diff --git "a/val_problems.json" "b/val_problems.json" new file mode 100644--- /dev/null +++ "b/val_problems.json" @@ -0,0 +1,16002 @@ +[ + { + "nums": [ + 6, + 88, + 41, + 38 + ], + "target": 79, + "solution": [ + "88-6=82", + "41-38=3", + "82-3=79" + ], + "optimal_path": "Current State: 79:[6, 88, 41, 38], Operations: []\nExploring Operation: 88-6=82, Resulting Numbers: [41, 38, 82]\nGenerated Node #2: [41, 38, 82] from Operation: 88-6=82\nCurrent State: 79:[41, 38, 82], Operations: ['88-6=82']\nExploring Operation: 41-38=3, Resulting Numbers: [82, 3]\nGenerated Node #3: [82, 3] from Operation: 41-38=3\nCurrent State: 79:[82, 3], Operations: ['88-6=82', '41-38=3']\nExploring Operation: 82-3=79, Resulting Numbers: [79]\n79,79 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 37, + 62, + 80, + 88 + ], + "target": 91, + "solution": [ + "37+62=99", + "88-80=8", + "99-8=91" + ], + "optimal_path": "Current State: 91:[37, 62, 80, 88], Operations: []\nExploring Operation: 37+62=99, Resulting Numbers: [80, 88, 99]\nGenerated Node #2: [80, 88, 99] from Operation: 37+62=99\nCurrent State: 91:[80, 88, 99], Operations: ['37+62=99']\nExploring Operation: 88-80=8, Resulting Numbers: [99, 8]\nGenerated Node #3: [99, 8] from Operation: 88-80=8\nCurrent State: 91:[99, 8], Operations: ['37+62=99', '88-80=8']\nExploring Operation: 99-8=91, Resulting Numbers: [91]\n91,91 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 34, + 57, + 24, + 80 + ], + "target": 81, + "solution": [ + "57-34=23", + "24+80=104", + "104-23=81" + ], + "optimal_path": "Current State: 81:[34, 57, 24, 80], Operations: []\nExploring Operation: 57-34=23, Resulting Numbers: [24, 80, 23]\nGenerated Node #2: [24, 80, 23] from Operation: 57-34=23\nCurrent State: 81:[24, 80, 23], Operations: ['57-34=23']\nExploring Operation: 24+80=104, Resulting Numbers: [23, 104]\nGenerated Node #3: [23, 104] from Operation: 24+80=104\nCurrent State: 81:[23, 104], Operations: ['57-34=23', '24+80=104']\nExploring Operation: 104-23=81, Resulting Numbers: [81]\n81,81 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 41, + 63, + 31, + 63 + ], + "target": 73, + "solution": [ + "41+31=72", + "63/63=1", + "72+1=73" + ], + "optimal_path": "Current State: 73:[41, 63, 31, 63], Operations: []\nExploring Operation: 41+31=72, Resulting Numbers: [63, 63, 72]\nGenerated Node #2: [63, 63, 72] from Operation: 41+31=72\nCurrent State: 73:[63, 63, 72], Operations: ['41+31=72']\nExploring Operation: 63/63=1, Resulting Numbers: [72, 1]\nGenerated Node #3: [72, 1] from Operation: 63/63=1\nCurrent State: 73:[72, 1], Operations: ['41+31=72', '63/63=1']\nExploring Operation: 72+1=73, Resulting Numbers: [73]\n73,73 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 94, + 47, + 28, + 94 + ], + "target": 58, + "solution": [ + "94*28=2632", + "94+2632=2726", + "2726/47=58" + ], + "optimal_path": "Current State: 58:[94, 47, 28, 94], Operations: []\nExploring Operation: 94*28=2632, Resulting Numbers: [47, 2632]\nGenerated Node #2: [47, 2632] from Operation: 94*28=2632\nCurrent State: 58:[47, 2632], Operations: ['94*28=2632']\nExploring Operation: 94+2632=2726, Resulting Numbers: [47, 2726]\nGenerated Node #3: [47, 2726] from Operation: 94+2632=2726\nCurrent State: 58:[47, 2726], Operations: ['94*28=2632', '94+2632=2726']\nExploring Operation: 2726/47=58, Resulting Numbers: [58]\n58,58 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 4, + 31, + 22, + 55 + ], + "target": 41, + "solution": [ + "4*55=220", + "220/22=10", + "31+10=41" + ], + "optimal_path": "Current State: 41:[4, 31, 22, 55], Operations: []\nExploring Operation: 4*55=220, Resulting Numbers: [31, 22, 220]\nGenerated Node #2: [31, 22, 220] from Operation: 4*55=220\nCurrent State: 41:[31, 22, 220], Operations: ['4*55=220']\nExploring Operation: 220/22=10, Resulting Numbers: [31, 10]\nGenerated Node #3: [31, 10] from Operation: 220/22=10\nCurrent State: 41:[31, 10], Operations: ['4*55=220', '220/22=10']\nExploring Operation: 31+10=41, Resulting Numbers: [41]\n41,41 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 33, + 92, + 82, + 30 + ], + "target": 54, + "solution": [ + "33*82=2706", + "92*30=2760", + "2760-2706=54" + ], + "optimal_path": "Current State: 54:[33, 92, 82, 30], Operations: []\nExploring Operation: 33*82=2706, Resulting Numbers: [92, 30, 2706]\nGenerated Node #2: [92, 30, 2706] from Operation: 33*82=2706\nCurrent State: 54:[92, 30, 2706], Operations: ['33*82=2706']\nExploring Operation: 92*30=2760, Resulting Numbers: [2706, 2760]\nGenerated Node #3: [2706, 2760] from Operation: 92*30=2760\nCurrent State: 54:[2706, 2760], Operations: ['33*82=2706', '92*30=2760']\nExploring Operation: 2760-2706=54, Resulting Numbers: [54]\n54,54 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 91, + 58, + 80, + 91 + ], + "target": 22, + "solution": [ + "91+58=149", + "80+91=171", + "171-149=22" + ], + "optimal_path": "Current State: 22:[91, 58, 80, 91], Operations: []\nExploring Operation: 91+58=149, Resulting Numbers: [80, 149]\nGenerated Node #2: [80, 149] from Operation: 91+58=149\nCurrent State: 22:[80, 149], Operations: ['91+58=149']\nExploring Operation: 80+91=171, Resulting Numbers: [149, 171]\nGenerated Node #3: [149, 171] from Operation: 80+91=171\nCurrent State: 22:[149, 171], Operations: ['91+58=149', '80+91=171']\nExploring Operation: 171-149=22, Resulting Numbers: [22]\n22,22 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 18, + 24, + 27, + 36 + ], + "target": 69, + "solution": [ + "24-18=6", + "27+36=63", + "6+63=69" + ], + "optimal_path": "Current State: 69:[18, 24, 27, 36], Operations: []\nExploring Operation: 24-18=6, Resulting Numbers: [27, 36, 6]\nGenerated Node #2: [27, 36, 6] from Operation: 24-18=6\nCurrent State: 69:[27, 36, 6], Operations: ['24-18=6']\nExploring Operation: 27+36=63, Resulting Numbers: [6, 63]\nGenerated Node #3: [6, 63] from Operation: 27+36=63\nCurrent State: 69:[6, 63], Operations: ['24-18=6', '27+36=63']\nExploring Operation: 6+63=69, Resulting Numbers: [69]\n69,69 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 39, + 24, + 6, + 68 + ], + "target": 22, + "solution": [ + "39-24=15", + "6*15=90", + "90-68=22" + ], + "optimal_path": "Current State: 22:[39, 24, 6, 68], Operations: []\nExploring Operation: 39-24=15, Resulting Numbers: [6, 68, 15]\nGenerated Node #2: [6, 68, 15] from Operation: 39-24=15\nCurrent State: 22:[6, 68, 15], Operations: ['39-24=15']\nExploring Operation: 6*15=90, Resulting Numbers: [68, 90]\nGenerated Node #3: [68, 90] from Operation: 6*15=90\nCurrent State: 22:[68, 90], Operations: ['39-24=15', '6*15=90']\nExploring Operation: 90-68=22, Resulting Numbers: [22]\n22,22 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 49, + 38, + 74, + 76 + ], + "target": 23, + "solution": [ + "74-49=25", + "76/38=2", + "25-2=23" + ], + "optimal_path": "Current State: 23:[49, 38, 74, 76], Operations: []\nExploring Operation: 74-49=25, Resulting Numbers: [38, 76, 25]\nGenerated Node #2: [38, 76, 25] from Operation: 74-49=25\nCurrent State: 23:[38, 76, 25], Operations: ['74-49=25']\nExploring Operation: 76/38=2, Resulting Numbers: [25, 2]\nGenerated Node #3: [25, 2] from Operation: 76/38=2\nCurrent State: 23:[25, 2], Operations: ['74-49=25', '76/38=2']\nExploring Operation: 25-2=23, Resulting Numbers: [23]\n23,23 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 79, + 17, + 80, + 93 + ], + "target": 77, + "solution": [ + "79+17=96", + "80+93=173", + "173-96=77" + ], + "optimal_path": "Current State: 77:[79, 17, 80, 93], Operations: []\nExploring Operation: 79+17=96, Resulting Numbers: [80, 93, 96]\nGenerated Node #2: [80, 93, 96] from Operation: 79+17=96\nCurrent State: 77:[80, 93, 96], Operations: ['79+17=96']\nExploring Operation: 80+93=173, Resulting Numbers: [96, 173]\nGenerated Node #3: [96, 173] from Operation: 80+93=173\nCurrent State: 77:[96, 173], Operations: ['79+17=96', '80+93=173']\nExploring Operation: 173-96=77, Resulting Numbers: [77]\n77,77 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 64, + 60, + 15, + 71 + ], + "target": 68, + "solution": [ + "64+60=124", + "71-15=56", + "124-56=68" + ], + "optimal_path": "Current State: 68:[64, 60, 15, 71], Operations: []\nExploring Operation: 64+60=124, Resulting Numbers: [15, 71, 124]\nGenerated Node #2: [15, 71, 124] from Operation: 64+60=124\nCurrent State: 68:[15, 71, 124], Operations: ['64+60=124']\nExploring Operation: 71-15=56, Resulting Numbers: [124, 56]\nGenerated Node #3: [124, 56] from Operation: 71-15=56\nCurrent State: 68:[124, 56], Operations: ['64+60=124', '71-15=56']\nExploring Operation: 124-56=68, Resulting Numbers: [68]\n68,68 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 76, + 93, + 52, + 90 + ], + "target": 95, + "solution": [ + "90-52=38", + "76/38=2", + "93+2=95" + ], + "optimal_path": "Current State: 95:[76, 93, 52, 90], Operations: []\nExploring Operation: 90-52=38, Resulting Numbers: [76, 93, 38]\nGenerated Node #2: [76, 93, 38] from Operation: 90-52=38\nCurrent State: 95:[76, 93, 38], Operations: ['90-52=38']\nExploring Operation: 76/38=2, Resulting Numbers: [93, 2]\nGenerated Node #3: [93, 2] from Operation: 76/38=2\nCurrent State: 95:[93, 2], Operations: ['90-52=38', '76/38=2']\nExploring Operation: 93+2=95, Resulting Numbers: [95]\n95,95 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 97, + 11, + 20, + 8 + ], + "target": 11, + "solution": [ + "97+11=108", + "108-20=88", + "88/8=11" + ], + "optimal_path": "Current State: 11:[97, 11, 20, 8], Operations: []\nExploring Operation: 97+11=108, Resulting Numbers: [20, 8, 108]\nGenerated Node #2: [20, 8, 108] from Operation: 97+11=108\nCurrent State: 11:[20, 8, 108], Operations: ['97+11=108']\nExploring Operation: 108-20=88, Resulting Numbers: [8, 88]\nGenerated Node #3: [8, 88] from Operation: 108-20=88\nCurrent State: 11:[8, 88], Operations: ['97+11=108', '108-20=88']\nExploring Operation: 88/8=11, Resulting Numbers: [11]\n11,11 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 17, + 4, + 80, + 85 + ], + "target": 82, + "solution": [ + "17+85=102", + "80/4=20", + "102-20=82" + ], + "optimal_path": "Current State: 82:[17, 4, 80, 85], Operations: []\nExploring Operation: 17+85=102, Resulting Numbers: [4, 80, 102]\nGenerated Node #2: [4, 80, 102] from Operation: 17+85=102\nCurrent State: 82:[4, 80, 102], Operations: ['17+85=102']\nExploring Operation: 80/4=20, Resulting Numbers: [102, 20]\nGenerated Node #3: [102, 20] from Operation: 80/4=20\nCurrent State: 82:[102, 20], Operations: ['17+85=102', '80/4=20']\nExploring Operation: 102-20=82, Resulting Numbers: [82]\n82,82 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 92, + 75, + 46, + 29 + ], + "target": 23, + "solution": [ + "92/46=2", + "75-29=46", + "46/2=23" + ], + "optimal_path": "Current State: 23:[92, 75, 46, 29], Operations: []\nExploring Operation: 92/46=2, Resulting Numbers: [75, 29, 2]\nGenerated Node #2: [75, 29, 2] from Operation: 92/46=2\nCurrent State: 23:[75, 29, 2], Operations: ['92/46=2']\nExploring Operation: 75-29=46, Resulting Numbers: [2, 46]\nGenerated Node #3: [2, 46] from Operation: 75-29=46\nCurrent State: 23:[2, 46], Operations: ['92/46=2', '75-29=46']\nExploring Operation: 46/2=23, Resulting Numbers: [23]\n23,23 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 70, + 24, + 5, + 22 + ], + "target": 60, + "solution": [ + "70/5=14", + "24+22=46", + "14+46=60" + ], + "optimal_path": "Current State: 60:[70, 24, 5, 22], Operations: []\nExploring Operation: 70/5=14, Resulting Numbers: [24, 22, 14]\nGenerated Node #2: [24, 22, 14] from Operation: 70/5=14\nCurrent State: 60:[24, 22, 14], Operations: ['70/5=14']\nExploring Operation: 24+22=46, Resulting Numbers: [14, 46]\nGenerated Node #3: [14, 46] from Operation: 24+22=46\nCurrent State: 60:[14, 46], Operations: ['70/5=14', '24+22=46']\nExploring Operation: 14+46=60, Resulting Numbers: [60]\n60,60 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 91, + 52, + 50, + 45 + ], + "target": 13, + "solution": [ + "91-50=41", + "45-41=4", + "52/4=13" + ], + "optimal_path": "Current State: 13:[91, 52, 50, 45], Operations: []\nExploring Operation: 91-50=41, Resulting Numbers: [52, 45, 41]\nGenerated Node #2: [52, 45, 41] from Operation: 91-50=41\nCurrent State: 13:[52, 45, 41], Operations: ['91-50=41']\nExploring Operation: 45-41=4, Resulting Numbers: [52, 4]\nGenerated Node #3: [52, 4] from Operation: 45-41=4\nCurrent State: 13:[52, 4], Operations: ['91-50=41', '45-41=4']\nExploring Operation: 52/4=13, Resulting Numbers: [13]\n13,13 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 82, + 95, + 21, + 80 + ], + "target": 53, + "solution": [ + "82-80=2", + "21*2=42", + "95-42=53" + ], + "optimal_path": "Current State: 53:[82, 95, 21, 80], Operations: []\nExploring Operation: 82-80=2, Resulting Numbers: [95, 21, 2]\nGenerated Node #2: [95, 21, 2] from Operation: 82-80=2\nCurrent State: 53:[95, 21, 2], Operations: ['82-80=2']\nExploring Operation: 21*2=42, Resulting Numbers: [95, 42]\nGenerated Node #3: [95, 42] from Operation: 21*2=42\nCurrent State: 53:[95, 42], Operations: ['82-80=2', '21*2=42']\nExploring Operation: 95-42=53, Resulting Numbers: [53]\n53,53 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 68, + 21, + 23, + 29 + ], + "target": 83, + "solution": [ + "68+21=89", + "29-23=6", + "89-6=83" + ], + "optimal_path": "Current State: 83:[68, 21, 23, 29], Operations: []\nExploring Operation: 68+21=89, Resulting Numbers: [23, 29, 89]\nGenerated Node #2: [23, 29, 89] from Operation: 68+21=89\nCurrent State: 83:[23, 29, 89], Operations: ['68+21=89']\nExploring Operation: 29-23=6, Resulting Numbers: [89, 6]\nGenerated Node #3: [89, 6] from Operation: 29-23=6\nCurrent State: 83:[89, 6], Operations: ['68+21=89', '29-23=6']\nExploring Operation: 89-6=83, Resulting Numbers: [83]\n83,83 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 40, + 95, + 70, + 75 + ], + "target": 60, + "solution": [ + "95-40=55", + "75-70=5", + "55+5=60" + ], + "optimal_path": "Current State: 60:[40, 95, 70, 75], Operations: []\nExploring Operation: 95-40=55, Resulting Numbers: [70, 75, 55]\nGenerated Node #2: [70, 75, 55] from Operation: 95-40=55\nCurrent State: 60:[70, 75, 55], Operations: ['95-40=55']\nExploring Operation: 75-70=5, Resulting Numbers: [55, 5]\nGenerated Node #3: [55, 5] from Operation: 75-70=5\nCurrent State: 60:[55, 5], Operations: ['95-40=55', '75-70=5']\nExploring Operation: 55+5=60, Resulting Numbers: [60]\n60,60 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 42, + 13, + 70, + 28 + ], + "target": 17, + "solution": [ + "42*13=546", + "546-70=476", + "476/28=17" + ], + "optimal_path": "Current State: 17:[42, 13, 70, 28], Operations: []\nExploring Operation: 42*13=546, Resulting Numbers: [70, 28, 546]\nGenerated Node #2: [70, 28, 546] from Operation: 42*13=546\nCurrent State: 17:[70, 28, 546], Operations: ['42*13=546']\nExploring Operation: 546-70=476, Resulting Numbers: [28, 476]\nGenerated Node #3: [28, 476] from Operation: 546-70=476\nCurrent State: 17:[28, 476], Operations: ['42*13=546', '546-70=476']\nExploring Operation: 476/28=17, Resulting Numbers: [17]\n17,17 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 87, + 34, + 71, + 2 + ], + "target": 90, + "solution": [ + "87+71=158", + "34*2=68", + "158-68=90" + ], + "optimal_path": "Current State: 90:[87, 34, 71, 2], Operations: []\nExploring Operation: 87+71=158, Resulting Numbers: [34, 2, 158]\nGenerated Node #2: [34, 2, 158] from Operation: 87+71=158\nCurrent State: 90:[34, 2, 158], Operations: ['87+71=158']\nExploring Operation: 34*2=68, Resulting Numbers: [158, 68]\nGenerated Node #3: [158, 68] from Operation: 34*2=68\nCurrent State: 90:[158, 68], Operations: ['87+71=158', '34*2=68']\nExploring Operation: 158-68=90, Resulting Numbers: [90]\n90,90 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 65, + 85, + 26, + 72 + ], + "target": 67, + "solution": [ + "85-72=13", + "26/13=2", + "65+2=67" + ], + "optimal_path": "Current State: 67:[65, 85, 26, 72], Operations: []\nExploring Operation: 85-72=13, Resulting Numbers: [65, 26, 13]\nGenerated Node #2: [65, 26, 13] from Operation: 85-72=13\nCurrent State: 67:[65, 26, 13], Operations: ['85-72=13']\nExploring Operation: 26/13=2, Resulting Numbers: [65, 2]\nGenerated Node #3: [65, 2] from Operation: 26/13=2\nCurrent State: 67:[65, 2], Operations: ['85-72=13', '26/13=2']\nExploring Operation: 65+2=67, Resulting Numbers: [67]\n67,67 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 81, + 32, + 96, + 48 + ], + "target": 17, + "solution": [ + "32*96=3072", + "3072/48=64", + "81-64=17" + ], + "optimal_path": "Current State: 17:[81, 32, 96, 48], Operations: []\nExploring Operation: 32*96=3072, Resulting Numbers: [81, 48, 3072]\nGenerated Node #2: [81, 48, 3072] from Operation: 32*96=3072\nCurrent State: 17:[81, 48, 3072], Operations: ['32*96=3072']\nExploring Operation: 3072/48=64, Resulting Numbers: [81, 64]\nGenerated Node #3: [81, 64] from Operation: 3072/48=64\nCurrent State: 17:[81, 64], Operations: ['32*96=3072', '3072/48=64']\nExploring Operation: 81-64=17, Resulting Numbers: [17]\n17,17 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 43, + 81, + 49, + 28 + ], + "target": 17, + "solution": [ + "81-43=38", + "49-28=21", + "38-21=17" + ], + "optimal_path": "Current State: 17:[43, 81, 49, 28], Operations: []\nExploring Operation: 81-43=38, Resulting Numbers: [49, 28, 38]\nGenerated Node #2: [49, 28, 38] from Operation: 81-43=38\nCurrent State: 17:[49, 28, 38], Operations: ['81-43=38']\nExploring Operation: 49-28=21, Resulting Numbers: [38, 21]\nGenerated Node #3: [38, 21] from Operation: 49-28=21\nCurrent State: 17:[38, 21], Operations: ['81-43=38', '49-28=21']\nExploring Operation: 38-21=17, Resulting Numbers: [17]\n17,17 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 3, + 70, + 90, + 14 + ], + "target": 46, + "solution": [ + "90-70=20", + "3*20=60", + "60-14=46" + ], + "optimal_path": "Current State: 46:[3, 70, 90, 14], Operations: []\nExploring Operation: 90-70=20, Resulting Numbers: [3, 14, 20]\nGenerated Node #2: [3, 14, 20] from Operation: 90-70=20\nCurrent State: 46:[3, 14, 20], Operations: ['90-70=20']\nExploring Operation: 3*20=60, Resulting Numbers: [14, 60]\nGenerated Node #3: [14, 60] from Operation: 3*20=60\nCurrent State: 46:[14, 60], Operations: ['90-70=20', '3*20=60']\nExploring Operation: 60-14=46, Resulting Numbers: [46]\n46,46 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 64, + 62, + 16, + 41 + ], + "target": 27, + "solution": [ + "64-62=2", + "41-16=25", + "2+25=27" + ], + "optimal_path": "Current State: 27:[64, 62, 16, 41], Operations: []\nExploring Operation: 64-62=2, Resulting Numbers: [16, 41, 2]\nGenerated Node #2: [16, 41, 2] from Operation: 64-62=2\nCurrent State: 27:[16, 41, 2], Operations: ['64-62=2']\nExploring Operation: 41-16=25, Resulting Numbers: [2, 25]\nGenerated Node #3: [2, 25] from Operation: 41-16=25\nCurrent State: 27:[2, 25], Operations: ['64-62=2', '41-16=25']\nExploring Operation: 2+25=27, Resulting Numbers: [27]\n27,27 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 48, + 6, + 49, + 3 + ], + "target": 17, + "solution": [ + "49-48=1", + "6*3=18", + "18-1=17" + ], + "optimal_path": "Current State: 17:[48, 6, 49, 3], Operations: []\nExploring Operation: 49-48=1, Resulting Numbers: [6, 3, 1]\nGenerated Node #2: [6, 3, 1] from Operation: 49-48=1\nCurrent State: 17:[6, 3, 1], Operations: ['49-48=1']\nExploring Operation: 6*3=18, Resulting Numbers: [1, 18]\nGenerated Node #3: [1, 18] from Operation: 6*3=18\nCurrent State: 17:[1, 18], Operations: ['49-48=1', '6*3=18']\nExploring Operation: 18-1=17, Resulting Numbers: [17]\n17,17 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 4, + 91, + 96, + 95 + ], + "target": 95, + "solution": [ + "4+91=95", + "96-95=1", + "95*1=95" + ], + "optimal_path": "Current State: 95:[4, 91, 96, 95], Operations: []\nExploring Operation: 4+91=95, Resulting Numbers: [96, 95, 95]\nGenerated Node #2: [96, 95, 95] from Operation: 4+91=95\nCurrent State: 95:[96, 95, 95], Operations: ['4+91=95']\nExploring Operation: 96-95=1, Resulting Numbers: [1]\n1,95 equal: Goal Reached\nExploring Operation: 95*1=95, Resulting Numbers: [95]\n95,95 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 48, + 4, + 60, + 85 + ], + "target": 69, + "solution": [ + "48-4=44", + "85-60=25", + "44+25=69" + ], + "optimal_path": "Current State: 69:[48, 4, 60, 85], Operations: []\nExploring Operation: 48-4=44, Resulting Numbers: [60, 85, 44]\nGenerated Node #2: [60, 85, 44] from Operation: 48-4=44\nCurrent State: 69:[60, 85, 44], Operations: ['48-4=44']\nExploring Operation: 85-60=25, Resulting Numbers: [44, 25]\nGenerated Node #3: [44, 25] from Operation: 85-60=25\nCurrent State: 69:[44, 25], Operations: ['48-4=44', '85-60=25']\nExploring Operation: 44+25=69, Resulting Numbers: [69]\n69,69 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 96, + 96, + 48, + 8 + ], + "target": 72, + "solution": [ + "96+96=192", + "192/8=24", + "48+24=72" + ], + "optimal_path": "Current State: 72:[96, 96, 48, 8], Operations: []\nExploring Operation: 96+96=192, Resulting Numbers: [48, 8, 192]\nGenerated Node #2: [48, 8, 192] from Operation: 96+96=192\nCurrent State: 72:[48, 8, 192], Operations: ['96+96=192']\nExploring Operation: 192/8=24, Resulting Numbers: [48, 24]\nGenerated Node #3: [48, 24] from Operation: 192/8=24\nCurrent State: 72:[48, 24], Operations: ['96+96=192', '192/8=24']\nExploring Operation: 48+24=72, Resulting Numbers: [72]\n72,72 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 64, + 37, + 16, + 31 + ], + "target": 24, + "solution": [ + "64/16=4", + "37-31=6", + "4*6=24" + ], + "optimal_path": "Current State: 24:[64, 37, 16, 31], Operations: []\nExploring Operation: 64/16=4, Resulting Numbers: [37, 31, 4]\nGenerated Node #2: [37, 31, 4] from Operation: 64/16=4\nCurrent State: 24:[37, 31, 4], Operations: ['64/16=4']\nExploring Operation: 37-31=6, Resulting Numbers: [4, 6]\nGenerated Node #3: [4, 6] from Operation: 37-31=6\nCurrent State: 24:[4, 6], Operations: ['64/16=4', '37-31=6']\nExploring Operation: 4*6=24, Resulting Numbers: [24]\n24,24 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 78, + 17, + 26, + 90 + ], + "target": 76, + "solution": [ + "78/26=3", + "90-17=73", + "3+73=76" + ], + "optimal_path": "Current State: 76:[78, 17, 26, 90], Operations: []\nExploring Operation: 78/26=3, Resulting Numbers: [17, 90, 3]\nGenerated Node #2: [17, 90, 3] from Operation: 78/26=3\nCurrent State: 76:[17, 90, 3], Operations: ['78/26=3']\nExploring Operation: 90-17=73, Resulting Numbers: [3, 73]\nGenerated Node #3: [3, 73] from Operation: 90-17=73\nCurrent State: 76:[3, 73], Operations: ['78/26=3', '90-17=73']\nExploring Operation: 3+73=76, Resulting Numbers: [76]\n76,76 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 8, + 68, + 74, + 42 + ], + "target": 90, + "solution": [ + "74-68=6", + "8*6=48", + "42+48=90" + ], + "optimal_path": "Current State: 90:[8, 68, 74, 42], Operations: []\nExploring Operation: 74-68=6, Resulting Numbers: [8, 42, 6]\nGenerated Node #2: [8, 42, 6] from Operation: 74-68=6\nCurrent State: 90:[8, 42, 6], Operations: ['74-68=6']\nExploring Operation: 8*6=48, Resulting Numbers: [42, 48]\nGenerated Node #3: [42, 48] from Operation: 8*6=48\nCurrent State: 90:[42, 48], Operations: ['74-68=6', '8*6=48']\nExploring Operation: 42+48=90, Resulting Numbers: [90]\n90,90 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 32, + 60, + 34, + 36 + ], + "target": 94, + "solution": [ + "32+60=92", + "36-34=2", + "92+2=94" + ], + "optimal_path": "Current State: 94:[32, 60, 34, 36], Operations: []\nExploring Operation: 32+60=92, Resulting Numbers: [34, 36, 92]\nGenerated Node #2: [34, 36, 92] from Operation: 32+60=92\nCurrent State: 94:[34, 36, 92], Operations: ['32+60=92']\nExploring Operation: 36-34=2, Resulting Numbers: [92, 2]\nGenerated Node #3: [92, 2] from Operation: 36-34=2\nCurrent State: 94:[92, 2], Operations: ['32+60=92', '36-34=2']\nExploring Operation: 92+2=94, Resulting Numbers: [94]\n94,94 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 37, + 65, + 84, + 57 + ], + "target": 19, + "solution": [ + "65-37=28", + "84/28=3", + "57/3=19" + ], + "optimal_path": "Current State: 19:[37, 65, 84, 57], Operations: []\nExploring Operation: 65-37=28, Resulting Numbers: [84, 57, 28]\nGenerated Node #2: [84, 57, 28] from Operation: 65-37=28\nCurrent State: 19:[84, 57, 28], Operations: ['65-37=28']\nExploring Operation: 84/28=3, Resulting Numbers: [57, 3]\nGenerated Node #3: [57, 3] from Operation: 84/28=3\nCurrent State: 19:[57, 3], Operations: ['65-37=28', '84/28=3']\nExploring Operation: 57/3=19, Resulting Numbers: [19]\n19,19 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 96, + 94, + 64, + 17 + ], + "target": 49, + "solution": [ + "96-94=2", + "64-17=47", + "2+47=49" + ], + "optimal_path": "Current State: 49:[96, 94, 64, 17], Operations: []\nExploring Operation: 96-94=2, Resulting Numbers: [64, 17, 2]\nGenerated Node #2: [64, 17, 2] from Operation: 96-94=2\nCurrent State: 49:[64, 17, 2], Operations: ['96-94=2']\nExploring Operation: 64-17=47, Resulting Numbers: [2, 47]\nGenerated Node #3: [2, 47] from Operation: 64-17=47\nCurrent State: 49:[2, 47], Operations: ['96-94=2', '64-17=47']\nExploring Operation: 2+47=49, Resulting Numbers: [49]\n49,49 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 33, + 6, + 44, + 82 + ], + "target": 90, + "solution": [ + "6*44=264", + "264/33=8", + "82+8=90" + ], + "optimal_path": "Current State: 90:[33, 6, 44, 82], Operations: []\nExploring Operation: 6*44=264, Resulting Numbers: [33, 82, 264]\nGenerated Node #2: [33, 82, 264] from Operation: 6*44=264\nCurrent State: 90:[33, 82, 264], Operations: ['6*44=264']\nExploring Operation: 264/33=8, Resulting Numbers: [82, 8]\nGenerated Node #3: [82, 8] from Operation: 264/33=8\nCurrent State: 90:[82, 8], Operations: ['6*44=264', '264/33=8']\nExploring Operation: 82+8=90, Resulting Numbers: [90]\n90,90 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 98, + 63, + 12, + 82 + ], + "target": 45, + "solution": [ + "82-12=70", + "63*70=4410", + "4410/98=45" + ], + "optimal_path": "Current State: 45:[98, 63, 12, 82], Operations: []\nExploring Operation: 82-12=70, Resulting Numbers: [98, 63, 70]\nGenerated Node #2: [98, 63, 70] from Operation: 82-12=70\nCurrent State: 45:[98, 63, 70], Operations: ['82-12=70']\nExploring Operation: 63*70=4410, Resulting Numbers: [98, 4410]\nGenerated Node #3: [98, 4410] from Operation: 63*70=4410\nCurrent State: 45:[98, 4410], Operations: ['82-12=70', '63*70=4410']\nExploring Operation: 4410/98=45, Resulting Numbers: [45]\n45,45 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 94, + 48, + 5, + 33 + ], + "target": 84, + "solution": [ + "94-48=46", + "5+33=38", + "46+38=84" + ], + "optimal_path": "Current State: 84:[94, 48, 5, 33], Operations: []\nExploring Operation: 94-48=46, Resulting Numbers: [5, 33, 46]\nGenerated Node #2: [5, 33, 46] from Operation: 94-48=46\nCurrent State: 84:[5, 33, 46], Operations: ['94-48=46']\nExploring Operation: 5+33=38, Resulting Numbers: [46, 38]\nGenerated Node #3: [46, 38] from Operation: 5+33=38\nCurrent State: 84:[46, 38], Operations: ['94-48=46', '5+33=38']\nExploring Operation: 46+38=84, Resulting Numbers: [84]\n84,84 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 4, + 72, + 74, + 8 + ], + "target": 34, + "solution": [ + "4*8=32", + "74-72=2", + "32+2=34" + ], + "optimal_path": "Current State: 34:[4, 72, 74, 8], Operations: []\nExploring Operation: 4*8=32, Resulting Numbers: [72, 74, 32]\nGenerated Node #2: [72, 74, 32] from Operation: 4*8=32\nCurrent State: 34:[72, 74, 32], Operations: ['4*8=32']\nExploring Operation: 74-72=2, Resulting Numbers: [32, 2]\nGenerated Node #3: [32, 2] from Operation: 74-72=2\nCurrent State: 34:[32, 2], Operations: ['4*8=32', '74-72=2']\nExploring Operation: 32+2=34, Resulting Numbers: [34]\n34,34 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 24, + 45, + 77, + 56 + ], + "target": 31, + "solution": [ + "56-45=11", + "77/11=7", + "24+7=31" + ], + "optimal_path": "Current State: 31:[24, 45, 77, 56], Operations: []\nExploring Operation: 56-45=11, Resulting Numbers: [24, 77, 11]\nGenerated Node #2: [24, 77, 11] from Operation: 56-45=11\nCurrent State: 31:[24, 77, 11], Operations: ['56-45=11']\nExploring Operation: 77/11=7, Resulting Numbers: [24, 7]\nGenerated Node #3: [24, 7] from Operation: 77/11=7\nCurrent State: 31:[24, 7], Operations: ['56-45=11', '77/11=7']\nExploring Operation: 24+7=31, Resulting Numbers: [31]\n31,31 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 66, + 63, + 15, + 71 + ], + "target": 66, + "solution": [ + "66-63=3", + "15/3=5", + "71-5=66" + ], + "optimal_path": "Current State: 66:[66, 63, 15, 71], Operations: []\nExploring Operation: 66-63=3, Resulting Numbers: [15, 71, 3]\nGenerated Node #2: [15, 71, 3] from Operation: 66-63=3\nCurrent State: 66:[15, 71, 3], Operations: ['66-63=3']\nExploring Operation: 15/3=5, Resulting Numbers: [71, 5]\nGenerated Node #3: [71, 5] from Operation: 15/3=5\nCurrent State: 66:[71, 5], Operations: ['66-63=3', '15/3=5']\nExploring Operation: 71-5=66, Resulting Numbers: [66]\n66,66 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 87, + 3, + 30, + 82 + ], + "target": 22, + "solution": [ + "87+3=90", + "30+82=112", + "112-90=22" + ], + "optimal_path": "Current State: 22:[87, 3, 30, 82], Operations: []\nExploring Operation: 87+3=90, Resulting Numbers: [30, 82, 90]\nGenerated Node #2: [30, 82, 90] from Operation: 87+3=90\nCurrent State: 22:[30, 82, 90], Operations: ['87+3=90']\nExploring Operation: 30+82=112, Resulting Numbers: [90, 112]\nGenerated Node #3: [90, 112] from Operation: 30+82=112\nCurrent State: 22:[90, 112], Operations: ['87+3=90', '30+82=112']\nExploring Operation: 112-90=22, Resulting Numbers: [22]\n22,22 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 57, + 99, + 56, + 22 + ], + "target": 78, + "solution": [ + "57+99=156", + "56+22=78", + "156-78=78" + ], + "optimal_path": "Current State: 78:[57, 99, 56, 22], Operations: []\nExploring Operation: 57+99=156, Resulting Numbers: [56, 22, 156]\nGenerated Node #2: [56, 22, 156] from Operation: 57+99=156\nCurrent State: 78:[56, 22, 156], Operations: ['57+99=156']\nExploring Operation: 56+22=78, Resulting Numbers: [156, 78]\nGenerated Node #3: [156, 78] from Operation: 56+22=78\nCurrent State: 78:[156, 78], Operations: ['57+99=156', '56+22=78']\nExploring Operation: 156-78=78, Resulting Numbers: [78]\n78,78 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 30, + 46, + 10, + 11 + ], + "target": 75, + "solution": [ + "30+46=76", + "11-10=1", + "76-1=75" + ], + "optimal_path": "Current State: 75:[30, 46, 10, 11], Operations: []\nExploring Operation: 30+46=76, Resulting Numbers: [10, 11, 76]\nGenerated Node #2: [10, 11, 76] from Operation: 30+46=76\nCurrent State: 75:[10, 11, 76], Operations: ['30+46=76']\nExploring Operation: 11-10=1, Resulting Numbers: [76, 1]\nGenerated Node #3: [76, 1] from Operation: 11-10=1\nCurrent State: 75:[76, 1], Operations: ['30+46=76', '11-10=1']\nExploring Operation: 76-1=75, Resulting Numbers: [75]\n75,75 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 83, + 37, + 27, + 67 + ], + "target": 48, + "solution": [ + "83-37=46", + "27+67=94", + "94-46=48" + ], + "optimal_path": "Current State: 48:[83, 37, 27, 67], Operations: []\nExploring Operation: 83-37=46, Resulting Numbers: [27, 67, 46]\nGenerated Node #2: [27, 67, 46] from Operation: 83-37=46\nCurrent State: 48:[27, 67, 46], Operations: ['83-37=46']\nExploring Operation: 27+67=94, Resulting Numbers: [46, 94]\nGenerated Node #3: [46, 94] from Operation: 27+67=94\nCurrent State: 48:[46, 94], Operations: ['83-37=46', '27+67=94']\nExploring Operation: 94-46=48, Resulting Numbers: [48]\n48,48 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 39, + 37, + 11, + 16 + ], + "target": 88, + "solution": [ + "39-37=2", + "11*16=176", + "176/2=88" + ], + "optimal_path": "Current State: 88:[39, 37, 11, 16], Operations: []\nExploring Operation: 39-37=2, Resulting Numbers: [11, 16, 2]\nGenerated Node #2: [11, 16, 2] from Operation: 39-37=2\nCurrent State: 88:[11, 16, 2], Operations: ['39-37=2']\nExploring Operation: 11*16=176, Resulting Numbers: [2, 176]\nGenerated Node #3: [2, 176] from Operation: 11*16=176\nCurrent State: 88:[2, 176], Operations: ['39-37=2', '11*16=176']\nExploring Operation: 176/2=88, Resulting Numbers: [88]\n88,88 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 77, + 86, + 97, + 2 + ], + "target": 23, + "solution": [ + "97-77=20", + "86/2=43", + "43-20=23" + ], + "optimal_path": "Current State: 23:[77, 86, 97, 2], Operations: []\nExploring Operation: 97-77=20, Resulting Numbers: [86, 2, 20]\nGenerated Node #2: [86, 2, 20] from Operation: 97-77=20\nCurrent State: 23:[86, 2, 20], Operations: ['97-77=20']\nExploring Operation: 86/2=43, Resulting Numbers: [20, 43]\nGenerated Node #3: [20, 43] from Operation: 86/2=43\nCurrent State: 23:[20, 43], Operations: ['97-77=20', '86/2=43']\nExploring Operation: 43-20=23, Resulting Numbers: [23]\n23,23 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 28, + 67, + 30, + 18 + ], + "target": 70, + "solution": [ + "28-18=10", + "30/10=3", + "67+3=70" + ], + "optimal_path": "Current State: 70:[28, 67, 30, 18], Operations: []\nExploring Operation: 28-18=10, Resulting Numbers: [67, 30, 10]\nGenerated Node #2: [67, 30, 10] from Operation: 28-18=10\nCurrent State: 70:[67, 30, 10], Operations: ['28-18=10']\nExploring Operation: 30/10=3, Resulting Numbers: [67, 3]\nGenerated Node #3: [67, 3] from Operation: 30/10=3\nCurrent State: 70:[67, 3], Operations: ['28-18=10', '30/10=3']\nExploring Operation: 67+3=70, Resulting Numbers: [70]\n70,70 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 68, + 38, + 47, + 27 + ], + "target": 65, + "solution": [ + "47-38=9", + "27/9=3", + "68-3=65" + ], + "optimal_path": "Current State: 65:[68, 38, 47, 27], Operations: []\nExploring Operation: 47-38=9, Resulting Numbers: [68, 27, 9]\nGenerated Node #2: [68, 27, 9] from Operation: 47-38=9\nCurrent State: 65:[68, 27, 9], Operations: ['47-38=9']\nExploring Operation: 27/9=3, Resulting Numbers: [68, 3]\nGenerated Node #3: [68, 3] from Operation: 27/9=3\nCurrent State: 65:[68, 3], Operations: ['47-38=9', '27/9=3']\nExploring Operation: 68-3=65, Resulting Numbers: [65]\n65,65 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 76, + 33, + 24, + 18 + ], + "target": 38, + "solution": [ + "33-24=9", + "76*9=684", + "684/18=38" + ], + "optimal_path": "Current State: 38:[76, 33, 24, 18], Operations: []\nExploring Operation: 33-24=9, Resulting Numbers: [76, 18, 9]\nGenerated Node #2: [76, 18, 9] from Operation: 33-24=9\nCurrent State: 38:[76, 18, 9], Operations: ['33-24=9']\nExploring Operation: 76*9=684, Resulting Numbers: [18, 684]\nGenerated Node #3: [18, 684] from Operation: 76*9=684\nCurrent State: 38:[18, 684], Operations: ['33-24=9', '76*9=684']\nExploring Operation: 684/18=38, Resulting Numbers: [38]\n38,38 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 99, + 35, + 9, + 67 + ], + "target": 43, + "solution": [ + "99/9=11", + "67-35=32", + "11+32=43" + ], + "optimal_path": "Current State: 43:[99, 35, 9, 67], Operations: []\nExploring Operation: 99/9=11, Resulting Numbers: [35, 67, 11]\nGenerated Node #2: [35, 67, 11] from Operation: 99/9=11\nCurrent State: 43:[35, 67, 11], Operations: ['99/9=11']\nExploring Operation: 67-35=32, Resulting Numbers: [11, 32]\nGenerated Node #3: [11, 32] from Operation: 67-35=32\nCurrent State: 43:[11, 32], Operations: ['99/9=11', '67-35=32']\nExploring Operation: 11+32=43, Resulting Numbers: [43]\n43,43 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 93, + 10, + 89, + 9 + ], + "target": 23, + "solution": [ + "93+10=103", + "89-9=80", + "103-80=23" + ], + "optimal_path": "Current State: 23:[93, 10, 89, 9], Operations: []\nExploring Operation: 93+10=103, Resulting Numbers: [89, 9, 103]\nGenerated Node #2: [89, 9, 103] from Operation: 93+10=103\nCurrent State: 23:[89, 9, 103], Operations: ['93+10=103']\nExploring Operation: 89-9=80, Resulting Numbers: [103, 80]\nGenerated Node #3: [103, 80] from Operation: 89-9=80\nCurrent State: 23:[103, 80], Operations: ['93+10=103', '89-9=80']\nExploring Operation: 103-80=23, Resulting Numbers: [23]\n23,23 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 69, + 92, + 92, + 60 + ], + "target": 12, + "solution": [ + "92*60=5520", + "5520/69=80", + "92-80=12" + ], + "optimal_path": "Current State: 12:[69, 92, 92, 60], Operations: []\nExploring Operation: 92*60=5520, Resulting Numbers: [69, 5520]\nGenerated Node #2: [69, 5520] from Operation: 92*60=5520\nCurrent State: 12:[69, 5520], Operations: ['92*60=5520']\nExploring Operation: 5520/69=80, Resulting Numbers: [80]\n80,12 equal: Goal Reached\nExploring Operation: 92-80=12, Resulting Numbers: [12]\n12,12 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 25, + 2, + 88, + 80 + ], + "target": 97, + "solution": [ + "88-25=63", + "2*80=160", + "160-63=97" + ], + "optimal_path": "Current State: 97:[25, 2, 88, 80], Operations: []\nExploring Operation: 88-25=63, Resulting Numbers: [2, 80, 63]\nGenerated Node #2: [2, 80, 63] from Operation: 88-25=63\nCurrent State: 97:[2, 80, 63], Operations: ['88-25=63']\nExploring Operation: 2*80=160, Resulting Numbers: [63, 160]\nGenerated Node #3: [63, 160] from Operation: 2*80=160\nCurrent State: 97:[63, 160], Operations: ['88-25=63', '2*80=160']\nExploring Operation: 160-63=97, Resulting Numbers: [97]\n97,97 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 68, + 35, + 46, + 75 + ], + "target": 77, + "solution": [ + "75-68=7", + "46-35=11", + "7*11=77" + ], + "optimal_path": "Current State: 77:[68, 35, 46, 75], Operations: []\nExploring Operation: 75-68=7, Resulting Numbers: [35, 46, 7]\nGenerated Node #2: [35, 46, 7] from Operation: 75-68=7\nCurrent State: 77:[35, 46, 7], Operations: ['75-68=7']\nExploring Operation: 46-35=11, Resulting Numbers: [7, 11]\nGenerated Node #3: [7, 11] from Operation: 46-35=11\nCurrent State: 77:[7, 11], Operations: ['75-68=7', '46-35=11']\nExploring Operation: 7*11=77, Resulting Numbers: [77]\n77,77 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 33, + 90, + 76, + 9 + ], + "target": 10, + "solution": [ + "90-33=57", + "76-9=67", + "67-57=10" + ], + "optimal_path": "Current State: 10:[33, 90, 76, 9], Operations: []\nExploring Operation: 90-33=57, Resulting Numbers: [76, 9, 57]\nGenerated Node #2: [76, 9, 57] from Operation: 90-33=57\nCurrent State: 10:[76, 9, 57], Operations: ['90-33=57']\nExploring Operation: 76-9=67, Resulting Numbers: [57, 67]\nGenerated Node #3: [57, 67] from Operation: 76-9=67\nCurrent State: 10:[57, 67], Operations: ['90-33=57', '76-9=67']\nExploring Operation: 67-57=10, Resulting Numbers: [10]\n10,10 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 82, + 39, + 78, + 44 + ], + "target": 77, + "solution": [ + "82-39=43", + "78-44=34", + "43+34=77" + ], + "optimal_path": "Current State: 77:[82, 39, 78, 44], Operations: []\nExploring Operation: 82-39=43, Resulting Numbers: [78, 44, 43]\nGenerated Node #2: [78, 44, 43] from Operation: 82-39=43\nCurrent State: 77:[78, 44, 43], Operations: ['82-39=43']\nExploring Operation: 78-44=34, Resulting Numbers: [43, 34]\nGenerated Node #3: [43, 34] from Operation: 78-44=34\nCurrent State: 77:[43, 34], Operations: ['82-39=43', '78-44=34']\nExploring Operation: 43+34=77, Resulting Numbers: [77]\n77,77 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 84, + 35, + 84, + 3 + ], + "target": 70, + "solution": [ + "84/84=1", + "3-1=2", + "35*2=70" + ], + "optimal_path": "Current State: 70:[84, 35, 84, 3], Operations: []\nExploring Operation: 84/84=1, Resulting Numbers: [35, 3, 1]\nGenerated Node #2: [35, 3, 1] from Operation: 84/84=1\nCurrent State: 70:[35, 3, 1], Operations: ['84/84=1']\nExploring Operation: 3-1=2, Resulting Numbers: [35, 2]\nGenerated Node #3: [35, 2] from Operation: 3-1=2\nCurrent State: 70:[35, 2], Operations: ['84/84=1', '3-1=2']\nExploring Operation: 35*2=70, Resulting Numbers: [70]\n70,70 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 33, + 77, + 73, + 47 + ], + "target": 10, + "solution": [ + "33+77=110", + "73+47=120", + "120-110=10" + ], + "optimal_path": "Current State: 10:[33, 77, 73, 47], Operations: []\nExploring Operation: 33+77=110, Resulting Numbers: [73, 47, 110]\nGenerated Node #2: [73, 47, 110] from Operation: 33+77=110\nCurrent State: 10:[73, 47, 110], Operations: ['33+77=110']\nExploring Operation: 73+47=120, Resulting Numbers: [110, 120]\nGenerated Node #3: [110, 120] from Operation: 73+47=120\nCurrent State: 10:[110, 120], Operations: ['33+77=110', '73+47=120']\nExploring Operation: 120-110=10, Resulting Numbers: [10]\n10,10 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 3, + 52, + 43, + 34 + ], + "target": 43, + "solution": [ + "3*43=129", + "52+34=86", + "129-86=43" + ], + "optimal_path": "Current State: 43:[3, 52, 43, 34], Operations: []\nExploring Operation: 3*43=129, Resulting Numbers: [52, 34, 129]\nGenerated Node #2: [52, 34, 129] from Operation: 3*43=129\nCurrent State: 43:[52, 34, 129], Operations: ['3*43=129']\nExploring Operation: 52+34=86, Resulting Numbers: [129, 86]\nGenerated Node #3: [129, 86] from Operation: 52+34=86\nCurrent State: 43:[129, 86], Operations: ['3*43=129', '52+34=86']\nExploring Operation: 129-86=43, Resulting Numbers: [43]\n43,43 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 36, + 79, + 10, + 94 + ], + "target": 41, + "solution": [ + "79-36=43", + "94-10=84", + "84-43=41" + ], + "optimal_path": "Current State: 41:[36, 79, 10, 94], Operations: []\nExploring Operation: 79-36=43, Resulting Numbers: [10, 94, 43]\nGenerated Node #2: [10, 94, 43] from Operation: 79-36=43\nCurrent State: 41:[10, 94, 43], Operations: ['79-36=43']\nExploring Operation: 94-10=84, Resulting Numbers: [43, 84]\nGenerated Node #3: [43, 84] from Operation: 94-10=84\nCurrent State: 41:[43, 84], Operations: ['79-36=43', '94-10=84']\nExploring Operation: 84-43=41, Resulting Numbers: [41]\n41,41 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 28, + 43, + 90, + 69 + ], + "target": 92, + "solution": [ + "28+43=71", + "90-69=21", + "71+21=92" + ], + "optimal_path": "Current State: 92:[28, 43, 90, 69], Operations: []\nExploring Operation: 28+43=71, Resulting Numbers: [90, 69, 71]\nGenerated Node #2: [90, 69, 71] from Operation: 28+43=71\nCurrent State: 92:[90, 69, 71], Operations: ['28+43=71']\nExploring Operation: 90-69=21, Resulting Numbers: [71, 21]\nGenerated Node #3: [71, 21] from Operation: 90-69=21\nCurrent State: 92:[71, 21], Operations: ['28+43=71', '90-69=21']\nExploring Operation: 71+21=92, Resulting Numbers: [92]\n92,92 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 49, + 37, + 35, + 6 + ], + "target": 70, + "solution": [ + "49-37=12", + "35*12=420", + "420/6=70" + ], + "optimal_path": "Current State: 70:[49, 37, 35, 6], Operations: []\nExploring Operation: 49-37=12, Resulting Numbers: [35, 6, 12]\nGenerated Node #2: [35, 6, 12] from Operation: 49-37=12\nCurrent State: 70:[35, 6, 12], Operations: ['49-37=12']\nExploring Operation: 35*12=420, Resulting Numbers: [6, 420]\nGenerated Node #3: [6, 420] from Operation: 35*12=420\nCurrent State: 70:[6, 420], Operations: ['49-37=12', '35*12=420']\nExploring Operation: 420/6=70, Resulting Numbers: [70]\n70,70 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 16, + 66, + 99, + 44 + ], + "target": 60, + "solution": [ + "66+99=165", + "16*165=2640", + "2640/44=60" + ], + "optimal_path": "Current State: 60:[16, 66, 99, 44], Operations: []\nExploring Operation: 66+99=165, Resulting Numbers: [16, 44, 165]\nGenerated Node #2: [16, 44, 165] from Operation: 66+99=165\nCurrent State: 60:[16, 44, 165], Operations: ['66+99=165']\nExploring Operation: 16*165=2640, Resulting Numbers: [44, 2640]\nGenerated Node #3: [44, 2640] from Operation: 16*165=2640\nCurrent State: 60:[44, 2640], Operations: ['66+99=165', '16*165=2640']\nExploring Operation: 2640/44=60, Resulting Numbers: [60]\n60,60 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 82, + 3, + 80, + 90 + ], + "target": 13, + "solution": [ + "90-82=8", + "80/8=10", + "3+10=13" + ], + "optimal_path": "Current State: 13:[82, 3, 80, 90], Operations: []\nExploring Operation: 90-82=8, Resulting Numbers: [3, 80, 8]\nGenerated Node #2: [3, 80, 8] from Operation: 90-82=8\nCurrent State: 13:[3, 80, 8], Operations: ['90-82=8']\nExploring Operation: 80/8=10, Resulting Numbers: [3, 10]\nGenerated Node #3: [3, 10] from Operation: 80/8=10\nCurrent State: 13:[3, 10], Operations: ['90-82=8', '80/8=10']\nExploring Operation: 3+10=13, Resulting Numbers: [13]\n13,13 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 51, + 97, + 9, + 85 + ], + "target": 72, + "solution": [ + "51+97=148", + "85-9=76", + "148-76=72" + ], + "optimal_path": "Current State: 72:[51, 97, 9, 85], Operations: []\nExploring Operation: 51+97=148, Resulting Numbers: [9, 85, 148]\nGenerated Node #2: [9, 85, 148] from Operation: 51+97=148\nCurrent State: 72:[9, 85, 148], Operations: ['51+97=148']\nExploring Operation: 85-9=76, Resulting Numbers: [148, 76]\nGenerated Node #3: [148, 76] from Operation: 85-9=76\nCurrent State: 72:[148, 76], Operations: ['51+97=148', '85-9=76']\nExploring Operation: 148-76=72, Resulting Numbers: [72]\n72,72 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 57, + 93, + 66, + 31 + ], + "target": 53, + "solution": [ + "57+93=150", + "66+31=97", + "150-97=53" + ], + "optimal_path": "Current State: 53:[57, 93, 66, 31], Operations: []\nExploring Operation: 57+93=150, Resulting Numbers: [66, 31, 150]\nGenerated Node #2: [66, 31, 150] from Operation: 57+93=150\nCurrent State: 53:[66, 31, 150], Operations: ['57+93=150']\nExploring Operation: 66+31=97, Resulting Numbers: [150, 97]\nGenerated Node #3: [150, 97] from Operation: 66+31=97\nCurrent State: 53:[150, 97], Operations: ['57+93=150', '66+31=97']\nExploring Operation: 150-97=53, Resulting Numbers: [53]\n53,53 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 31, + 84, + 44, + 29 + ], + "target": 68, + "solution": [ + "84-31=53", + "44-29=15", + "53+15=68" + ], + "optimal_path": "Current State: 68:[31, 84, 44, 29], Operations: []\nExploring Operation: 84-31=53, Resulting Numbers: [44, 29, 53]\nGenerated Node #2: [44, 29, 53] from Operation: 84-31=53\nCurrent State: 68:[44, 29, 53], Operations: ['84-31=53']\nExploring Operation: 44-29=15, Resulting Numbers: [53, 15]\nGenerated Node #3: [53, 15] from Operation: 44-29=15\nCurrent State: 68:[53, 15], Operations: ['84-31=53', '44-29=15']\nExploring Operation: 53+15=68, Resulting Numbers: [68]\n68,68 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 9, + 95, + 61, + 41 + ], + "target": 67, + "solution": [ + "95-41=54", + "54/9=6", + "61+6=67" + ], + "optimal_path": "Current State: 67:[9, 95, 61, 41], Operations: []\nExploring Operation: 95-41=54, Resulting Numbers: [9, 61, 54]\nGenerated Node #2: [9, 61, 54] from Operation: 95-41=54\nCurrent State: 67:[9, 61, 54], Operations: ['95-41=54']\nExploring Operation: 54/9=6, Resulting Numbers: [61, 6]\nGenerated Node #3: [61, 6] from Operation: 54/9=6\nCurrent State: 67:[61, 6], Operations: ['95-41=54', '54/9=6']\nExploring Operation: 61+6=67, Resulting Numbers: [67]\n67,67 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 65, + 48, + 14, + 17 + ], + "target": 49, + "solution": [ + "17-14=3", + "48/3=16", + "65-16=49" + ], + "optimal_path": "Current State: 49:[65, 48, 14, 17], Operations: []\nExploring Operation: 17-14=3, Resulting Numbers: [65, 48, 3]\nGenerated Node #2: [65, 48, 3] from Operation: 17-14=3\nCurrent State: 49:[65, 48, 3], Operations: ['17-14=3']\nExploring Operation: 48/3=16, Resulting Numbers: [65, 16]\nGenerated Node #3: [65, 16] from Operation: 48/3=16\nCurrent State: 49:[65, 16], Operations: ['17-14=3', '48/3=16']\nExploring Operation: 65-16=49, Resulting Numbers: [49]\n49,49 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 73, + 94, + 26, + 17 + ], + "target": 19, + "solution": [ + "73-26=47", + "94/47=2", + "17+2=19" + ], + "optimal_path": "Current State: 19:[73, 94, 26, 17], Operations: []\nExploring Operation: 73-26=47, Resulting Numbers: [94, 17, 47]\nGenerated Node #2: [94, 17, 47] from Operation: 73-26=47\nCurrent State: 19:[94, 17, 47], Operations: ['73-26=47']\nExploring Operation: 94/47=2, Resulting Numbers: [17, 2]\nGenerated Node #3: [17, 2] from Operation: 94/47=2\nCurrent State: 19:[17, 2], Operations: ['73-26=47', '94/47=2']\nExploring Operation: 17+2=19, Resulting Numbers: [19]\n19,19 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 4, + 7, + 67, + 5 + ], + "target": 75, + "solution": [ + "7-4=3", + "67+5=72", + "3+72=75" + ], + "optimal_path": "Current State: 75:[4, 7, 67, 5], Operations: []\nExploring Operation: 7-4=3, Resulting Numbers: [67, 5, 3]\nGenerated Node #2: [67, 5, 3] from Operation: 7-4=3\nCurrent State: 75:[67, 5, 3], Operations: ['7-4=3']\nExploring Operation: 67+5=72, Resulting Numbers: [3, 72]\nGenerated Node #3: [3, 72] from Operation: 67+5=72\nCurrent State: 75:[3, 72], Operations: ['7-4=3', '67+5=72']\nExploring Operation: 3+72=75, Resulting Numbers: [75]\n75,75 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 64, + 16, + 37, + 53 + ], + "target": 95, + "solution": [ + "64/16=4", + "37*4=148", + "148-53=95" + ], + "optimal_path": "Current State: 95:[64, 16, 37, 53], Operations: []\nExploring Operation: 64/16=4, Resulting Numbers: [37, 53, 4]\nGenerated Node #2: [37, 53, 4] from Operation: 64/16=4\nCurrent State: 95:[37, 53, 4], Operations: ['64/16=4']\nExploring Operation: 37*4=148, Resulting Numbers: [53, 148]\nGenerated Node #3: [53, 148] from Operation: 37*4=148\nCurrent State: 95:[53, 148], Operations: ['64/16=4', '37*4=148']\nExploring Operation: 148-53=95, Resulting Numbers: [95]\n95,95 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 32, + 33, + 75, + 57 + ], + "target": 36, + "solution": [ + "57-32=25", + "75/25=3", + "33+3=36" + ], + "optimal_path": "Current State: 36:[32, 33, 75, 57], Operations: []\nExploring Operation: 57-32=25, Resulting Numbers: [33, 75, 25]\nGenerated Node #2: [33, 75, 25] from Operation: 57-32=25\nCurrent State: 36:[33, 75, 25], Operations: ['57-32=25']\nExploring Operation: 75/25=3, Resulting Numbers: [33, 3]\nGenerated Node #3: [33, 3] from Operation: 75/25=3\nCurrent State: 36:[33, 3], Operations: ['57-32=25', '75/25=3']\nExploring Operation: 33+3=36, Resulting Numbers: [36]\n36,36 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 17, + 51, + 61, + 59 + ], + "target": 32, + "solution": [ + "51-17=34", + "61-59=2", + "34-2=32" + ], + "optimal_path": "Current State: 32:[17, 51, 61, 59], Operations: []\nExploring Operation: 51-17=34, Resulting Numbers: [61, 59, 34]\nGenerated Node #2: [61, 59, 34] from Operation: 51-17=34\nCurrent State: 32:[61, 59, 34], Operations: ['51-17=34']\nExploring Operation: 61-59=2, Resulting Numbers: [34, 2]\nGenerated Node #3: [34, 2] from Operation: 61-59=2\nCurrent State: 32:[34, 2], Operations: ['51-17=34', '61-59=2']\nExploring Operation: 34-2=32, Resulting Numbers: [32]\n32,32 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 49, + 25, + 52, + 54 + ], + "target": 21, + "solution": [ + "52-49=3", + "25*3=75", + "75-54=21" + ], + "optimal_path": "Current State: 21:[49, 25, 52, 54], Operations: []\nExploring Operation: 52-49=3, Resulting Numbers: [25, 54, 3]\nGenerated Node #2: [25, 54, 3] from Operation: 52-49=3\nCurrent State: 21:[25, 54, 3], Operations: ['52-49=3']\nExploring Operation: 25*3=75, Resulting Numbers: [54, 75]\nGenerated Node #3: [54, 75] from Operation: 25*3=75\nCurrent State: 21:[54, 75], Operations: ['52-49=3', '25*3=75']\nExploring Operation: 75-54=21, Resulting Numbers: [21]\n21,21 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 6, + 51, + 59, + 87 + ], + "target": 17, + "solution": [ + "51-6=45", + "87-59=28", + "45-28=17" + ], + "optimal_path": "Current State: 17:[6, 51, 59, 87], Operations: []\nExploring Operation: 51-6=45, Resulting Numbers: [59, 87, 45]\nGenerated Node #2: [59, 87, 45] from Operation: 51-6=45\nCurrent State: 17:[59, 87, 45], Operations: ['51-6=45']\nExploring Operation: 87-59=28, Resulting Numbers: [45, 28]\nGenerated Node #3: [45, 28] from Operation: 87-59=28\nCurrent State: 17:[45, 28], Operations: ['51-6=45', '87-59=28']\nExploring Operation: 45-28=17, Resulting Numbers: [17]\n17,17 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 34, + 60, + 69, + 7 + ], + "target": 68, + "solution": [ + "69-60=9", + "9-7=2", + "34*2=68" + ], + "optimal_path": "Current State: 68:[34, 60, 69, 7], Operations: []\nExploring Operation: 69-60=9, Resulting Numbers: [34, 7, 9]\nGenerated Node #2: [34, 7, 9] from Operation: 69-60=9\nCurrent State: 68:[34, 7, 9], Operations: ['69-60=9']\nExploring Operation: 9-7=2, Resulting Numbers: [34, 2]\nGenerated Node #3: [34, 2] from Operation: 9-7=2\nCurrent State: 68:[34, 2], Operations: ['69-60=9', '9-7=2']\nExploring Operation: 34*2=68, Resulting Numbers: [68]\n68,68 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 87, + 23, + 58, + 85 + ], + "target": 10, + "solution": [ + "87+58=145", + "85+145=230", + "230/23=10" + ], + "optimal_path": "Current State: 10:[87, 23, 58, 85], Operations: []\nExploring Operation: 87+58=145, Resulting Numbers: [23, 85, 145]\nGenerated Node #2: [23, 85, 145] from Operation: 87+58=145\nCurrent State: 10:[23, 85, 145], Operations: ['87+58=145']\nExploring Operation: 85+145=230, Resulting Numbers: [23, 230]\nGenerated Node #3: [23, 230] from Operation: 85+145=230\nCurrent State: 10:[23, 230], Operations: ['87+58=145', '85+145=230']\nExploring Operation: 230/23=10, Resulting Numbers: [10]\n10,10 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 49, + 56, + 34, + 17 + ], + "target": 85, + "solution": [ + "56-49=7", + "17*7=119", + "119-34=85" + ], + "optimal_path": "Current State: 85:[49, 56, 34, 17], Operations: []\nExploring Operation: 56-49=7, Resulting Numbers: [34, 17, 7]\nGenerated Node #2: [34, 17, 7] from Operation: 56-49=7\nCurrent State: 85:[34, 17, 7], Operations: ['56-49=7']\nExploring Operation: 17*7=119, Resulting Numbers: [34, 119]\nGenerated Node #3: [34, 119] from Operation: 17*7=119\nCurrent State: 85:[34, 119], Operations: ['56-49=7', '17*7=119']\nExploring Operation: 119-34=85, Resulting Numbers: [85]\n85,85 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 94, + 71, + 30, + 24 + ], + "target": 28, + "solution": [ + "71-24=47", + "94/47=2", + "30-2=28" + ], + "optimal_path": "Current State: 28:[94, 71, 30, 24], Operations: []\nExploring Operation: 71-24=47, Resulting Numbers: [94, 30, 47]\nGenerated Node #2: [94, 30, 47] from Operation: 71-24=47\nCurrent State: 28:[94, 30, 47], Operations: ['71-24=47']\nExploring Operation: 94/47=2, Resulting Numbers: [30, 2]\nGenerated Node #3: [30, 2] from Operation: 94/47=2\nCurrent State: 28:[30, 2], Operations: ['71-24=47', '94/47=2']\nExploring Operation: 30-2=28, Resulting Numbers: [28]\n28,28 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 70, + 90, + 64, + 31 + ], + "target": 46, + "solution": [ + "70-64=6", + "90/6=15", + "31+15=46" + ], + "optimal_path": "Current State: 46:[70, 90, 64, 31], Operations: []\nExploring Operation: 70-64=6, Resulting Numbers: [90, 31, 6]\nGenerated Node #2: [90, 31, 6] from Operation: 70-64=6\nCurrent State: 46:[90, 31, 6], Operations: ['70-64=6']\nExploring Operation: 90/6=15, Resulting Numbers: [31, 15]\nGenerated Node #3: [31, 15] from Operation: 90/6=15\nCurrent State: 46:[31, 15], Operations: ['70-64=6', '90/6=15']\nExploring Operation: 31+15=46, Resulting Numbers: [46]\n46,46 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 76, + 68, + 64, + 60 + ], + "target": 96, + "solution": [ + "76-64=12", + "68-60=8", + "12*8=96" + ], + "optimal_path": "Current State: 96:[76, 68, 64, 60], Operations: []\nExploring Operation: 76-64=12, Resulting Numbers: [68, 60, 12]\nGenerated Node #2: [68, 60, 12] from Operation: 76-64=12\nCurrent State: 96:[68, 60, 12], Operations: ['76-64=12']\nExploring Operation: 68-60=8, Resulting Numbers: [12, 8]\nGenerated Node #3: [12, 8] from Operation: 68-60=8\nCurrent State: 96:[12, 8], Operations: ['76-64=12', '68-60=8']\nExploring Operation: 12*8=96, Resulting Numbers: [96]\n96,96 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 96, + 49, + 39, + 32 + ], + "target": 30, + "solution": [ + "96/32=3", + "49-39=10", + "3*10=30" + ], + "optimal_path": "Current State: 30:[96, 49, 39, 32], Operations: []\nExploring Operation: 96/32=3, Resulting Numbers: [49, 39, 3]\nGenerated Node #2: [49, 39, 3] from Operation: 96/32=3\nCurrent State: 30:[49, 39, 3], Operations: ['96/32=3']\nExploring Operation: 49-39=10, Resulting Numbers: [3, 10]\nGenerated Node #3: [3, 10] from Operation: 49-39=10\nCurrent State: 30:[3, 10], Operations: ['96/32=3', '49-39=10']\nExploring Operation: 3*10=30, Resulting Numbers: [30]\n30,30 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 94, + 73, + 93, + 27 + ], + "target": 87, + "solution": [ + "94-73=21", + "93-27=66", + "21+66=87" + ], + "optimal_path": "Current State: 87:[94, 73, 93, 27], Operations: []\nExploring Operation: 94-73=21, Resulting Numbers: [93, 27, 21]\nGenerated Node #2: [93, 27, 21] from Operation: 94-73=21\nCurrent State: 87:[93, 27, 21], Operations: ['94-73=21']\nExploring Operation: 93-27=66, Resulting Numbers: [21, 66]\nGenerated Node #3: [21, 66] from Operation: 93-27=66\nCurrent State: 87:[21, 66], Operations: ['94-73=21', '93-27=66']\nExploring Operation: 21+66=87, Resulting Numbers: [87]\n87,87 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 63, + 46, + 92, + 93 + ], + "target": 32, + "solution": [ + "93-63=30", + "92/46=2", + "30+2=32" + ], + "optimal_path": "Current State: 32:[63, 46, 92, 93], Operations: []\nExploring Operation: 93-63=30, Resulting Numbers: [46, 92, 30]\nGenerated Node #2: [46, 92, 30] from Operation: 93-63=30\nCurrent State: 32:[46, 92, 30], Operations: ['93-63=30']\nExploring Operation: 92/46=2, Resulting Numbers: [30, 2]\nGenerated Node #3: [30, 2] from Operation: 92/46=2\nCurrent State: 32:[30, 2], Operations: ['93-63=30', '92/46=2']\nExploring Operation: 30+2=32, Resulting Numbers: [32]\n32,32 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 58, + 32, + 79, + 25 + ], + "target": 80, + "solution": [ + "58-32=26", + "79-25=54", + "26+54=80" + ], + "optimal_path": "Current State: 67:[55, 36, 46, 49], Operations: []\nExploring Operation: 49-46=3, Resulting Numbers: [55, 36, 3]\nGenerated Node #2: [55, 36, 3] from Operation: 49-46=3\nCurrent State: 67:[55, 36, 3], Operations: ['49-46=3']\nExploring Operation: 36/3=12, Resulting Numbers: [55, 12]\nGenerated Node #3: [55, 12] from Operation: 36/3=12\nCurrent State: 67:[55, 12], Operations: ['49-46=3', '36/3=12']\nExploring Operation: 55+12=67, Resulting Numbers: [67]\n67,67 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 4, + 20, + 68, + 22 + ], + "target": 32, + "solution": [ + "68-4=64", + "22-20=2", + "64/2=32" + ], + "optimal_path": "Current State: 32:[4, 20, 68, 22], Operations: []\nExploring Operation: 68-4=64, Resulting Numbers: [20, 22, 64]\nGenerated Node #2: [20, 22, 64] from Operation: 68-4=64\nCurrent State: 32:[20, 22, 64], Operations: ['68-4=64']\nExploring Operation: 22-20=2, Resulting Numbers: [64, 2]\nGenerated Node #3: [64, 2] from Operation: 22-20=2\nCurrent State: 32:[64, 2], Operations: ['68-4=64', '22-20=2']\nExploring Operation: 64/2=32, Resulting Numbers: [32]\n32,32 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 2, + 86, + 37, + 29 + ], + "target": 80, + "solution": [ + "2+86=88", + "37-29=8", + "88-8=80" + ], + "optimal_path": "Current State: 80:[2, 86, 37, 29], Operations: []\nExploring Operation: 2+86=88, Resulting Numbers: [37, 29, 88]\nGenerated Node #2: [37, 29, 88] from Operation: 2+86=88\nCurrent State: 80:[37, 29, 88], Operations: ['2+86=88']\nExploring Operation: 37-29=8, Resulting Numbers: [88, 8]\nGenerated Node #3: [88, 8] from Operation: 37-29=8\nCurrent State: 80:[88, 8], Operations: ['2+86=88', '37-29=8']\nExploring Operation: 88-8=80, Resulting Numbers: [80]\n80,80 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 78, + 1, + 77, + 67 + ], + "target": 66, + "solution": [ + "78*1=78", + "77+67=144", + "144-78=66" + ], + "optimal_path": "Current State: 66:[78, 1, 77, 67], Operations: []\nExploring Operation: 78*1=78, Resulting Numbers: [77, 67, 78]\nGenerated Node #2: [77, 67, 78] from Operation: 78*1=78\nCurrent State: 66:[77, 67, 78], Operations: ['78*1=78']\nExploring Operation: 77+67=144, Resulting Numbers: [78, 144]\nGenerated Node #3: [78, 144] from Operation: 77+67=144\nCurrent State: 66:[78, 144], Operations: ['78*1=78', '77+67=144']\nExploring Operation: 144-78=66, Resulting Numbers: [66]\n66,66 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 45, + 10, + 18, + 72 + ], + "target": 12, + "solution": [ + "18+72=90", + "90/45=2", + "10+2=12" + ], + "optimal_path": "Current State: 12:[45, 10, 18, 72], Operations: []\nExploring Operation: 18+72=90, Resulting Numbers: [45, 10, 90]\nGenerated Node #2: [45, 10, 90] from Operation: 18+72=90\nCurrent State: 12:[45, 10, 90], Operations: ['18+72=90']\nExploring Operation: 90/45=2, Resulting Numbers: [10, 2]\nGenerated Node #3: [10, 2] from Operation: 90/45=2\nCurrent State: 12:[10, 2], Operations: ['18+72=90', '90/45=2']\nExploring Operation: 10+2=12, Resulting Numbers: [12]\n12,12 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 1, + 72, + 22, + 75 + ], + "target": 66, + "solution": [ + "1*72=72", + "75-72=3", + "22*3=66" + ], + "optimal_path": "Current State: 66:[1, 72, 22, 75], Operations: []\nExploring Operation: 1*72=72, Resulting Numbers: [22, 75, 72]\nGenerated Node #2: [22, 75, 72] from Operation: 1*72=72\nCurrent State: 66:[22, 75, 72], Operations: ['1*72=72']\nExploring Operation: 75-72=3, Resulting Numbers: [22, 3]\nGenerated Node #3: [22, 3] from Operation: 75-72=3\nCurrent State: 66:[22, 3], Operations: ['1*72=72', '75-72=3']\nExploring Operation: 22*3=66, Resulting Numbers: [66]\n66,66 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 47, + 7, + 2, + 39 + ], + "target": 12, + "solution": [ + "47+7=54", + "54/2=27", + "39-27=12" + ], + "optimal_path": "Current State: 12:[47, 7, 2, 39], Operations: []\nExploring Operation: 47+7=54, Resulting Numbers: [2, 39, 54]\nGenerated Node #2: [2, 39, 54] from Operation: 47+7=54\nCurrent State: 12:[2, 39, 54], Operations: ['47+7=54']\nExploring Operation: 54/2=27, Resulting Numbers: [39, 27]\nGenerated Node #3: [39, 27] from Operation: 54/2=27\nCurrent State: 12:[39, 27], Operations: ['47+7=54', '54/2=27']\nExploring Operation: 39-27=12, Resulting Numbers: [12]\n12,12 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 13, + 52, + 56, + 29 + ], + "target": 38, + "solution": [ + "13+52=65", + "56-29=27", + "65-27=38" + ], + "optimal_path": "Current State: 38:[13, 52, 56, 29], Operations: []\nExploring Operation: 13+52=65, Resulting Numbers: [56, 29, 65]\nGenerated Node #2: [56, 29, 65] from Operation: 13+52=65\nCurrent State: 38:[56, 29, 65], Operations: ['13+52=65']\nExploring Operation: 56-29=27, Resulting Numbers: [65, 27]\nGenerated Node #3: [65, 27] from Operation: 56-29=27\nCurrent State: 38:[65, 27], Operations: ['13+52=65', '56-29=27']\nExploring Operation: 65-27=38, Resulting Numbers: [38]\n38,38 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 56, + 16, + 6, + 13 + ], + "target": 25, + "solution": [ + "56+16=72", + "72/6=12", + "13+12=25" + ], + "optimal_path": "Current State: 25:[56, 16, 6, 13], Operations: []\nExploring Operation: 56+16=72, Resulting Numbers: [6, 13, 72]\nGenerated Node #2: [6, 13, 72] from Operation: 56+16=72\nCurrent State: 25:[6, 13, 72], Operations: ['56+16=72']\nExploring Operation: 72/6=12, Resulting Numbers: [13, 12]\nGenerated Node #3: [13, 12] from Operation: 72/6=12\nCurrent State: 25:[13, 12], Operations: ['56+16=72', '72/6=12']\nExploring Operation: 13+12=25, Resulting Numbers: [25]\n25,25 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 74, + 51, + 72, + 73 + ], + "target": 62, + "solution": [ + "74-72=2", + "51+73=124", + "124/2=62" + ], + "optimal_path": "Current State: 62:[74, 51, 72, 73], Operations: []\nExploring Operation: 74-72=2, Resulting Numbers: [51, 73, 2]\nGenerated Node #2: [51, 73, 2] from Operation: 74-72=2\nCurrent State: 62:[51, 73, 2], Operations: ['74-72=2']\nExploring Operation: 51+73=124, Resulting Numbers: [2, 124]\nGenerated Node #3: [2, 124] from Operation: 51+73=124\nCurrent State: 62:[2, 124], Operations: ['74-72=2', '51+73=124']\nExploring Operation: 124/2=62, Resulting Numbers: [62]\n62,62 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 97, + 24, + 85, + 33 + ], + "target": 66, + "solution": [ + "97-85=12", + "24*33=792", + "792/12=66" + ], + "optimal_path": "Current State: 66:[97, 24, 85, 33], Operations: []\nExploring Operation: 97-85=12, Resulting Numbers: [24, 33, 12]\nGenerated Node #2: [24, 33, 12] from Operation: 97-85=12\nCurrent State: 66:[24, 33, 12], Operations: ['97-85=12']\nExploring Operation: 24*33=792, Resulting Numbers: [12, 792]\nGenerated Node #3: [12, 792] from Operation: 24*33=792\nCurrent State: 66:[12, 792], Operations: ['97-85=12', '24*33=792']\nExploring Operation: 792/12=66, Resulting Numbers: [66]\n66,66 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 15, + 25, + 10, + 6 + ], + "target": 94, + "solution": [ + "25-15=10", + "10*10=100", + "100-6=94" + ], + "optimal_path": "Current State: 94:[15, 25, 10, 6], Operations: []\nExploring Operation: 25-15=10, Resulting Numbers: [10, 6, 10]\nGenerated Node #2: [10, 6, 10] from Operation: 25-15=10\nCurrent State: 94:[10, 6, 10], Operations: ['25-15=10']\nExploring Operation: 10*10=100, Resulting Numbers: [6, 100]\nGenerated Node #3: [6, 100] from Operation: 10*10=100\nCurrent State: 94:[6, 100], Operations: ['25-15=10', '10*10=100']\nExploring Operation: 100-6=94, Resulting Numbers: [94]\n94,94 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 27, + 87, + 90, + 45 + ], + "target": 92, + "solution": [ + "45-27=18", + "90/18=5", + "87+5=92" + ], + "optimal_path": "Current State: 92:[27, 87, 90, 45], Operations: []\nExploring Operation: 45-27=18, Resulting Numbers: [87, 90, 18]\nGenerated Node #2: [87, 90, 18] from Operation: 45-27=18\nCurrent State: 92:[87, 90, 18], Operations: ['45-27=18']\nExploring Operation: 90/18=5, Resulting Numbers: [87, 5]\nGenerated Node #3: [87, 5] from Operation: 90/18=5\nCurrent State: 92:[87, 5], Operations: ['45-27=18', '90/18=5']\nExploring Operation: 87+5=92, Resulting Numbers: [92]\n92,92 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 11, + 37, + 63, + 4 + ], + "target": 36, + "solution": [ + "37+63=100", + "100/4=25", + "11+25=36" + ], + "optimal_path": "Current State: 36:[11, 37, 63, 4], Operations: []\nExploring Operation: 37+63=100, Resulting Numbers: [11, 4, 100]\nGenerated Node #2: [11, 4, 100] from Operation: 37+63=100\nCurrent State: 36:[11, 4, 100], Operations: ['37+63=100']\nExploring Operation: 100/4=25, Resulting Numbers: [11, 25]\nGenerated Node #3: [11, 25] from Operation: 100/4=25\nCurrent State: 36:[11, 25], Operations: ['37+63=100', '100/4=25']\nExploring Operation: 11+25=36, Resulting Numbers: [36]\n36,36 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 80, + 61, + 70, + 22 + ], + "target": 93, + "solution": [ + "80+61=141", + "70-22=48", + "141-48=93" + ], + "optimal_path": "Current State: 93:[80, 61, 70, 22], Operations: []\nExploring Operation: 80+61=141, Resulting Numbers: [70, 22, 141]\nGenerated Node #2: [70, 22, 141] from Operation: 80+61=141\nCurrent State: 93:[70, 22, 141], Operations: ['80+61=141']\nExploring Operation: 70-22=48, Resulting Numbers: [141, 48]\nGenerated Node #3: [141, 48] from Operation: 70-22=48\nCurrent State: 93:[141, 48], Operations: ['80+61=141', '70-22=48']\nExploring Operation: 141-48=93, Resulting Numbers: [93]\n93,93 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 77, + 63, + 5, + 3 + ], + "target": 47, + "solution": [ + "77-63=14", + "3*14=42", + "5+42=47" + ], + "optimal_path": "Current State: 47:[77, 63, 5, 3], Operations: []\nExploring Operation: 77-63=14, Resulting Numbers: [5, 3, 14]\nGenerated Node #2: [5, 3, 14] from Operation: 77-63=14\nCurrent State: 47:[5, 3, 14], Operations: ['77-63=14']\nExploring Operation: 3*14=42, Resulting Numbers: [5, 42]\nGenerated Node #3: [5, 42] from Operation: 3*14=42\nCurrent State: 47:[5, 42], Operations: ['77-63=14', '3*14=42']\nExploring Operation: 5+42=47, Resulting Numbers: [47]\n47,47 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 18, + 42, + 54, + 75 + ], + "target": 20, + "solution": [ + "75-54=21", + "42/21=2", + "18+2=20" + ], + "optimal_path": "Current State: 20:[18, 42, 54, 75], Operations: []\nExploring Operation: 75-54=21, Resulting Numbers: [18, 42, 21]\nGenerated Node #2: [18, 42, 21] from Operation: 75-54=21\nCurrent State: 20:[18, 42, 21], Operations: ['75-54=21']\nExploring Operation: 42/21=2, Resulting Numbers: [18, 2]\nGenerated Node #3: [18, 2] from Operation: 42/21=2\nCurrent State: 20:[18, 2], Operations: ['75-54=21', '42/21=2']\nExploring Operation: 18+2=20, Resulting Numbers: [20]\n20,20 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 19, + 40, + 74, + 96 + ], + "target": 43, + "solution": [ + "40-19=21", + "96-74=22", + "21+22=43" + ], + "optimal_path": "Current State: 43:[19, 40, 74, 96], Operations: []\nExploring Operation: 40-19=21, Resulting Numbers: [74, 96, 21]\nGenerated Node #2: [74, 96, 21] from Operation: 40-19=21\nCurrent State: 43:[74, 96, 21], Operations: ['40-19=21']\nExploring Operation: 96-74=22, Resulting Numbers: [21, 22]\nGenerated Node #3: [21, 22] from Operation: 96-74=22\nCurrent State: 43:[21, 22], Operations: ['40-19=21', '96-74=22']\nExploring Operation: 21+22=43, Resulting Numbers: [43]\n43,43 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 4, + 53, + 69, + 5 + ], + "target": 100, + "solution": [ + "53-4=49", + "69-49=20", + "5*20=100" + ], + "optimal_path": "Current State: 100:[4, 53, 69, 5], Operations: []\nExploring Operation: 53-4=49, Resulting Numbers: [69, 5, 49]\nGenerated Node #2: [69, 5, 49] from Operation: 53-4=49\nCurrent State: 100:[69, 5, 49], Operations: ['53-4=49']\nExploring Operation: 69-49=20, Resulting Numbers: [5, 20]\nGenerated Node #3: [5, 20] from Operation: 69-49=20\nCurrent State: 100:[5, 20], Operations: ['53-4=49', '69-49=20']\nExploring Operation: 5*20=100, Resulting Numbers: [100]\n100,100 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 65, + 90, + 45, + 19 + ], + "target": 36, + "solution": [ + "45-19=26", + "90*26=2340", + "2340/65=36" + ], + "optimal_path": "Current State: 36:[65, 90, 45, 19], Operations: []\nExploring Operation: 45-19=26, Resulting Numbers: [65, 90, 26]\nGenerated Node #2: [65, 90, 26] from Operation: 45-19=26\nCurrent State: 36:[65, 90, 26], Operations: ['45-19=26']\nExploring Operation: 90*26=2340, Resulting Numbers: [65, 2340]\nGenerated Node #3: [65, 2340] from Operation: 90*26=2340\nCurrent State: 36:[65, 2340], Operations: ['45-19=26', '90*26=2340']\nExploring Operation: 2340/65=36, Resulting Numbers: [36]\n36,36 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 97, + 14, + 14, + 97 + ], + "target": 29, + "solution": [ + "97/97=1", + "14+14=28", + "1+28=29" + ], + "optimal_path": "Current State: 29:[97, 14, 14, 97], Operations: []\nExploring Operation: 97/97=1, Resulting Numbers: [14, 14, 1]\nGenerated Node #2: [14, 14, 1] from Operation: 97/97=1\nCurrent State: 29:[14, 14, 1], Operations: ['97/97=1']\nExploring Operation: 14+14=28, Resulting Numbers: [1, 28]\nGenerated Node #3: [1, 28] from Operation: 14+14=28\nCurrent State: 29:[1, 28], Operations: ['97/97=1', '14+14=28']\nExploring Operation: 1+28=29, Resulting Numbers: [29]\n29,29 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 28, + 39, + 83, + 97 + ], + "target": 41, + "solution": [ + "97-83=14", + "28/14=2", + "39+2=41" + ], + "optimal_path": "Current State: 41:[28, 39, 83, 97], Operations: []\nExploring Operation: 97-83=14, Resulting Numbers: [28, 39, 14]\nGenerated Node #2: [28, 39, 14] from Operation: 97-83=14\nCurrent State: 41:[28, 39, 14], Operations: ['97-83=14']\nExploring Operation: 28/14=2, Resulting Numbers: [39, 2]\nGenerated Node #3: [39, 2] from Operation: 28/14=2\nCurrent State: 41:[39, 2], Operations: ['97-83=14', '28/14=2']\nExploring Operation: 39+2=41, Resulting Numbers: [41]\n41,41 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 75, + 28, + 51, + 92 + ], + "target": 25, + "solution": [ + "92-75=17", + "51/17=3", + "28-3=25" + ], + "optimal_path": "Current State: 25:[75, 28, 51, 92], Operations: []\nExploring Operation: 92-75=17, Resulting Numbers: [28, 51, 17]\nGenerated Node #2: [28, 51, 17] from Operation: 92-75=17\nCurrent State: 25:[28, 51, 17], Operations: ['92-75=17']\nExploring Operation: 51/17=3, Resulting Numbers: [28, 3]\nGenerated Node #3: [28, 3] from Operation: 51/17=3\nCurrent State: 25:[28, 3], Operations: ['92-75=17', '51/17=3']\nExploring Operation: 28-3=25, Resulting Numbers: [25]\n25,25 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 12, + 2, + 5, + 24 + ], + "target": 29, + "solution": [ + "12-2=10", + "24-5=19", + "10+19=29" + ], + "optimal_path": "Current State: 29:[12, 2, 5, 24], Operations: []\nExploring Operation: 12-2=10, Resulting Numbers: [5, 24, 10]\nGenerated Node #2: [5, 24, 10] from Operation: 12-2=10\nCurrent State: 29:[5, 24, 10], Operations: ['12-2=10']\nExploring Operation: 24-5=19, Resulting Numbers: [10, 19]\nGenerated Node #3: [10, 19] from Operation: 24-5=19\nCurrent State: 29:[10, 19], Operations: ['12-2=10', '24-5=19']\nExploring Operation: 10+19=29, Resulting Numbers: [29]\n29,29 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 5, + 52, + 60, + 90 + ], + "target": 46, + "solution": [ + "90-60=30", + "30/5=6", + "52-6=46" + ], + "optimal_path": "Current State: 46:[5, 52, 60, 90], Operations: []\nExploring Operation: 90-60=30, Resulting Numbers: [5, 52, 30]\nGenerated Node #2: [5, 52, 30] from Operation: 90-60=30\nCurrent State: 46:[5, 52, 30], Operations: ['90-60=30']\nExploring Operation: 30/5=6, Resulting Numbers: [52, 6]\nGenerated Node #3: [52, 6] from Operation: 30/5=6\nCurrent State: 46:[52, 6], Operations: ['90-60=30', '30/5=6']\nExploring Operation: 52-6=46, Resulting Numbers: [46]\n46,46 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 32, + 23, + 2, + 35 + ], + "target": 43, + "solution": [ + "35-32=3", + "23*2=46", + "46-3=43" + ], + "optimal_path": "Current State: 43:[32, 23, 2, 35], Operations: []\nExploring Operation: 35-32=3, Resulting Numbers: [23, 2, 3]\nGenerated Node #2: [23, 2, 3] from Operation: 35-32=3\nCurrent State: 43:[23, 2, 3], Operations: ['35-32=3']\nExploring Operation: 23*2=46, Resulting Numbers: [3, 46]\nGenerated Node #3: [3, 46] from Operation: 23*2=46\nCurrent State: 43:[3, 46], Operations: ['35-32=3', '23*2=46']\nExploring Operation: 46-3=43, Resulting Numbers: [43]\n43,43 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 30, + 90, + 24, + 6 + ], + "target": 49, + "solution": [ + "90+24=114", + "114/6=19", + "30+19=49" + ], + "optimal_path": "Current State: 49:[30, 90, 24, 6], Operations: []\nExploring Operation: 90+24=114, Resulting Numbers: [30, 6, 114]\nGenerated Node #2: [30, 6, 114] from Operation: 90+24=114\nCurrent State: 49:[30, 6, 114], Operations: ['90+24=114']\nExploring Operation: 114/6=19, Resulting Numbers: [30, 19]\nGenerated Node #3: [30, 19] from Operation: 114/6=19\nCurrent State: 49:[30, 19], Operations: ['90+24=114', '114/6=19']\nExploring Operation: 30+19=49, Resulting Numbers: [49]\n49,49 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 67, + 80, + 99, + 25 + ], + "target": 23, + "solution": [ + "67+80=147", + "99+25=124", + "147-124=23" + ], + "optimal_path": "Current State: 23:[67, 80, 99, 25], Operations: []\nExploring Operation: 67+80=147, Resulting Numbers: [99, 25, 147]\nGenerated Node #2: [99, 25, 147] from Operation: 67+80=147\nCurrent State: 23:[99, 25, 147], Operations: ['67+80=147']\nExploring Operation: 99+25=124, Resulting Numbers: [147, 124]\nGenerated Node #3: [147, 124] from Operation: 99+25=124\nCurrent State: 23:[147, 124], Operations: ['67+80=147', '99+25=124']\nExploring Operation: 147-124=23, Resulting Numbers: [23]\n23,23 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 29, + 52, + 57, + 23 + ], + "target": 86, + "solution": [ + "57-52=5", + "23*5=115", + "115-29=86" + ], + "optimal_path": "Current State: 86:[29, 52, 57, 23], Operations: []\nExploring Operation: 57-52=5, Resulting Numbers: [29, 23, 5]\nGenerated Node #2: [29, 23, 5] from Operation: 57-52=5\nCurrent State: 86:[29, 23, 5], Operations: ['57-52=5']\nExploring Operation: 23*5=115, Resulting Numbers: [29, 115]\nGenerated Node #3: [29, 115] from Operation: 23*5=115\nCurrent State: 86:[29, 115], Operations: ['57-52=5', '23*5=115']\nExploring Operation: 115-29=86, Resulting Numbers: [86]\n86,86 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 18, + 11, + 92, + 60 + ], + "target": 50, + "solution": [ + "18+92=110", + "110/11=10", + "60-10=50" + ], + "optimal_path": "Current State: 50:[18, 11, 92, 60], Operations: []\nExploring Operation: 18+92=110, Resulting Numbers: [11, 60, 110]\nGenerated Node #2: [11, 60, 110] from Operation: 18+92=110\nCurrent State: 50:[11, 60, 110], Operations: ['18+92=110']\nExploring Operation: 110/11=10, Resulting Numbers: [60, 10]\nGenerated Node #3: [60, 10] from Operation: 110/11=10\nCurrent State: 50:[60, 10], Operations: ['18+92=110', '110/11=10']\nExploring Operation: 60-10=50, Resulting Numbers: [50]\n50,50 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 98, + 79, + 10, + 81 + ], + "target": 10, + "solution": [ + "98-79=19", + "81+19=100", + "100/10=10" + ], + "optimal_path": "Current State: 10:[98, 79, 10, 81], Operations: []\nExploring Operation: 98-79=19, Resulting Numbers: [10, 81, 19]\nGenerated Node #2: [10, 81, 19] from Operation: 98-79=19\nCurrent State: 10:[10, 81, 19], Operations: ['98-79=19']\nExploring Operation: 81+19=100, Resulting Numbers: [10, 100]\nGenerated Node #3: [10, 100] from Operation: 81+19=100\nCurrent State: 10:[10, 100], Operations: ['98-79=19', '81+19=100']\nExploring Operation: 100/10=10, Resulting Numbers: [10]\n10,10 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 64, + 67, + 95, + 38 + ], + "target": 74, + "solution": [ + "64+67=131", + "95-38=57", + "131-57=74" + ], + "optimal_path": "Current State: 74:[64, 67, 95, 38], Operations: []\nExploring Operation: 64+67=131, Resulting Numbers: [95, 38, 131]\nGenerated Node #2: [95, 38, 131] from Operation: 64+67=131\nCurrent State: 74:[95, 38, 131], Operations: ['64+67=131']\nExploring Operation: 95-38=57, Resulting Numbers: [131, 57]\nGenerated Node #3: [131, 57] from Operation: 95-38=57\nCurrent State: 74:[131, 57], Operations: ['64+67=131', '95-38=57']\nExploring Operation: 131-57=74, Resulting Numbers: [74]\n74,74 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 43, + 98, + 32, + 70 + ], + "target": 93, + "solution": [ + "98-43=55", + "70-32=38", + "55+38=93" + ], + "optimal_path": "Current State: 93:[43, 98, 32, 70], Operations: []\nExploring Operation: 98-43=55, Resulting Numbers: [32, 70, 55]\nGenerated Node #2: [32, 70, 55] from Operation: 98-43=55\nCurrent State: 93:[32, 70, 55], Operations: ['98-43=55']\nExploring Operation: 70-32=38, Resulting Numbers: [55, 38]\nGenerated Node #3: [55, 38] from Operation: 70-32=38\nCurrent State: 93:[55, 38], Operations: ['98-43=55', '70-32=38']\nExploring Operation: 55+38=93, Resulting Numbers: [93]\n93,93 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 33, + 31, + 81, + 64 + ], + "target": 98, + "solution": [ + "33-31=2", + "81*2=162", + "162-64=98" + ], + "optimal_path": "Current State: 98:[33, 31, 81, 64], Operations: []\nExploring Operation: 33-31=2, Resulting Numbers: [81, 64, 2]\nGenerated Node #2: [81, 64, 2] from Operation: 33-31=2\nCurrent State: 98:[81, 64, 2], Operations: ['33-31=2']\nExploring Operation: 81*2=162, Resulting Numbers: [64, 162]\nGenerated Node #3: [64, 162] from Operation: 81*2=162\nCurrent State: 98:[64, 162], Operations: ['33-31=2', '81*2=162']\nExploring Operation: 162-64=98, Resulting Numbers: [98]\n98,98 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 27, + 93, + 14, + 81 + ], + "target": 54, + "solution": [ + "93-14=79", + "81-79=2", + "27*2=54" + ], + "optimal_path": "Current State: 54:[27, 93, 14, 81], Operations: []\nExploring Operation: 93-14=79, Resulting Numbers: [27, 81, 79]\nGenerated Node #2: [27, 81, 79] from Operation: 93-14=79\nCurrent State: 54:[27, 81, 79], Operations: ['93-14=79']\nExploring Operation: 81-79=2, Resulting Numbers: [27, 2]\nGenerated Node #3: [27, 2] from Operation: 81-79=2\nCurrent State: 54:[27, 2], Operations: ['93-14=79', '81-79=2']\nExploring Operation: 27*2=54, Resulting Numbers: [54]\n54,54 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 40, + 63, + 6, + 48 + ], + "target": 65, + "solution": [ + "63-40=23", + "48-6=42", + "23+42=65" + ], + "optimal_path": "Current State: 65:[40, 63, 6, 48], Operations: []\nExploring Operation: 63-40=23, Resulting Numbers: [6, 48, 23]\nGenerated Node #2: [6, 48, 23] from Operation: 63-40=23\nCurrent State: 65:[6, 48, 23], Operations: ['63-40=23']\nExploring Operation: 48-6=42, Resulting Numbers: [23, 42]\nGenerated Node #3: [23, 42] from Operation: 48-6=42\nCurrent State: 65:[23, 42], Operations: ['63-40=23', '48-6=42']\nExploring Operation: 23+42=65, Resulting Numbers: [65]\n65,65 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 54, + 50, + 16, + 7 + ], + "target": 28, + "solution": [ + "54-50=4", + "16*7=112", + "112/4=28" + ], + "optimal_path": "Current State: 28:[54, 50, 16, 7], Operations: []\nExploring Operation: 54-50=4, Resulting Numbers: [16, 7, 4]\nGenerated Node #2: [16, 7, 4] from Operation: 54-50=4\nCurrent State: 28:[16, 7, 4], Operations: ['54-50=4']\nExploring Operation: 16*7=112, Resulting Numbers: [4, 112]\nGenerated Node #3: [4, 112] from Operation: 16*7=112\nCurrent State: 28:[4, 112], Operations: ['54-50=4', '16*7=112']\nExploring Operation: 112/4=28, Resulting Numbers: [28]\n28,28 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 56, + 28, + 60, + 63 + ], + "target": 96, + "solution": [ + "56*60=3360", + "63-28=35", + "3360/35=96" + ], + "optimal_path": "Current State: 96:[56, 28, 60, 63], Operations: []\nExploring Operation: 56*60=3360, Resulting Numbers: [28, 63, 3360]\nGenerated Node #2: [28, 63, 3360] from Operation: 56*60=3360\nCurrent State: 96:[28, 63, 3360], Operations: ['56*60=3360']\nExploring Operation: 63-28=35, Resulting Numbers: [3360, 35]\nGenerated Node #3: [3360, 35] from Operation: 63-28=35\nCurrent State: 96:[3360, 35], Operations: ['56*60=3360', '63-28=35']\nExploring Operation: 3360/35=96, Resulting Numbers: [96]\n96,96 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 5, + 81, + 54, + 27 + ], + "target": 17, + "solution": [ + "5*81=405", + "54+405=459", + "459/27=17" + ], + "optimal_path": "Current State: 17:[5, 81, 54, 27], Operations: []\nExploring Operation: 5*81=405, Resulting Numbers: [54, 27, 405]\nGenerated Node #2: [54, 27, 405] from Operation: 5*81=405\nCurrent State: 17:[54, 27, 405], Operations: ['5*81=405']\nExploring Operation: 54+405=459, Resulting Numbers: [27, 459]\nGenerated Node #3: [27, 459] from Operation: 54+405=459\nCurrent State: 17:[27, 459], Operations: ['5*81=405', '54+405=459']\nExploring Operation: 459/27=17, Resulting Numbers: [17]\n17,17 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 16, + 74, + 83, + 85 + ], + "target": 66, + "solution": [ + "85-83=2", + "16/2=8", + "74-8=66" + ], + "optimal_path": "Current State: 66:[16, 74, 83, 85], Operations: []\nExploring Operation: 85-83=2, Resulting Numbers: [16, 74, 2]\nGenerated Node #2: [16, 74, 2] from Operation: 85-83=2\nCurrent State: 66:[16, 74, 2], Operations: ['85-83=2']\nExploring Operation: 16/2=8, Resulting Numbers: [74, 8]\nGenerated Node #3: [74, 8] from Operation: 16/2=8\nCurrent State: 66:[74, 8], Operations: ['85-83=2', '16/2=8']\nExploring Operation: 74-8=66, Resulting Numbers: [66]\n66,66 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 56, + 42, + 68, + 25 + ], + "target": 52, + "solution": [ + "42-25=17", + "68/17=4", + "56-4=52" + ], + "optimal_path": "Current State: 52:[56, 42, 68, 25], Operations: []\nExploring Operation: 42-25=17, Resulting Numbers: [56, 68, 17]\nGenerated Node #2: [56, 68, 17] from Operation: 42-25=17\nCurrent State: 52:[56, 68, 17], Operations: ['42-25=17']\nExploring Operation: 68/17=4, Resulting Numbers: [56, 4]\nGenerated Node #3: [56, 4] from Operation: 68/17=4\nCurrent State: 52:[56, 4], Operations: ['42-25=17', '68/17=4']\nExploring Operation: 56-4=52, Resulting Numbers: [52]\n52,52 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 38, + 12, + 2, + 40 + ], + "target": 71, + "solution": [ + "38/2=19", + "12+40=52", + "19+52=71" + ], + "optimal_path": "Current State: 71:[38, 12, 2, 40], Operations: []\nExploring Operation: 38/2=19, Resulting Numbers: [12, 40, 19]\nGenerated Node #2: [12, 40, 19] from Operation: 38/2=19\nCurrent State: 71:[12, 40, 19], Operations: ['38/2=19']\nExploring Operation: 12+40=52, Resulting Numbers: [19, 52]\nGenerated Node #3: [19, 52] from Operation: 12+40=52\nCurrent State: 71:[19, 52], Operations: ['38/2=19', '12+40=52']\nExploring Operation: 19+52=71, Resulting Numbers: [71]\n71,71 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 89, + 93, + 49, + 47 + ], + "target": 86, + "solution": [ + "89+93=182", + "49+47=96", + "182-96=86" + ], + "optimal_path": "Current State: 86:[89, 93, 49, 47], Operations: []\nExploring Operation: 89+93=182, Resulting Numbers: [49, 47, 182]\nGenerated Node #2: [49, 47, 182] from Operation: 89+93=182\nCurrent State: 86:[49, 47, 182], Operations: ['89+93=182']\nExploring Operation: 49+47=96, Resulting Numbers: [182, 96]\nGenerated Node #3: [182, 96] from Operation: 49+47=96\nCurrent State: 86:[182, 96], Operations: ['89+93=182', '49+47=96']\nExploring Operation: 182-96=86, Resulting Numbers: [86]\n86,86 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 76, + 79, + 37, + 81 + ], + "target": 37, + "solution": [ + "76+79=155", + "37+81=118", + "155-118=37" + ], + "optimal_path": "Current State: 37:[76, 79, 37, 81], Operations: []\nExploring Operation: 76+79=155, Resulting Numbers: [37, 81, 155]\nGenerated Node #2: [37, 81, 155] from Operation: 76+79=155\nCurrent State: 37:[37, 81, 155], Operations: ['76+79=155']\nExploring Operation: 37+81=118, Resulting Numbers: [155, 118]\nGenerated Node #3: [155, 118] from Operation: 37+81=118\nCurrent State: 37:[155, 118], Operations: ['76+79=155', '37+81=118']\nExploring Operation: 155-118=37, Resulting Numbers: [37]\n37,37 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 97, + 8, + 7, + 54 + ], + "target": 67, + "solution": [ + "97+7=104", + "104/8=13", + "54+13=67" + ], + "optimal_path": "Current State: 67:[97, 8, 7, 54], Operations: []\nExploring Operation: 97+7=104, Resulting Numbers: [8, 54, 104]\nGenerated Node #2: [8, 54, 104] from Operation: 97+7=104\nCurrent State: 67:[8, 54, 104], Operations: ['97+7=104']\nExploring Operation: 104/8=13, Resulting Numbers: [54, 13]\nGenerated Node #3: [54, 13] from Operation: 104/8=13\nCurrent State: 67:[54, 13], Operations: ['97+7=104', '104/8=13']\nExploring Operation: 54+13=67, Resulting Numbers: [67]\n67,67 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 83, + 16, + 24, + 12 + ], + "target": 85, + "solution": [ + "83+24=107", + "16*12=192", + "192-107=85" + ], + "optimal_path": "Current State: 85:[83, 16, 24, 12], Operations: []\nExploring Operation: 83+24=107, Resulting Numbers: [16, 12, 107]\nGenerated Node #2: [16, 12, 107] from Operation: 83+24=107\nCurrent State: 85:[16, 12, 107], Operations: ['83+24=107']\nExploring Operation: 16*12=192, Resulting Numbers: [107, 192]\nGenerated Node #3: [107, 192] from Operation: 16*12=192\nCurrent State: 85:[107, 192], Operations: ['83+24=107', '16*12=192']\nExploring Operation: 192-107=85, Resulting Numbers: [85]\n85,85 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 46, + 57, + 43, + 75 + ], + "target": 43, + "solution": [ + "57-46=11", + "75-43=32", + "11+32=43" + ], + "optimal_path": "Current State: 43:[46, 57, 43, 75], Operations: []\nExploring Operation: 57-46=11, Resulting Numbers: [43, 75, 11]\nGenerated Node #2: [43, 75, 11] from Operation: 57-46=11\nCurrent State: 43:[43, 75, 11], Operations: ['57-46=11']\nExploring Operation: 75-43=32, Resulting Numbers: [11, 32]\nGenerated Node #3: [11, 32] from Operation: 75-43=32\nCurrent State: 43:[11, 32], Operations: ['57-46=11', '75-43=32']\nExploring Operation: 11+32=43, Resulting Numbers: [43]\n43,43 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 99, + 76, + 47, + 49 + ], + "target": 46, + "solution": [ + "99-76=23", + "49-47=2", + "23*2=46" + ], + "optimal_path": "Current State: 46:[99, 76, 47, 49], Operations: []\nExploring Operation: 99-76=23, Resulting Numbers: [47, 49, 23]\nGenerated Node #2: [47, 49, 23] from Operation: 99-76=23\nCurrent State: 46:[47, 49, 23], Operations: ['99-76=23']\nExploring Operation: 49-47=2, Resulting Numbers: [23, 2]\nGenerated Node #3: [23, 2] from Operation: 49-47=2\nCurrent State: 46:[23, 2], Operations: ['99-76=23', '49-47=2']\nExploring Operation: 23*2=46, Resulting Numbers: [46]\n46,46 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 90, + 87, + 17, + 46 + ], + "target": 79, + "solution": [ + "90+46=136", + "136/17=8", + "87-8=79" + ], + "optimal_path": "Current State: 79:[90, 87, 17, 46], Operations: []\nExploring Operation: 90+46=136, Resulting Numbers: [87, 17, 136]\nGenerated Node #2: [87, 17, 136] from Operation: 90+46=136\nCurrent State: 79:[87, 17, 136], Operations: ['90+46=136']\nExploring Operation: 136/17=8, Resulting Numbers: [87, 8]\nGenerated Node #3: [87, 8] from Operation: 136/17=8\nCurrent State: 79:[87, 8], Operations: ['90+46=136', '136/17=8']\nExploring Operation: 87-8=79, Resulting Numbers: [79]\n79,79 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 3, + 27, + 93, + 77 + ], + "target": 89, + "solution": [ + "3*27=81", + "93+77=170", + "170-81=89" + ], + "optimal_path": "Current State: 89:[3, 27, 93, 77], Operations: []\nExploring Operation: 3*27=81, Resulting Numbers: [93, 77, 81]\nGenerated Node #2: [93, 77, 81] from Operation: 3*27=81\nCurrent State: 89:[93, 77, 81], Operations: ['3*27=81']\nExploring Operation: 93+77=170, Resulting Numbers: [81, 170]\nGenerated Node #3: [81, 170] from Operation: 93+77=170\nCurrent State: 89:[81, 170], Operations: ['3*27=81', '93+77=170']\nExploring Operation: 170-81=89, Resulting Numbers: [89]\n89,89 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 59, + 57, + 32, + 26 + ], + "target": 45, + "solution": [ + "59-57=2", + "26/2=13", + "32+13=45" + ], + "optimal_path": "Current State: 45:[59, 57, 32, 26], Operations: []\nExploring Operation: 59-57=2, Resulting Numbers: [32, 26, 2]\nGenerated Node #2: [32, 26, 2] from Operation: 59-57=2\nCurrent State: 45:[32, 26, 2], Operations: ['59-57=2']\nExploring Operation: 26/2=13, Resulting Numbers: [32, 13]\nGenerated Node #3: [32, 13] from Operation: 26/2=13\nCurrent State: 45:[32, 13], Operations: ['59-57=2', '26/2=13']\nExploring Operation: 32+13=45, Resulting Numbers: [45]\n45,45 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 68, + 36, + 85, + 80 + ], + "target": 34, + "solution": [ + "68-36=32", + "85*32=2720", + "2720/80=34" + ], + "optimal_path": "Current State: 34:[68, 36, 85, 80], Operations: []\nExploring Operation: 68-36=32, Resulting Numbers: [85, 80, 32]\nGenerated Node #2: [85, 80, 32] from Operation: 68-36=32\nCurrent State: 34:[85, 80, 32], Operations: ['68-36=32']\nExploring Operation: 85*32=2720, Resulting Numbers: [80, 2720]\nGenerated Node #3: [80, 2720] from Operation: 85*32=2720\nCurrent State: 34:[80, 2720], Operations: ['68-36=32', '85*32=2720']\nExploring Operation: 2720/80=34, Resulting Numbers: [34]\n34,34 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 90, + 54, + 69, + 25 + ], + "target": 58, + "solution": [ + "90-54=36", + "69+25=94", + "94-36=58" + ], + "optimal_path": "Current State: 58:[90, 54, 69, 25], Operations: []\nExploring Operation: 90-54=36, Resulting Numbers: [69, 25, 36]\nGenerated Node #2: [69, 25, 36] from Operation: 90-54=36\nCurrent State: 58:[69, 25, 36], Operations: ['90-54=36']\nExploring Operation: 69+25=94, Resulting Numbers: [36, 94]\nGenerated Node #3: [36, 94] from Operation: 69+25=94\nCurrent State: 58:[36, 94], Operations: ['90-54=36', '69+25=94']\nExploring Operation: 94-36=58, Resulting Numbers: [58]\n58,58 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 96, + 11, + 33, + 35 + ], + "target": 83, + "solution": [ + "96-11=85", + "35-33=2", + "85-2=83" + ], + "optimal_path": "Current State: 83:[96, 11, 33, 35], Operations: []\nExploring Operation: 96-11=85, Resulting Numbers: [33, 35, 85]\nGenerated Node #2: [33, 35, 85] from Operation: 96-11=85\nCurrent State: 83:[33, 35, 85], Operations: ['96-11=85']\nExploring Operation: 35-33=2, Resulting Numbers: [85, 2]\nGenerated Node #3: [85, 2] from Operation: 35-33=2\nCurrent State: 83:[85, 2], Operations: ['96-11=85', '35-33=2']\nExploring Operation: 85-2=83, Resulting Numbers: [83]\n83,83 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 20, + 21, + 19, + 5 + ], + "target": 50, + "solution": [ + "20+5=25", + "21-19=2", + "25*2=50" + ], + "optimal_path": "Current State: 50:[20, 21, 19, 5], Operations: []\nExploring Operation: 20+5=25, Resulting Numbers: [21, 19, 25]\nGenerated Node #2: [21, 19, 25] from Operation: 20+5=25\nCurrent State: 50:[21, 19, 25], Operations: ['20+5=25']\nExploring Operation: 21-19=2, Resulting Numbers: [25, 2]\nGenerated Node #3: [25, 2] from Operation: 21-19=2\nCurrent State: 50:[25, 2], Operations: ['20+5=25', '21-19=2']\nExploring Operation: 25*2=50, Resulting Numbers: [50]\n50,50 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 1, + 36, + 50, + 7 + ], + "target": 29, + "solution": [ + "50-1=49", + "49/7=7", + "36-7=29" + ], + "optimal_path": "Current State: 29:[1, 36, 50, 7], Operations: []\nExploring Operation: 50-1=49, Resulting Numbers: [36, 7, 49]\nGenerated Node #2: [36, 7, 49] from Operation: 50-1=49\nCurrent State: 29:[36, 7, 49], Operations: ['50-1=49']\nExploring Operation: 49/7=7, Resulting Numbers: [36, 7]\nGenerated Node #3: [36, 7] from Operation: 49/7=7\nCurrent State: 29:[36, 7], Operations: ['50-1=49', '49/7=7']\nExploring Operation: 36-7=29, Resulting Numbers: [29]\n29,29 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 3, + 18, + 77, + 72 + ], + "target": 49, + "solution": [ + "3*18=54", + "77-72=5", + "54-5=49" + ], + "optimal_path": "Current State: 49:[3, 18, 77, 72], Operations: []\nExploring Operation: 3*18=54, Resulting Numbers: [77, 72, 54]\nGenerated Node #2: [77, 72, 54] from Operation: 3*18=54\nCurrent State: 49:[77, 72, 54], Operations: ['3*18=54']\nExploring Operation: 77-72=5, Resulting Numbers: [54, 5]\nGenerated Node #3: [54, 5] from Operation: 77-72=5\nCurrent State: 49:[54, 5], Operations: ['3*18=54', '77-72=5']\nExploring Operation: 54-5=49, Resulting Numbers: [49]\n49,49 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 88, + 20, + 85, + 51 + ], + "target": 34, + "solution": [ + "88-20=68", + "85-51=34", + "68-34=34" + ], + "optimal_path": "Current State: 34:[88, 20, 85, 51], Operations: []\nExploring Operation: 88-20=68, Resulting Numbers: [85, 51, 68]\nGenerated Node #2: [85, 51, 68] from Operation: 88-20=68\nCurrent State: 34:[85, 51, 68], Operations: ['88-20=68']\nExploring Operation: 85-51=34, Resulting Numbers: [68, 34]\nGenerated Node #3: [68, 34] from Operation: 85-51=34\nCurrent State: 34:[68, 34], Operations: ['88-20=68', '85-51=34']\nExploring Operation: 68-34=34, Resulting Numbers: [34]\n34,34 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 1, + 19, + 82, + 82 + ], + "target": 17, + "solution": [ + "19-1=18", + "82/82=1", + "18-1=17" + ], + "optimal_path": "Current State: 17:[1, 19, 82, 82], Operations: []\nExploring Operation: 19-1=18, Resulting Numbers: [82, 82, 18]\nGenerated Node #2: [82, 82, 18] from Operation: 19-1=18\nCurrent State: 17:[82, 82, 18], Operations: ['19-1=18']\nExploring Operation: 82/82=1, Resulting Numbers: [18, 1]\nGenerated Node #3: [18, 1] from Operation: 82/82=1\nCurrent State: 17:[18, 1], Operations: ['19-1=18', '82/82=1']\nExploring Operation: 18-1=17, Resulting Numbers: [17]\n17,17 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 7, + 26, + 18, + 12 + ], + "target": 27, + "solution": [ + "7+26=33", + "18-12=6", + "33-6=27" + ], + "optimal_path": "Current State: 27:[7, 26, 18, 12], Operations: []\nExploring Operation: 7+26=33, Resulting Numbers: [18, 12, 33]\nGenerated Node #2: [18, 12, 33] from Operation: 7+26=33\nCurrent State: 27:[18, 12, 33], Operations: ['7+26=33']\nExploring Operation: 18-12=6, Resulting Numbers: [33, 6]\nGenerated Node #3: [33, 6] from Operation: 18-12=6\nCurrent State: 27:[33, 6], Operations: ['7+26=33', '18-12=6']\nExploring Operation: 33-6=27, Resulting Numbers: [27]\n27,27 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 97, + 70, + 91, + 33 + ], + "target": 31, + "solution": [ + "97-70=27", + "91-33=58", + "58-27=31" + ], + "optimal_path": "Current State: 31:[97, 70, 91, 33], Operations: []\nExploring Operation: 97-70=27, Resulting Numbers: [91, 33, 27]\nGenerated Node #2: [91, 33, 27] from Operation: 97-70=27\nCurrent State: 31:[91, 33, 27], Operations: ['97-70=27']\nExploring Operation: 91-33=58, Resulting Numbers: [27, 58]\nGenerated Node #3: [27, 58] from Operation: 91-33=58\nCurrent State: 31:[27, 58], Operations: ['97-70=27', '91-33=58']\nExploring Operation: 58-27=31, Resulting Numbers: [31]\n31,31 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 49, + 26, + 42, + 16 + ], + "target": 81, + "solution": [ + "49-26=23", + "42+16=58", + "23+58=81" + ], + "optimal_path": "Current State: 81:[49, 26, 42, 16], Operations: []\nExploring Operation: 49-26=23, Resulting Numbers: [42, 16, 23]\nGenerated Node #2: [42, 16, 23] from Operation: 49-26=23\nCurrent State: 81:[42, 16, 23], Operations: ['49-26=23']\nExploring Operation: 42+16=58, Resulting Numbers: [23, 58]\nGenerated Node #3: [23, 58] from Operation: 42+16=58\nCurrent State: 81:[23, 58], Operations: ['49-26=23', '42+16=58']\nExploring Operation: 23+58=81, Resulting Numbers: [81]\n81,81 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 27, + 10, + 2, + 88 + ], + "target": 95, + "solution": [ + "27+88=115", + "10*2=20", + "115-20=95" + ], + "optimal_path": "Current State: 95:[27, 10, 2, 88], Operations: []\nExploring Operation: 27+88=115, Resulting Numbers: [10, 2, 115]\nGenerated Node #2: [10, 2, 115] from Operation: 27+88=115\nCurrent State: 95:[10, 2, 115], Operations: ['27+88=115']\nExploring Operation: 10*2=20, Resulting Numbers: [115, 20]\nGenerated Node #3: [115, 20] from Operation: 10*2=20\nCurrent State: 95:[115, 20], Operations: ['27+88=115', '10*2=20']\nExploring Operation: 115-20=95, Resulting Numbers: [95]\n95,95 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 25, + 69, + 3, + 72 + ], + "target": 22, + "solution": [ + "69+72=141", + "141/3=47", + "47-25=22" + ], + "optimal_path": "Current State: 22:[25, 69, 3, 72], Operations: []\nExploring Operation: 69+72=141, Resulting Numbers: [25, 3, 141]\nGenerated Node #2: [25, 3, 141] from Operation: 69+72=141\nCurrent State: 22:[25, 3, 141], Operations: ['69+72=141']\nExploring Operation: 141/3=47, Resulting Numbers: [25, 47]\nGenerated Node #3: [25, 47] from Operation: 141/3=47\nCurrent State: 22:[25, 47], Operations: ['69+72=141', '141/3=47']\nExploring Operation: 47-25=22, Resulting Numbers: [22]\n22,22 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 58, + 29, + 85, + 1 + ], + "target": 83, + "solution": [ + "58/29=2", + "85*1=85", + "85-2=83" + ], + "optimal_path": "Current State: 83:[58, 29, 85, 1], Operations: []\nExploring Operation: 58/29=2, Resulting Numbers: [85, 1, 2]\nGenerated Node #2: [85, 1, 2] from Operation: 58/29=2\nCurrent State: 83:[85, 1, 2], Operations: ['58/29=2']\nExploring Operation: 85*1=85, Resulting Numbers: [2, 85]\nGenerated Node #3: [2, 85] from Operation: 85*1=85\nCurrent State: 83:[2, 85], Operations: ['58/29=2', '85*1=85']\nExploring Operation: 85-2=83, Resulting Numbers: [83]\n83,83 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 52, + 54, + 81, + 90 + ], + "target": 65, + "solution": [ + "52+54=106", + "81+90=171", + "171-106=65" + ], + "optimal_path": "Current State: 65:[52, 54, 81, 90], Operations: []\nExploring Operation: 52+54=106, Resulting Numbers: [81, 90, 106]\nGenerated Node #2: [81, 90, 106] from Operation: 52+54=106\nCurrent State: 65:[81, 90, 106], Operations: ['52+54=106']\nExploring Operation: 81+90=171, Resulting Numbers: [106, 171]\nGenerated Node #3: [106, 171] from Operation: 81+90=171\nCurrent State: 65:[106, 171], Operations: ['52+54=106', '81+90=171']\nExploring Operation: 171-106=65, Resulting Numbers: [65]\n65,65 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 36, + 21, + 27, + 50 + ], + "target": 66, + "solution": [ + "27*50=1350", + "36+1350=1386", + "1386/21=66" + ], + "optimal_path": "Current State: 66:[36, 21, 27, 50], Operations: []\nExploring Operation: 27*50=1350, Resulting Numbers: [36, 21, 1350]\nGenerated Node #2: [36, 21, 1350] from Operation: 27*50=1350\nCurrent State: 66:[36, 21, 1350], Operations: ['27*50=1350']\nExploring Operation: 36+1350=1386, Resulting Numbers: [21, 1386]\nGenerated Node #3: [21, 1386] from Operation: 36+1350=1386\nCurrent State: 66:[21, 1386], Operations: ['27*50=1350', '36+1350=1386']\nExploring Operation: 1386/21=66, Resulting Numbers: [66]\n66,66 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 2, + 10, + 66, + 96 + ], + "target": 73, + "solution": [ + "66/2=33", + "10+96=106", + "106-33=73" + ], + "optimal_path": "Current State: 73:[2, 10, 66, 96], Operations: []\nExploring Operation: 66/2=33, Resulting Numbers: [10, 96, 33]\nGenerated Node #2: [10, 96, 33] from Operation: 66/2=33\nCurrent State: 73:[10, 96, 33], Operations: ['66/2=33']\nExploring Operation: 10+96=106, Resulting Numbers: [33, 106]\nGenerated Node #3: [33, 106] from Operation: 10+96=106\nCurrent State: 73:[33, 106], Operations: ['66/2=33', '10+96=106']\nExploring Operation: 106-33=73, Resulting Numbers: [73]\n73,73 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 74, + 72, + 24, + 24 + ], + "target": 71, + "solution": [ + "74*24=1776", + "1776-72=1704", + "1704/24=71" + ], + "optimal_path": "Current State: 71:[74, 72, 24, 24], Operations: []\nExploring Operation: 74*24=1776, Resulting Numbers: [72, 1776]\nGenerated Node #2: [72, 1776] from Operation: 74*24=1776\nCurrent State: 71:[72, 1776], Operations: ['74*24=1776']\nExploring Operation: 1776-72=1704, Resulting Numbers: [1704]\n1704,71 equal: Goal Reached\nExploring Operation: 1704/24=71, Resulting Numbers: [71]\n71,71 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 1, + 11, + 28, + 94 + ], + "target": 54, + "solution": [ + "1+11=12", + "94-28=66", + "66-12=54" + ], + "optimal_path": "Current State: 54:[1, 11, 28, 94], Operations: []\nExploring Operation: 1+11=12, Resulting Numbers: [28, 94, 12]\nGenerated Node #2: [28, 94, 12] from Operation: 1+11=12\nCurrent State: 54:[28, 94, 12], Operations: ['1+11=12']\nExploring Operation: 94-28=66, Resulting Numbers: [12, 66]\nGenerated Node #3: [12, 66] from Operation: 94-28=66\nCurrent State: 54:[12, 66], Operations: ['1+11=12', '94-28=66']\nExploring Operation: 66-12=54, Resulting Numbers: [54]\n54,54 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 3, + 41, + 52, + 60 + ], + "target": 11, + "solution": [ + "3*41=123", + "52+60=112", + "123-112=11" + ], + "optimal_path": "Current State: 11:[3, 41, 52, 60], Operations: []\nExploring Operation: 3*41=123, Resulting Numbers: [52, 60, 123]\nGenerated Node #2: [52, 60, 123] from Operation: 3*41=123\nCurrent State: 11:[52, 60, 123], Operations: ['3*41=123']\nExploring Operation: 52+60=112, Resulting Numbers: [123, 112]\nGenerated Node #3: [123, 112] from Operation: 52+60=112\nCurrent State: 11:[123, 112], Operations: ['3*41=123', '52+60=112']\nExploring Operation: 123-112=11, Resulting Numbers: [11]\n11,11 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 2, + 75, + 31, + 89 + ], + "target": 51, + "solution": [ + "75+89=164", + "164/2=82", + "82-31=51" + ], + "optimal_path": "Current State: 51:[2, 75, 31, 89], Operations: []\nExploring Operation: 75+89=164, Resulting Numbers: [2, 31, 164]\nGenerated Node #2: [2, 31, 164] from Operation: 75+89=164\nCurrent State: 51:[2, 31, 164], Operations: ['75+89=164']\nExploring Operation: 164/2=82, Resulting Numbers: [31, 82]\nGenerated Node #3: [31, 82] from Operation: 164/2=82\nCurrent State: 51:[31, 82], Operations: ['75+89=164', '164/2=82']\nExploring Operation: 82-31=51, Resulting Numbers: [51]\n51,51 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 40, + 12, + 79, + 66 + ], + "target": 40, + "solution": [ + "79-12=67", + "67-66=1", + "40*1=40" + ], + "optimal_path": "Current State: 40:[40, 12, 79, 66], Operations: []\nExploring Operation: 79-12=67, Resulting Numbers: [40, 66, 67]\nGenerated Node #2: [40, 66, 67] from Operation: 79-12=67\nCurrent State: 40:[40, 66, 67], Operations: ['79-12=67']\nExploring Operation: 67-66=1, Resulting Numbers: [40, 1]\nGenerated Node #3: [40, 1] from Operation: 67-66=1\nCurrent State: 40:[40, 1], Operations: ['79-12=67', '67-66=1']\nExploring Operation: 40*1=40, Resulting Numbers: [40]\n40,40 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 26, + 7, + 77, + 99 + ], + "target": 55, + "solution": [ + "26+7=33", + "99-77=22", + "33+22=55" + ], + "optimal_path": "Current State: 55:[26, 7, 77, 99], Operations: []\nExploring Operation: 26+7=33, Resulting Numbers: [77, 99, 33]\nGenerated Node #2: [77, 99, 33] from Operation: 26+7=33\nCurrent State: 55:[77, 99, 33], Operations: ['26+7=33']\nExploring Operation: 99-77=22, Resulting Numbers: [33, 22]\nGenerated Node #3: [33, 22] from Operation: 99-77=22\nCurrent State: 55:[33, 22], Operations: ['26+7=33', '99-77=22']\nExploring Operation: 33+22=55, Resulting Numbers: [55]\n55,55 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 1, + 22, + 7, + 5 + ], + "target": 46, + "solution": [ + "1+22=23", + "7-5=2", + "23*2=46" + ], + "optimal_path": "Current State: 46:[1, 22, 7, 5], Operations: []\nExploring Operation: 1+22=23, Resulting Numbers: [7, 5, 23]\nGenerated Node #2: [7, 5, 23] from Operation: 1+22=23\nCurrent State: 46:[7, 5, 23], Operations: ['1+22=23']\nExploring Operation: 7-5=2, Resulting Numbers: [23, 2]\nGenerated Node #3: [23, 2] from Operation: 7-5=2\nCurrent State: 46:[23, 2], Operations: ['1+22=23', '7-5=2']\nExploring Operation: 23*2=46, Resulting Numbers: [46]\n46,46 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 3, + 12, + 6, + 24 + ], + "target": 36, + "solution": [ + "12-3=9", + "24/6=4", + "9*4=36" + ], + "optimal_path": "Current State: 36:[3, 12, 6, 24], Operations: []\nExploring Operation: 12-3=9, Resulting Numbers: [6, 24, 9]\nGenerated Node #2: [6, 24, 9] from Operation: 12-3=9\nCurrent State: 36:[6, 24, 9], Operations: ['12-3=9']\nExploring Operation: 24/6=4, Resulting Numbers: [9, 4]\nGenerated Node #3: [9, 4] from Operation: 24/6=4\nCurrent State: 36:[9, 4], Operations: ['12-3=9', '24/6=4']\nExploring Operation: 9*4=36, Resulting Numbers: [36]\n36,36 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 91, + 66, + 70, + 92 + ], + "target": 20, + "solution": [ + "92-66=26", + "70*26=1820", + "1820/91=20" + ], + "optimal_path": "Current State: 20:[91, 66, 70, 92], Operations: []\nExploring Operation: 92-66=26, Resulting Numbers: [91, 70, 26]\nGenerated Node #2: [91, 70, 26] from Operation: 92-66=26\nCurrent State: 20:[91, 70, 26], Operations: ['92-66=26']\nExploring Operation: 70*26=1820, Resulting Numbers: [91, 1820]\nGenerated Node #3: [91, 1820] from Operation: 70*26=1820\nCurrent State: 20:[91, 1820], Operations: ['92-66=26', '70*26=1820']\nExploring Operation: 1820/91=20, Resulting Numbers: [20]\n20,20 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 91, + 21, + 29, + 54 + ], + "target": 95, + "solution": [ + "91-21=70", + "54-29=25", + "70+25=95" + ], + "optimal_path": "Current State: 95:[91, 21, 29, 54], Operations: []\nExploring Operation: 91-21=70, Resulting Numbers: [29, 54, 70]\nGenerated Node #2: [29, 54, 70] from Operation: 91-21=70\nCurrent State: 95:[29, 54, 70], Operations: ['91-21=70']\nExploring Operation: 54-29=25, Resulting Numbers: [70, 25]\nGenerated Node #3: [70, 25] from Operation: 54-29=25\nCurrent State: 95:[70, 25], Operations: ['91-21=70', '54-29=25']\nExploring Operation: 70+25=95, Resulting Numbers: [95]\n95,95 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 5, + 16, + 47, + 9 + ], + "target": 94, + "solution": [ + "16-5=11", + "11-9=2", + "47*2=94" + ], + "optimal_path": "Current State: 94:[5, 16, 47, 9], Operations: []\nExploring Operation: 16-5=11, Resulting Numbers: [47, 9, 11]\nGenerated Node #2: [47, 9, 11] from Operation: 16-5=11\nCurrent State: 94:[47, 9, 11], Operations: ['16-5=11']\nExploring Operation: 11-9=2, Resulting Numbers: [47, 2]\nGenerated Node #3: [47, 2] from Operation: 11-9=2\nCurrent State: 94:[47, 2], Operations: ['16-5=11', '11-9=2']\nExploring Operation: 47*2=94, Resulting Numbers: [94]\n94,94 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 1, + 74, + 11, + 3 + ], + "target": 83, + "solution": [ + "1+74=75", + "11-3=8", + "75+8=83" + ], + "optimal_path": "Current State: 83:[1, 74, 11, 3], Operations: []\nExploring Operation: 1+74=75, Resulting Numbers: [11, 3, 75]\nGenerated Node #2: [11, 3, 75] from Operation: 1+74=75\nCurrent State: 83:[11, 3, 75], Operations: ['1+74=75']\nExploring Operation: 11-3=8, Resulting Numbers: [75, 8]\nGenerated Node #3: [75, 8] from Operation: 11-3=8\nCurrent State: 83:[75, 8], Operations: ['1+74=75', '11-3=8']\nExploring Operation: 75+8=83, Resulting Numbers: [83]\n83,83 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 84, + 11, + 87, + 9 + ], + "target": 66, + "solution": [ + "87-84=3", + "9-3=6", + "11*6=66" + ], + "optimal_path": "Current State: 66:[84, 11, 87, 9], Operations: []\nExploring Operation: 87-84=3, Resulting Numbers: [11, 9, 3]\nGenerated Node #2: [11, 9, 3] from Operation: 87-84=3\nCurrent State: 66:[11, 9, 3], Operations: ['87-84=3']\nExploring Operation: 9-3=6, Resulting Numbers: [11, 6]\nGenerated Node #3: [11, 6] from Operation: 9-3=6\nCurrent State: 66:[11, 6], Operations: ['87-84=3', '9-3=6']\nExploring Operation: 11*6=66, Resulting Numbers: [66]\n66,66 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 28, + 45, + 79, + 33 + ], + "target": 95, + "solution": [ + "45-28=17", + "79+33=112", + "112-17=95" + ], + "optimal_path": "Current State: 95:[28, 45, 79, 33], Operations: []\nExploring Operation: 45-28=17, Resulting Numbers: [79, 33, 17]\nGenerated Node #2: [79, 33, 17] from Operation: 45-28=17\nCurrent State: 95:[79, 33, 17], Operations: ['45-28=17']\nExploring Operation: 79+33=112, Resulting Numbers: [17, 112]\nGenerated Node #3: [17, 112] from Operation: 79+33=112\nCurrent State: 95:[17, 112], Operations: ['45-28=17', '79+33=112']\nExploring Operation: 112-17=95, Resulting Numbers: [95]\n95,95 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 61, + 90, + 97, + 76 + ], + "target": 50, + "solution": [ + "90-61=29", + "97-76=21", + "29+21=50" + ], + "optimal_path": "Current State: 50:[61, 90, 97, 76], Operations: []\nExploring Operation: 90-61=29, Resulting Numbers: [97, 76, 29]\nGenerated Node #2: [97, 76, 29] from Operation: 90-61=29\nCurrent State: 50:[97, 76, 29], Operations: ['90-61=29']\nExploring Operation: 97-76=21, Resulting Numbers: [29, 21]\nGenerated Node #3: [29, 21] from Operation: 97-76=21\nCurrent State: 50:[29, 21], Operations: ['90-61=29', '97-76=21']\nExploring Operation: 29+21=50, Resulting Numbers: [50]\n50,50 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 41, + 63, + 22, + 27 + ], + "target": 99, + "solution": [ + "41+63=104", + "27-22=5", + "104-5=99" + ], + "optimal_path": "Current State: 99:[41, 63, 22, 27], Operations: []\nExploring Operation: 41+63=104, Resulting Numbers: [22, 27, 104]\nGenerated Node #2: [22, 27, 104] from Operation: 41+63=104\nCurrent State: 99:[22, 27, 104], Operations: ['41+63=104']\nExploring Operation: 27-22=5, Resulting Numbers: [104, 5]\nGenerated Node #3: [104, 5] from Operation: 27-22=5\nCurrent State: 99:[104, 5], Operations: ['41+63=104', '27-22=5']\nExploring Operation: 104-5=99, Resulting Numbers: [99]\n99,99 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 22, + 26, + 31, + 53 + ], + "target": 27, + "solution": [ + "22+31=53", + "53/53=1", + "26+1=27" + ], + "optimal_path": "Current State: 27:[22, 26, 31, 53], Operations: []\nExploring Operation: 22+31=53, Resulting Numbers: [26, 53, 53]\nGenerated Node #2: [26, 53, 53] from Operation: 22+31=53\nCurrent State: 27:[26, 53, 53], Operations: ['22+31=53']\nExploring Operation: 53/53=1, Resulting Numbers: [26, 1]\nGenerated Node #3: [26, 1] from Operation: 53/53=1\nCurrent State: 27:[26, 1], Operations: ['22+31=53', '53/53=1']\nExploring Operation: 26+1=27, Resulting Numbers: [27]\n27,27 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 73, + 76, + 9, + 56 + ], + "target": 53, + "solution": [ + "76-73=3", + "9/3=3", + "56-3=53" + ], + "optimal_path": "Current State: 53:[73, 76, 9, 56], Operations: []\nExploring Operation: 76-73=3, Resulting Numbers: [9, 56, 3]\nGenerated Node #2: [9, 56, 3] from Operation: 76-73=3\nCurrent State: 53:[9, 56, 3], Operations: ['76-73=3']\nExploring Operation: 9/3=3, Resulting Numbers: [56, 3]\nGenerated Node #3: [56, 3] from Operation: 9/3=3\nCurrent State: 53:[56, 3], Operations: ['76-73=3', '9/3=3']\nExploring Operation: 56-3=53, Resulting Numbers: [53]\n53,53 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 88, + 41, + 52, + 60 + ], + "target": 49, + "solution": [ + "41*60=2460", + "88+2460=2548", + "2548/52=49" + ], + "optimal_path": "Current State: 49:[88, 41, 52, 60], Operations: []\nExploring Operation: 41*60=2460, Resulting Numbers: [88, 52, 2460]\nGenerated Node #2: [88, 52, 2460] from Operation: 41*60=2460\nCurrent State: 49:[88, 52, 2460], Operations: ['41*60=2460']\nExploring Operation: 88+2460=2548, Resulting Numbers: [52, 2548]\nGenerated Node #3: [52, 2548] from Operation: 88+2460=2548\nCurrent State: 49:[52, 2548], Operations: ['41*60=2460', '88+2460=2548']\nExploring Operation: 2548/52=49, Resulting Numbers: [49]\n49,49 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 62, + 23, + 2, + 73 + ], + "target": 89, + "solution": [ + "62+73=135", + "23*2=46", + "135-46=89" + ], + "optimal_path": "Current State: 89:[62, 23, 2, 73], Operations: []\nExploring Operation: 62+73=135, Resulting Numbers: [23, 2, 135]\nGenerated Node #2: [23, 2, 135] from Operation: 62+73=135\nCurrent State: 89:[23, 2, 135], Operations: ['62+73=135']\nExploring Operation: 23*2=46, Resulting Numbers: [135, 46]\nGenerated Node #3: [135, 46] from Operation: 23*2=46\nCurrent State: 89:[135, 46], Operations: ['62+73=135', '23*2=46']\nExploring Operation: 135-46=89, Resulting Numbers: [89]\n89,89 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 61, + 39, + 20, + 83 + ], + "target": 10, + "solution": [ + "61*20=1220", + "39+83=122", + "1220/122=10" + ], + "optimal_path": "Current State: 10:[61, 39, 20, 83], Operations: []\nExploring Operation: 61*20=1220, Resulting Numbers: [39, 83, 1220]\nGenerated Node #2: [39, 83, 1220] from Operation: 61*20=1220\nCurrent State: 10:[39, 83, 1220], Operations: ['61*20=1220']\nExploring Operation: 39+83=122, Resulting Numbers: [1220, 122]\nGenerated Node #3: [1220, 122] from Operation: 39+83=122\nCurrent State: 10:[1220, 122], Operations: ['61*20=1220', '39+83=122']\nExploring Operation: 1220/122=10, Resulting Numbers: [10]\n10,10 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 69, + 65, + 23, + 17 + ], + "target": 51, + "solution": [ + "69/23=3", + "65-17=48", + "3+48=51" + ], + "optimal_path": "Current State: 51:[69, 65, 23, 17], Operations: []\nExploring Operation: 69/23=3, Resulting Numbers: [65, 17, 3]\nGenerated Node #2: [65, 17, 3] from Operation: 69/23=3\nCurrent State: 51:[65, 17, 3], Operations: ['69/23=3']\nExploring Operation: 65-17=48, Resulting Numbers: [3, 48]\nGenerated Node #3: [3, 48] from Operation: 65-17=48\nCurrent State: 51:[3, 48], Operations: ['69/23=3', '65-17=48']\nExploring Operation: 3+48=51, Resulting Numbers: [51]\n51,51 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 84, + 80, + 66, + 90 + ], + "target": 75, + "solution": [ + "84-66=18", + "90/18=5", + "80-5=75" + ], + "optimal_path": "Current State: 75:[84, 80, 66, 90], Operations: []\nExploring Operation: 84-66=18, Resulting Numbers: [80, 90, 18]\nGenerated Node #2: [80, 90, 18] from Operation: 84-66=18\nCurrent State: 75:[80, 90, 18], Operations: ['84-66=18']\nExploring Operation: 90/18=5, Resulting Numbers: [80, 5]\nGenerated Node #3: [80, 5] from Operation: 90/18=5\nCurrent State: 75:[80, 5], Operations: ['84-66=18', '90/18=5']\nExploring Operation: 80-5=75, Resulting Numbers: [75]\n75,75 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 48, + 70, + 75, + 35 + ], + "target": 21, + "solution": [ + "48*70=3360", + "3360/35=96", + "96-75=21" + ], + "optimal_path": "Current State: 21:[48, 70, 75, 35], Operations: []\nExploring Operation: 48*70=3360, Resulting Numbers: [75, 35, 3360]\nGenerated Node #2: [75, 35, 3360] from Operation: 48*70=3360\nCurrent State: 21:[75, 35, 3360], Operations: ['48*70=3360']\nExploring Operation: 3360/35=96, Resulting Numbers: [75, 96]\nGenerated Node #3: [75, 96] from Operation: 3360/35=96\nCurrent State: 21:[75, 96], Operations: ['48*70=3360', '3360/35=96']\nExploring Operation: 96-75=21, Resulting Numbers: [21]\n21,21 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 8, + 32, + 37, + 27 + ], + "target": 88, + "solution": [ + "32-8=24", + "37+27=64", + "24+64=88" + ], + "optimal_path": "Current State: 88:[8, 32, 37, 27], Operations: []\nExploring Operation: 32-8=24, Resulting Numbers: [37, 27, 24]\nGenerated Node #2: [37, 27, 24] from Operation: 32-8=24\nCurrent State: 88:[37, 27, 24], Operations: ['32-8=24']\nExploring Operation: 37+27=64, Resulting Numbers: [24, 64]\nGenerated Node #3: [24, 64] from Operation: 37+27=64\nCurrent State: 88:[24, 64], Operations: ['32-8=24', '37+27=64']\nExploring Operation: 24+64=88, Resulting Numbers: [88]\n88,88 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 32, + 44, + 86, + 11 + ], + "target": 63, + "solution": [ + "44-32=12", + "86-11=75", + "75-12=63" + ], + "optimal_path": "Current State: 63:[32, 44, 86, 11], Operations: []\nExploring Operation: 44-32=12, Resulting Numbers: [86, 11, 12]\nGenerated Node #2: [86, 11, 12] from Operation: 44-32=12\nCurrent State: 63:[86, 11, 12], Operations: ['44-32=12']\nExploring Operation: 86-11=75, Resulting Numbers: [12, 75]\nGenerated Node #3: [12, 75] from Operation: 86-11=75\nCurrent State: 63:[12, 75], Operations: ['44-32=12', '86-11=75']\nExploring Operation: 75-12=63, Resulting Numbers: [63]\n63,63 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 51, + 3, + 44, + 91 + ], + "target": 81, + "solution": [ + "51+3=54", + "44+91=135", + "135-54=81" + ], + "optimal_path": "Current State: 81:[51, 3, 44, 91], Operations: []\nExploring Operation: 51+3=54, Resulting Numbers: [44, 91, 54]\nGenerated Node #2: [44, 91, 54] from Operation: 51+3=54\nCurrent State: 81:[44, 91, 54], Operations: ['51+3=54']\nExploring Operation: 44+91=135, Resulting Numbers: [54, 135]\nGenerated Node #3: [54, 135] from Operation: 44+91=135\nCurrent State: 81:[54, 135], Operations: ['51+3=54', '44+91=135']\nExploring Operation: 135-54=81, Resulting Numbers: [81]\n81,81 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 42, + 23, + 6, + 11 + ], + "target": 60, + "solution": [ + "42+23=65", + "11-6=5", + "65-5=60" + ], + "optimal_path": "Current State: 60:[42, 23, 6, 11], Operations: []\nExploring Operation: 42+23=65, Resulting Numbers: [6, 11, 65]\nGenerated Node #2: [6, 11, 65] from Operation: 42+23=65\nCurrent State: 60:[6, 11, 65], Operations: ['42+23=65']\nExploring Operation: 11-6=5, Resulting Numbers: [65, 5]\nGenerated Node #3: [65, 5] from Operation: 11-6=5\nCurrent State: 60:[65, 5], Operations: ['42+23=65', '11-6=5']\nExploring Operation: 65-5=60, Resulting Numbers: [60]\n60,60 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 6, + 84, + 42, + 84 + ], + "target": 24, + "solution": [ + "42/6=7", + "84+84=168", + "168/7=24" + ], + "optimal_path": "Current State: 24:[6, 84, 42, 84], Operations: []\nExploring Operation: 42/6=7, Resulting Numbers: [84, 84, 7]\nGenerated Node #2: [84, 84, 7] from Operation: 42/6=7\nCurrent State: 24:[84, 84, 7], Operations: ['42/6=7']\nExploring Operation: 84+84=168, Resulting Numbers: [7, 168]\nGenerated Node #3: [7, 168] from Operation: 84+84=168\nCurrent State: 24:[7, 168], Operations: ['42/6=7', '84+84=168']\nExploring Operation: 168/7=24, Resulting Numbers: [24]\n24,24 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 72, + 58, + 12, + 3 + ], + "target": 94, + "solution": [ + "72+58=130", + "12*3=36", + "130-36=94" + ], + "optimal_path": "Current State: 94:[72, 58, 12, 3], Operations: []\nExploring Operation: 72+58=130, Resulting Numbers: [12, 3, 130]\nGenerated Node #2: [12, 3, 130] from Operation: 72+58=130\nCurrent State: 94:[12, 3, 130], Operations: ['72+58=130']\nExploring Operation: 12*3=36, Resulting Numbers: [130, 36]\nGenerated Node #3: [130, 36] from Operation: 12*3=36\nCurrent State: 94:[130, 36], Operations: ['72+58=130', '12*3=36']\nExploring Operation: 130-36=94, Resulting Numbers: [94]\n94,94 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 79, + 4, + 87, + 43 + ], + "target": 31, + "solution": [ + "79-4=75", + "87-43=44", + "75-44=31" + ], + "optimal_path": "Current State: 31:[79, 4, 87, 43], Operations: []\nExploring Operation: 79-4=75, Resulting Numbers: [87, 43, 75]\nGenerated Node #2: [87, 43, 75] from Operation: 79-4=75\nCurrent State: 31:[87, 43, 75], Operations: ['79-4=75']\nExploring Operation: 87-43=44, Resulting Numbers: [75, 44]\nGenerated Node #3: [75, 44] from Operation: 87-43=44\nCurrent State: 31:[75, 44], Operations: ['79-4=75', '87-43=44']\nExploring Operation: 75-44=31, Resulting Numbers: [31]\n31,31 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 64, + 98, + 97, + 4 + ], + "target": 69, + "solution": [ + "64+98=162", + "97-4=93", + "162-93=69" + ], + "optimal_path": "Current State: 69:[64, 98, 97, 4], Operations: []\nExploring Operation: 64+98=162, Resulting Numbers: [97, 4, 162]\nGenerated Node #2: [97, 4, 162] from Operation: 64+98=162\nCurrent State: 69:[97, 4, 162], Operations: ['64+98=162']\nExploring Operation: 97-4=93, Resulting Numbers: [162, 93]\nGenerated Node #3: [162, 93] from Operation: 97-4=93\nCurrent State: 69:[162, 93], Operations: ['64+98=162', '97-4=93']\nExploring Operation: 162-93=69, Resulting Numbers: [69]\n69,69 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 19, + 21, + 81, + 27 + ], + "target": 12, + "solution": [ + "21*27=567", + "567/81=7", + "19-7=12" + ], + "optimal_path": "Current State: 12:[19, 21, 81, 27], Operations: []\nExploring Operation: 21*27=567, Resulting Numbers: [19, 81, 567]\nGenerated Node #2: [19, 81, 567] from Operation: 21*27=567\nCurrent State: 12:[19, 81, 567], Operations: ['21*27=567']\nExploring Operation: 567/81=7, Resulting Numbers: [19, 7]\nGenerated Node #3: [19, 7] from Operation: 567/81=7\nCurrent State: 12:[19, 7], Operations: ['21*27=567', '567/81=7']\nExploring Operation: 19-7=12, Resulting Numbers: [12]\n12,12 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 41, + 45, + 12, + 82 + ], + "target": 39, + "solution": [ + "41*12=492", + "492/82=6", + "45-6=39" + ], + "optimal_path": "Current State: 39:[41, 45, 12, 82], Operations: []\nExploring Operation: 41*12=492, Resulting Numbers: [45, 82, 492]\nGenerated Node #2: [45, 82, 492] from Operation: 41*12=492\nCurrent State: 39:[45, 82, 492], Operations: ['41*12=492']\nExploring Operation: 492/82=6, Resulting Numbers: [45, 6]\nGenerated Node #3: [45, 6] from Operation: 492/82=6\nCurrent State: 39:[45, 6], Operations: ['41*12=492', '492/82=6']\nExploring Operation: 45-6=39, Resulting Numbers: [39]\n39,39 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 12, + 98, + 27, + 24 + ], + "target": 62, + "solution": [ + "27-24=3", + "12*3=36", + "98-36=62" + ], + "optimal_path": "Current State: 62:[12, 98, 27, 24], Operations: []\nExploring Operation: 27-24=3, Resulting Numbers: [12, 98, 3]\nGenerated Node #2: [12, 98, 3] from Operation: 27-24=3\nCurrent State: 62:[12, 98, 3], Operations: ['27-24=3']\nExploring Operation: 12*3=36, Resulting Numbers: [98, 36]\nGenerated Node #3: [98, 36] from Operation: 12*3=36\nCurrent State: 62:[98, 36], Operations: ['27-24=3', '12*3=36']\nExploring Operation: 98-36=62, Resulting Numbers: [62]\n62,62 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 26, + 4, + 47, + 82 + ], + "target": 74, + "solution": [ + "26+82=108", + "108/4=27", + "47+27=74" + ], + "optimal_path": "Current State: 74:[26, 4, 47, 82], Operations: []\nExploring Operation: 26+82=108, Resulting Numbers: [4, 47, 108]\nGenerated Node #2: [4, 47, 108] from Operation: 26+82=108\nCurrent State: 74:[4, 47, 108], Operations: ['26+82=108']\nExploring Operation: 108/4=27, Resulting Numbers: [47, 27]\nGenerated Node #3: [47, 27] from Operation: 108/4=27\nCurrent State: 74:[47, 27], Operations: ['26+82=108', '108/4=27']\nExploring Operation: 47+27=74, Resulting Numbers: [74]\n74,74 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 96, + 32, + 53, + 74 + ], + "target": 63, + "solution": [ + "96-32=64", + "53+74=127", + "127-64=63" + ], + "optimal_path": "Current State: 63:[96, 32, 53, 74], Operations: []\nExploring Operation: 96-32=64, Resulting Numbers: [53, 74, 64]\nGenerated Node #2: [53, 74, 64] from Operation: 96-32=64\nCurrent State: 63:[53, 74, 64], Operations: ['96-32=64']\nExploring Operation: 53+74=127, Resulting Numbers: [64, 127]\nGenerated Node #3: [64, 127] from Operation: 53+74=127\nCurrent State: 63:[64, 127], Operations: ['96-32=64', '53+74=127']\nExploring Operation: 127-64=63, Resulting Numbers: [63]\n63,63 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 11, + 98, + 66, + 20 + ], + "target": 84, + "solution": [ + "66/11=6", + "98-20=78", + "6+78=84" + ], + "optimal_path": "Current State: 84:[11, 98, 66, 20], Operations: []\nExploring Operation: 66/11=6, Resulting Numbers: [98, 20, 6]\nGenerated Node #2: [98, 20, 6] from Operation: 66/11=6\nCurrent State: 84:[98, 20, 6], Operations: ['66/11=6']\nExploring Operation: 98-20=78, Resulting Numbers: [6, 78]\nGenerated Node #3: [6, 78] from Operation: 98-20=78\nCurrent State: 84:[6, 78], Operations: ['66/11=6', '98-20=78']\nExploring Operation: 6+78=84, Resulting Numbers: [84]\n84,84 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 68, + 17, + 6, + 44 + ], + "target": 42, + "solution": [ + "68-17=51", + "51-44=7", + "6*7=42" + ], + "optimal_path": "Current State: 42:[68, 17, 6, 44], Operations: []\nExploring Operation: 68-17=51, Resulting Numbers: [6, 44, 51]\nGenerated Node #2: [6, 44, 51] from Operation: 68-17=51\nCurrent State: 42:[6, 44, 51], Operations: ['68-17=51']\nExploring Operation: 51-44=7, Resulting Numbers: [6, 7]\nGenerated Node #3: [6, 7] from Operation: 51-44=7\nCurrent State: 42:[6, 7], Operations: ['68-17=51', '51-44=7']\nExploring Operation: 6*7=42, Resulting Numbers: [42]\n42,42 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 68, + 66, + 64, + 30 + ], + "target": 47, + "solution": [ + "68-66=2", + "64+30=94", + "94/2=47" + ], + "optimal_path": "Current State: 47:[68, 66, 64, 30], Operations: []\nExploring Operation: 68-66=2, Resulting Numbers: [64, 30, 2]\nGenerated Node #2: [64, 30, 2] from Operation: 68-66=2\nCurrent State: 47:[64, 30, 2], Operations: ['68-66=2']\nExploring Operation: 64+30=94, Resulting Numbers: [2, 94]\nGenerated Node #3: [2, 94] from Operation: 64+30=94\nCurrent State: 47:[2, 94], Operations: ['68-66=2', '64+30=94']\nExploring Operation: 94/2=47, Resulting Numbers: [47]\n47,47 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 69, + 87, + 47, + 2 + ], + "target": 38, + "solution": [ + "87-69=18", + "18/2=9", + "47-9=38" + ], + "optimal_path": "Current State: 38:[69, 87, 47, 2], Operations: []\nExploring Operation: 87-69=18, Resulting Numbers: [47, 2, 18]\nGenerated Node #2: [47, 2, 18] from Operation: 87-69=18\nCurrent State: 38:[47, 2, 18], Operations: ['87-69=18']\nExploring Operation: 18/2=9, Resulting Numbers: [47, 9]\nGenerated Node #3: [47, 9] from Operation: 18/2=9\nCurrent State: 38:[47, 9], Operations: ['87-69=18', '18/2=9']\nExploring Operation: 47-9=38, Resulting Numbers: [38]\n38,38 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 54, + 67, + 94, + 70 + ], + "target": 97, + "solution": [ + "54+67=121", + "94-70=24", + "121-24=97" + ], + "optimal_path": "Current State: 97:[54, 67, 94, 70], Operations: []\nExploring Operation: 54+67=121, Resulting Numbers: [94, 70, 121]\nGenerated Node #2: [94, 70, 121] from Operation: 54+67=121\nCurrent State: 97:[94, 70, 121], Operations: ['54+67=121']\nExploring Operation: 94-70=24, Resulting Numbers: [121, 24]\nGenerated Node #3: [121, 24] from Operation: 94-70=24\nCurrent State: 97:[121, 24], Operations: ['54+67=121', '94-70=24']\nExploring Operation: 121-24=97, Resulting Numbers: [97]\n97,97 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 44, + 29, + 12, + 87 + ], + "target": 96, + "solution": [ + "44-12=32", + "87/29=3", + "32*3=96" + ], + "optimal_path": "Current State: 96:[44, 29, 12, 87], Operations: []\nExploring Operation: 44-12=32, Resulting Numbers: [29, 87, 32]\nGenerated Node #2: [29, 87, 32] from Operation: 44-12=32\nCurrent State: 96:[29, 87, 32], Operations: ['44-12=32']\nExploring Operation: 87/29=3, Resulting Numbers: [32, 3]\nGenerated Node #3: [32, 3] from Operation: 87/29=3\nCurrent State: 96:[32, 3], Operations: ['44-12=32', '87/29=3']\nExploring Operation: 32*3=96, Resulting Numbers: [96]\n96,96 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 84, + 74, + 45, + 55 + ], + "target": 90, + "solution": [ + "84-74=10", + "45+55=100", + "100-10=90" + ], + "optimal_path": "Current State: 90:[84, 74, 45, 55], Operations: []\nExploring Operation: 84-74=10, Resulting Numbers: [45, 55, 10]\nGenerated Node #2: [45, 55, 10] from Operation: 84-74=10\nCurrent State: 90:[45, 55, 10], Operations: ['84-74=10']\nExploring Operation: 45+55=100, Resulting Numbers: [10, 100]\nGenerated Node #3: [10, 100] from Operation: 45+55=100\nCurrent State: 90:[10, 100], Operations: ['84-74=10', '45+55=100']\nExploring Operation: 100-10=90, Resulting Numbers: [90]\n90,90 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 51, + 50, + 55, + 53 + ], + "target": 99, + "solution": [ + "51+50=101", + "55-53=2", + "101-2=99" + ], + "optimal_path": "Current State: 99:[51, 50, 55, 53], Operations: []\nExploring Operation: 51+50=101, Resulting Numbers: [55, 53, 101]\nGenerated Node #2: [55, 53, 101] from Operation: 51+50=101\nCurrent State: 99:[55, 53, 101], Operations: ['51+50=101']\nExploring Operation: 55-53=2, Resulting Numbers: [101, 2]\nGenerated Node #3: [101, 2] from Operation: 55-53=2\nCurrent State: 99:[101, 2], Operations: ['51+50=101', '55-53=2']\nExploring Operation: 101-2=99, Resulting Numbers: [99]\n99,99 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 67, + 2, + 94, + 87 + ], + "target": 33, + "solution": [ + "94-67=27", + "2*27=54", + "87-54=33" + ], + "optimal_path": "Current State: 33:[67, 2, 94, 87], Operations: []\nExploring Operation: 94-67=27, Resulting Numbers: [2, 87, 27]\nGenerated Node #2: [2, 87, 27] from Operation: 94-67=27\nCurrent State: 33:[2, 87, 27], Operations: ['94-67=27']\nExploring Operation: 2*27=54, Resulting Numbers: [87, 54]\nGenerated Node #3: [87, 54] from Operation: 2*27=54\nCurrent State: 33:[87, 54], Operations: ['94-67=27', '2*27=54']\nExploring Operation: 87-54=33, Resulting Numbers: [33]\n33,33 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 93, + 91, + 58, + 80 + ], + "target": 36, + "solution": [ + "93-91=2", + "58*2=116", + "116-80=36" + ], + "optimal_path": "Current State: 36:[93, 91, 58, 80], Operations: []\nExploring Operation: 93-91=2, Resulting Numbers: [58, 80, 2]\nGenerated Node #2: [58, 80, 2] from Operation: 93-91=2\nCurrent State: 36:[58, 80, 2], Operations: ['93-91=2']\nExploring Operation: 58*2=116, Resulting Numbers: [80, 116]\nGenerated Node #3: [80, 116] from Operation: 58*2=116\nCurrent State: 36:[80, 116], Operations: ['93-91=2', '58*2=116']\nExploring Operation: 116-80=36, Resulting Numbers: [36]\n36,36 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 15, + 46, + 6, + 90 + ], + "target": 36, + "solution": [ + "15-6=9", + "90/9=10", + "46-10=36" + ], + "optimal_path": "Current State: 36:[15, 46, 6, 90], Operations: []\nExploring Operation: 15-6=9, Resulting Numbers: [46, 90, 9]\nGenerated Node #2: [46, 90, 9] from Operation: 15-6=9\nCurrent State: 36:[46, 90, 9], Operations: ['15-6=9']\nExploring Operation: 90/9=10, Resulting Numbers: [46, 10]\nGenerated Node #3: [46, 10] from Operation: 90/9=10\nCurrent State: 36:[46, 10], Operations: ['15-6=9', '90/9=10']\nExploring Operation: 46-10=36, Resulting Numbers: [36]\n36,36 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 41, + 15, + 62, + 95 + ], + "target": 25, + "solution": [ + "15*62=930", + "95+930=1025", + "1025/41=25" + ], + "optimal_path": "Current State: 25:[41, 15, 62, 95], Operations: []\nExploring Operation: 15*62=930, Resulting Numbers: [41, 95, 930]\nGenerated Node #2: [41, 95, 930] from Operation: 15*62=930\nCurrent State: 25:[41, 95, 930], Operations: ['15*62=930']\nExploring Operation: 95+930=1025, Resulting Numbers: [41, 1025]\nGenerated Node #3: [41, 1025] from Operation: 95+930=1025\nCurrent State: 25:[41, 1025], Operations: ['15*62=930', '95+930=1025']\nExploring Operation: 1025/41=25, Resulting Numbers: [25]\n25,25 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 5, + 42, + 51, + 11 + ], + "target": 50, + "solution": [ + "51-11=40", + "40/5=8", + "42+8=50" + ], + "optimal_path": "Current State: 50:[5, 42, 51, 11], Operations: []\nExploring Operation: 51-11=40, Resulting Numbers: [5, 42, 40]\nGenerated Node #2: [5, 42, 40] from Operation: 51-11=40\nCurrent State: 50:[5, 42, 40], Operations: ['51-11=40']\nExploring Operation: 40/5=8, Resulting Numbers: [42, 8]\nGenerated Node #3: [42, 8] from Operation: 40/5=8\nCurrent State: 50:[42, 8], Operations: ['51-11=40', '40/5=8']\nExploring Operation: 42+8=50, Resulting Numbers: [50]\n50,50 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 80, + 99, + 27, + 2 + ], + "target": 91, + "solution": [ + "80+27=107", + "99*2=198", + "198-107=91" + ], + "optimal_path": "Current State: 91:[80, 99, 27, 2], Operations: []\nExploring Operation: 80+27=107, Resulting Numbers: [99, 2, 107]\nGenerated Node #2: [99, 2, 107] from Operation: 80+27=107\nCurrent State: 91:[99, 2, 107], Operations: ['80+27=107']\nExploring Operation: 99*2=198, Resulting Numbers: [107, 198]\nGenerated Node #3: [107, 198] from Operation: 99*2=198\nCurrent State: 91:[107, 198], Operations: ['80+27=107', '99*2=198']\nExploring Operation: 198-107=91, Resulting Numbers: [91]\n91,91 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 5, + 23, + 90, + 65 + ], + "target": 100, + "solution": [ + "65/5=13", + "23+90=113", + "113-13=100" + ], + "optimal_path": "Current State: 100:[5, 23, 90, 65], Operations: []\nExploring Operation: 65/5=13, Resulting Numbers: [23, 90, 13]\nGenerated Node #2: [23, 90, 13] from Operation: 65/5=13\nCurrent State: 100:[23, 90, 13], Operations: ['65/5=13']\nExploring Operation: 23+90=113, Resulting Numbers: [13, 113]\nGenerated Node #3: [13, 113] from Operation: 23+90=113\nCurrent State: 100:[13, 113], Operations: ['65/5=13', '23+90=113']\nExploring Operation: 113-13=100, Resulting Numbers: [100]\n100,100 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 56, + 50, + 20, + 14 + ], + "target": 45, + "solution": [ + "56/14=4", + "20/4=5", + "50-5=45" + ], + "optimal_path": "Current State: 45:[56, 50, 20, 14], Operations: []\nExploring Operation: 56/14=4, Resulting Numbers: [50, 20, 4]\nGenerated Node #2: [50, 20, 4] from Operation: 56/14=4\nCurrent State: 45:[50, 20, 4], Operations: ['56/14=4']\nExploring Operation: 20/4=5, Resulting Numbers: [50, 5]\nGenerated Node #3: [50, 5] from Operation: 20/4=5\nCurrent State: 45:[50, 5], Operations: ['56/14=4', '20/4=5']\nExploring Operation: 50-5=45, Resulting Numbers: [45]\n45,45 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 41, + 1, + 34, + 99 + ], + "target": 25, + "solution": [ + "41-1=40", + "99-34=65", + "65-40=25" + ], + "optimal_path": "Current State: 25:[41, 1, 34, 99], Operations: []\nExploring Operation: 41-1=40, Resulting Numbers: [34, 99, 40]\nGenerated Node #2: [34, 99, 40] from Operation: 41-1=40\nCurrent State: 25:[34, 99, 40], Operations: ['41-1=40']\nExploring Operation: 99-34=65, Resulting Numbers: [40, 65]\nGenerated Node #3: [40, 65] from Operation: 99-34=65\nCurrent State: 25:[40, 65], Operations: ['41-1=40', '99-34=65']\nExploring Operation: 65-40=25, Resulting Numbers: [25]\n25,25 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 43, + 50, + 35, + 3 + ], + "target": 98, + "solution": [ + "50-43=7", + "35*3=105", + "105-7=98" + ], + "optimal_path": "Current State: 98:[43, 50, 35, 3], Operations: []\nExploring Operation: 50-43=7, Resulting Numbers: [35, 3, 7]\nGenerated Node #2: [35, 3, 7] from Operation: 50-43=7\nCurrent State: 98:[35, 3, 7], Operations: ['50-43=7']\nExploring Operation: 35*3=105, Resulting Numbers: [7, 105]\nGenerated Node #3: [7, 105] from Operation: 35*3=105\nCurrent State: 98:[7, 105], Operations: ['50-43=7', '35*3=105']\nExploring Operation: 105-7=98, Resulting Numbers: [98]\n98,98 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 69, + 40, + 48, + 44 + ], + "target": 63, + "solution": [ + "69-40=29", + "48+44=92", + "92-29=63" + ], + "optimal_path": "Current State: 63:[69, 40, 48, 44], Operations: []\nExploring Operation: 69-40=29, Resulting Numbers: [48, 44, 29]\nGenerated Node #2: [48, 44, 29] from Operation: 69-40=29\nCurrent State: 63:[48, 44, 29], Operations: ['69-40=29']\nExploring Operation: 48+44=92, Resulting Numbers: [29, 92]\nGenerated Node #3: [29, 92] from Operation: 48+44=92\nCurrent State: 63:[29, 92], Operations: ['69-40=29', '48+44=92']\nExploring Operation: 92-29=63, Resulting Numbers: [63]\n63,63 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 2, + 13, + 34, + 21 + ], + "target": 21, + "solution": [ + "2*21=42", + "34-13=21", + "42-21=21" + ], + "optimal_path": "Current State: 21:[2, 13, 34, 21], Operations: []\nExploring Operation: 2*21=42, Resulting Numbers: [13, 34, 42]\nGenerated Node #2: [13, 34, 42] from Operation: 2*21=42\nCurrent State: 21:[13, 34, 42], Operations: ['2*21=42']\nExploring Operation: 34-13=21, Resulting Numbers: [42, 21]\nGenerated Node #3: [42, 21] from Operation: 34-13=21\nCurrent State: 21:[42, 21], Operations: ['2*21=42', '34-13=21']\nExploring Operation: 42-21=21, Resulting Numbers: [21]\n21,21 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 55, + 37, + 3, + 68 + ], + "target": 74, + "solution": [ + "55-37=18", + "18/3=6", + "68+6=74" + ], + "optimal_path": "Current State: 74:[55, 37, 3, 68], Operations: []\nExploring Operation: 55-37=18, Resulting Numbers: [3, 68, 18]\nGenerated Node #2: [3, 68, 18] from Operation: 55-37=18\nCurrent State: 74:[3, 68, 18], Operations: ['55-37=18']\nExploring Operation: 18/3=6, Resulting Numbers: [68, 6]\nGenerated Node #3: [68, 6] from Operation: 18/3=6\nCurrent State: 74:[68, 6], Operations: ['55-37=18', '18/3=6']\nExploring Operation: 68+6=74, Resulting Numbers: [74]\n74,74 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 35, + 19, + 88, + 79 + ], + "target": 38, + "solution": [ + "79-35=44", + "19*88=1672", + "1672/44=38" + ], + "optimal_path": "Current State: 38:[35, 19, 88, 79], Operations: []\nExploring Operation: 79-35=44, Resulting Numbers: [19, 88, 44]\nGenerated Node #2: [19, 88, 44] from Operation: 79-35=44\nCurrent State: 38:[19, 88, 44], Operations: ['79-35=44']\nExploring Operation: 19*88=1672, Resulting Numbers: [44, 1672]\nGenerated Node #3: [44, 1672] from Operation: 19*88=1672\nCurrent State: 38:[44, 1672], Operations: ['79-35=44', '19*88=1672']\nExploring Operation: 1672/44=38, Resulting Numbers: [38]\n38,38 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 75, + 41, + 53, + 40 + ], + "target": 59, + "solution": [ + "75-41=34", + "53+40=93", + "93-34=59" + ], + "optimal_path": "Current State: 59:[75, 41, 53, 40], Operations: []\nExploring Operation: 75-41=34, Resulting Numbers: [53, 40, 34]\nGenerated Node #2: [53, 40, 34] from Operation: 75-41=34\nCurrent State: 59:[53, 40, 34], Operations: ['75-41=34']\nExploring Operation: 53+40=93, Resulting Numbers: [34, 93]\nGenerated Node #3: [34, 93] from Operation: 53+40=93\nCurrent State: 59:[34, 93], Operations: ['75-41=34', '53+40=93']\nExploring Operation: 93-34=59, Resulting Numbers: [59]\n59,59 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 97, + 45, + 84, + 27 + ], + "target": 43, + "solution": [ + "45*84=3780", + "3780/27=140", + "140-97=43" + ], + "optimal_path": "Current State: 43:[97, 45, 84, 27], Operations: []\nExploring Operation: 45*84=3780, Resulting Numbers: [97, 27, 3780]\nGenerated Node #2: [97, 27, 3780] from Operation: 45*84=3780\nCurrent State: 43:[97, 27, 3780], Operations: ['45*84=3780']\nExploring Operation: 3780/27=140, Resulting Numbers: [97, 140]\nGenerated Node #3: [97, 140] from Operation: 3780/27=140\nCurrent State: 43:[97, 140], Operations: ['45*84=3780', '3780/27=140']\nExploring Operation: 140-97=43, Resulting Numbers: [43]\n43,43 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 61, + 15, + 40, + 51 + ], + "target": 60, + "solution": [ + "61-51=10", + "15*40=600", + "600/10=60" + ], + "optimal_path": "Current State: 60:[61, 15, 40, 51], Operations: []\nExploring Operation: 61-51=10, Resulting Numbers: [15, 40, 10]\nGenerated Node #2: [15, 40, 10] from Operation: 61-51=10\nCurrent State: 60:[15, 40, 10], Operations: ['61-51=10']\nExploring Operation: 15*40=600, Resulting Numbers: [10, 600]\nGenerated Node #3: [10, 600] from Operation: 15*40=600\nCurrent State: 60:[10, 600], Operations: ['61-51=10', '15*40=600']\nExploring Operation: 600/10=60, Resulting Numbers: [60]\n60,60 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 38, + 40, + 85, + 54 + ], + "target": 58, + "solution": [ + "40-38=2", + "54/2=27", + "85-27=58" + ], + "optimal_path": "Current State: 58:[38, 40, 85, 54], Operations: []\nExploring Operation: 40-38=2, Resulting Numbers: [85, 54, 2]\nGenerated Node #2: [85, 54, 2] from Operation: 40-38=2\nCurrent State: 58:[85, 54, 2], Operations: ['40-38=2']\nExploring Operation: 54/2=27, Resulting Numbers: [85, 27]\nGenerated Node #3: [85, 27] from Operation: 54/2=27\nCurrent State: 58:[85, 27], Operations: ['40-38=2', '54/2=27']\nExploring Operation: 85-27=58, Resulting Numbers: [58]\n58,58 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 18, + 2, + 73, + 5 + ], + "target": 59, + "solution": [ + "18/2=9", + "73-5=68", + "68-9=59" + ], + "optimal_path": "Current State: 59:[18, 2, 73, 5], Operations: []\nExploring Operation: 18/2=9, Resulting Numbers: [73, 5, 9]\nGenerated Node #2: [73, 5, 9] from Operation: 18/2=9\nCurrent State: 59:[73, 5, 9], Operations: ['18/2=9']\nExploring Operation: 73-5=68, Resulting Numbers: [9, 68]\nGenerated Node #3: [9, 68] from Operation: 73-5=68\nCurrent State: 59:[9, 68], Operations: ['18/2=9', '73-5=68']\nExploring Operation: 68-9=59, Resulting Numbers: [59]\n59,59 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 52, + 44, + 85, + 13 + ], + "target": 74, + "solution": [ + "52/13=4", + "44/4=11", + "85-11=74" + ], + "optimal_path": "Current State: 74:[52, 44, 85, 13], Operations: []\nExploring Operation: 52/13=4, Resulting Numbers: [44, 85, 4]\nGenerated Node #2: [44, 85, 4] from Operation: 52/13=4\nCurrent State: 74:[44, 85, 4], Operations: ['52/13=4']\nExploring Operation: 44/4=11, Resulting Numbers: [85, 11]\nGenerated Node #3: [85, 11] from Operation: 44/4=11\nCurrent State: 74:[85, 11], Operations: ['52/13=4', '44/4=11']\nExploring Operation: 85-11=74, Resulting Numbers: [74]\n74,74 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 97, + 93, + 1, + 96 + ], + "target": 91, + "solution": [ + "97-93=4", + "96-1=95", + "95-4=91" + ], + "optimal_path": "Current State: 91:[97, 93, 1, 96], Operations: []\nExploring Operation: 97-93=4, Resulting Numbers: [1, 96, 4]\nGenerated Node #2: [1, 96, 4] from Operation: 97-93=4\nCurrent State: 91:[1, 96, 4], Operations: ['97-93=4']\nExploring Operation: 96-1=95, Resulting Numbers: [4, 95]\nGenerated Node #3: [4, 95] from Operation: 96-1=95\nCurrent State: 91:[4, 95], Operations: ['97-93=4', '96-1=95']\nExploring Operation: 95-4=91, Resulting Numbers: [91]\n91,91 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 81, + 78, + 53, + 90 + ], + "target": 40, + "solution": [ + "81-78=3", + "90-53=37", + "3+37=40" + ], + "optimal_path": "Current State: 40:[81, 78, 53, 90], Operations: []\nExploring Operation: 81-78=3, Resulting Numbers: [53, 90, 3]\nGenerated Node #2: [53, 90, 3] from Operation: 81-78=3\nCurrent State: 40:[53, 90, 3], Operations: ['81-78=3']\nExploring Operation: 90-53=37, Resulting Numbers: [3, 37]\nGenerated Node #3: [3, 37] from Operation: 90-53=37\nCurrent State: 40:[3, 37], Operations: ['81-78=3', '90-53=37']\nExploring Operation: 3+37=40, Resulting Numbers: [40]\n40,40 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 96, + 24, + 34, + 54 + ], + "target": 16, + "solution": [ + "96-24=72", + "34+54=88", + "88-72=16" + ], + "optimal_path": "Current State: 16:[96, 24, 34, 54], Operations: []\nExploring Operation: 96-24=72, Resulting Numbers: [34, 54, 72]\nGenerated Node #2: [34, 54, 72] from Operation: 96-24=72\nCurrent State: 16:[34, 54, 72], Operations: ['96-24=72']\nExploring Operation: 34+54=88, Resulting Numbers: [72, 88]\nGenerated Node #3: [72, 88] from Operation: 34+54=88\nCurrent State: 16:[72, 88], Operations: ['96-24=72', '34+54=88']\nExploring Operation: 88-72=16, Resulting Numbers: [16]\n16,16 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 64, + 37, + 32, + 54 + ], + "target": 20, + "solution": [ + "64*37=2368", + "2368/32=74", + "74-54=20" + ], + "optimal_path": "Current State: 20:[64, 37, 32, 54], Operations: []\nExploring Operation: 64*37=2368, Resulting Numbers: [32, 54, 2368]\nGenerated Node #2: [32, 54, 2368] from Operation: 64*37=2368\nCurrent State: 20:[32, 54, 2368], Operations: ['64*37=2368']\nExploring Operation: 2368/32=74, Resulting Numbers: [54, 74]\nGenerated Node #3: [54, 74] from Operation: 2368/32=74\nCurrent State: 20:[54, 74], Operations: ['64*37=2368', '2368/32=74']\nExploring Operation: 74-54=20, Resulting Numbers: [20]\n20,20 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 73, + 79, + 53, + 15 + ], + "target": 37, + "solution": [ + "79-73=6", + "15*6=90", + "90-53=37" + ], + "optimal_path": "Current State: 37:[73, 79, 53, 15], Operations: []\nExploring Operation: 79-73=6, Resulting Numbers: [53, 15, 6]\nGenerated Node #2: [53, 15, 6] from Operation: 79-73=6\nCurrent State: 37:[53, 15, 6], Operations: ['79-73=6']\nExploring Operation: 15*6=90, Resulting Numbers: [53, 90]\nGenerated Node #3: [53, 90] from Operation: 15*6=90\nCurrent State: 37:[53, 90], Operations: ['79-73=6', '15*6=90']\nExploring Operation: 90-53=37, Resulting Numbers: [37]\n37,37 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 21, + 32, + 69, + 84 + ], + "target": 41, + "solution": [ + "84/21=4", + "69-32=37", + "4+37=41" + ], + "optimal_path": "Current State: 41:[21, 32, 69, 84], Operations: []\nExploring Operation: 84/21=4, Resulting Numbers: [32, 69, 4]\nGenerated Node #2: [32, 69, 4] from Operation: 84/21=4\nCurrent State: 41:[32, 69, 4], Operations: ['84/21=4']\nExploring Operation: 69-32=37, Resulting Numbers: [4, 37]\nGenerated Node #3: [4, 37] from Operation: 69-32=37\nCurrent State: 41:[4, 37], Operations: ['84/21=4', '69-32=37']\nExploring Operation: 4+37=41, Resulting Numbers: [41]\n41,41 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 82, + 49, + 40, + 68 + ], + "target": 52, + "solution": [ + "82*40=3280", + "49*68=3332", + "3332-3280=52" + ], + "optimal_path": "Current State: 52:[82, 49, 40, 68], Operations: []\nExploring Operation: 82*40=3280, Resulting Numbers: [49, 68, 3280]\nGenerated Node #2: [49, 68, 3280] from Operation: 82*40=3280\nCurrent State: 52:[49, 68, 3280], Operations: ['82*40=3280']\nExploring Operation: 49*68=3332, Resulting Numbers: [3280, 3332]\nGenerated Node #3: [3280, 3332] from Operation: 49*68=3332\nCurrent State: 52:[3280, 3332], Operations: ['82*40=3280', '49*68=3332']\nExploring Operation: 3332-3280=52, Resulting Numbers: [52]\n52,52 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 35, + 3, + 56, + 1 + ], + "target": 14, + "solution": [ + "3-1=2", + "35*2=70", + "70-56=14" + ], + "optimal_path": "Current State: 14:[35, 3, 56, 1], Operations: []\nExploring Operation: 3-1=2, Resulting Numbers: [35, 56, 2]\nGenerated Node #2: [35, 56, 2] from Operation: 3-1=2\nCurrent State: 14:[35, 56, 2], Operations: ['3-1=2']\nExploring Operation: 35*2=70, Resulting Numbers: [56, 70]\nGenerated Node #3: [56, 70] from Operation: 35*2=70\nCurrent State: 14:[56, 70], Operations: ['3-1=2', '35*2=70']\nExploring Operation: 70-56=14, Resulting Numbers: [14]\n14,14 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 68, + 61, + 42, + 69 + ], + "target": 63, + "solution": [ + "68-61=7", + "42/7=6", + "69-6=63" + ], + "optimal_path": "Current State: 63:[68, 61, 42, 69], Operations: []\nExploring Operation: 68-61=7, Resulting Numbers: [42, 69, 7]\nGenerated Node #2: [42, 69, 7] from Operation: 68-61=7\nCurrent State: 63:[42, 69, 7], Operations: ['68-61=7']\nExploring Operation: 42/7=6, Resulting Numbers: [69, 6]\nGenerated Node #3: [69, 6] from Operation: 42/7=6\nCurrent State: 63:[69, 6], Operations: ['68-61=7', '42/7=6']\nExploring Operation: 69-6=63, Resulting Numbers: [63]\n63,63 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 35, + 55, + 12, + 77 + ], + "target": 37, + "solution": [ + "35*55=1925", + "1925/77=25", + "12+25=37" + ], + "optimal_path": "Current State: 37:[35, 55, 12, 77], Operations: []\nExploring Operation: 35*55=1925, Resulting Numbers: [12, 77, 1925]\nGenerated Node #2: [12, 77, 1925] from Operation: 35*55=1925\nCurrent State: 37:[12, 77, 1925], Operations: ['35*55=1925']\nExploring Operation: 1925/77=25, Resulting Numbers: [12, 25]\nGenerated Node #3: [12, 25] from Operation: 1925/77=25\nCurrent State: 37:[12, 25], Operations: ['35*55=1925', '1925/77=25']\nExploring Operation: 12+25=37, Resulting Numbers: [37]\n37,37 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 32, + 10, + 10, + 11 + ], + "target": 12, + "solution": [ + "32-10=22", + "22/11=2", + "10+2=12" + ], + "optimal_path": "Current State: 12:[32, 10, 10, 11], Operations: []\nExploring Operation: 32-10=22, Resulting Numbers: [11, 22]\nGenerated Node #2: [11, 22] from Operation: 32-10=22\nCurrent State: 12:[11, 22], Operations: ['32-10=22']\nExploring Operation: 22/11=2, Resulting Numbers: [2]\n2,12 equal: Goal Reached\nExploring Operation: 10+2=12, Resulting Numbers: [12]\n12,12 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 50, + 63, + 55, + 41 + ], + "target": 83, + "solution": [ + "63-50=13", + "55+41=96", + "96-13=83" + ], + "optimal_path": "Current State: 83:[50, 63, 55, 41], Operations: []\nExploring Operation: 63-50=13, Resulting Numbers: [55, 41, 13]\nGenerated Node #2: [55, 41, 13] from Operation: 63-50=13\nCurrent State: 83:[55, 41, 13], Operations: ['63-50=13']\nExploring Operation: 55+41=96, Resulting Numbers: [13, 96]\nGenerated Node #3: [13, 96] from Operation: 55+41=96\nCurrent State: 83:[13, 96], Operations: ['63-50=13', '55+41=96']\nExploring Operation: 96-13=83, Resulting Numbers: [83]\n83,83 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 37, + 96, + 64, + 24 + ], + "target": 99, + "solution": [ + "96-37=59", + "64-24=40", + "59+40=99" + ], + "optimal_path": "Current State: 99:[37, 96, 64, 24], Operations: []\nExploring Operation: 96-37=59, Resulting Numbers: [64, 24, 59]\nGenerated Node #2: [64, 24, 59] from Operation: 96-37=59\nCurrent State: 99:[64, 24, 59], Operations: ['96-37=59']\nExploring Operation: 64-24=40, Resulting Numbers: [59, 40]\nGenerated Node #3: [59, 40] from Operation: 64-24=40\nCurrent State: 99:[59, 40], Operations: ['96-37=59', '64-24=40']\nExploring Operation: 59+40=99, Resulting Numbers: [99]\n99,99 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 31, + 45, + 34, + 27 + ], + "target": 98, + "solution": [ + "45-31=14", + "34-27=7", + "14*7=98" + ], + "optimal_path": "Current State: 98:[31, 45, 34, 27], Operations: []\nExploring Operation: 45-31=14, Resulting Numbers: [34, 27, 14]\nGenerated Node #2: [34, 27, 14] from Operation: 45-31=14\nCurrent State: 98:[34, 27, 14], Operations: ['45-31=14']\nExploring Operation: 34-27=7, Resulting Numbers: [14, 7]\nGenerated Node #3: [14, 7] from Operation: 34-27=7\nCurrent State: 98:[14, 7], Operations: ['45-31=14', '34-27=7']\nExploring Operation: 14*7=98, Resulting Numbers: [98]\n98,98 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 79, + 29, + 5, + 7 + ], + "target": 21, + "solution": [ + "7-5=2", + "29*2=58", + "79-58=21" + ], + "optimal_path": "Current State: 21:[79, 29, 5, 7], Operations: []\nExploring Operation: 7-5=2, Resulting Numbers: [79, 29, 2]\nGenerated Node #2: [79, 29, 2] from Operation: 7-5=2\nCurrent State: 21:[79, 29, 2], Operations: ['7-5=2']\nExploring Operation: 29*2=58, Resulting Numbers: [79, 58]\nGenerated Node #3: [79, 58] from Operation: 29*2=58\nCurrent State: 21:[79, 58], Operations: ['7-5=2', '29*2=58']\nExploring Operation: 79-58=21, Resulting Numbers: [21]\n21,21 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 39, + 31, + 3, + 43 + ], + "target": 81, + "solution": [ + "39+31=70", + "70-43=27", + "3*27=81" + ], + "optimal_path": "Current State: 81:[39, 31, 3, 43], Operations: []\nExploring Operation: 39+31=70, Resulting Numbers: [3, 43, 70]\nGenerated Node #2: [3, 43, 70] from Operation: 39+31=70\nCurrent State: 81:[3, 43, 70], Operations: ['39+31=70']\nExploring Operation: 70-43=27, Resulting Numbers: [3, 27]\nGenerated Node #3: [3, 27] from Operation: 70-43=27\nCurrent State: 81:[3, 27], Operations: ['39+31=70', '70-43=27']\nExploring Operation: 3*27=81, Resulting Numbers: [81]\n81,81 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 75, + 23, + 28, + 44 + ], + "target": 100, + "solution": [ + "75*28=2100", + "44-23=21", + "2100/21=100" + ], + "optimal_path": "Current State: 100:[75, 23, 28, 44], Operations: []\nExploring Operation: 75*28=2100, Resulting Numbers: [23, 44, 2100]\nGenerated Node #2: [23, 44, 2100] from Operation: 75*28=2100\nCurrent State: 100:[23, 44, 2100], Operations: ['75*28=2100']\nExploring Operation: 44-23=21, Resulting Numbers: [2100, 21]\nGenerated Node #3: [2100, 21] from Operation: 44-23=21\nCurrent State: 100:[2100, 21], Operations: ['75*28=2100', '44-23=21']\nExploring Operation: 2100/21=100, Resulting Numbers: [100]\n100,100 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 90, + 21, + 21, + 2 + ], + "target": 24, + "solution": [ + "90-21=69", + "69-21=48", + "48/2=24" + ], + "optimal_path": "Current State: 24:[90, 21, 21, 2], Operations: []\nExploring Operation: 90-21=69, Resulting Numbers: [2, 69]\nGenerated Node #2: [2, 69] from Operation: 90-21=69\nCurrent State: 24:[2, 69], Operations: ['90-21=69']\nExploring Operation: 69-21=48, Resulting Numbers: [2, 48]\nGenerated Node #3: [2, 48] from Operation: 69-21=48\nCurrent State: 24:[2, 48], Operations: ['90-21=69', '69-21=48']\nExploring Operation: 48/2=24, Resulting Numbers: [24]\n24,24 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 7, + 14, + 5, + 70 + ], + "target": 52, + "solution": [ + "5*70=350", + "14+350=364", + "364/7=52" + ], + "optimal_path": "Current State: 52:[7, 14, 5, 70], Operations: []\nExploring Operation: 5*70=350, Resulting Numbers: [7, 14, 350]\nGenerated Node #2: [7, 14, 350] from Operation: 5*70=350\nCurrent State: 52:[7, 14, 350], Operations: ['5*70=350']\nExploring Operation: 14+350=364, Resulting Numbers: [7, 364]\nGenerated Node #3: [7, 364] from Operation: 14+350=364\nCurrent State: 52:[7, 364], Operations: ['5*70=350', '14+350=364']\nExploring Operation: 364/7=52, Resulting Numbers: [52]\n52,52 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 97, + 31, + 30, + 31 + ], + "target": 66, + "solution": [ + "97-31=66", + "31-30=1", + "66*1=66" + ], + "optimal_path": "Current State: 66:[97, 31, 30, 31], Operations: []\nExploring Operation: 97-31=66, Resulting Numbers: [30, 66]\nGenerated Node #2: [30, 66] from Operation: 97-31=66\nCurrent State: 66:[30, 66], Operations: ['97-31=66']\nExploring Operation: 31-30=1, Resulting Numbers: [66, 1]\nGenerated Node #3: [66, 1] from Operation: 31-30=1\nCurrent State: 66:[66, 1], Operations: ['97-31=66', '31-30=1']\nExploring Operation: 66*1=66, Resulting Numbers: [66]\n66,66 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 17, + 48, + 83, + 26 + ], + "target": 88, + "solution": [ + "48-17=31", + "83-26=57", + "31+57=88" + ], + "optimal_path": "Current State: 88:[17, 48, 83, 26], Operations: []\nExploring Operation: 48-17=31, Resulting Numbers: [83, 26, 31]\nGenerated Node #2: [83, 26, 31] from Operation: 48-17=31\nCurrent State: 88:[83, 26, 31], Operations: ['48-17=31']\nExploring Operation: 83-26=57, Resulting Numbers: [31, 57]\nGenerated Node #3: [31, 57] from Operation: 83-26=57\nCurrent State: 88:[31, 57], Operations: ['48-17=31', '83-26=57']\nExploring Operation: 31+57=88, Resulting Numbers: [88]\n88,88 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 75, + 43, + 9, + 86 + ], + "target": 93, + "solution": [ + "86/43=2", + "9*2=18", + "75+18=93" + ], + "optimal_path": "Current State: 93:[75, 43, 9, 86], Operations: []\nExploring Operation: 86/43=2, Resulting Numbers: [75, 9, 2]\nGenerated Node #2: [75, 9, 2] from Operation: 86/43=2\nCurrent State: 93:[75, 9, 2], Operations: ['86/43=2']\nExploring Operation: 9*2=18, Resulting Numbers: [75, 18]\nGenerated Node #3: [75, 18] from Operation: 9*2=18\nCurrent State: 93:[75, 18], Operations: ['86/43=2', '9*2=18']\nExploring Operation: 75+18=93, Resulting Numbers: [93]\n93,93 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 39, + 21, + 34, + 83 + ], + "target": 86, + "solution": [ + "34-21=13", + "39/13=3", + "83+3=86" + ], + "optimal_path": "Current State: 86:[39, 21, 34, 83], Operations: []\nExploring Operation: 34-21=13, Resulting Numbers: [39, 83, 13]\nGenerated Node #2: [39, 83, 13] from Operation: 34-21=13\nCurrent State: 86:[39, 83, 13], Operations: ['34-21=13']\nExploring Operation: 39/13=3, Resulting Numbers: [83, 3]\nGenerated Node #3: [83, 3] from Operation: 39/13=3\nCurrent State: 86:[83, 3], Operations: ['34-21=13', '39/13=3']\nExploring Operation: 83+3=86, Resulting Numbers: [86]\n86,86 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 37, + 6, + 17, + 93 + ], + "target": 27, + "solution": [ + "37-17=20", + "6*20=120", + "120-93=27" + ], + "optimal_path": "Current State: 27:[37, 6, 17, 93], Operations: []\nExploring Operation: 37-17=20, Resulting Numbers: [6, 93, 20]\nGenerated Node #2: [6, 93, 20] from Operation: 37-17=20\nCurrent State: 27:[6, 93, 20], Operations: ['37-17=20']\nExploring Operation: 6*20=120, Resulting Numbers: [93, 120]\nGenerated Node #3: [93, 120] from Operation: 6*20=120\nCurrent State: 27:[93, 120], Operations: ['37-17=20', '6*20=120']\nExploring Operation: 120-93=27, Resulting Numbers: [27]\n27,27 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 87, + 97, + 37, + 53 + ], + "target": 80, + "solution": [ + "97-87=10", + "37+53=90", + "90-10=80" + ], + "optimal_path": "Current State: 80:[87, 97, 37, 53], Operations: []\nExploring Operation: 97-87=10, Resulting Numbers: [37, 53, 10]\nGenerated Node #2: [37, 53, 10] from Operation: 97-87=10\nCurrent State: 80:[37, 53, 10], Operations: ['97-87=10']\nExploring Operation: 37+53=90, Resulting Numbers: [10, 90]\nGenerated Node #3: [10, 90] from Operation: 37+53=90\nCurrent State: 80:[10, 90], Operations: ['97-87=10', '37+53=90']\nExploring Operation: 90-10=80, Resulting Numbers: [80]\n80,80 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 86, + 96, + 7, + 49 + ], + "target": 23, + "solution": [ + "86+96=182", + "182/7=26", + "49-26=23" + ], + "optimal_path": "Current State: 23:[86, 96, 7, 49], Operations: []\nExploring Operation: 86+96=182, Resulting Numbers: [7, 49, 182]\nGenerated Node #2: [7, 49, 182] from Operation: 86+96=182\nCurrent State: 23:[7, 49, 182], Operations: ['86+96=182']\nExploring Operation: 182/7=26, Resulting Numbers: [49, 26]\nGenerated Node #3: [49, 26] from Operation: 182/7=26\nCurrent State: 23:[49, 26], Operations: ['86+96=182', '182/7=26']\nExploring Operation: 49-26=23, Resulting Numbers: [23]\n23,23 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 45, + 4, + 47, + 98 + ], + "target": 100, + "solution": [ + "45+4=49", + "98-47=51", + "49+51=100" + ], + "optimal_path": "Current State: 100:[45, 4, 47, 98], Operations: []\nExploring Operation: 45+4=49, Resulting Numbers: [47, 98, 49]\nGenerated Node #2: [47, 98, 49] from Operation: 45+4=49\nCurrent State: 100:[47, 98, 49], Operations: ['45+4=49']\nExploring Operation: 98-47=51, Resulting Numbers: [49, 51]\nGenerated Node #3: [49, 51] from Operation: 98-47=51\nCurrent State: 100:[49, 51], Operations: ['45+4=49', '98-47=51']\nExploring Operation: 49+51=100, Resulting Numbers: [100]\n100,100 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 3, + 44, + 11, + 92 + ], + "target": 15, + "solution": [ + "3*11=33", + "92-44=48", + "48-33=15" + ], + "optimal_path": "Current State: 15:[3, 44, 11, 92], Operations: []\nExploring Operation: 3*11=33, Resulting Numbers: [44, 92, 33]\nGenerated Node #2: [44, 92, 33] from Operation: 3*11=33\nCurrent State: 15:[44, 92, 33], Operations: ['3*11=33']\nExploring Operation: 92-44=48, Resulting Numbers: [33, 48]\nGenerated Node #3: [33, 48] from Operation: 92-44=48\nCurrent State: 15:[33, 48], Operations: ['3*11=33', '92-44=48']\nExploring Operation: 48-33=15, Resulting Numbers: [15]\n15,15 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 75, + 39, + 29, + 2 + ], + "target": 14, + "solution": [ + "75-39=36", + "36-29=7", + "2*7=14" + ], + "optimal_path": "Current State: 14:[75, 39, 29, 2], Operations: []\nExploring Operation: 75-39=36, Resulting Numbers: [29, 2, 36]\nGenerated Node #2: [29, 2, 36] from Operation: 75-39=36\nCurrent State: 14:[29, 2, 36], Operations: ['75-39=36']\nExploring Operation: 36-29=7, Resulting Numbers: [2, 7]\nGenerated Node #3: [2, 7] from Operation: 36-29=7\nCurrent State: 14:[2, 7], Operations: ['75-39=36', '36-29=7']\nExploring Operation: 2*7=14, Resulting Numbers: [14]\n14,14 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 6, + 62, + 34, + 59 + ], + "target": 88, + "solution": [ + "59-34=25", + "6*25=150", + "150-62=88" + ], + "optimal_path": "Current State: 88:[6, 62, 34, 59], Operations: []\nExploring Operation: 59-34=25, Resulting Numbers: [6, 62, 25]\nGenerated Node #2: [6, 62, 25] from Operation: 59-34=25\nCurrent State: 88:[6, 62, 25], Operations: ['59-34=25']\nExploring Operation: 6*25=150, Resulting Numbers: [62, 150]\nGenerated Node #3: [62, 150] from Operation: 6*25=150\nCurrent State: 88:[62, 150], Operations: ['59-34=25', '6*25=150']\nExploring Operation: 150-62=88, Resulting Numbers: [88]\n88,88 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 49, + 12, + 56, + 28 + ], + "target": 39, + "solution": [ + "49-12=37", + "56/28=2", + "37+2=39" + ], + "optimal_path": "Current State: 39:[49, 12, 56, 28], Operations: []\nExploring Operation: 49-12=37, Resulting Numbers: [56, 28, 37]\nGenerated Node #2: [56, 28, 37] from Operation: 49-12=37\nCurrent State: 39:[56, 28, 37], Operations: ['49-12=37']\nExploring Operation: 56/28=2, Resulting Numbers: [37, 2]\nGenerated Node #3: [37, 2] from Operation: 56/28=2\nCurrent State: 39:[37, 2], Operations: ['49-12=37', '56/28=2']\nExploring Operation: 37+2=39, Resulting Numbers: [39]\n39,39 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 85, + 98, + 22, + 67 + ], + "target": 58, + "solution": [ + "98-85=13", + "67-22=45", + "13+45=58" + ], + "optimal_path": "Current State: 58:[85, 98, 22, 67], Operations: []\nExploring Operation: 98-85=13, Resulting Numbers: [22, 67, 13]\nGenerated Node #2: [22, 67, 13] from Operation: 98-85=13\nCurrent State: 58:[22, 67, 13], Operations: ['98-85=13']\nExploring Operation: 67-22=45, Resulting Numbers: [13, 45]\nGenerated Node #3: [13, 45] from Operation: 67-22=45\nCurrent State: 58:[13, 45], Operations: ['98-85=13', '67-22=45']\nExploring Operation: 13+45=58, Resulting Numbers: [58]\n58,58 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 22, + 17, + 28, + 79 + ], + "target": 46, + "solution": [ + "22-17=5", + "79-28=51", + "51-5=46" + ], + "optimal_path": "Current State: 46:[22, 17, 28, 79], Operations: []\nExploring Operation: 22-17=5, Resulting Numbers: [28, 79, 5]\nGenerated Node #2: [28, 79, 5] from Operation: 22-17=5\nCurrent State: 46:[28, 79, 5], Operations: ['22-17=5']\nExploring Operation: 79-28=51, Resulting Numbers: [5, 51]\nGenerated Node #3: [5, 51] from Operation: 79-28=51\nCurrent State: 46:[5, 51], Operations: ['22-17=5', '79-28=51']\nExploring Operation: 51-5=46, Resulting Numbers: [46]\n46,46 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 6, + 26, + 68, + 58 + ], + "target": 70, + "solution": [ + "58-6=52", + "52/26=2", + "68+2=70" + ], + "optimal_path": "Current State: 70:[6, 26, 68, 58], Operations: []\nExploring Operation: 58-6=52, Resulting Numbers: [26, 68, 52]\nGenerated Node #2: [26, 68, 52] from Operation: 58-6=52\nCurrent State: 70:[26, 68, 52], Operations: ['58-6=52']\nExploring Operation: 52/26=2, Resulting Numbers: [68, 2]\nGenerated Node #3: [68, 2] from Operation: 52/26=2\nCurrent State: 70:[68, 2], Operations: ['58-6=52', '52/26=2']\nExploring Operation: 68+2=70, Resulting Numbers: [70]\n70,70 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 10, + 56, + 53, + 24 + ], + "target": 75, + "solution": [ + "56-10=46", + "53-24=29", + "46+29=75" + ], + "optimal_path": "Current State: 75:[10, 56, 53, 24], Operations: []\nExploring Operation: 56-10=46, Resulting Numbers: [53, 24, 46]\nGenerated Node #2: [53, 24, 46] from Operation: 56-10=46\nCurrent State: 75:[53, 24, 46], Operations: ['56-10=46']\nExploring Operation: 53-24=29, Resulting Numbers: [46, 29]\nGenerated Node #3: [46, 29] from Operation: 53-24=29\nCurrent State: 75:[46, 29], Operations: ['56-10=46', '53-24=29']\nExploring Operation: 46+29=75, Resulting Numbers: [75]\n75,75 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 7, + 2, + 14, + 46 + ], + "target": 65, + "solution": [ + "7-2=5", + "14+46=60", + "5+60=65" + ], + "optimal_path": "Current State: 65:[7, 2, 14, 46], Operations: []\nExploring Operation: 7-2=5, Resulting Numbers: [14, 46, 5]\nGenerated Node #2: [14, 46, 5] from Operation: 7-2=5\nCurrent State: 65:[14, 46, 5], Operations: ['7-2=5']\nExploring Operation: 14+46=60, Resulting Numbers: [5, 60]\nGenerated Node #3: [5, 60] from Operation: 14+46=60\nCurrent State: 65:[5, 60], Operations: ['7-2=5', '14+46=60']\nExploring Operation: 5+60=65, Resulting Numbers: [65]\n65,65 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 29, + 44, + 23, + 22 + ], + "target": 74, + "solution": [ + "29+44=73", + "23-22=1", + "73+1=74" + ], + "optimal_path": "Current State: 74:[29, 44, 23, 22], Operations: []\nExploring Operation: 29+44=73, Resulting Numbers: [23, 22, 73]\nGenerated Node #2: [23, 22, 73] from Operation: 29+44=73\nCurrent State: 74:[23, 22, 73], Operations: ['29+44=73']\nExploring Operation: 23-22=1, Resulting Numbers: [73, 1]\nGenerated Node #3: [73, 1] from Operation: 23-22=1\nCurrent State: 74:[73, 1], Operations: ['29+44=73', '23-22=1']\nExploring Operation: 73+1=74, Resulting Numbers: [74]\n74,74 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 44, + 19, + 1, + 4 + ], + "target": 30, + "solution": [ + "44-19=25", + "1+4=5", + "25+5=30" + ], + "optimal_path": "Current State: 30:[44, 19, 1, 4], Operations: []\nExploring Operation: 44-19=25, Resulting Numbers: [1, 4, 25]\nGenerated Node #2: [1, 4, 25] from Operation: 44-19=25\nCurrent State: 30:[1, 4, 25], Operations: ['44-19=25']\nExploring Operation: 1+4=5, Resulting Numbers: [25, 5]\nGenerated Node #3: [25, 5] from Operation: 1+4=5\nCurrent State: 30:[25, 5], Operations: ['44-19=25', '1+4=5']\nExploring Operation: 25+5=30, Resulting Numbers: [30]\n30,30 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 70, + 67, + 17, + 79 + ], + "target": 99, + "solution": [ + "70-67=3", + "17+79=96", + "3+96=99" + ], + "optimal_path": "Current State: 99:[70, 67, 17, 79], Operations: []\nExploring Operation: 70-67=3, Resulting Numbers: [17, 79, 3]\nGenerated Node #2: [17, 79, 3] from Operation: 70-67=3\nCurrent State: 99:[17, 79, 3], Operations: ['70-67=3']\nExploring Operation: 17+79=96, Resulting Numbers: [3, 96]\nGenerated Node #3: [3, 96] from Operation: 17+79=96\nCurrent State: 99:[3, 96], Operations: ['70-67=3', '17+79=96']\nExploring Operation: 3+96=99, Resulting Numbers: [99]\n99,99 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 62, + 20, + 82, + 43 + ], + "target": 42, + "solution": [ + "62+20=82", + "82/82=1", + "43-1=42" + ], + "optimal_path": "Current State: 42:[62, 20, 82, 43], Operations: []\nExploring Operation: 62+20=82, Resulting Numbers: [82, 43, 82]\nGenerated Node #2: [82, 43, 82] from Operation: 62+20=82\nCurrent State: 42:[82, 43, 82], Operations: ['62+20=82']\nExploring Operation: 82/82=1, Resulting Numbers: [43, 1]\nGenerated Node #3: [43, 1] from Operation: 82/82=1\nCurrent State: 42:[43, 1], Operations: ['62+20=82', '82/82=1']\nExploring Operation: 43-1=42, Resulting Numbers: [42]\n42,42 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 97, + 10, + 46, + 48 + ], + "target": 85, + "solution": [ + "97-10=87", + "48-46=2", + "87-2=85" + ], + "optimal_path": "Current State: 85:[97, 10, 46, 48], Operations: []\nExploring Operation: 97-10=87, Resulting Numbers: [46, 48, 87]\nGenerated Node #2: [46, 48, 87] from Operation: 97-10=87\nCurrent State: 85:[46, 48, 87], Operations: ['97-10=87']\nExploring Operation: 48-46=2, Resulting Numbers: [87, 2]\nGenerated Node #3: [87, 2] from Operation: 48-46=2\nCurrent State: 85:[87, 2], Operations: ['97-10=87', '48-46=2']\nExploring Operation: 87-2=85, Resulting Numbers: [85]\n85,85 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 26, + 48, + 78, + 63 + ], + "target": 37, + "solution": [ + "48-26=22", + "78-63=15", + "22+15=37" + ], + "optimal_path": "Current State: 37:[26, 48, 78, 63], Operations: []\nExploring Operation: 48-26=22, Resulting Numbers: [78, 63, 22]\nGenerated Node #2: [78, 63, 22] from Operation: 48-26=22\nCurrent State: 37:[78, 63, 22], Operations: ['48-26=22']\nExploring Operation: 78-63=15, Resulting Numbers: [22, 15]\nGenerated Node #3: [22, 15] from Operation: 78-63=15\nCurrent State: 37:[22, 15], Operations: ['48-26=22', '78-63=15']\nExploring Operation: 22+15=37, Resulting Numbers: [37]\n37,37 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 44, + 6, + 24, + 22 + ], + "target": 64, + "solution": [ + "44+24=68", + "6*22=132", + "132-68=64" + ], + "optimal_path": "Current State: 64:[44, 6, 24, 22], Operations: []\nExploring Operation: 44+24=68, Resulting Numbers: [6, 22, 68]\nGenerated Node #2: [6, 22, 68] from Operation: 44+24=68\nCurrent State: 64:[6, 22, 68], Operations: ['44+24=68']\nExploring Operation: 6*22=132, Resulting Numbers: [68, 132]\nGenerated Node #3: [68, 132] from Operation: 6*22=132\nCurrent State: 64:[68, 132], Operations: ['44+24=68', '6*22=132']\nExploring Operation: 132-68=64, Resulting Numbers: [64]\n64,64 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 89, + 84, + 16, + 39 + ], + "target": 18, + "solution": [ + "89-84=5", + "39-16=23", + "23-5=18" + ], + "optimal_path": "Current State: 18:[89, 84, 16, 39], Operations: []\nExploring Operation: 89-84=5, Resulting Numbers: [16, 39, 5]\nGenerated Node #2: [16, 39, 5] from Operation: 89-84=5\nCurrent State: 18:[16, 39, 5], Operations: ['89-84=5']\nExploring Operation: 39-16=23, Resulting Numbers: [5, 23]\nGenerated Node #3: [5, 23] from Operation: 39-16=23\nCurrent State: 18:[5, 23], Operations: ['89-84=5', '39-16=23']\nExploring Operation: 23-5=18, Resulting Numbers: [18]\n18,18 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 98, + 59, + 17, + 32 + ], + "target": 10, + "solution": [ + "98-59=39", + "17+32=49", + "49-39=10" + ], + "optimal_path": "Current State: 10:[98, 59, 17, 32], Operations: []\nExploring Operation: 98-59=39, Resulting Numbers: [17, 32, 39]\nGenerated Node #2: [17, 32, 39] from Operation: 98-59=39\nCurrent State: 10:[17, 32, 39], Operations: ['98-59=39']\nExploring Operation: 17+32=49, Resulting Numbers: [39, 49]\nGenerated Node #3: [39, 49] from Operation: 17+32=49\nCurrent State: 10:[39, 49], Operations: ['98-59=39', '17+32=49']\nExploring Operation: 49-39=10, Resulting Numbers: [10]\n10,10 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 71, + 91, + 10, + 82 + ], + "target": 84, + "solution": [ + "91-71=20", + "20/10=2", + "82+2=84" + ], + "optimal_path": "Current State: 84:[71, 91, 10, 82], Operations: []\nExploring Operation: 91-71=20, Resulting Numbers: [10, 82, 20]\nGenerated Node #2: [10, 82, 20] from Operation: 91-71=20\nCurrent State: 84:[10, 82, 20], Operations: ['91-71=20']\nExploring Operation: 20/10=2, Resulting Numbers: [82, 2]\nGenerated Node #3: [82, 2] from Operation: 20/10=2\nCurrent State: 84:[82, 2], Operations: ['91-71=20', '20/10=2']\nExploring Operation: 82+2=84, Resulting Numbers: [84]\n84,84 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 51, + 58, + 15, + 16 + ], + "target": 38, + "solution": [ + "58-51=7", + "15+16=31", + "7+31=38" + ], + "optimal_path": "Current State: 38:[51, 58, 15, 16], Operations: []\nExploring Operation: 58-51=7, Resulting Numbers: [15, 16, 7]\nGenerated Node #2: [15, 16, 7] from Operation: 58-51=7\nCurrent State: 38:[15, 16, 7], Operations: ['58-51=7']\nExploring Operation: 15+16=31, Resulting Numbers: [7, 31]\nGenerated Node #3: [7, 31] from Operation: 15+16=31\nCurrent State: 38:[7, 31], Operations: ['58-51=7', '15+16=31']\nExploring Operation: 7+31=38, Resulting Numbers: [38]\n38,38 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 16, + 64, + 3, + 73 + ], + "target": 51, + "solution": [ + "16+64=80", + "73+80=153", + "153/3=51" + ], + "optimal_path": "Current State: 51:[16, 64, 3, 73], Operations: []\nExploring Operation: 16+64=80, Resulting Numbers: [3, 73, 80]\nGenerated Node #2: [3, 73, 80] from Operation: 16+64=80\nCurrent State: 51:[3, 73, 80], Operations: ['16+64=80']\nExploring Operation: 73+80=153, Resulting Numbers: [3, 153]\nGenerated Node #3: [3, 153] from Operation: 73+80=153\nCurrent State: 51:[3, 153], Operations: ['16+64=80', '73+80=153']\nExploring Operation: 153/3=51, Resulting Numbers: [51]\n51,51 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 46, + 6, + 15, + 23 + ], + "target": 60, + "solution": [ + "46+6=52", + "23-15=8", + "52+8=60" + ], + "optimal_path": "Current State: 78:[59, 91, 99, 88], Operations: []\nExploring Operation: 91-88=3, Resulting Numbers: [59, 99, 3]\nGenerated Node #2: [59, 99, 3] from Operation: 91-88=3\nCurrent State: 78:[59, 99, 3], Operations: ['91-88=3']\nExploring Operation: 59*3=177, Resulting Numbers: [99, 177]\nGenerated Node #3: [99, 177] from Operation: 59*3=177\nCurrent State: 78:[99, 177], Operations: ['91-88=3', '59*3=177']\nExploring Operation: 177-99=78, Resulting Numbers: [78]\n78,78 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 2, + 40, + 50, + 72 + ], + "target": 21, + "solution": [ + "50+72=122", + "122/2=61", + "61-40=21" + ], + "optimal_path": "Current State: 21:[2, 40, 50, 72], Operations: []\nExploring Operation: 50+72=122, Resulting Numbers: [2, 40, 122]\nGenerated Node #2: [2, 40, 122] from Operation: 50+72=122\nCurrent State: 21:[2, 40, 122], Operations: ['50+72=122']\nExploring Operation: 122/2=61, Resulting Numbers: [40, 61]\nGenerated Node #3: [40, 61] from Operation: 122/2=61\nCurrent State: 21:[40, 61], Operations: ['50+72=122', '122/2=61']\nExploring Operation: 61-40=21, Resulting Numbers: [21]\n21,21 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 35, + 30, + 61, + 4 + ], + "target": 52, + "solution": [ + "35-30=5", + "61-4=57", + "57-5=52" + ], + "optimal_path": "Current State: 52:[35, 30, 61, 4], Operations: []\nExploring Operation: 35-30=5, Resulting Numbers: [61, 4, 5]\nGenerated Node #2: [61, 4, 5] from Operation: 35-30=5\nCurrent State: 52:[61, 4, 5], Operations: ['35-30=5']\nExploring Operation: 61-4=57, Resulting Numbers: [5, 57]\nGenerated Node #3: [5, 57] from Operation: 61-4=57\nCurrent State: 52:[5, 57], Operations: ['35-30=5', '61-4=57']\nExploring Operation: 57-5=52, Resulting Numbers: [52]\n52,52 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 75, + 96, + 74, + 27 + ], + "target": 70, + "solution": [ + "75+96=171", + "74+27=101", + "171-101=70" + ], + "optimal_path": "Current State: 70:[75, 96, 74, 27], Operations: []\nExploring Operation: 75+96=171, Resulting Numbers: [74, 27, 171]\nGenerated Node #2: [74, 27, 171] from Operation: 75+96=171\nCurrent State: 70:[74, 27, 171], Operations: ['75+96=171']\nExploring Operation: 74+27=101, Resulting Numbers: [171, 101]\nGenerated Node #3: [171, 101] from Operation: 74+27=101\nCurrent State: 70:[171, 101], Operations: ['75+96=171', '74+27=101']\nExploring Operation: 171-101=70, Resulting Numbers: [70]\n70,70 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 21, + 2, + 84, + 91 + ], + "target": 85, + "solution": [ + "84/21=4", + "91-2=89", + "89-4=85" + ], + "optimal_path": "Current State: 85:[21, 2, 84, 91], Operations: []\nExploring Operation: 84/21=4, Resulting Numbers: [2, 91, 4]\nGenerated Node #2: [2, 91, 4] from Operation: 84/21=4\nCurrent State: 85:[2, 91, 4], Operations: ['84/21=4']\nExploring Operation: 91-2=89, Resulting Numbers: [4, 89]\nGenerated Node #3: [4, 89] from Operation: 91-2=89\nCurrent State: 85:[4, 89], Operations: ['84/21=4', '91-2=89']\nExploring Operation: 89-4=85, Resulting Numbers: [85]\n85,85 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 46, + 48, + 96, + 60 + ], + "target": 58, + "solution": [ + "46+48=94", + "96-60=36", + "94-36=58" + ], + "optimal_path": "Current State: 58:[46, 48, 96, 60], Operations: []\nExploring Operation: 46+48=94, Resulting Numbers: [96, 60, 94]\nGenerated Node #2: [96, 60, 94] from Operation: 46+48=94\nCurrent State: 58:[96, 60, 94], Operations: ['46+48=94']\nExploring Operation: 96-60=36, Resulting Numbers: [94, 36]\nGenerated Node #3: [94, 36] from Operation: 96-60=36\nCurrent State: 58:[94, 36], Operations: ['46+48=94', '96-60=36']\nExploring Operation: 94-36=58, Resulting Numbers: [58]\n58,58 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 13, + 67, + 94, + 75 + ], + "target": 61, + "solution": [ + "13+67=80", + "94-75=19", + "80-19=61" + ], + "optimal_path": "Current State: 61:[13, 67, 94, 75], Operations: []\nExploring Operation: 13+67=80, Resulting Numbers: [94, 75, 80]\nGenerated Node #2: [94, 75, 80] from Operation: 13+67=80\nCurrent State: 61:[94, 75, 80], Operations: ['13+67=80']\nExploring Operation: 94-75=19, Resulting Numbers: [80, 19]\nGenerated Node #3: [80, 19] from Operation: 94-75=19\nCurrent State: 61:[80, 19], Operations: ['13+67=80', '94-75=19']\nExploring Operation: 80-19=61, Resulting Numbers: [61]\n61,61 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 94, + 34, + 4, + 15 + ], + "target": 47, + "solution": [ + "94+34=128", + "128/4=32", + "15+32=47" + ], + "optimal_path": "Current State: 47:[94, 34, 4, 15], Operations: []\nExploring Operation: 94+34=128, Resulting Numbers: [4, 15, 128]\nGenerated Node #2: [4, 15, 128] from Operation: 94+34=128\nCurrent State: 47:[4, 15, 128], Operations: ['94+34=128']\nExploring Operation: 128/4=32, Resulting Numbers: [15, 32]\nGenerated Node #3: [15, 32] from Operation: 128/4=32\nCurrent State: 47:[15, 32], Operations: ['94+34=128', '128/4=32']\nExploring Operation: 15+32=47, Resulting Numbers: [47]\n47,47 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 52, + 5, + 62, + 28 + ], + "target": 33, + "solution": [ + "52+5=57", + "62+28=90", + "90-57=33" + ], + "optimal_path": "Current State: 33:[52, 5, 62, 28], Operations: []\nExploring Operation: 52+5=57, Resulting Numbers: [62, 28, 57]\nGenerated Node #2: [62, 28, 57] from Operation: 52+5=57\nCurrent State: 33:[62, 28, 57], Operations: ['52+5=57']\nExploring Operation: 62+28=90, Resulting Numbers: [57, 90]\nGenerated Node #3: [57, 90] from Operation: 62+28=90\nCurrent State: 33:[57, 90], Operations: ['52+5=57', '62+28=90']\nExploring Operation: 90-57=33, Resulting Numbers: [33]\n33,33 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 91, + 12, + 66, + 26 + ], + "target": 13, + "solution": [ + "91-12=79", + "66+26=92", + "92-79=13" + ], + "optimal_path": "Current State: 13:[91, 12, 66, 26], Operations: []\nExploring Operation: 91-12=79, Resulting Numbers: [66, 26, 79]\nGenerated Node #2: [66, 26, 79] from Operation: 91-12=79\nCurrent State: 13:[66, 26, 79], Operations: ['91-12=79']\nExploring Operation: 66+26=92, Resulting Numbers: [79, 92]\nGenerated Node #3: [79, 92] from Operation: 66+26=92\nCurrent State: 13:[79, 92], Operations: ['91-12=79', '66+26=92']\nExploring Operation: 92-79=13, Resulting Numbers: [13]\n13,13 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 88, + 77, + 4, + 59 + ], + "target": 40, + "solution": [ + "88/4=22", + "77-59=18", + "22+18=40" + ], + "optimal_path": "Current State: 40:[88, 77, 4, 59], Operations: []\nExploring Operation: 88/4=22, Resulting Numbers: [77, 59, 22]\nGenerated Node #2: [77, 59, 22] from Operation: 88/4=22\nCurrent State: 40:[77, 59, 22], Operations: ['88/4=22']\nExploring Operation: 77-59=18, Resulting Numbers: [22, 18]\nGenerated Node #3: [22, 18] from Operation: 77-59=18\nCurrent State: 40:[22, 18], Operations: ['88/4=22', '77-59=18']\nExploring Operation: 22+18=40, Resulting Numbers: [40]\n40,40 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 8, + 42, + 2, + 77 + ], + "target": 51, + "solution": [ + "8*2=16", + "77-42=35", + "16+35=51" + ], + "optimal_path": "Current State: 51:[8, 42, 2, 77], Operations: []\nExploring Operation: 8*2=16, Resulting Numbers: [42, 77, 16]\nGenerated Node #2: [42, 77, 16] from Operation: 8*2=16\nCurrent State: 51:[42, 77, 16], Operations: ['8*2=16']\nExploring Operation: 77-42=35, Resulting Numbers: [16, 35]\nGenerated Node #3: [16, 35] from Operation: 77-42=35\nCurrent State: 51:[16, 35], Operations: ['8*2=16', '77-42=35']\nExploring Operation: 16+35=51, Resulting Numbers: [51]\n51,51 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 67, + 94, + 2, + 77 + ], + "target": 99, + "solution": [ + "77-67=10", + "10/2=5", + "94+5=99" + ], + "optimal_path": "Current State: 99:[67, 94, 2, 77], Operations: []\nExploring Operation: 77-67=10, Resulting Numbers: [94, 2, 10]\nGenerated Node #2: [94, 2, 10] from Operation: 77-67=10\nCurrent State: 99:[94, 2, 10], Operations: ['77-67=10']\nExploring Operation: 10/2=5, Resulting Numbers: [94, 5]\nGenerated Node #3: [94, 5] from Operation: 10/2=5\nCurrent State: 99:[94, 5], Operations: ['77-67=10', '10/2=5']\nExploring Operation: 94+5=99, Resulting Numbers: [99]\n99,99 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 15, + 54, + 64, + 9 + ], + "target": 45, + "solution": [ + "15+54=69", + "69-64=5", + "9*5=45" + ], + "optimal_path": "Current State: 45:[15, 54, 64, 9], Operations: []\nExploring Operation: 15+54=69, Resulting Numbers: [64, 9, 69]\nGenerated Node #2: [64, 9, 69] from Operation: 15+54=69\nCurrent State: 45:[64, 9, 69], Operations: ['15+54=69']\nExploring Operation: 69-64=5, Resulting Numbers: [9, 5]\nGenerated Node #3: [9, 5] from Operation: 69-64=5\nCurrent State: 45:[9, 5], Operations: ['15+54=69', '69-64=5']\nExploring Operation: 9*5=45, Resulting Numbers: [45]\n45,45 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 3, + 67, + 34, + 2 + ], + "target": 33, + "solution": [ + "3*34=102", + "67+2=69", + "102-69=33" + ], + "optimal_path": "Current State: 33:[3, 67, 34, 2], Operations: []\nExploring Operation: 3*34=102, Resulting Numbers: [67, 2, 102]\nGenerated Node #2: [67, 2, 102] from Operation: 3*34=102\nCurrent State: 33:[67, 2, 102], Operations: ['3*34=102']\nExploring Operation: 67+2=69, Resulting Numbers: [102, 69]\nGenerated Node #3: [102, 69] from Operation: 67+2=69\nCurrent State: 33:[102, 69], Operations: ['3*34=102', '67+2=69']\nExploring Operation: 102-69=33, Resulting Numbers: [33]\n33,33 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 25, + 59, + 51, + 44 + ], + "target": 27, + "solution": [ + "59-25=34", + "51-44=7", + "34-7=27" + ], + "optimal_path": "Current State: 27:[25, 59, 51, 44], Operations: []\nExploring Operation: 59-25=34, Resulting Numbers: [51, 44, 34]\nGenerated Node #2: [51, 44, 34] from Operation: 59-25=34\nCurrent State: 27:[51, 44, 34], Operations: ['59-25=34']\nExploring Operation: 51-44=7, Resulting Numbers: [34, 7]\nGenerated Node #3: [34, 7] from Operation: 51-44=7\nCurrent State: 27:[34, 7], Operations: ['59-25=34', '51-44=7']\nExploring Operation: 34-7=27, Resulting Numbers: [27]\n27,27 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 80, + 3, + 46, + 26 + ], + "target": 44, + "solution": [ + "80-46=34", + "3*26=78", + "78-34=44" + ], + "optimal_path": "Current State: 44:[80, 3, 46, 26], Operations: []\nExploring Operation: 80-46=34, Resulting Numbers: [3, 26, 34]\nGenerated Node #2: [3, 26, 34] from Operation: 80-46=34\nCurrent State: 44:[3, 26, 34], Operations: ['80-46=34']\nExploring Operation: 3*26=78, Resulting Numbers: [34, 78]\nGenerated Node #3: [34, 78] from Operation: 3*26=78\nCurrent State: 44:[34, 78], Operations: ['80-46=34', '3*26=78']\nExploring Operation: 78-34=44, Resulting Numbers: [44]\n44,44 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 26, + 80, + 77, + 27 + ], + "target": 56, + "solution": [ + "26+80=106", + "77-27=50", + "106-50=56" + ], + "optimal_path": "Current State: 56:[26, 80, 77, 27], Operations: []\nExploring Operation: 26+80=106, Resulting Numbers: [77, 27, 106]\nGenerated Node #2: [77, 27, 106] from Operation: 26+80=106\nCurrent State: 56:[77, 27, 106], Operations: ['26+80=106']\nExploring Operation: 77-27=50, Resulting Numbers: [106, 50]\nGenerated Node #3: [106, 50] from Operation: 77-27=50\nCurrent State: 56:[106, 50], Operations: ['26+80=106', '77-27=50']\nExploring Operation: 106-50=56, Resulting Numbers: [56]\n56,56 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 52, + 4, + 99, + 32 + ], + "target": 81, + "solution": [ + "99-52=47", + "4*32=128", + "128-47=81" + ], + "optimal_path": "Current State: 81:[52, 4, 99, 32], Operations: []\nExploring Operation: 99-52=47, Resulting Numbers: [4, 32, 47]\nGenerated Node #2: [4, 32, 47] from Operation: 99-52=47\nCurrent State: 81:[4, 32, 47], Operations: ['99-52=47']\nExploring Operation: 4*32=128, Resulting Numbers: [47, 128]\nGenerated Node #3: [47, 128] from Operation: 4*32=128\nCurrent State: 81:[47, 128], Operations: ['99-52=47', '4*32=128']\nExploring Operation: 128-47=81, Resulting Numbers: [81]\n81,81 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 35, + 85, + 97, + 84 + ], + "target": 37, + "solution": [ + "85-35=50", + "97-84=13", + "50-13=37" + ], + "optimal_path": "Current State: 37:[35, 85, 97, 84], Operations: []\nExploring Operation: 85-35=50, Resulting Numbers: [97, 84, 50]\nGenerated Node #2: [97, 84, 50] from Operation: 85-35=50\nCurrent State: 37:[97, 84, 50], Operations: ['85-35=50']\nExploring Operation: 97-84=13, Resulting Numbers: [50, 13]\nGenerated Node #3: [50, 13] from Operation: 97-84=13\nCurrent State: 37:[50, 13], Operations: ['85-35=50', '97-84=13']\nExploring Operation: 50-13=37, Resulting Numbers: [37]\n37,37 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 83, + 28, + 6, + 7 + ], + "target": 78, + "solution": [ + "83+7=90", + "28*6=168", + "168-90=78" + ], + "optimal_path": "Current State: 78:[83, 28, 6, 7], Operations: []\nExploring Operation: 83+7=90, Resulting Numbers: [28, 6, 90]\nGenerated Node #2: [28, 6, 90] from Operation: 83+7=90\nCurrent State: 78:[28, 6, 90], Operations: ['83+7=90']\nExploring Operation: 28*6=168, Resulting Numbers: [90, 168]\nGenerated Node #3: [90, 168] from Operation: 28*6=168\nCurrent State: 78:[90, 168], Operations: ['83+7=90', '28*6=168']\nExploring Operation: 168-90=78, Resulting Numbers: [78]\n78,78 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 93, + 2, + 28, + 88 + ], + "target": 66, + "solution": [ + "93+28=121", + "121-88=33", + "2*33=66" + ], + "optimal_path": "Current State: 66:[93, 2, 28, 88], Operations: []\nExploring Operation: 93+28=121, Resulting Numbers: [2, 88, 121]\nGenerated Node #2: [2, 88, 121] from Operation: 93+28=121\nCurrent State: 66:[2, 88, 121], Operations: ['93+28=121']\nExploring Operation: 121-88=33, Resulting Numbers: [2, 33]\nGenerated Node #3: [2, 33] from Operation: 121-88=33\nCurrent State: 66:[2, 33], Operations: ['93+28=121', '121-88=33']\nExploring Operation: 2*33=66, Resulting Numbers: [66]\n66,66 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 30, + 14, + 96, + 63 + ], + "target": 57, + "solution": [ + "30-14=16", + "96/16=6", + "63-6=57" + ], + "optimal_path": "Current State: 57:[30, 14, 96, 63], Operations: []\nExploring Operation: 30-14=16, Resulting Numbers: [96, 63, 16]\nGenerated Node #2: [96, 63, 16] from Operation: 30-14=16\nCurrent State: 57:[96, 63, 16], Operations: ['30-14=16']\nExploring Operation: 96/16=6, Resulting Numbers: [63, 6]\nGenerated Node #3: [63, 6] from Operation: 96/16=6\nCurrent State: 57:[63, 6], Operations: ['30-14=16', '96/16=6']\nExploring Operation: 63-6=57, Resulting Numbers: [57]\n57,57 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 17, + 9, + 78, + 70 + ], + "target": 64, + "solution": [ + "17-9=8", + "78-70=8", + "8*8=64" + ], + "optimal_path": "Current State: 64:[17, 9, 78, 70], Operations: []\nExploring Operation: 17-9=8, Resulting Numbers: [78, 70, 8]\nGenerated Node #2: [78, 70, 8] from Operation: 17-9=8\nCurrent State: 64:[78, 70, 8], Operations: ['17-9=8']\nExploring Operation: 78-70=8, Resulting Numbers: [8, 8]\nGenerated Node #3: [8, 8] from Operation: 78-70=8\nCurrent State: 64:[8, 8], Operations: ['17-9=8', '78-70=8']\nExploring Operation: 8*8=64, Resulting Numbers: [64]\n64,64 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 90, + 90, + 20, + 16 + ], + "target": 35, + "solution": [ + "90/90=1", + "20+16=36", + "36-1=35" + ], + "optimal_path": "Current State: 35:[90, 90, 20, 16], Operations: []\nExploring Operation: 90/90=1, Resulting Numbers: [20, 16, 1]\nGenerated Node #2: [20, 16, 1] from Operation: 90/90=1\nCurrent State: 35:[20, 16, 1], Operations: ['90/90=1']\nExploring Operation: 20+16=36, Resulting Numbers: [1, 36]\nGenerated Node #3: [1, 36] from Operation: 20+16=36\nCurrent State: 35:[1, 36], Operations: ['90/90=1', '20+16=36']\nExploring Operation: 36-1=35, Resulting Numbers: [35]\n35,35 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 48, + 87, + 89, + 68 + ], + "target": 28, + "solution": [ + "89-87=2", + "48*2=96", + "96-68=28" + ], + "optimal_path": "Current State: 28:[48, 87, 89, 68], Operations: []\nExploring Operation: 89-87=2, Resulting Numbers: [48, 68, 2]\nGenerated Node #2: [48, 68, 2] from Operation: 89-87=2\nCurrent State: 28:[48, 68, 2], Operations: ['89-87=2']\nExploring Operation: 48*2=96, Resulting Numbers: [68, 96]\nGenerated Node #3: [68, 96] from Operation: 48*2=96\nCurrent State: 28:[68, 96], Operations: ['89-87=2', '48*2=96']\nExploring Operation: 96-68=28, Resulting Numbers: [28]\n28,28 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 82, + 13, + 22, + 19 + ], + "target": 89, + "solution": [ + "22-13=9", + "19*9=171", + "171-82=89" + ], + "optimal_path": "Current State: 89:[82, 13, 22, 19], Operations: []\nExploring Operation: 22-13=9, Resulting Numbers: [82, 19, 9]\nGenerated Node #2: [82, 19, 9] from Operation: 22-13=9\nCurrent State: 89:[82, 19, 9], Operations: ['22-13=9']\nExploring Operation: 19*9=171, Resulting Numbers: [82, 171]\nGenerated Node #3: [82, 171] from Operation: 19*9=171\nCurrent State: 89:[82, 171], Operations: ['22-13=9', '19*9=171']\nExploring Operation: 171-82=89, Resulting Numbers: [89]\n89,89 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 88, + 86, + 11, + 31 + ], + "target": 73, + "solution": [ + "88-86=2", + "31*2=62", + "11+62=73" + ], + "optimal_path": "Current State: 73:[88, 86, 11, 31], Operations: []\nExploring Operation: 88-86=2, Resulting Numbers: [11, 31, 2]\nGenerated Node #2: [11, 31, 2] from Operation: 88-86=2\nCurrent State: 73:[11, 31, 2], Operations: ['88-86=2']\nExploring Operation: 31*2=62, Resulting Numbers: [11, 62]\nGenerated Node #3: [11, 62] from Operation: 31*2=62\nCurrent State: 73:[11, 62], Operations: ['88-86=2', '31*2=62']\nExploring Operation: 11+62=73, Resulting Numbers: [73]\n73,73 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 25, + 79, + 6, + 31 + ], + "target": 79, + "solution": [ + "25+79=104", + "31-6=25", + "104-25=79" + ], + "optimal_path": "Current State: 79:[25, 79, 6, 31], Operations: []\nExploring Operation: 25+79=104, Resulting Numbers: [6, 31, 104]\nGenerated Node #2: [6, 31, 104] from Operation: 25+79=104\nCurrent State: 79:[6, 31, 104], Operations: ['25+79=104']\nExploring Operation: 31-6=25, Resulting Numbers: [104, 25]\nGenerated Node #3: [104, 25] from Operation: 31-6=25\nCurrent State: 79:[104, 25], Operations: ['25+79=104', '31-6=25']\nExploring Operation: 104-25=79, Resulting Numbers: [79]\n79,79 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 92, + 31, + 40, + 98 + ], + "target": 77, + "solution": [ + "92-31=61", + "40+98=138", + "138-61=77" + ], + "optimal_path": "Current State: 77:[92, 31, 40, 98], Operations: []\nExploring Operation: 92-31=61, Resulting Numbers: [40, 98, 61]\nGenerated Node #2: [40, 98, 61] from Operation: 92-31=61\nCurrent State: 77:[40, 98, 61], Operations: ['92-31=61']\nExploring Operation: 40+98=138, Resulting Numbers: [61, 138]\nGenerated Node #3: [61, 138] from Operation: 40+98=138\nCurrent State: 77:[61, 138], Operations: ['92-31=61', '40+98=138']\nExploring Operation: 138-61=77, Resulting Numbers: [77]\n77,77 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 92, + 63, + 13, + 58 + ], + "target": 84, + "solution": [ + "92+63=155", + "13+58=71", + "155-71=84" + ], + "optimal_path": "Current State: 84:[92, 63, 13, 58], Operations: []\nExploring Operation: 92+63=155, Resulting Numbers: [13, 58, 155]\nGenerated Node #2: [13, 58, 155] from Operation: 92+63=155\nCurrent State: 84:[13, 58, 155], Operations: ['92+63=155']\nExploring Operation: 13+58=71, Resulting Numbers: [155, 71]\nGenerated Node #3: [155, 71] from Operation: 13+58=71\nCurrent State: 84:[155, 71], Operations: ['92+63=155', '13+58=71']\nExploring Operation: 155-71=84, Resulting Numbers: [84]\n84,84 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 40, + 51, + 32, + 7 + ], + "target": 93, + "solution": [ + "51-32=19", + "7*19=133", + "133-40=93" + ], + "optimal_path": "Current State: 93:[40, 51, 32, 7], Operations: []\nExploring Operation: 51-32=19, Resulting Numbers: [40, 7, 19]\nGenerated Node #2: [40, 7, 19] from Operation: 51-32=19\nCurrent State: 93:[40, 7, 19], Operations: ['51-32=19']\nExploring Operation: 7*19=133, Resulting Numbers: [40, 133]\nGenerated Node #3: [40, 133] from Operation: 7*19=133\nCurrent State: 93:[40, 133], Operations: ['51-32=19', '7*19=133']\nExploring Operation: 133-40=93, Resulting Numbers: [93]\n93,93 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 78, + 92, + 76, + 82 + ], + "target": 72, + "solution": [ + "78-76=2", + "82*2=164", + "164-92=72" + ], + "optimal_path": "Current State: 72:[78, 92, 76, 82], Operations: []\nExploring Operation: 78-76=2, Resulting Numbers: [92, 82, 2]\nGenerated Node #2: [92, 82, 2] from Operation: 78-76=2\nCurrent State: 72:[92, 82, 2], Operations: ['78-76=2']\nExploring Operation: 82*2=164, Resulting Numbers: [92, 164]\nGenerated Node #3: [92, 164] from Operation: 82*2=164\nCurrent State: 72:[92, 164], Operations: ['78-76=2', '82*2=164']\nExploring Operation: 164-92=72, Resulting Numbers: [72]\n72,72 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 71, + 50, + 11, + 73 + ], + "target": 78, + "solution": [ + "73-71=2", + "50-11=39", + "2*39=78" + ], + "optimal_path": "Current State: 78:[71, 50, 11, 73], Operations: []\nExploring Operation: 73-71=2, Resulting Numbers: [50, 11, 2]\nGenerated Node #2: [50, 11, 2] from Operation: 73-71=2\nCurrent State: 78:[50, 11, 2], Operations: ['73-71=2']\nExploring Operation: 50-11=39, Resulting Numbers: [2, 39]\nGenerated Node #3: [2, 39] from Operation: 50-11=39\nCurrent State: 78:[2, 39], Operations: ['73-71=2', '50-11=39']\nExploring Operation: 2*39=78, Resulting Numbers: [78]\n78,78 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 83, + 69, + 67, + 6 + ], + "target": 71, + "solution": [ + "69-67=2", + "6*2=12", + "83-12=71" + ], + "optimal_path": "Current State: 71:[83, 69, 67, 6], Operations: []\nExploring Operation: 69-67=2, Resulting Numbers: [83, 6, 2]\nGenerated Node #2: [83, 6, 2] from Operation: 69-67=2\nCurrent State: 71:[83, 6, 2], Operations: ['69-67=2']\nExploring Operation: 6*2=12, Resulting Numbers: [83, 12]\nGenerated Node #3: [83, 12] from Operation: 6*2=12\nCurrent State: 71:[83, 12], Operations: ['69-67=2', '6*2=12']\nExploring Operation: 83-12=71, Resulting Numbers: [71]\n71,71 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 39, + 40, + 96, + 22 + ], + "target": 39, + "solution": [ + "39+40=79", + "96+22=118", + "118-79=39" + ], + "optimal_path": "Current State: 39:[39, 40, 96, 22], Operations: []\nExploring Operation: 39+40=79, Resulting Numbers: [96, 22, 79]\nGenerated Node #2: [96, 22, 79] from Operation: 39+40=79\nCurrent State: 39:[96, 22, 79], Operations: ['39+40=79']\nExploring Operation: 96+22=118, Resulting Numbers: [79, 118]\nGenerated Node #3: [79, 118] from Operation: 96+22=118\nCurrent State: 39:[79, 118], Operations: ['39+40=79', '96+22=118']\nExploring Operation: 118-79=39, Resulting Numbers: [39]\n39,39 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 46, + 50, + 63, + 26 + ], + "target": 93, + "solution": [ + "50-46=4", + "63+26=89", + "4+89=93" + ], + "optimal_path": "Current State: 93:[46, 50, 63, 26], Operations: []\nExploring Operation: 50-46=4, Resulting Numbers: [63, 26, 4]\nGenerated Node #2: [63, 26, 4] from Operation: 50-46=4\nCurrent State: 93:[63, 26, 4], Operations: ['50-46=4']\nExploring Operation: 63+26=89, Resulting Numbers: [4, 89]\nGenerated Node #3: [4, 89] from Operation: 63+26=89\nCurrent State: 93:[4, 89], Operations: ['50-46=4', '63+26=89']\nExploring Operation: 4+89=93, Resulting Numbers: [93]\n93,93 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 18, + 24, + 89, + 6 + ], + "target": 81, + "solution": [ + "18/6=3", + "24/3=8", + "89-8=81" + ], + "optimal_path": "Current State: 81:[18, 24, 89, 6], Operations: []\nExploring Operation: 18/6=3, Resulting Numbers: [24, 89, 3]\nGenerated Node #2: [24, 89, 3] from Operation: 18/6=3\nCurrent State: 81:[24, 89, 3], Operations: ['18/6=3']\nExploring Operation: 24/3=8, Resulting Numbers: [89, 8]\nGenerated Node #3: [89, 8] from Operation: 24/3=8\nCurrent State: 81:[89, 8], Operations: ['18/6=3', '24/3=8']\nExploring Operation: 89-8=81, Resulting Numbers: [81]\n81,81 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 11, + 17, + 99, + 52 + ], + "target": 75, + "solution": [ + "11+17=28", + "99-52=47", + "28+47=75" + ], + "optimal_path": "Current State: 75:[11, 17, 99, 52], Operations: []\nExploring Operation: 11+17=28, Resulting Numbers: [99, 52, 28]\nGenerated Node #2: [99, 52, 28] from Operation: 11+17=28\nCurrent State: 75:[99, 52, 28], Operations: ['11+17=28']\nExploring Operation: 99-52=47, Resulting Numbers: [28, 47]\nGenerated Node #3: [28, 47] from Operation: 99-52=47\nCurrent State: 75:[28, 47], Operations: ['11+17=28', '99-52=47']\nExploring Operation: 28+47=75, Resulting Numbers: [75]\n75,75 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 9, + 31, + 41, + 36 + ], + "target": 99, + "solution": [ + "31-9=22", + "41+36=77", + "22+77=99" + ], + "optimal_path": "Current State: 99:[9, 31, 41, 36], Operations: []\nExploring Operation: 31-9=22, Resulting Numbers: [41, 36, 22]\nGenerated Node #2: [41, 36, 22] from Operation: 31-9=22\nCurrent State: 99:[41, 36, 22], Operations: ['31-9=22']\nExploring Operation: 41+36=77, Resulting Numbers: [22, 77]\nGenerated Node #3: [22, 77] from Operation: 41+36=77\nCurrent State: 99:[22, 77], Operations: ['31-9=22', '41+36=77']\nExploring Operation: 22+77=99, Resulting Numbers: [99]\n99,99 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 78, + 44, + 83, + 91 + ], + "target": 52, + "solution": [ + "78+44=122", + "83+91=174", + "174-122=52" + ], + "optimal_path": "Current State: 52:[78, 44, 83, 91], Operations: []\nExploring Operation: 78+44=122, Resulting Numbers: [83, 91, 122]\nGenerated Node #2: [83, 91, 122] from Operation: 78+44=122\nCurrent State: 52:[83, 91, 122], Operations: ['78+44=122']\nExploring Operation: 83+91=174, Resulting Numbers: [122, 174]\nGenerated Node #3: [122, 174] from Operation: 83+91=174\nCurrent State: 52:[122, 174], Operations: ['78+44=122', '83+91=174']\nExploring Operation: 174-122=52, Resulting Numbers: [52]\n52,52 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 16, + 79, + 87, + 93 + ], + "target": 35, + "solution": [ + "87-79=8", + "16*8=128", + "128-93=35" + ], + "optimal_path": "Current State: 35:[16, 79, 87, 93], Operations: []\nExploring Operation: 87-79=8, Resulting Numbers: [16, 93, 8]\nGenerated Node #2: [16, 93, 8] from Operation: 87-79=8\nCurrent State: 35:[16, 93, 8], Operations: ['87-79=8']\nExploring Operation: 16*8=128, Resulting Numbers: [93, 128]\nGenerated Node #3: [93, 128] from Operation: 16*8=128\nCurrent State: 35:[93, 128], Operations: ['87-79=8', '16*8=128']\nExploring Operation: 128-93=35, Resulting Numbers: [35]\n35,35 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 60, + 55, + 75, + 30 + ], + "target": 100, + "solution": [ + "60-55=5", + "75+30=105", + "105-5=100" + ], + "optimal_path": "Current State: 100:[60, 55, 75, 30], Operations: []\nExploring Operation: 60-55=5, Resulting Numbers: [75, 30, 5]\nGenerated Node #2: [75, 30, 5] from Operation: 60-55=5\nCurrent State: 100:[75, 30, 5], Operations: ['60-55=5']\nExploring Operation: 75+30=105, Resulting Numbers: [5, 105]\nGenerated Node #3: [5, 105] from Operation: 75+30=105\nCurrent State: 100:[5, 105], Operations: ['60-55=5', '75+30=105']\nExploring Operation: 105-5=100, Resulting Numbers: [100]\n100,100 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 65, + 9, + 68, + 47 + ], + "target": 59, + "solution": [ + "65-9=56", + "68+47=115", + "115-56=59" + ], + "optimal_path": "Current State: 59:[65, 9, 68, 47], Operations: []\nExploring Operation: 65-9=56, Resulting Numbers: [68, 47, 56]\nGenerated Node #2: [68, 47, 56] from Operation: 65-9=56\nCurrent State: 59:[68, 47, 56], Operations: ['65-9=56']\nExploring Operation: 68+47=115, Resulting Numbers: [56, 115]\nGenerated Node #3: [56, 115] from Operation: 68+47=115\nCurrent State: 59:[56, 115], Operations: ['65-9=56', '68+47=115']\nExploring Operation: 115-56=59, Resulting Numbers: [59]\n59,59 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 10, + 53, + 5, + 4 + ], + "target": 34, + "solution": [ + "53-10=43", + "5+4=9", + "43-9=34" + ], + "optimal_path": "Current State: 34:[10, 53, 5, 4], Operations: []\nExploring Operation: 53-10=43, Resulting Numbers: [5, 4, 43]\nGenerated Node #2: [5, 4, 43] from Operation: 53-10=43\nCurrent State: 34:[5, 4, 43], Operations: ['53-10=43']\nExploring Operation: 5+4=9, Resulting Numbers: [43, 9]\nGenerated Node #3: [43, 9] from Operation: 5+4=9\nCurrent State: 34:[43, 9], Operations: ['53-10=43', '5+4=9']\nExploring Operation: 43-9=34, Resulting Numbers: [34]\n34,34 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 74, + 3, + 60, + 76 + ], + "target": 90, + "solution": [ + "76-74=2", + "3*60=180", + "180/2=90" + ], + "optimal_path": "Current State: 90:[74, 3, 60, 76], Operations: []\nExploring Operation: 76-74=2, Resulting Numbers: [3, 60, 2]\nGenerated Node #2: [3, 60, 2] from Operation: 76-74=2\nCurrent State: 90:[3, 60, 2], Operations: ['76-74=2']\nExploring Operation: 3*60=180, Resulting Numbers: [2, 180]\nGenerated Node #3: [2, 180] from Operation: 3*60=180\nCurrent State: 90:[2, 180], Operations: ['76-74=2', '3*60=180']\nExploring Operation: 180/2=90, Resulting Numbers: [90]\n90,90 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 37, + 47, + 39, + 73 + ], + "target": 60, + "solution": [ + "39-37=2", + "47+73=120", + "120/2=60" + ], + "optimal_path": "Current State: 60:[37, 47, 39, 73], Operations: []\nExploring Operation: 39-37=2, Resulting Numbers: [47, 73, 2]\nGenerated Node #2: [47, 73, 2] from Operation: 39-37=2\nCurrent State: 60:[47, 73, 2], Operations: ['39-37=2']\nExploring Operation: 47+73=120, Resulting Numbers: [2, 120]\nGenerated Node #3: [2, 120] from Operation: 47+73=120\nCurrent State: 60:[2, 120], Operations: ['39-37=2', '47+73=120']\nExploring Operation: 120/2=60, Resulting Numbers: [60]\n60,60 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 5, + 72, + 67, + 48 + ], + "target": 86, + "solution": [ + "72-5=67", + "67-48=19", + "67+19=86" + ], + "optimal_path": "Current State: 86:[5, 72, 67, 48], Operations: []\nExploring Operation: 72-5=67, Resulting Numbers: [67, 48, 67]\nGenerated Node #2: [67, 48, 67] from Operation: 72-5=67\nCurrent State: 86:[67, 48, 67], Operations: ['72-5=67']\nExploring Operation: 67-48=19, Resulting Numbers: [19]\n19,86 equal: Goal Reached\nExploring Operation: 67+19=86, Resulting Numbers: [86]\n86,86 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 21, + 76, + 95, + 83 + ], + "target": 52, + "solution": [ + "83-76=7", + "21*7=147", + "147-95=52" + ], + "optimal_path": "Current State: 52:[21, 76, 95, 83], Operations: []\nExploring Operation: 83-76=7, Resulting Numbers: [21, 95, 7]\nGenerated Node #2: [21, 95, 7] from Operation: 83-76=7\nCurrent State: 52:[21, 95, 7], Operations: ['83-76=7']\nExploring Operation: 21*7=147, Resulting Numbers: [95, 147]\nGenerated Node #3: [95, 147] from Operation: 21*7=147\nCurrent State: 52:[95, 147], Operations: ['83-76=7', '21*7=147']\nExploring Operation: 147-95=52, Resulting Numbers: [52]\n52,52 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 99, + 19, + 6, + 30 + ], + "target": 100, + "solution": [ + "99-19=80", + "6*30=180", + "180-80=100" + ], + "optimal_path": "Current State: 100:[99, 19, 6, 30], Operations: []\nExploring Operation: 99-19=80, Resulting Numbers: [6, 30, 80]\nGenerated Node #2: [6, 30, 80] from Operation: 99-19=80\nCurrent State: 100:[6, 30, 80], Operations: ['99-19=80']\nExploring Operation: 6*30=180, Resulting Numbers: [80, 180]\nGenerated Node #3: [80, 180] from Operation: 6*30=180\nCurrent State: 100:[80, 180], Operations: ['99-19=80', '6*30=180']\nExploring Operation: 180-80=100, Resulting Numbers: [100]\n100,100 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 23, + 31, + 93, + 8 + ], + "target": 94, + "solution": [ + "31-23=8", + "8/8=1", + "93+1=94" + ], + "optimal_path": "Current State: 94:[23, 31, 93, 8], Operations: []\nExploring Operation: 31-23=8, Resulting Numbers: [93, 8, 8]\nGenerated Node #2: [93, 8, 8] from Operation: 31-23=8\nCurrent State: 94:[93, 8, 8], Operations: ['31-23=8']\nExploring Operation: 8/8=1, Resulting Numbers: [93, 1]\nGenerated Node #3: [93, 1] from Operation: 8/8=1\nCurrent State: 94:[93, 1], Operations: ['31-23=8', '8/8=1']\nExploring Operation: 93+1=94, Resulting Numbers: [94]\n94,94 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 67, + 69, + 82, + 23 + ], + "target": 18, + "solution": [ + "69-67=2", + "82/2=41", + "41-23=18" + ], + "optimal_path": "Current State: 18:[67, 69, 82, 23], Operations: []\nExploring Operation: 69-67=2, Resulting Numbers: [82, 23, 2]\nGenerated Node #2: [82, 23, 2] from Operation: 69-67=2\nCurrent State: 18:[82, 23, 2], Operations: ['69-67=2']\nExploring Operation: 82/2=41, Resulting Numbers: [23, 41]\nGenerated Node #3: [23, 41] from Operation: 82/2=41\nCurrent State: 18:[23, 41], Operations: ['69-67=2', '82/2=41']\nExploring Operation: 41-23=18, Resulting Numbers: [18]\n18,18 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 17, + 36, + 88, + 8 + ], + "target": 43, + "solution": [ + "17+36=53", + "88+8=96", + "96-53=43" + ], + "optimal_path": "Current State: 43:[17, 36, 88, 8], Operations: []\nExploring Operation: 17+36=53, Resulting Numbers: [88, 8, 53]\nGenerated Node #2: [88, 8, 53] from Operation: 17+36=53\nCurrent State: 43:[88, 8, 53], Operations: ['17+36=53']\nExploring Operation: 88+8=96, Resulting Numbers: [53, 96]\nGenerated Node #3: [53, 96] from Operation: 88+8=96\nCurrent State: 43:[53, 96], Operations: ['17+36=53', '88+8=96']\nExploring Operation: 96-53=43, Resulting Numbers: [43]\n43,43 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 30, + 19, + 2, + 98 + ], + "target": 38, + "solution": [ + "30-19=11", + "98/2=49", + "49-11=38" + ], + "optimal_path": "Current State: 38:[30, 19, 2, 98], Operations: []\nExploring Operation: 30-19=11, Resulting Numbers: [2, 98, 11]\nGenerated Node #2: [2, 98, 11] from Operation: 30-19=11\nCurrent State: 38:[2, 98, 11], Operations: ['30-19=11']\nExploring Operation: 98/2=49, Resulting Numbers: [11, 49]\nGenerated Node #3: [11, 49] from Operation: 98/2=49\nCurrent State: 38:[11, 49], Operations: ['30-19=11', '98/2=49']\nExploring Operation: 49-11=38, Resulting Numbers: [38]\n38,38 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 75, + 69, + 63, + 51 + ], + "target": 71, + "solution": [ + "75+51=126", + "126/63=2", + "69+2=71" + ], + "optimal_path": "Current State: 71:[75, 69, 63, 51], Operations: []\nExploring Operation: 75+51=126, Resulting Numbers: [69, 63, 126]\nGenerated Node #2: [69, 63, 126] from Operation: 75+51=126\nCurrent State: 71:[69, 63, 126], Operations: ['75+51=126']\nExploring Operation: 126/63=2, Resulting Numbers: [69, 2]\nGenerated Node #3: [69, 2] from Operation: 126/63=2\nCurrent State: 71:[69, 2], Operations: ['75+51=126', '126/63=2']\nExploring Operation: 69+2=71, Resulting Numbers: [71]\n71,71 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 94, + 42, + 5, + 96 + ], + "target": 39, + "solution": [ + "94-42=52", + "96-5=91", + "91-52=39" + ], + "optimal_path": "Current State: 39:[94, 42, 5, 96], Operations: []\nExploring Operation: 94-42=52, Resulting Numbers: [5, 96, 52]\nGenerated Node #2: [5, 96, 52] from Operation: 94-42=52\nCurrent State: 39:[5, 96, 52], Operations: ['94-42=52']\nExploring Operation: 96-5=91, Resulting Numbers: [52, 91]\nGenerated Node #3: [52, 91] from Operation: 96-5=91\nCurrent State: 39:[52, 91], Operations: ['94-42=52', '96-5=91']\nExploring Operation: 91-52=39, Resulting Numbers: [39]\n39,39 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 46, + 62, + 28, + 32 + ], + "target": 64, + "solution": [ + "62-46=16", + "32-28=4", + "16*4=64" + ], + "optimal_path": "Current State: 64:[46, 62, 28, 32], Operations: []\nExploring Operation: 62-46=16, Resulting Numbers: [28, 32, 16]\nGenerated Node #2: [28, 32, 16] from Operation: 62-46=16\nCurrent State: 64:[28, 32, 16], Operations: ['62-46=16']\nExploring Operation: 32-28=4, Resulting Numbers: [16, 4]\nGenerated Node #3: [16, 4] from Operation: 32-28=4\nCurrent State: 64:[16, 4], Operations: ['62-46=16', '32-28=4']\nExploring Operation: 16*4=64, Resulting Numbers: [64]\n64,64 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 64, + 97, + 57, + 30 + ], + "target": 60, + "solution": [ + "97-64=33", + "57-30=27", + "33+27=60" + ], + "optimal_path": "Current State: 60:[64, 97, 57, 30], Operations: []\nExploring Operation: 97-64=33, Resulting Numbers: [57, 30, 33]\nGenerated Node #2: [57, 30, 33] from Operation: 97-64=33\nCurrent State: 60:[57, 30, 33], Operations: ['97-64=33']\nExploring Operation: 57-30=27, Resulting Numbers: [33, 27]\nGenerated Node #3: [33, 27] from Operation: 57-30=27\nCurrent State: 60:[33, 27], Operations: ['97-64=33', '57-30=27']\nExploring Operation: 33+27=60, Resulting Numbers: [60]\n60,60 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 38, + 64, + 47, + 52 + ], + "target": 97, + "solution": [ + "38+64=102", + "52-47=5", + "102-5=97" + ], + "optimal_path": "Current State: 97:[38, 64, 47, 52], Operations: []\nExploring Operation: 38+64=102, Resulting Numbers: [47, 52, 102]\nGenerated Node #2: [47, 52, 102] from Operation: 38+64=102\nCurrent State: 97:[47, 52, 102], Operations: ['38+64=102']\nExploring Operation: 52-47=5, Resulting Numbers: [102, 5]\nGenerated Node #3: [102, 5] from Operation: 52-47=5\nCurrent State: 97:[102, 5], Operations: ['38+64=102', '52-47=5']\nExploring Operation: 102-5=97, Resulting Numbers: [97]\n97,97 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 21, + 89, + 61, + 55 + ], + "target": 62, + "solution": [ + "89-21=68", + "61-55=6", + "68-6=62" + ], + "optimal_path": "Current State: 62:[21, 89, 61, 55], Operations: []\nExploring Operation: 89-21=68, Resulting Numbers: [61, 55, 68]\nGenerated Node #2: [61, 55, 68] from Operation: 89-21=68\nCurrent State: 62:[61, 55, 68], Operations: ['89-21=68']\nExploring Operation: 61-55=6, Resulting Numbers: [68, 6]\nGenerated Node #3: [68, 6] from Operation: 61-55=6\nCurrent State: 62:[68, 6], Operations: ['89-21=68', '61-55=6']\nExploring Operation: 68-6=62, Resulting Numbers: [62]\n62,62 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 86, + 29, + 85, + 2 + ], + "target": 71, + "solution": [ + "86-29=57", + "85+57=142", + "142/2=71" + ], + "optimal_path": "Current State: 71:[86, 29, 85, 2], Operations: []\nExploring Operation: 86-29=57, Resulting Numbers: [85, 2, 57]\nGenerated Node #2: [85, 2, 57] from Operation: 86-29=57\nCurrent State: 71:[85, 2, 57], Operations: ['86-29=57']\nExploring Operation: 85+57=142, Resulting Numbers: [2, 142]\nGenerated Node #3: [2, 142] from Operation: 85+57=142\nCurrent State: 71:[2, 142], Operations: ['86-29=57', '85+57=142']\nExploring Operation: 142/2=71, Resulting Numbers: [71]\n71,71 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 13, + 44, + 2, + 7 + ], + "target": 100, + "solution": [ + "13+44=57", + "57-7=50", + "2*50=100" + ], + "optimal_path": "Current State: 100:[13, 44, 2, 7], Operations: []\nExploring Operation: 13+44=57, Resulting Numbers: [2, 7, 57]\nGenerated Node #2: [2, 7, 57] from Operation: 13+44=57\nCurrent State: 100:[2, 7, 57], Operations: ['13+44=57']\nExploring Operation: 57-7=50, Resulting Numbers: [2, 50]\nGenerated Node #3: [2, 50] from Operation: 57-7=50\nCurrent State: 100:[2, 50], Operations: ['13+44=57', '57-7=50']\nExploring Operation: 2*50=100, Resulting Numbers: [100]\n100,100 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 30, + 23, + 4, + 6 + ], + "target": 69, + "solution": [ + "30*23=690", + "4+6=10", + "690/10=69" + ], + "optimal_path": "Current State: 69:[30, 23, 4, 6], Operations: []\nExploring Operation: 30*23=690, Resulting Numbers: [4, 6, 690]\nGenerated Node #2: [4, 6, 690] from Operation: 30*23=690\nCurrent State: 69:[4, 6, 690], Operations: ['30*23=690']\nExploring Operation: 4+6=10, Resulting Numbers: [690, 10]\nGenerated Node #3: [690, 10] from Operation: 4+6=10\nCurrent State: 69:[690, 10], Operations: ['30*23=690', '4+6=10']\nExploring Operation: 690/10=69, Resulting Numbers: [69]\n69,69 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 19, + 42, + 31, + 63 + ], + "target": 71, + "solution": [ + "42-19=23", + "31+63=94", + "94-23=71" + ], + "optimal_path": "Current State: 71:[19, 42, 31, 63], Operations: []\nExploring Operation: 42-19=23, Resulting Numbers: [31, 63, 23]\nGenerated Node #2: [31, 63, 23] from Operation: 42-19=23\nCurrent State: 71:[31, 63, 23], Operations: ['42-19=23']\nExploring Operation: 31+63=94, Resulting Numbers: [23, 94]\nGenerated Node #3: [23, 94] from Operation: 31+63=94\nCurrent State: 71:[23, 94], Operations: ['42-19=23', '31+63=94']\nExploring Operation: 94-23=71, Resulting Numbers: [71]\n71,71 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 18, + 44, + 68, + 40 + ], + "target": 38, + "solution": [ + "68+40=108", + "108/18=6", + "44-6=38" + ], + "optimal_path": "Current State: 38:[18, 44, 68, 40], Operations: []\nExploring Operation: 68+40=108, Resulting Numbers: [18, 44, 108]\nGenerated Node #2: [18, 44, 108] from Operation: 68+40=108\nCurrent State: 38:[18, 44, 108], Operations: ['68+40=108']\nExploring Operation: 108/18=6, Resulting Numbers: [44, 6]\nGenerated Node #3: [44, 6] from Operation: 108/18=6\nCurrent State: 38:[44, 6], Operations: ['68+40=108', '108/18=6']\nExploring Operation: 44-6=38, Resulting Numbers: [38]\n38,38 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 99, + 87, + 92, + 39 + ], + "target": 58, + "solution": [ + "99+39=138", + "87*92=8004", + "8004/138=58" + ], + "optimal_path": "Current State: 58:[99, 87, 92, 39], Operations: []\nExploring Operation: 99+39=138, Resulting Numbers: [87, 92, 138]\nGenerated Node #2: [87, 92, 138] from Operation: 99+39=138\nCurrent State: 58:[87, 92, 138], Operations: ['99+39=138']\nExploring Operation: 87*92=8004, Resulting Numbers: [138, 8004]\nGenerated Node #3: [138, 8004] from Operation: 87*92=8004\nCurrent State: 58:[138, 8004], Operations: ['99+39=138', '87*92=8004']\nExploring Operation: 8004/138=58, Resulting Numbers: [58]\n58,58 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 64, + 26, + 6, + 64 + ], + "target": 31, + "solution": [ + "64/64=1", + "26+6=32", + "32-1=31" + ], + "optimal_path": "Current State: 31:[64, 26, 6, 64], Operations: []\nExploring Operation: 64/64=1, Resulting Numbers: [26, 6, 1]\nGenerated Node #2: [26, 6, 1] from Operation: 64/64=1\nCurrent State: 31:[26, 6, 1], Operations: ['64/64=1']\nExploring Operation: 26+6=32, Resulting Numbers: [1, 32]\nGenerated Node #3: [1, 32] from Operation: 26+6=32\nCurrent State: 31:[1, 32], Operations: ['64/64=1', '26+6=32']\nExploring Operation: 32-1=31, Resulting Numbers: [31]\n31,31 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 39, + 46, + 91, + 55 + ], + "target": 29, + "solution": [ + "46-39=7", + "91-55=36", + "36-7=29" + ], + "optimal_path": "Current State: 29:[39, 46, 91, 55], Operations: []\nExploring Operation: 46-39=7, Resulting Numbers: [91, 55, 7]\nGenerated Node #2: [91, 55, 7] from Operation: 46-39=7\nCurrent State: 29:[91, 55, 7], Operations: ['46-39=7']\nExploring Operation: 91-55=36, Resulting Numbers: [7, 36]\nGenerated Node #3: [7, 36] from Operation: 91-55=36\nCurrent State: 29:[7, 36], Operations: ['46-39=7', '91-55=36']\nExploring Operation: 36-7=29, Resulting Numbers: [29]\n29,29 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 50, + 16, + 43, + 59 + ], + "target": 68, + "solution": [ + "50-16=34", + "43+59=102", + "102-34=68" + ], + "optimal_path": "Current State: 68:[50, 16, 43, 59], Operations: []\nExploring Operation: 50-16=34, Resulting Numbers: [43, 59, 34]\nGenerated Node #2: [43, 59, 34] from Operation: 50-16=34\nCurrent State: 68:[43, 59, 34], Operations: ['50-16=34']\nExploring Operation: 43+59=102, Resulting Numbers: [34, 102]\nGenerated Node #3: [34, 102] from Operation: 43+59=102\nCurrent State: 68:[34, 102], Operations: ['50-16=34', '43+59=102']\nExploring Operation: 102-34=68, Resulting Numbers: [68]\n68,68 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 25, + 37, + 24, + 51 + ], + "target": 63, + "solution": [ + "37-25=12", + "24+51=75", + "75-12=63" + ], + "optimal_path": "Current State: 63:[25, 37, 24, 51], Operations: []\nExploring Operation: 37-25=12, Resulting Numbers: [24, 51, 12]\nGenerated Node #2: [24, 51, 12] from Operation: 37-25=12\nCurrent State: 63:[24, 51, 12], Operations: ['37-25=12']\nExploring Operation: 24+51=75, Resulting Numbers: [12, 75]\nGenerated Node #3: [12, 75] from Operation: 24+51=75\nCurrent State: 63:[12, 75], Operations: ['37-25=12', '24+51=75']\nExploring Operation: 75-12=63, Resulting Numbers: [63]\n63,63 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 63, + 52, + 41, + 93 + ], + "target": 44, + "solution": [ + "63+93=156", + "156/52=3", + "41+3=44" + ], + "optimal_path": "Current State: 44:[63, 52, 41, 93], Operations: []\nExploring Operation: 63+93=156, Resulting Numbers: [52, 41, 156]\nGenerated Node #2: [52, 41, 156] from Operation: 63+93=156\nCurrent State: 44:[52, 41, 156], Operations: ['63+93=156']\nExploring Operation: 156/52=3, Resulting Numbers: [41, 3]\nGenerated Node #3: [41, 3] from Operation: 156/52=3\nCurrent State: 44:[41, 3], Operations: ['63+93=156', '156/52=3']\nExploring Operation: 41+3=44, Resulting Numbers: [44]\n44,44 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 92, + 47, + 2, + 72 + ], + "target": 29, + "solution": [ + "92-47=45", + "2+72=74", + "74-45=29" + ], + "optimal_path": "Current State: 29:[92, 47, 2, 72], Operations: []\nExploring Operation: 92-47=45, Resulting Numbers: [2, 72, 45]\nGenerated Node #2: [2, 72, 45] from Operation: 92-47=45\nCurrent State: 29:[2, 72, 45], Operations: ['92-47=45']\nExploring Operation: 2+72=74, Resulting Numbers: [45, 74]\nGenerated Node #3: [45, 74] from Operation: 2+72=74\nCurrent State: 29:[45, 74], Operations: ['92-47=45', '2+72=74']\nExploring Operation: 74-45=29, Resulting Numbers: [29]\n29,29 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 97, + 68, + 58, + 87 + ], + "target": 85, + "solution": [ + "97-68=29", + "58/29=2", + "87-2=85" + ], + "optimal_path": "Current State: 85:[97, 68, 58, 87], Operations: []\nExploring Operation: 97-68=29, Resulting Numbers: [58, 87, 29]\nGenerated Node #2: [58, 87, 29] from Operation: 97-68=29\nCurrent State: 85:[58, 87, 29], Operations: ['97-68=29']\nExploring Operation: 58/29=2, Resulting Numbers: [87, 2]\nGenerated Node #3: [87, 2] from Operation: 58/29=2\nCurrent State: 85:[87, 2], Operations: ['97-68=29', '58/29=2']\nExploring Operation: 87-2=85, Resulting Numbers: [85]\n85,85 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 93, + 29, + 49, + 63 + ], + "target": 48, + "solution": [ + "93-29=64", + "49+63=112", + "112-64=48" + ], + "optimal_path": "Current State: 48:[93, 29, 49, 63], Operations: []\nExploring Operation: 93-29=64, Resulting Numbers: [49, 63, 64]\nGenerated Node #2: [49, 63, 64] from Operation: 93-29=64\nCurrent State: 48:[49, 63, 64], Operations: ['93-29=64']\nExploring Operation: 49+63=112, Resulting Numbers: [64, 112]\nGenerated Node #3: [64, 112] from Operation: 49+63=112\nCurrent State: 48:[64, 112], Operations: ['93-29=64', '49+63=112']\nExploring Operation: 112-64=48, Resulting Numbers: [48]\n48,48 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 60, + 32, + 15, + 51 + ], + "target": 59, + "solution": [ + "60/15=4", + "32/4=8", + "51+8=59" + ], + "optimal_path": "Current State: 59:[60, 32, 15, 51], Operations: []\nExploring Operation: 60/15=4, Resulting Numbers: [32, 51, 4]\nGenerated Node #2: [32, 51, 4] from Operation: 60/15=4\nCurrent State: 59:[32, 51, 4], Operations: ['60/15=4']\nExploring Operation: 32/4=8, Resulting Numbers: [51, 8]\nGenerated Node #3: [51, 8] from Operation: 32/4=8\nCurrent State: 59:[51, 8], Operations: ['60/15=4', '32/4=8']\nExploring Operation: 51+8=59, Resulting Numbers: [59]\n59,59 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 45, + 12, + 70, + 76 + ], + "target": 47, + "solution": [ + "76-70=6", + "12/6=2", + "45+2=47" + ], + "optimal_path": "Current State: 47:[45, 12, 70, 76], Operations: []\nExploring Operation: 76-70=6, Resulting Numbers: [45, 12, 6]\nGenerated Node #2: [45, 12, 6] from Operation: 76-70=6\nCurrent State: 47:[45, 12, 6], Operations: ['76-70=6']\nExploring Operation: 12/6=2, Resulting Numbers: [45, 2]\nGenerated Node #3: [45, 2] from Operation: 12/6=2\nCurrent State: 47:[45, 2], Operations: ['76-70=6', '12/6=2']\nExploring Operation: 45+2=47, Resulting Numbers: [47]\n47,47 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 29, + 2, + 43, + 98 + ], + "target": 70, + "solution": [ + "43-29=14", + "2*14=28", + "98-28=70" + ], + "optimal_path": "Current State: 70:[29, 2, 43, 98], Operations: []\nExploring Operation: 43-29=14, Resulting Numbers: [2, 98, 14]\nGenerated Node #2: [2, 98, 14] from Operation: 43-29=14\nCurrent State: 70:[2, 98, 14], Operations: ['43-29=14']\nExploring Operation: 2*14=28, Resulting Numbers: [98, 28]\nGenerated Node #3: [98, 28] from Operation: 2*14=28\nCurrent State: 70:[98, 28], Operations: ['43-29=14', '2*14=28']\nExploring Operation: 98-28=70, Resulting Numbers: [70]\n70,70 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 7, + 15, + 35, + 62 + ], + "target": 91, + "solution": [ + "7*62=434", + "15*35=525", + "525-434=91" + ], + "optimal_path": "Current State: 91:[7, 15, 35, 62], Operations: []\nExploring Operation: 7*62=434, Resulting Numbers: [15, 35, 434]\nGenerated Node #2: [15, 35, 434] from Operation: 7*62=434\nCurrent State: 91:[15, 35, 434], Operations: ['7*62=434']\nExploring Operation: 15*35=525, Resulting Numbers: [434, 525]\nGenerated Node #3: [434, 525] from Operation: 15*35=525\nCurrent State: 91:[434, 525], Operations: ['7*62=434', '15*35=525']\nExploring Operation: 525-434=91, Resulting Numbers: [91]\n91,91 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 51, + 82, + 18, + 91 + ], + "target": 42, + "solution": [ + "82-51=31", + "91-18=73", + "73-31=42" + ], + "optimal_path": "Current State: 42:[51, 82, 18, 91], Operations: []\nExploring Operation: 82-51=31, Resulting Numbers: [18, 91, 31]\nGenerated Node #2: [18, 91, 31] from Operation: 82-51=31\nCurrent State: 42:[18, 91, 31], Operations: ['82-51=31']\nExploring Operation: 91-18=73, Resulting Numbers: [31, 73]\nGenerated Node #3: [31, 73] from Operation: 91-18=73\nCurrent State: 42:[31, 73], Operations: ['82-51=31', '91-18=73']\nExploring Operation: 73-31=42, Resulting Numbers: [42]\n42,42 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 72, + 10, + 50, + 68 + ], + "target": 80, + "solution": [ + "72-10=62", + "68-50=18", + "62+18=80" + ], + "optimal_path": "Current State: 80:[72, 10, 50, 68], Operations: []\nExploring Operation: 72-10=62, Resulting Numbers: [50, 68, 62]\nGenerated Node #2: [50, 68, 62] from Operation: 72-10=62\nCurrent State: 80:[50, 68, 62], Operations: ['72-10=62']\nExploring Operation: 68-50=18, Resulting Numbers: [62, 18]\nGenerated Node #3: [62, 18] from Operation: 68-50=18\nCurrent State: 80:[62, 18], Operations: ['72-10=62', '68-50=18']\nExploring Operation: 62+18=80, Resulting Numbers: [80]\n80,80 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 65, + 60, + 30, + 20 + ], + "target": 26, + "solution": [ + "65-60=5", + "30/5=6", + "20+6=26" + ], + "optimal_path": "Current State: 26:[65, 60, 30, 20], Operations: []\nExploring Operation: 65-60=5, Resulting Numbers: [30, 20, 5]\nGenerated Node #2: [30, 20, 5] from Operation: 65-60=5\nCurrent State: 26:[30, 20, 5], Operations: ['65-60=5']\nExploring Operation: 30/5=6, Resulting Numbers: [20, 6]\nGenerated Node #3: [20, 6] from Operation: 30/5=6\nCurrent State: 26:[20, 6], Operations: ['65-60=5', '30/5=6']\nExploring Operation: 20+6=26, Resulting Numbers: [26]\n26,26 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 30, + 35, + 50, + 40 + ], + "target": 37, + "solution": [ + "30+50=80", + "80/40=2", + "35+2=37" + ], + "optimal_path": "Current State: 37:[30, 35, 50, 40], Operations: []\nExploring Operation: 30+50=80, Resulting Numbers: [35, 40, 80]\nGenerated Node #2: [35, 40, 80] from Operation: 30+50=80\nCurrent State: 37:[35, 40, 80], Operations: ['30+50=80']\nExploring Operation: 80/40=2, Resulting Numbers: [35, 2]\nGenerated Node #3: [35, 2] from Operation: 80/40=2\nCurrent State: 37:[35, 2], Operations: ['30+50=80', '80/40=2']\nExploring Operation: 35+2=37, Resulting Numbers: [37]\n37,37 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 25, + 2, + 18, + 4 + ], + "target": 44, + "solution": [ + "2*18=36", + "36-25=11", + "4*11=44" + ], + "optimal_path": "Current State: 44:[25, 2, 18, 4], Operations: []\nExploring Operation: 2*18=36, Resulting Numbers: [25, 4, 36]\nGenerated Node #2: [25, 4, 36] from Operation: 2*18=36\nCurrent State: 44:[25, 4, 36], Operations: ['2*18=36']\nExploring Operation: 36-25=11, Resulting Numbers: [4, 11]\nGenerated Node #3: [4, 11] from Operation: 36-25=11\nCurrent State: 44:[4, 11], Operations: ['2*18=36', '36-25=11']\nExploring Operation: 4*11=44, Resulting Numbers: [44]\n44,44 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 68, + 73, + 68, + 80 + ], + "target": 52, + "solution": [ + "73-68=5", + "80/5=16", + "68-16=52" + ], + "optimal_path": "Current State: 52:[68, 73, 68, 80], Operations: []\nExploring Operation: 73-68=5, Resulting Numbers: [80, 5]\nGenerated Node #2: [80, 5] from Operation: 73-68=5\nCurrent State: 52:[80, 5], Operations: ['73-68=5']\nExploring Operation: 80/5=16, Resulting Numbers: [16]\n16,52 equal: Goal Reached\nExploring Operation: 68-16=52, Resulting Numbers: [52]\n52,52 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 46, + 33, + 3, + 85 + ], + "target": 46, + "solution": [ + "46-33=13", + "3*13=39", + "85-39=46" + ], + "optimal_path": "Current State: 46:[46, 33, 3, 85], Operations: []\nExploring Operation: 46-33=13, Resulting Numbers: [3, 85, 13]\nGenerated Node #2: [3, 85, 13] from Operation: 46-33=13\nCurrent State: 46:[3, 85, 13], Operations: ['46-33=13']\nExploring Operation: 3*13=39, Resulting Numbers: [85, 39]\nGenerated Node #3: [85, 39] from Operation: 3*13=39\nCurrent State: 46:[85, 39], Operations: ['46-33=13', '3*13=39']\nExploring Operation: 85-39=46, Resulting Numbers: [46]\n46,46 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 38, + 15, + 69, + 73 + ], + "target": 70, + "solution": [ + "38-15=23", + "69/23=3", + "73-3=70" + ], + "optimal_path": "Current State: 70:[38, 15, 69, 73], Operations: []\nExploring Operation: 38-15=23, Resulting Numbers: [69, 73, 23]\nGenerated Node #2: [69, 73, 23] from Operation: 38-15=23\nCurrent State: 70:[69, 73, 23], Operations: ['38-15=23']\nExploring Operation: 69/23=3, Resulting Numbers: [73, 3]\nGenerated Node #3: [73, 3] from Operation: 69/23=3\nCurrent State: 70:[73, 3], Operations: ['38-15=23', '69/23=3']\nExploring Operation: 73-3=70, Resulting Numbers: [70]\n70,70 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 16, + 93, + 99, + 25 + ], + "target": 37, + "solution": [ + "93+99=192", + "192/16=12", + "25+12=37" + ], + "optimal_path": "Current State: 37:[16, 93, 99, 25], Operations: []\nExploring Operation: 93+99=192, Resulting Numbers: [16, 25, 192]\nGenerated Node #2: [16, 25, 192] from Operation: 93+99=192\nCurrent State: 37:[16, 25, 192], Operations: ['93+99=192']\nExploring Operation: 192/16=12, Resulting Numbers: [25, 12]\nGenerated Node #3: [25, 12] from Operation: 192/16=12\nCurrent State: 37:[25, 12], Operations: ['93+99=192', '192/16=12']\nExploring Operation: 25+12=37, Resulting Numbers: [37]\n37,37 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 20, + 23, + 10, + 73 + ], + "target": 48, + "solution": [ + "20/10=2", + "23+73=96", + "96/2=48" + ], + "optimal_path": "Current State: 48:[20, 23, 10, 73], Operations: []\nExploring Operation: 20/10=2, Resulting Numbers: [23, 73, 2]\nGenerated Node #2: [23, 73, 2] from Operation: 20/10=2\nCurrent State: 48:[23, 73, 2], Operations: ['20/10=2']\nExploring Operation: 23+73=96, Resulting Numbers: [2, 96]\nGenerated Node #3: [2, 96] from Operation: 23+73=96\nCurrent State: 48:[2, 96], Operations: ['20/10=2', '23+73=96']\nExploring Operation: 96/2=48, Resulting Numbers: [48]\n48,48 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 72, + 9, + 36, + 28 + ], + "target": 73, + "solution": [ + "72+9=81", + "36-28=8", + "81-8=73" + ], + "optimal_path": "Current State: 73:[72, 9, 36, 28], Operations: []\nExploring Operation: 72+9=81, Resulting Numbers: [36, 28, 81]\nGenerated Node #2: [36, 28, 81] from Operation: 72+9=81\nCurrent State: 73:[36, 28, 81], Operations: ['72+9=81']\nExploring Operation: 36-28=8, Resulting Numbers: [81, 8]\nGenerated Node #3: [81, 8] from Operation: 36-28=8\nCurrent State: 73:[81, 8], Operations: ['72+9=81', '36-28=8']\nExploring Operation: 81-8=73, Resulting Numbers: [73]\n73,73 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 19, + 75, + 46, + 7 + ], + "target": 70, + "solution": [ + "75-19=56", + "56-46=10", + "7*10=70" + ], + "optimal_path": "Current State: 70:[19, 75, 46, 7], Operations: []\nExploring Operation: 75-19=56, Resulting Numbers: [46, 7, 56]\nGenerated Node #2: [46, 7, 56] from Operation: 75-19=56\nCurrent State: 70:[46, 7, 56], Operations: ['75-19=56']\nExploring Operation: 56-46=10, Resulting Numbers: [7, 10]\nGenerated Node #3: [7, 10] from Operation: 56-46=10\nCurrent State: 70:[7, 10], Operations: ['75-19=56', '56-46=10']\nExploring Operation: 7*10=70, Resulting Numbers: [70]\n70,70 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 70, + 6, + 87, + 88 + ], + "target": 76, + "solution": [ + "70+6=76", + "88-87=1", + "76*1=76" + ], + "optimal_path": "Current State: 76:[70, 6, 87, 88], Operations: []\nExploring Operation: 70+6=76, Resulting Numbers: [87, 88, 76]\nGenerated Node #2: [87, 88, 76] from Operation: 70+6=76\nCurrent State: 76:[87, 88, 76], Operations: ['70+6=76']\nExploring Operation: 88-87=1, Resulting Numbers: [76, 1]\nGenerated Node #3: [76, 1] from Operation: 88-87=1\nCurrent State: 76:[76, 1], Operations: ['70+6=76', '88-87=1']\nExploring Operation: 76*1=76, Resulting Numbers: [76]\n76,76 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 57, + 42, + 36, + 39 + ], + "target": 44, + "solution": [ + "57-39=18", + "36/18=2", + "42+2=44" + ], + "optimal_path": "Current State: 44:[57, 42, 36, 39], Operations: []\nExploring Operation: 57-39=18, Resulting Numbers: [42, 36, 18]\nGenerated Node #2: [42, 36, 18] from Operation: 57-39=18\nCurrent State: 44:[42, 36, 18], Operations: ['57-39=18']\nExploring Operation: 36/18=2, Resulting Numbers: [42, 2]\nGenerated Node #3: [42, 2] from Operation: 36/18=2\nCurrent State: 44:[42, 2], Operations: ['57-39=18', '36/18=2']\nExploring Operation: 42+2=44, Resulting Numbers: [44]\n44,44 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 50, + 43, + 28, + 10 + ], + "target": 97, + "solution": [ + "50*28=1400", + "1400/10=140", + "140-43=97" + ], + "optimal_path": "Current State: 97:[50, 43, 28, 10], Operations: []\nExploring Operation: 50*28=1400, Resulting Numbers: [43, 10, 1400]\nGenerated Node #2: [43, 10, 1400] from Operation: 50*28=1400\nCurrent State: 97:[43, 10, 1400], Operations: ['50*28=1400']\nExploring Operation: 1400/10=140, Resulting Numbers: [43, 140]\nGenerated Node #3: [43, 140] from Operation: 1400/10=140\nCurrent State: 97:[43, 140], Operations: ['50*28=1400', '1400/10=140']\nExploring Operation: 140-43=97, Resulting Numbers: [97]\n97,97 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 61, + 43, + 71, + 32 + ], + "target": 12, + "solution": [ + "61+71=132", + "43-32=11", + "132/11=12" + ], + "optimal_path": "Current State: 12:[61, 43, 71, 32], Operations: []\nExploring Operation: 61+71=132, Resulting Numbers: [43, 32, 132]\nGenerated Node #2: [43, 32, 132] from Operation: 61+71=132\nCurrent State: 12:[43, 32, 132], Operations: ['61+71=132']\nExploring Operation: 43-32=11, Resulting Numbers: [132, 11]\nGenerated Node #3: [132, 11] from Operation: 43-32=11\nCurrent State: 12:[132, 11], Operations: ['61+71=132', '43-32=11']\nExploring Operation: 132/11=12, Resulting Numbers: [12]\n12,12 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 77, + 54, + 79, + 25 + ], + "target": 52, + "solution": [ + "79-77=2", + "54/2=27", + "25+27=52" + ], + "optimal_path": "Current State: 52:[77, 54, 79, 25], Operations: []\nExploring Operation: 79-77=2, Resulting Numbers: [54, 25, 2]\nGenerated Node #2: [54, 25, 2] from Operation: 79-77=2\nCurrent State: 52:[54, 25, 2], Operations: ['79-77=2']\nExploring Operation: 54/2=27, Resulting Numbers: [25, 27]\nGenerated Node #3: [25, 27] from Operation: 54/2=27\nCurrent State: 52:[25, 27], Operations: ['79-77=2', '54/2=27']\nExploring Operation: 25+27=52, Resulting Numbers: [52]\n52,52 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 69, + 98, + 46, + 6 + ], + "target": 94, + "solution": [ + "46*6=276", + "276/69=4", + "98-4=94" + ], + "optimal_path": "Current State: 94:[69, 98, 46, 6], Operations: []\nExploring Operation: 46*6=276, Resulting Numbers: [69, 98, 276]\nGenerated Node #2: [69, 98, 276] from Operation: 46*6=276\nCurrent State: 94:[69, 98, 276], Operations: ['46*6=276']\nExploring Operation: 276/69=4, Resulting Numbers: [98, 4]\nGenerated Node #3: [98, 4] from Operation: 276/69=4\nCurrent State: 94:[98, 4], Operations: ['46*6=276', '276/69=4']\nExploring Operation: 98-4=94, Resulting Numbers: [94]\n94,94 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 9, + 4, + 3, + 28 + ], + "target": 21, + "solution": [ + "9/3=3", + "28-4=24", + "24-3=21" + ], + "optimal_path": "Current State: 21:[9, 4, 3, 28], Operations: []\nExploring Operation: 9/3=3, Resulting Numbers: [4, 28, 3]\nGenerated Node #2: [4, 28, 3] from Operation: 9/3=3\nCurrent State: 21:[4, 28, 3], Operations: ['9/3=3']\nExploring Operation: 28-4=24, Resulting Numbers: [3, 24]\nGenerated Node #3: [3, 24] from Operation: 28-4=24\nCurrent State: 21:[3, 24], Operations: ['9/3=3', '28-4=24']\nExploring Operation: 24-3=21, Resulting Numbers: [21]\n21,21 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 25, + 16, + 4, + 5 + ], + "target": 100, + "solution": [ + "25/5=5", + "16+4=20", + "5*20=100" + ], + "optimal_path": "Current State: 100:[25, 16, 4, 5], Operations: []\nExploring Operation: 25/5=5, Resulting Numbers: [16, 4, 5]\nGenerated Node #2: [16, 4, 5] from Operation: 25/5=5\nCurrent State: 100:[16, 4, 5], Operations: ['25/5=5']\nExploring Operation: 16+4=20, Resulting Numbers: [5, 20]\nGenerated Node #3: [5, 20] from Operation: 16+4=20\nCurrent State: 100:[5, 20], Operations: ['25/5=5', '16+4=20']\nExploring Operation: 5*20=100, Resulting Numbers: [100]\n100,100 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 41, + 38, + 34, + 99 + ], + "target": 54, + "solution": [ + "41+38=79", + "34+99=133", + "133-79=54" + ], + "optimal_path": "Current State: 54:[41, 38, 34, 99], Operations: []\nExploring Operation: 41+38=79, Resulting Numbers: [34, 99, 79]\nGenerated Node #2: [34, 99, 79] from Operation: 41+38=79\nCurrent State: 54:[34, 99, 79], Operations: ['41+38=79']\nExploring Operation: 34+99=133, Resulting Numbers: [79, 133]\nGenerated Node #3: [79, 133] from Operation: 34+99=133\nCurrent State: 54:[79, 133], Operations: ['41+38=79', '34+99=133']\nExploring Operation: 133-79=54, Resulting Numbers: [54]\n54,54 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 35, + 43, + 42, + 49 + ], + "target": 73, + "solution": [ + "35*42=1470", + "1470/49=30", + "43+30=73" + ], + "optimal_path": "Current State: 73:[35, 43, 42, 49], Operations: []\nExploring Operation: 35*42=1470, Resulting Numbers: [43, 49, 1470]\nGenerated Node #2: [43, 49, 1470] from Operation: 35*42=1470\nCurrent State: 73:[43, 49, 1470], Operations: ['35*42=1470']\nExploring Operation: 1470/49=30, Resulting Numbers: [43, 30]\nGenerated Node #3: [43, 30] from Operation: 1470/49=30\nCurrent State: 73:[43, 30], Operations: ['35*42=1470', '1470/49=30']\nExploring Operation: 43+30=73, Resulting Numbers: [73]\n73,73 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 1, + 73, + 52, + 5 + ], + "target": 84, + "solution": [ + "5-1=4", + "73-52=21", + "4*21=84" + ], + "optimal_path": "Current State: 84:[1, 73, 52, 5], Operations: []\nExploring Operation: 5-1=4, Resulting Numbers: [73, 52, 4]\nGenerated Node #2: [73, 52, 4] from Operation: 5-1=4\nCurrent State: 84:[73, 52, 4], Operations: ['5-1=4']\nExploring Operation: 73-52=21, Resulting Numbers: [4, 21]\nGenerated Node #3: [4, 21] from Operation: 73-52=21\nCurrent State: 84:[4, 21], Operations: ['5-1=4', '73-52=21']\nExploring Operation: 4*21=84, Resulting Numbers: [84]\n84,84 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 74, + 11, + 60, + 58 + ], + "target": 83, + "solution": [ + "74+11=85", + "60-58=2", + "85-2=83" + ], + "optimal_path": "Current State: 83:[74, 11, 60, 58], Operations: []\nExploring Operation: 74+11=85, Resulting Numbers: [60, 58, 85]\nGenerated Node #2: [60, 58, 85] from Operation: 74+11=85\nCurrent State: 83:[60, 58, 85], Operations: ['74+11=85']\nExploring Operation: 60-58=2, Resulting Numbers: [85, 2]\nGenerated Node #3: [85, 2] from Operation: 60-58=2\nCurrent State: 83:[85, 2], Operations: ['74+11=85', '60-58=2']\nExploring Operation: 85-2=83, Resulting Numbers: [83]\n83,83 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 76, + 95, + 29, + 87 + ], + "target": 57, + "solution": [ + "76+95=171", + "87/29=3", + "171/3=57" + ], + "optimal_path": "Current State: 57:[76, 95, 29, 87], Operations: []\nExploring Operation: 76+95=171, Resulting Numbers: [29, 87, 171]\nGenerated Node #2: [29, 87, 171] from Operation: 76+95=171\nCurrent State: 57:[29, 87, 171], Operations: ['76+95=171']\nExploring Operation: 87/29=3, Resulting Numbers: [171, 3]\nGenerated Node #3: [171, 3] from Operation: 87/29=3\nCurrent State: 57:[171, 3], Operations: ['76+95=171', '87/29=3']\nExploring Operation: 171/3=57, Resulting Numbers: [57]\n57,57 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 84, + 82, + 3, + 43 + ], + "target": 48, + "solution": [ + "84-82=2", + "3+43=46", + "2+46=48" + ], + "optimal_path": "Current State: 48:[84, 82, 3, 43], Operations: []\nExploring Operation: 84-82=2, Resulting Numbers: [3, 43, 2]\nGenerated Node #2: [3, 43, 2] from Operation: 84-82=2\nCurrent State: 48:[3, 43, 2], Operations: ['84-82=2']\nExploring Operation: 3+43=46, Resulting Numbers: [2, 46]\nGenerated Node #3: [2, 46] from Operation: 3+43=46\nCurrent State: 48:[2, 46], Operations: ['84-82=2', '3+43=46']\nExploring Operation: 2+46=48, Resulting Numbers: [48]\n48,48 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 42, + 45, + 53, + 11 + ], + "target": 39, + "solution": [ + "45-42=3", + "53-11=42", + "42-3=39" + ], + "optimal_path": "Current State: 39:[42, 45, 53, 11], Operations: []\nExploring Operation: 45-42=3, Resulting Numbers: [53, 11, 3]\nGenerated Node #2: [53, 11, 3] from Operation: 45-42=3\nCurrent State: 39:[53, 11, 3], Operations: ['45-42=3']\nExploring Operation: 53-11=42, Resulting Numbers: [3, 42]\nGenerated Node #3: [3, 42] from Operation: 53-11=42\nCurrent State: 39:[3, 42], Operations: ['45-42=3', '53-11=42']\nExploring Operation: 42-3=39, Resulting Numbers: [39]\n39,39 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 81, + 91, + 26, + 22 + ], + "target": 14, + "solution": [ + "91-81=10", + "26-22=4", + "10+4=14" + ], + "optimal_path": "Current State: 14:[81, 91, 26, 22], Operations: []\nExploring Operation: 91-81=10, Resulting Numbers: [26, 22, 10]\nGenerated Node #2: [26, 22, 10] from Operation: 91-81=10\nCurrent State: 14:[26, 22, 10], Operations: ['91-81=10']\nExploring Operation: 26-22=4, Resulting Numbers: [10, 4]\nGenerated Node #3: [10, 4] from Operation: 26-22=4\nCurrent State: 14:[10, 4], Operations: ['91-81=10', '26-22=4']\nExploring Operation: 10+4=14, Resulting Numbers: [14]\n14,14 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 34, + 24, + 78, + 37 + ], + "target": 17, + "solution": [ + "34+24=58", + "78-37=41", + "58-41=17" + ], + "optimal_path": "Current State: 17:[34, 24, 78, 37], Operations: []\nExploring Operation: 34+24=58, Resulting Numbers: [78, 37, 58]\nGenerated Node #2: [78, 37, 58] from Operation: 34+24=58\nCurrent State: 17:[78, 37, 58], Operations: ['34+24=58']\nExploring Operation: 78-37=41, Resulting Numbers: [58, 41]\nGenerated Node #3: [58, 41] from Operation: 78-37=41\nCurrent State: 17:[58, 41], Operations: ['34+24=58', '78-37=41']\nExploring Operation: 58-41=17, Resulting Numbers: [17]\n17,17 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 91, + 86, + 23, + 41 + ], + "target": 13, + "solution": [ + "91-86=5", + "41-23=18", + "18-5=13" + ], + "optimal_path": "Current State: 13:[91, 86, 23, 41], Operations: []\nExploring Operation: 91-86=5, Resulting Numbers: [23, 41, 5]\nGenerated Node #2: [23, 41, 5] from Operation: 91-86=5\nCurrent State: 13:[23, 41, 5], Operations: ['91-86=5']\nExploring Operation: 41-23=18, Resulting Numbers: [5, 18]\nGenerated Node #3: [5, 18] from Operation: 41-23=18\nCurrent State: 13:[5, 18], Operations: ['91-86=5', '41-23=18']\nExploring Operation: 18-5=13, Resulting Numbers: [13]\n13,13 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 72, + 19, + 51, + 61 + ], + "target": 59, + "solution": [ + "72-19=53", + "51+61=112", + "112-53=59" + ], + "optimal_path": "Current State: 59:[72, 19, 51, 61], Operations: []\nExploring Operation: 72-19=53, Resulting Numbers: [51, 61, 53]\nGenerated Node #2: [51, 61, 53] from Operation: 72-19=53\nCurrent State: 59:[51, 61, 53], Operations: ['72-19=53']\nExploring Operation: 51+61=112, Resulting Numbers: [53, 112]\nGenerated Node #3: [53, 112] from Operation: 51+61=112\nCurrent State: 59:[53, 112], Operations: ['72-19=53', '51+61=112']\nExploring Operation: 112-53=59, Resulting Numbers: [59]\n59,59 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 4, + 66, + 91, + 38 + ], + "target": 65, + "solution": [ + "66+38=104", + "104/4=26", + "91-26=65" + ], + "optimal_path": "Current State: 65:[4, 66, 91, 38], Operations: []\nExploring Operation: 66+38=104, Resulting Numbers: [4, 91, 104]\nGenerated Node #2: [4, 91, 104] from Operation: 66+38=104\nCurrent State: 65:[4, 91, 104], Operations: ['66+38=104']\nExploring Operation: 104/4=26, Resulting Numbers: [91, 26]\nGenerated Node #3: [91, 26] from Operation: 104/4=26\nCurrent State: 65:[91, 26], Operations: ['66+38=104', '104/4=26']\nExploring Operation: 91-26=65, Resulting Numbers: [65]\n65,65 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 16, + 27, + 19, + 24 + ], + "target": 29, + "solution": [ + "27-24=3", + "16*3=48", + "48-19=29" + ], + "optimal_path": "Current State: 29:[16, 27, 19, 24], Operations: []\nExploring Operation: 27-24=3, Resulting Numbers: [16, 19, 3]\nGenerated Node #2: [16, 19, 3] from Operation: 27-24=3\nCurrent State: 29:[16, 19, 3], Operations: ['27-24=3']\nExploring Operation: 16*3=48, Resulting Numbers: [19, 48]\nGenerated Node #3: [19, 48] from Operation: 16*3=48\nCurrent State: 29:[19, 48], Operations: ['27-24=3', '16*3=48']\nExploring Operation: 48-19=29, Resulting Numbers: [29]\n29,29 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 49, + 70, + 10, + 28 + ], + "target": 81, + "solution": [ + "49+70=119", + "10+28=38", + "119-38=81" + ], + "optimal_path": "Current State: 81:[49, 70, 10, 28], Operations: []\nExploring Operation: 49+70=119, Resulting Numbers: [10, 28, 119]\nGenerated Node #2: [10, 28, 119] from Operation: 49+70=119\nCurrent State: 81:[10, 28, 119], Operations: ['49+70=119']\nExploring Operation: 10+28=38, Resulting Numbers: [119, 38]\nGenerated Node #3: [119, 38] from Operation: 10+28=38\nCurrent State: 81:[119, 38], Operations: ['49+70=119', '10+28=38']\nExploring Operation: 119-38=81, Resulting Numbers: [81]\n81,81 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 61, + 64, + 32, + 82 + ], + "target": 48, + "solution": [ + "61*64=3904", + "32+3904=3936", + "3936/82=48" + ], + "optimal_path": "Current State: 48:[61, 64, 32, 82], Operations: []\nExploring Operation: 61*64=3904, Resulting Numbers: [32, 82, 3904]\nGenerated Node #2: [32, 82, 3904] from Operation: 61*64=3904\nCurrent State: 48:[32, 82, 3904], Operations: ['61*64=3904']\nExploring Operation: 32+3904=3936, Resulting Numbers: [82, 3936]\nGenerated Node #3: [82, 3936] from Operation: 32+3904=3936\nCurrent State: 48:[82, 3936], Operations: ['61*64=3904', '32+3904=3936']\nExploring Operation: 3936/82=48, Resulting Numbers: [48]\n48,48 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 36, + 16, + 35, + 33 + ], + "target": 50, + "solution": [ + "36+16=52", + "35-33=2", + "52-2=50" + ], + "optimal_path": "Current State: 50:[36, 16, 35, 33], Operations: []\nExploring Operation: 36+16=52, Resulting Numbers: [35, 33, 52]\nGenerated Node #2: [35, 33, 52] from Operation: 36+16=52\nCurrent State: 50:[35, 33, 52], Operations: ['36+16=52']\nExploring Operation: 35-33=2, Resulting Numbers: [52, 2]\nGenerated Node #3: [52, 2] from Operation: 35-33=2\nCurrent State: 50:[52, 2], Operations: ['36+16=52', '35-33=2']\nExploring Operation: 52-2=50, Resulting Numbers: [50]\n50,50 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 7, + 92, + 54, + 46 + ], + "target": 94, + "solution": [ + "54-7=47", + "92/46=2", + "47*2=94" + ], + "optimal_path": "Current State: 94:[7, 92, 54, 46], Operations: []\nExploring Operation: 54-7=47, Resulting Numbers: [92, 46, 47]\nGenerated Node #2: [92, 46, 47] from Operation: 54-7=47\nCurrent State: 94:[92, 46, 47], Operations: ['54-7=47']\nExploring Operation: 92/46=2, Resulting Numbers: [47, 2]\nGenerated Node #3: [47, 2] from Operation: 92/46=2\nCurrent State: 94:[47, 2], Operations: ['54-7=47', '92/46=2']\nExploring Operation: 47*2=94, Resulting Numbers: [94]\n94,94 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 56, + 61, + 42, + 20 + ], + "target": 17, + "solution": [ + "61-56=5", + "42-20=22", + "22-5=17" + ], + "optimal_path": "Current State: 17:[56, 61, 42, 20], Operations: []\nExploring Operation: 61-56=5, Resulting Numbers: [42, 20, 5]\nGenerated Node #2: [42, 20, 5] from Operation: 61-56=5\nCurrent State: 17:[42, 20, 5], Operations: ['61-56=5']\nExploring Operation: 42-20=22, Resulting Numbers: [5, 22]\nGenerated Node #3: [5, 22] from Operation: 42-20=22\nCurrent State: 17:[5, 22], Operations: ['61-56=5', '42-20=22']\nExploring Operation: 22-5=17, Resulting Numbers: [17]\n17,17 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 20, + 98, + 96, + 57 + ], + "target": 75, + "solution": [ + "98-20=78", + "96+57=153", + "153-78=75" + ], + "optimal_path": "Current State: 75:[20, 98, 96, 57], Operations: []\nExploring Operation: 98-20=78, Resulting Numbers: [96, 57, 78]\nGenerated Node #2: [96, 57, 78] from Operation: 98-20=78\nCurrent State: 75:[96, 57, 78], Operations: ['98-20=78']\nExploring Operation: 96+57=153, Resulting Numbers: [78, 153]\nGenerated Node #3: [78, 153] from Operation: 96+57=153\nCurrent State: 75:[78, 153], Operations: ['98-20=78', '96+57=153']\nExploring Operation: 153-78=75, Resulting Numbers: [75]\n75,75 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 4, + 58, + 42, + 63 + ], + "target": 43, + "solution": [ + "4+58=62", + "42+63=105", + "105-62=43" + ], + "optimal_path": "Current State: 43:[4, 58, 42, 63], Operations: []\nExploring Operation: 4+58=62, Resulting Numbers: [42, 63, 62]\nGenerated Node #2: [42, 63, 62] from Operation: 4+58=62\nCurrent State: 43:[42, 63, 62], Operations: ['4+58=62']\nExploring Operation: 42+63=105, Resulting Numbers: [62, 105]\nGenerated Node #3: [62, 105] from Operation: 42+63=105\nCurrent State: 43:[62, 105], Operations: ['4+58=62', '42+63=105']\nExploring Operation: 105-62=43, Resulting Numbers: [43]\n43,43 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 27, + 72, + 75, + 33 + ], + "target": 48, + "solution": [ + "75-72=3", + "27*3=81", + "81-33=48" + ], + "optimal_path": "Current State: 48:[27, 72, 75, 33], Operations: []\nExploring Operation: 75-72=3, Resulting Numbers: [27, 33, 3]\nGenerated Node #2: [27, 33, 3] from Operation: 75-72=3\nCurrent State: 48:[27, 33, 3], Operations: ['75-72=3']\nExploring Operation: 27*3=81, Resulting Numbers: [33, 81]\nGenerated Node #3: [33, 81] from Operation: 27*3=81\nCurrent State: 48:[33, 81], Operations: ['75-72=3', '27*3=81']\nExploring Operation: 81-33=48, Resulting Numbers: [48]\n48,48 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 31, + 25, + 2, + 68 + ], + "target": 55, + "solution": [ + "68-25=43", + "2*43=86", + "86-31=55" + ], + "optimal_path": "Current State: 55:[31, 25, 2, 68], Operations: []\nExploring Operation: 68-25=43, Resulting Numbers: [31, 2, 43]\nGenerated Node #2: [31, 2, 43] from Operation: 68-25=43\nCurrent State: 55:[31, 2, 43], Operations: ['68-25=43']\nExploring Operation: 2*43=86, Resulting Numbers: [31, 86]\nGenerated Node #3: [31, 86] from Operation: 2*43=86\nCurrent State: 55:[31, 86], Operations: ['68-25=43', '2*43=86']\nExploring Operation: 86-31=55, Resulting Numbers: [55]\n55,55 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 23, + 44, + 7, + 69 + ], + "target": 83, + "solution": [ + "44-23=21", + "69-7=62", + "21+62=83" + ], + "optimal_path": "Current State: 83:[23, 44, 7, 69], Operations: []\nExploring Operation: 44-23=21, Resulting Numbers: [7, 69, 21]\nGenerated Node #2: [7, 69, 21] from Operation: 44-23=21\nCurrent State: 83:[7, 69, 21], Operations: ['44-23=21']\nExploring Operation: 69-7=62, Resulting Numbers: [21, 62]\nGenerated Node #3: [21, 62] from Operation: 69-7=62\nCurrent State: 83:[21, 62], Operations: ['44-23=21', '69-7=62']\nExploring Operation: 21+62=83, Resulting Numbers: [83]\n83,83 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 7, + 9, + 90, + 10 + ], + "target": 63, + "solution": [ + "7+10=17", + "9*17=153", + "153-90=63" + ], + "optimal_path": "Current State: 63:[7, 9, 90, 10], Operations: []\nExploring Operation: 7+10=17, Resulting Numbers: [9, 90, 17]\nGenerated Node #2: [9, 90, 17] from Operation: 7+10=17\nCurrent State: 63:[9, 90, 17], Operations: ['7+10=17']\nExploring Operation: 9*17=153, Resulting Numbers: [90, 153]\nGenerated Node #3: [90, 153] from Operation: 9*17=153\nCurrent State: 63:[90, 153], Operations: ['7+10=17', '9*17=153']\nExploring Operation: 153-90=63, Resulting Numbers: [63]\n63,63 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 52, + 63, + 50, + 43 + ], + "target": 43, + "solution": [ + "52-43=9", + "63/9=7", + "50-7=43" + ], + "optimal_path": "Current State: 43:[52, 63, 50, 43], Operations: []\nExploring Operation: 52-43=9, Resulting Numbers: [63, 50, 9]\nGenerated Node #2: [63, 50, 9] from Operation: 52-43=9\nCurrent State: 43:[63, 50, 9], Operations: ['52-43=9']\nExploring Operation: 63/9=7, Resulting Numbers: [50, 7]\nGenerated Node #3: [50, 7] from Operation: 63/9=7\nCurrent State: 43:[50, 7], Operations: ['52-43=9', '63/9=7']\nExploring Operation: 50-7=43, Resulting Numbers: [43]\n43,43 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 88, + 30, + 84, + 58 + ], + "target": 22, + "solution": [ + "88-84=4", + "30+58=88", + "88/4=22" + ], + "optimal_path": "Current State: 22:[88, 30, 84, 58], Operations: []\nExploring Operation: 88-84=4, Resulting Numbers: [30, 58, 4]\nGenerated Node #2: [30, 58, 4] from Operation: 88-84=4\nCurrent State: 22:[30, 58, 4], Operations: ['88-84=4']\nExploring Operation: 30+58=88, Resulting Numbers: [4, 88]\nGenerated Node #3: [4, 88] from Operation: 30+58=88\nCurrent State: 22:[4, 88], Operations: ['88-84=4', '30+58=88']\nExploring Operation: 88/4=22, Resulting Numbers: [22]\n22,22 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 24, + 85, + 30, + 14 + ], + "target": 45, + "solution": [ + "85-24=61", + "30-14=16", + "61-16=45" + ], + "optimal_path": "Current State: 45:[24, 85, 30, 14], Operations: []\nExploring Operation: 85-24=61, Resulting Numbers: [30, 14, 61]\nGenerated Node #2: [30, 14, 61] from Operation: 85-24=61\nCurrent State: 45:[30, 14, 61], Operations: ['85-24=61']\nExploring Operation: 30-14=16, Resulting Numbers: [61, 16]\nGenerated Node #3: [61, 16] from Operation: 30-14=16\nCurrent State: 45:[61, 16], Operations: ['85-24=61', '30-14=16']\nExploring Operation: 61-16=45, Resulting Numbers: [45]\n45,45 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 28, + 10, + 21, + 36 + ], + "target": 34, + "solution": [ + "28-21=7", + "10*7=70", + "70-36=34" + ], + "optimal_path": "Current State: 34:[28, 10, 21, 36], Operations: []\nExploring Operation: 28-21=7, Resulting Numbers: [10, 36, 7]\nGenerated Node #2: [10, 36, 7] from Operation: 28-21=7\nCurrent State: 34:[10, 36, 7], Operations: ['28-21=7']\nExploring Operation: 10*7=70, Resulting Numbers: [36, 70]\nGenerated Node #3: [36, 70] from Operation: 10*7=70\nCurrent State: 34:[36, 70], Operations: ['28-21=7', '10*7=70']\nExploring Operation: 70-36=34, Resulting Numbers: [34]\n34,34 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 68, + 88, + 47, + 34 + ], + "target": 33, + "solution": [ + "88-68=20", + "47-34=13", + "20+13=33" + ], + "optimal_path": "Current State: 33:[68, 88, 47, 34], Operations: []\nExploring Operation: 88-68=20, Resulting Numbers: [47, 34, 20]\nGenerated Node #2: [47, 34, 20] from Operation: 88-68=20\nCurrent State: 33:[47, 34, 20], Operations: ['88-68=20']\nExploring Operation: 47-34=13, Resulting Numbers: [20, 13]\nGenerated Node #3: [20, 13] from Operation: 47-34=13\nCurrent State: 33:[20, 13], Operations: ['88-68=20', '47-34=13']\nExploring Operation: 20+13=33, Resulting Numbers: [33]\n33,33 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 75, + 64, + 93, + 96 + ], + "target": 14, + "solution": [ + "75-64=11", + "96-93=3", + "11+3=14" + ], + "optimal_path": "Current State: 14:[75, 64, 93, 96], Operations: []\nExploring Operation: 75-64=11, Resulting Numbers: [93, 96, 11]\nGenerated Node #2: [93, 96, 11] from Operation: 75-64=11\nCurrent State: 14:[93, 96, 11], Operations: ['75-64=11']\nExploring Operation: 96-93=3, Resulting Numbers: [11, 3]\nGenerated Node #3: [11, 3] from Operation: 96-93=3\nCurrent State: 14:[11, 3], Operations: ['75-64=11', '96-93=3']\nExploring Operation: 11+3=14, Resulting Numbers: [14]\n14,14 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 16, + 80, + 78, + 1 + ], + "target": 31, + "solution": [ + "80-78=2", + "16*2=32", + "32-1=31" + ], + "optimal_path": "Current State: 31:[16, 80, 78, 1], Operations: []\nExploring Operation: 80-78=2, Resulting Numbers: [16, 1, 2]\nGenerated Node #2: [16, 1, 2] from Operation: 80-78=2\nCurrent State: 31:[16, 1, 2], Operations: ['80-78=2']\nExploring Operation: 16*2=32, Resulting Numbers: [1, 32]\nGenerated Node #3: [1, 32] from Operation: 16*2=32\nCurrent State: 31:[1, 32], Operations: ['80-78=2', '16*2=32']\nExploring Operation: 32-1=31, Resulting Numbers: [31]\n31,31 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 20, + 63, + 21, + 39 + ], + "target": 62, + "solution": [ + "20+39=59", + "63/21=3", + "59+3=62" + ], + "optimal_path": "Current State: 62:[20, 63, 21, 39], Operations: []\nExploring Operation: 20+39=59, Resulting Numbers: [63, 21, 59]\nGenerated Node #2: [63, 21, 59] from Operation: 20+39=59\nCurrent State: 62:[63, 21, 59], Operations: ['20+39=59']\nExploring Operation: 63/21=3, Resulting Numbers: [59, 3]\nGenerated Node #3: [59, 3] from Operation: 63/21=3\nCurrent State: 62:[59, 3], Operations: ['20+39=59', '63/21=3']\nExploring Operation: 59+3=62, Resulting Numbers: [62]\n62,62 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 26, + 77, + 29, + 6 + ], + "target": 71, + "solution": [ + "26+77=103", + "29*6=174", + "174-103=71" + ], + "optimal_path": "Current State: 71:[26, 77, 29, 6], Operations: []\nExploring Operation: 26+77=103, Resulting Numbers: [29, 6, 103]\nGenerated Node #2: [29, 6, 103] from Operation: 26+77=103\nCurrent State: 71:[29, 6, 103], Operations: ['26+77=103']\nExploring Operation: 29*6=174, Resulting Numbers: [103, 174]\nGenerated Node #3: [103, 174] from Operation: 29*6=174\nCurrent State: 71:[103, 174], Operations: ['26+77=103', '29*6=174']\nExploring Operation: 174-103=71, Resulting Numbers: [71]\n71,71 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 50, + 3, + 14, + 56 + ], + "target": 42, + "solution": [ + "50+3=53", + "56-53=3", + "14*3=42" + ], + "optimal_path": "Current State: 42:[50, 3, 14, 56], Operations: []\nExploring Operation: 50+3=53, Resulting Numbers: [14, 56, 53]\nGenerated Node #2: [14, 56, 53] from Operation: 50+3=53\nCurrent State: 42:[14, 56, 53], Operations: ['50+3=53']\nExploring Operation: 56-53=3, Resulting Numbers: [14, 3]\nGenerated Node #3: [14, 3] from Operation: 56-53=3\nCurrent State: 42:[14, 3], Operations: ['50+3=53', '56-53=3']\nExploring Operation: 14*3=42, Resulting Numbers: [42]\n42,42 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 21, + 59, + 77, + 63 + ], + "target": 100, + "solution": [ + "63/21=3", + "59*3=177", + "177-77=100" + ], + "optimal_path": "Current State: 100:[21, 59, 77, 63], Operations: []\nExploring Operation: 63/21=3, Resulting Numbers: [59, 77, 3]\nGenerated Node #2: [59, 77, 3] from Operation: 63/21=3\nCurrent State: 100:[59, 77, 3], Operations: ['63/21=3']\nExploring Operation: 59*3=177, Resulting Numbers: [77, 177]\nGenerated Node #3: [77, 177] from Operation: 59*3=177\nCurrent State: 100:[77, 177], Operations: ['63/21=3', '59*3=177']\nExploring Operation: 177-77=100, Resulting Numbers: [100]\n100,100 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 52, + 49, + 68, + 20 + ], + "target": 16, + "solution": [ + "52-49=3", + "68-20=48", + "48/3=16" + ], + "optimal_path": "Current State: 16:[52, 49, 68, 20], Operations: []\nExploring Operation: 52-49=3, Resulting Numbers: [68, 20, 3]\nGenerated Node #2: [68, 20, 3] from Operation: 52-49=3\nCurrent State: 16:[68, 20, 3], Operations: ['52-49=3']\nExploring Operation: 68-20=48, Resulting Numbers: [3, 48]\nGenerated Node #3: [3, 48] from Operation: 68-20=48\nCurrent State: 16:[3, 48], Operations: ['52-49=3', '68-20=48']\nExploring Operation: 48/3=16, Resulting Numbers: [16]\n16,16 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 19, + 56, + 91, + 77 + ], + "target": 23, + "solution": [ + "56-19=37", + "91-77=14", + "37-14=23" + ], + "optimal_path": "Current State: 23:[19, 56, 91, 77], Operations: []\nExploring Operation: 56-19=37, Resulting Numbers: [91, 77, 37]\nGenerated Node #2: [91, 77, 37] from Operation: 56-19=37\nCurrent State: 23:[91, 77, 37], Operations: ['56-19=37']\nExploring Operation: 91-77=14, Resulting Numbers: [37, 14]\nGenerated Node #3: [37, 14] from Operation: 91-77=14\nCurrent State: 23:[37, 14], Operations: ['56-19=37', '91-77=14']\nExploring Operation: 37-14=23, Resulting Numbers: [23]\n23,23 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 12, + 63, + 91, + 19 + ], + "target": 59, + "solution": [ + "63-12=51", + "91+19=110", + "110-51=59" + ], + "optimal_path": "Current State: 59:[12, 63, 91, 19], Operations: []\nExploring Operation: 63-12=51, Resulting Numbers: [91, 19, 51]\nGenerated Node #2: [91, 19, 51] from Operation: 63-12=51\nCurrent State: 59:[91, 19, 51], Operations: ['63-12=51']\nExploring Operation: 91+19=110, Resulting Numbers: [51, 110]\nGenerated Node #3: [51, 110] from Operation: 91+19=110\nCurrent State: 59:[51, 110], Operations: ['63-12=51', '91+19=110']\nExploring Operation: 110-51=59, Resulting Numbers: [59]\n59,59 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 53, + 42, + 28, + 10 + ], + "target": 28, + "solution": [ + "53-42=11", + "11-10=1", + "28*1=28" + ], + "optimal_path": "Current State: 28:[53, 42, 28, 10], Operations: []\nExploring Operation: 53-42=11, Resulting Numbers: [28, 10, 11]\nGenerated Node #2: [28, 10, 11] from Operation: 53-42=11\nCurrent State: 28:[28, 10, 11], Operations: ['53-42=11']\nExploring Operation: 11-10=1, Resulting Numbers: [28, 1]\nGenerated Node #3: [28, 1] from Operation: 11-10=1\nCurrent State: 28:[28, 1], Operations: ['53-42=11', '11-10=1']\nExploring Operation: 28*1=28, Resulting Numbers: [28]\n28,28 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 82, + 32, + 14, + 16 + ], + "target": 55, + "solution": [ + "82*16=1312", + "1312/32=41", + "14+41=55" + ], + "optimal_path": "Current State: 55:[82, 32, 14, 16], Operations: []\nExploring Operation: 82*16=1312, Resulting Numbers: [32, 14, 1312]\nGenerated Node #2: [32, 14, 1312] from Operation: 82*16=1312\nCurrent State: 55:[32, 14, 1312], Operations: ['82*16=1312']\nExploring Operation: 1312/32=41, Resulting Numbers: [14, 41]\nGenerated Node #3: [14, 41] from Operation: 1312/32=41\nCurrent State: 55:[14, 41], Operations: ['82*16=1312', '1312/32=41']\nExploring Operation: 14+41=55, Resulting Numbers: [55]\n55,55 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 3, + 83, + 81, + 37 + ], + "target": 67, + "solution": [ + "83+81=164", + "37+164=201", + "201/3=67" + ], + "optimal_path": "Current State: 67:[3, 83, 81, 37], Operations: []\nExploring Operation: 83+81=164, Resulting Numbers: [3, 37, 164]\nGenerated Node #2: [3, 37, 164] from Operation: 83+81=164\nCurrent State: 67:[3, 37, 164], Operations: ['83+81=164']\nExploring Operation: 37+164=201, Resulting Numbers: [3, 201]\nGenerated Node #3: [3, 201] from Operation: 37+164=201\nCurrent State: 67:[3, 201], Operations: ['83+81=164', '37+164=201']\nExploring Operation: 201/3=67, Resulting Numbers: [67]\n67,67 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 7, + 86, + 31, + 67 + ], + "target": 19, + "solution": [ + "86-7=79", + "31+67=98", + "98-79=19" + ], + "optimal_path": "Current State: 19:[7, 86, 31, 67], Operations: []\nExploring Operation: 86-7=79, Resulting Numbers: [31, 67, 79]\nGenerated Node #2: [31, 67, 79] from Operation: 86-7=79\nCurrent State: 19:[31, 67, 79], Operations: ['86-7=79']\nExploring Operation: 31+67=98, Resulting Numbers: [79, 98]\nGenerated Node #3: [79, 98] from Operation: 31+67=98\nCurrent State: 19:[79, 98], Operations: ['86-7=79', '31+67=98']\nExploring Operation: 98-79=19, Resulting Numbers: [19]\n19,19 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 44, + 2, + 98, + 95 + ], + "target": 44, + "solution": [ + "98-2=96", + "96-95=1", + "44*1=44" + ], + "optimal_path": "Current State: 44:[44, 2, 98, 95], Operations: []\nExploring Operation: 98-2=96, Resulting Numbers: [44, 95, 96]\nGenerated Node #2: [44, 95, 96] from Operation: 98-2=96\nCurrent State: 44:[44, 95, 96], Operations: ['98-2=96']\nExploring Operation: 96-95=1, Resulting Numbers: [44, 1]\nGenerated Node #3: [44, 1] from Operation: 96-95=1\nCurrent State: 44:[44, 1], Operations: ['98-2=96', '96-95=1']\nExploring Operation: 44*1=44, Resulting Numbers: [44]\n44,44 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 15, + 51, + 45, + 82 + ], + "target": 28, + "solution": [ + "45/15=3", + "82-51=31", + "31-3=28" + ], + "optimal_path": "Current State: 28:[15, 51, 45, 82], Operations: []\nExploring Operation: 45/15=3, Resulting Numbers: [51, 82, 3]\nGenerated Node #2: [51, 82, 3] from Operation: 45/15=3\nCurrent State: 28:[51, 82, 3], Operations: ['45/15=3']\nExploring Operation: 82-51=31, Resulting Numbers: [3, 31]\nGenerated Node #3: [3, 31] from Operation: 82-51=31\nCurrent State: 28:[3, 31], Operations: ['45/15=3', '82-51=31']\nExploring Operation: 31-3=28, Resulting Numbers: [28]\n28,28 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 6, + 52, + 62, + 38 + ], + "target": 82, + "solution": [ + "6+52=58", + "62-38=24", + "58+24=82" + ], + "optimal_path": "Current State: 82:[6, 52, 62, 38], Operations: []\nExploring Operation: 6+52=58, Resulting Numbers: [62, 38, 58]\nGenerated Node #2: [62, 38, 58] from Operation: 6+52=58\nCurrent State: 82:[62, 38, 58], Operations: ['6+52=58']\nExploring Operation: 62-38=24, Resulting Numbers: [58, 24]\nGenerated Node #3: [58, 24] from Operation: 62-38=24\nCurrent State: 82:[58, 24], Operations: ['6+52=58', '62-38=24']\nExploring Operation: 58+24=82, Resulting Numbers: [82]\n82,82 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 67, + 12, + 10, + 28 + ], + "target": 61, + "solution": [ + "67+12=79", + "28-10=18", + "79-18=61" + ], + "optimal_path": "Current State: 61:[67, 12, 10, 28], Operations: []\nExploring Operation: 67+12=79, Resulting Numbers: [10, 28, 79]\nGenerated Node #2: [10, 28, 79] from Operation: 67+12=79\nCurrent State: 61:[10, 28, 79], Operations: ['67+12=79']\nExploring Operation: 28-10=18, Resulting Numbers: [79, 18]\nGenerated Node #3: [79, 18] from Operation: 28-10=18\nCurrent State: 61:[79, 18], Operations: ['67+12=79', '28-10=18']\nExploring Operation: 79-18=61, Resulting Numbers: [61]\n61,61 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 48, + 54, + 54, + 32 + ], + "target": 81, + "solution": [ + "48+32=80", + "54/54=1", + "80+1=81" + ], + "optimal_path": "Current State: 81:[48, 54, 54, 32], Operations: []\nExploring Operation: 48+32=80, Resulting Numbers: [54, 54, 80]\nGenerated Node #2: [54, 54, 80] from Operation: 48+32=80\nCurrent State: 81:[54, 54, 80], Operations: ['48+32=80']\nExploring Operation: 54/54=1, Resulting Numbers: [80, 1]\nGenerated Node #3: [80, 1] from Operation: 54/54=1\nCurrent State: 81:[80, 1], Operations: ['48+32=80', '54/54=1']\nExploring Operation: 80+1=81, Resulting Numbers: [81]\n81,81 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 18, + 46, + 86, + 31 + ], + "target": 53, + "solution": [ + "18+46=64", + "86+31=117", + "117-64=53" + ], + "optimal_path": "Current State: 53:[18, 46, 86, 31], Operations: []\nExploring Operation: 18+46=64, Resulting Numbers: [86, 31, 64]\nGenerated Node #2: [86, 31, 64] from Operation: 18+46=64\nCurrent State: 53:[86, 31, 64], Operations: ['18+46=64']\nExploring Operation: 86+31=117, Resulting Numbers: [64, 117]\nGenerated Node #3: [64, 117] from Operation: 86+31=117\nCurrent State: 53:[64, 117], Operations: ['18+46=64', '86+31=117']\nExploring Operation: 117-64=53, Resulting Numbers: [53]\n53,53 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 24, + 54, + 52, + 37 + ], + "target": 11, + "solution": [ + "24+54=78", + "52+37=89", + "89-78=11" + ], + "optimal_path": "Current State: 11:[24, 54, 52, 37], Operations: []\nExploring Operation: 24+54=78, Resulting Numbers: [52, 37, 78]\nGenerated Node #2: [52, 37, 78] from Operation: 24+54=78\nCurrent State: 11:[52, 37, 78], Operations: ['24+54=78']\nExploring Operation: 52+37=89, Resulting Numbers: [78, 89]\nGenerated Node #3: [78, 89] from Operation: 52+37=89\nCurrent State: 11:[78, 89], Operations: ['24+54=78', '52+37=89']\nExploring Operation: 89-78=11, Resulting Numbers: [11]\n11,11 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 8, + 30, + 18, + 1 + ], + "target": 15, + "solution": [ + "8+1=9", + "30*9=270", + "270/18=15" + ], + "optimal_path": "Current State: 15:[8, 30, 18, 1], Operations: []\nExploring Operation: 8+1=9, Resulting Numbers: [30, 18, 9]\nGenerated Node #2: [30, 18, 9] from Operation: 8+1=9\nCurrent State: 15:[30, 18, 9], Operations: ['8+1=9']\nExploring Operation: 30*9=270, Resulting Numbers: [18, 270]\nGenerated Node #3: [18, 270] from Operation: 30*9=270\nCurrent State: 15:[18, 270], Operations: ['8+1=9', '30*9=270']\nExploring Operation: 270/18=15, Resulting Numbers: [15]\n15,15 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 25, + 75, + 16, + 23 + ], + "target": 85, + "solution": [ + "75/25=3", + "23*3=69", + "16+69=85" + ], + "optimal_path": "Current State: 85:[25, 75, 16, 23], Operations: []\nExploring Operation: 75/25=3, Resulting Numbers: [16, 23, 3]\nGenerated Node #2: [16, 23, 3] from Operation: 75/25=3\nCurrent State: 85:[16, 23, 3], Operations: ['75/25=3']\nExploring Operation: 23*3=69, Resulting Numbers: [16, 69]\nGenerated Node #3: [16, 69] from Operation: 23*3=69\nCurrent State: 85:[16, 69], Operations: ['75/25=3', '23*3=69']\nExploring Operation: 16+69=85, Resulting Numbers: [85]\n85,85 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 34, + 73, + 56, + 74 + ], + "target": 91, + "solution": [ + "73-34=39", + "56+74=130", + "130-39=91" + ], + "optimal_path": "Current State: 91:[34, 73, 56, 74], Operations: []\nExploring Operation: 73-34=39, Resulting Numbers: [56, 74, 39]\nGenerated Node #2: [56, 74, 39] from Operation: 73-34=39\nCurrent State: 91:[56, 74, 39], Operations: ['73-34=39']\nExploring Operation: 56+74=130, Resulting Numbers: [39, 130]\nGenerated Node #3: [39, 130] from Operation: 56+74=130\nCurrent State: 91:[39, 130], Operations: ['73-34=39', '56+74=130']\nExploring Operation: 130-39=91, Resulting Numbers: [91]\n91,91 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 68, + 39, + 39, + 15 + ], + "target": 25, + "solution": [ + "68-39=29", + "39+15=54", + "54-29=25" + ], + "optimal_path": "Current State: 25:[68, 39, 39, 15], Operations: []\nExploring Operation: 68-39=29, Resulting Numbers: [15, 29]\nGenerated Node #2: [15, 29] from Operation: 68-39=29\nCurrent State: 25:[15, 29], Operations: ['68-39=29']\nExploring Operation: 39+15=54, Resulting Numbers: [29, 54]\nGenerated Node #3: [29, 54] from Operation: 39+15=54\nCurrent State: 25:[29, 54], Operations: ['68-39=29', '39+15=54']\nExploring Operation: 54-29=25, Resulting Numbers: [25]\n25,25 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 32, + 16, + 79, + 33 + ], + "target": 30, + "solution": [ + "32-16=16", + "79-33=46", + "46-16=30" + ], + "optimal_path": "Current State: 30:[32, 16, 79, 33], Operations: []\nExploring Operation: 32-16=16, Resulting Numbers: [79, 33, 16]\nGenerated Node #2: [79, 33, 16] from Operation: 32-16=16\nCurrent State: 30:[79, 33, 16], Operations: ['32-16=16']\nExploring Operation: 79-33=46, Resulting Numbers: [16, 46]\nGenerated Node #3: [16, 46] from Operation: 79-33=46\nCurrent State: 30:[16, 46], Operations: ['32-16=16', '79-33=46']\nExploring Operation: 46-16=30, Resulting Numbers: [30]\n30,30 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 32, + 53, + 76, + 41 + ], + "target": 96, + "solution": [ + "53-32=21", + "76+41=117", + "117-21=96" + ], + "optimal_path": "Current State: 96:[32, 53, 76, 41], Operations: []\nExploring Operation: 53-32=21, Resulting Numbers: [76, 41, 21]\nGenerated Node #2: [76, 41, 21] from Operation: 53-32=21\nCurrent State: 96:[76, 41, 21], Operations: ['53-32=21']\nExploring Operation: 76+41=117, Resulting Numbers: [21, 117]\nGenerated Node #3: [21, 117] from Operation: 76+41=117\nCurrent State: 96:[21, 117], Operations: ['53-32=21', '76+41=117']\nExploring Operation: 117-21=96, Resulting Numbers: [96]\n96,96 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 13, + 20, + 46, + 91 + ], + "target": 94, + "solution": [ + "91/13=7", + "20*7=140", + "140-46=94" + ], + "optimal_path": "Current State: 94:[13, 20, 46, 91], Operations: []\nExploring Operation: 91/13=7, Resulting Numbers: [20, 46, 7]\nGenerated Node #2: [20, 46, 7] from Operation: 91/13=7\nCurrent State: 94:[20, 46, 7], Operations: ['91/13=7']\nExploring Operation: 20*7=140, Resulting Numbers: [46, 140]\nGenerated Node #3: [46, 140] from Operation: 20*7=140\nCurrent State: 94:[46, 140], Operations: ['91/13=7', '20*7=140']\nExploring Operation: 140-46=94, Resulting Numbers: [94]\n94,94 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 25, + 70, + 15, + 7 + ], + "target": 60, + "solution": [ + "70-25=45", + "15*7=105", + "105-45=60" + ], + "optimal_path": "Current State: 60:[25, 70, 15, 7], Operations: []\nExploring Operation: 70-25=45, Resulting Numbers: [15, 7, 45]\nGenerated Node #2: [15, 7, 45] from Operation: 70-25=45\nCurrent State: 60:[15, 7, 45], Operations: ['70-25=45']\nExploring Operation: 15*7=105, Resulting Numbers: [45, 105]\nGenerated Node #3: [45, 105] from Operation: 15*7=105\nCurrent State: 60:[45, 105], Operations: ['70-25=45', '15*7=105']\nExploring Operation: 105-45=60, Resulting Numbers: [60]\n60,60 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 3, + 8, + 75, + 15 + ], + "target": 64, + "solution": [ + "75/15=5", + "3+5=8", + "8*8=64" + ], + "optimal_path": "Current State: 64:[3, 8, 75, 15], Operations: []\nExploring Operation: 75/15=5, Resulting Numbers: [3, 8, 5]\nGenerated Node #2: [3, 8, 5] from Operation: 75/15=5\nCurrent State: 64:[3, 8, 5], Operations: ['75/15=5']\nExploring Operation: 3+5=8, Resulting Numbers: [8, 8]\nGenerated Node #3: [8, 8] from Operation: 3+5=8\nCurrent State: 64:[8, 8], Operations: ['75/15=5', '3+5=8']\nExploring Operation: 8*8=64, Resulting Numbers: [64]\n64,64 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 35, + 81, + 95, + 37 + ], + "target": 86, + "solution": [ + "81-35=46", + "95+37=132", + "132-46=86" + ], + "optimal_path": "Current State: 86:[35, 81, 95, 37], Operations: []\nExploring Operation: 81-35=46, Resulting Numbers: [95, 37, 46]\nGenerated Node #2: [95, 37, 46] from Operation: 81-35=46\nCurrent State: 86:[95, 37, 46], Operations: ['81-35=46']\nExploring Operation: 95+37=132, Resulting Numbers: [46, 132]\nGenerated Node #3: [46, 132] from Operation: 95+37=132\nCurrent State: 86:[46, 132], Operations: ['81-35=46', '95+37=132']\nExploring Operation: 132-46=86, Resulting Numbers: [86]\n86,86 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 76, + 3, + 74, + 81 + ], + "target": 89, + "solution": [ + "81-76=5", + "3*5=15", + "74+15=89" + ], + "optimal_path": "Current State: 89:[76, 3, 74, 81], Operations: []\nExploring Operation: 81-76=5, Resulting Numbers: [3, 74, 5]\nGenerated Node #2: [3, 74, 5] from Operation: 81-76=5\nCurrent State: 89:[3, 74, 5], Operations: ['81-76=5']\nExploring Operation: 3*5=15, Resulting Numbers: [74, 15]\nGenerated Node #3: [74, 15] from Operation: 3*5=15\nCurrent State: 89:[74, 15], Operations: ['81-76=5', '3*5=15']\nExploring Operation: 74+15=89, Resulting Numbers: [89]\n89,89 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 54, + 69, + 96, + 8 + ], + "target": 64, + "solution": [ + "54-8=46", + "96*46=4416", + "4416/69=64" + ], + "optimal_path": "Current State: 64:[54, 69, 96, 8], Operations: []\nExploring Operation: 54-8=46, Resulting Numbers: [69, 96, 46]\nGenerated Node #2: [69, 96, 46] from Operation: 54-8=46\nCurrent State: 64:[69, 96, 46], Operations: ['54-8=46']\nExploring Operation: 96*46=4416, Resulting Numbers: [69, 4416]\nGenerated Node #3: [69, 4416] from Operation: 96*46=4416\nCurrent State: 64:[69, 4416], Operations: ['54-8=46', '96*46=4416']\nExploring Operation: 4416/69=64, Resulting Numbers: [64]\n64,64 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 8, + 11, + 32, + 33 + ], + "target": 77, + "solution": [ + "8+32=40", + "40-33=7", + "11*7=77" + ], + "optimal_path": "Current State: 77:[8, 11, 32, 33], Operations: []\nExploring Operation: 8+32=40, Resulting Numbers: [11, 33, 40]\nGenerated Node #2: [11, 33, 40] from Operation: 8+32=40\nCurrent State: 77:[11, 33, 40], Operations: ['8+32=40']\nExploring Operation: 40-33=7, Resulting Numbers: [11, 7]\nGenerated Node #3: [11, 7] from Operation: 40-33=7\nCurrent State: 77:[11, 7], Operations: ['8+32=40', '40-33=7']\nExploring Operation: 11*7=77, Resulting Numbers: [77]\n77,77 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 98, + 43, + 83, + 81 + ], + "target": 23, + "solution": [ + "98+43=141", + "83+81=164", + "164-141=23" + ], + "optimal_path": "Current State: 23:[98, 43, 83, 81], Operations: []\nExploring Operation: 98+43=141, Resulting Numbers: [83, 81, 141]\nGenerated Node #2: [83, 81, 141] from Operation: 98+43=141\nCurrent State: 23:[83, 81, 141], Operations: ['98+43=141']\nExploring Operation: 83+81=164, Resulting Numbers: [141, 164]\nGenerated Node #3: [141, 164] from Operation: 83+81=164\nCurrent State: 23:[141, 164], Operations: ['98+43=141', '83+81=164']\nExploring Operation: 164-141=23, Resulting Numbers: [23]\n23,23 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 74, + 38, + 27, + 70 + ], + "target": 61, + "solution": [ + "74-38=36", + "27+70=97", + "97-36=61" + ], + "optimal_path": "Current State: 61:[74, 38, 27, 70], Operations: []\nExploring Operation: 74-38=36, Resulting Numbers: [27, 70, 36]\nGenerated Node #2: [27, 70, 36] from Operation: 74-38=36\nCurrent State: 61:[27, 70, 36], Operations: ['74-38=36']\nExploring Operation: 27+70=97, Resulting Numbers: [36, 97]\nGenerated Node #3: [36, 97] from Operation: 27+70=97\nCurrent State: 61:[36, 97], Operations: ['74-38=36', '27+70=97']\nExploring Operation: 97-36=61, Resulting Numbers: [61]\n61,61 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 57, + 35, + 96, + 77 + ], + "target": 32, + "solution": [ + "96-77=19", + "57/19=3", + "35-3=32" + ], + "optimal_path": "Current State: 32:[57, 35, 96, 77], Operations: []\nExploring Operation: 96-77=19, Resulting Numbers: [57, 35, 19]\nGenerated Node #2: [57, 35, 19] from Operation: 96-77=19\nCurrent State: 32:[57, 35, 19], Operations: ['96-77=19']\nExploring Operation: 57/19=3, Resulting Numbers: [35, 3]\nGenerated Node #3: [35, 3] from Operation: 57/19=3\nCurrent State: 32:[35, 3], Operations: ['96-77=19', '57/19=3']\nExploring Operation: 35-3=32, Resulting Numbers: [32]\n32,32 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 47, + 65, + 50, + 30 + ], + "target": 38, + "solution": [ + "65-47=18", + "50-30=20", + "18+20=38" + ], + "optimal_path": "Current State: 38:[47, 65, 50, 30], Operations: []\nExploring Operation: 65-47=18, Resulting Numbers: [50, 30, 18]\nGenerated Node #2: [50, 30, 18] from Operation: 65-47=18\nCurrent State: 38:[50, 30, 18], Operations: ['65-47=18']\nExploring Operation: 50-30=20, Resulting Numbers: [18, 20]\nGenerated Node #3: [18, 20] from Operation: 50-30=20\nCurrent State: 38:[18, 20], Operations: ['65-47=18', '50-30=20']\nExploring Operation: 18+20=38, Resulting Numbers: [38]\n38,38 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 36, + 54, + 11, + 85 + ], + "target": 55, + "solution": [ + "36+54=90", + "90-85=5", + "11*5=55" + ], + "optimal_path": "Current State: 55:[36, 54, 11, 85], Operations: []\nExploring Operation: 36+54=90, Resulting Numbers: [11, 85, 90]\nGenerated Node #2: [11, 85, 90] from Operation: 36+54=90\nCurrent State: 55:[11, 85, 90], Operations: ['36+54=90']\nExploring Operation: 90-85=5, Resulting Numbers: [11, 5]\nGenerated Node #3: [11, 5] from Operation: 90-85=5\nCurrent State: 55:[11, 5], Operations: ['36+54=90', '90-85=5']\nExploring Operation: 11*5=55, Resulting Numbers: [55]\n55,55 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 93, + 8, + 11, + 60 + ], + "target": 73, + "solution": [ + "93+11=104", + "104/8=13", + "60+13=73" + ], + "optimal_path": "Current State: 73:[93, 8, 11, 60], Operations: []\nExploring Operation: 93+11=104, Resulting Numbers: [8, 60, 104]\nGenerated Node #2: [8, 60, 104] from Operation: 93+11=104\nCurrent State: 73:[8, 60, 104], Operations: ['93+11=104']\nExploring Operation: 104/8=13, Resulting Numbers: [60, 13]\nGenerated Node #3: [60, 13] from Operation: 104/8=13\nCurrent State: 73:[60, 13], Operations: ['93+11=104', '104/8=13']\nExploring Operation: 60+13=73, Resulting Numbers: [73]\n73,73 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 6, + 52, + 37, + 3 + ], + "target": 80, + "solution": [ + "52-6=46", + "37-3=34", + "46+34=80" + ], + "optimal_path": "Current State: 80:[6, 52, 37, 3], Operations: []\nExploring Operation: 52-6=46, Resulting Numbers: [37, 3, 46]\nGenerated Node #2: [37, 3, 46] from Operation: 52-6=46\nCurrent State: 80:[37, 3, 46], Operations: ['52-6=46']\nExploring Operation: 37-3=34, Resulting Numbers: [46, 34]\nGenerated Node #3: [46, 34] from Operation: 37-3=34\nCurrent State: 80:[46, 34], Operations: ['52-6=46', '37-3=34']\nExploring Operation: 46+34=80, Resulting Numbers: [80]\n80,80 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 63, + 47, + 83, + 62 + ], + "target": 89, + "solution": [ + "63+47=110", + "83-62=21", + "110-21=89" + ], + "optimal_path": "Current State: 89:[63, 47, 83, 62], Operations: []\nExploring Operation: 63+47=110, Resulting Numbers: [83, 62, 110]\nGenerated Node #2: [83, 62, 110] from Operation: 63+47=110\nCurrent State: 89:[83, 62, 110], Operations: ['63+47=110']\nExploring Operation: 83-62=21, Resulting Numbers: [110, 21]\nGenerated Node #3: [110, 21] from Operation: 83-62=21\nCurrent State: 89:[110, 21], Operations: ['63+47=110', '83-62=21']\nExploring Operation: 110-21=89, Resulting Numbers: [89]\n89,89 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 2, + 10, + 55, + 66 + ], + "target": 14, + "solution": [ + "10*66=660", + "660/55=12", + "2+12=14" + ], + "optimal_path": "Current State: 14:[2, 10, 55, 66], Operations: []\nExploring Operation: 10*66=660, Resulting Numbers: [2, 55, 660]\nGenerated Node #2: [2, 55, 660] from Operation: 10*66=660\nCurrent State: 14:[2, 55, 660], Operations: ['10*66=660']\nExploring Operation: 660/55=12, Resulting Numbers: [2, 12]\nGenerated Node #3: [2, 12] from Operation: 660/55=12\nCurrent State: 14:[2, 12], Operations: ['10*66=660', '660/55=12']\nExploring Operation: 2+12=14, Resulting Numbers: [14]\n14,14 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 46, + 13, + 55, + 11 + ], + "target": 32, + "solution": [ + "13-11=2", + "46/2=23", + "55-23=32" + ], + "optimal_path": "Current State: 32:[46, 13, 55, 11], Operations: []\nExploring Operation: 13-11=2, Resulting Numbers: [46, 55, 2]\nGenerated Node #2: [46, 55, 2] from Operation: 13-11=2\nCurrent State: 32:[46, 55, 2], Operations: ['13-11=2']\nExploring Operation: 46/2=23, Resulting Numbers: [55, 23]\nGenerated Node #3: [55, 23] from Operation: 46/2=23\nCurrent State: 32:[55, 23], Operations: ['13-11=2', '46/2=23']\nExploring Operation: 55-23=32, Resulting Numbers: [32]\n32,32 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 84, + 63, + 11, + 3 + ], + "target": 14, + "solution": [ + "84*11=924", + "63+3=66", + "924/66=14" + ], + "optimal_path": "Current State: 14:[84, 63, 11, 3], Operations: []\nExploring Operation: 84*11=924, Resulting Numbers: [63, 3, 924]\nGenerated Node #2: [63, 3, 924] from Operation: 84*11=924\nCurrent State: 14:[63, 3, 924], Operations: ['84*11=924']\nExploring Operation: 63+3=66, Resulting Numbers: [924, 66]\nGenerated Node #3: [924, 66] from Operation: 63+3=66\nCurrent State: 14:[924, 66], Operations: ['84*11=924', '63+3=66']\nExploring Operation: 924/66=14, Resulting Numbers: [14]\n14,14 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 31, + 19, + 11, + 54 + ], + "target": 93, + "solution": [ + "31+19=50", + "54-11=43", + "50+43=93" + ], + "optimal_path": "Current State: 93:[31, 19, 11, 54], Operations: []\nExploring Operation: 31+19=50, Resulting Numbers: [11, 54, 50]\nGenerated Node #2: [11, 54, 50] from Operation: 31+19=50\nCurrent State: 93:[11, 54, 50], Operations: ['31+19=50']\nExploring Operation: 54-11=43, Resulting Numbers: [50, 43]\nGenerated Node #3: [50, 43] from Operation: 54-11=43\nCurrent State: 93:[50, 43], Operations: ['31+19=50', '54-11=43']\nExploring Operation: 50+43=93, Resulting Numbers: [93]\n93,93 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 2, + 33, + 75, + 40 + ], + "target": 66, + "solution": [ + "33-2=31", + "75-40=35", + "31+35=66" + ], + "optimal_path": "Current State: 66:[2, 33, 75, 40], Operations: []\nExploring Operation: 33-2=31, Resulting Numbers: [75, 40, 31]\nGenerated Node #2: [75, 40, 31] from Operation: 33-2=31\nCurrent State: 66:[75, 40, 31], Operations: ['33-2=31']\nExploring Operation: 75-40=35, Resulting Numbers: [31, 35]\nGenerated Node #3: [31, 35] from Operation: 75-40=35\nCurrent State: 66:[31, 35], Operations: ['33-2=31', '75-40=35']\nExploring Operation: 31+35=66, Resulting Numbers: [66]\n66,66 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 49, + 89, + 40, + 32 + ], + "target": 31, + "solution": [ + "89-49=40", + "40/40=1", + "32-1=31" + ], + "optimal_path": "Current State: 31:[49, 89, 40, 32], Operations: []\nExploring Operation: 89-49=40, Resulting Numbers: [40, 32, 40]\nGenerated Node #2: [40, 32, 40] from Operation: 89-49=40\nCurrent State: 31:[40, 32, 40], Operations: ['89-49=40']\nExploring Operation: 40/40=1, Resulting Numbers: [32, 1]\nGenerated Node #3: [32, 1] from Operation: 40/40=1\nCurrent State: 31:[32, 1], Operations: ['89-49=40', '40/40=1']\nExploring Operation: 32-1=31, Resulting Numbers: [31]\n31,31 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 65, + 69, + 29, + 66 + ], + "target": 40, + "solution": [ + "66-65=1", + "69-29=40", + "1*40=40" + ], + "optimal_path": "Current State: 40:[65, 69, 29, 66], Operations: []\nExploring Operation: 66-65=1, Resulting Numbers: [69, 29, 1]\nGenerated Node #2: [69, 29, 1] from Operation: 66-65=1\nCurrent State: 40:[69, 29, 1], Operations: ['66-65=1']\nExploring Operation: 69-29=40, Resulting Numbers: [1, 40]\nGenerated Node #3: [1, 40] from Operation: 69-29=40\nCurrent State: 40:[1, 40], Operations: ['66-65=1', '69-29=40']\nExploring Operation: 1*40=40, Resulting Numbers: [40]\n40,40 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 35, + 1, + 45, + 76 + ], + "target": 65, + "solution": [ + "35-1=34", + "76-45=31", + "34+31=65" + ], + "optimal_path": "Current State: 65:[35, 1, 45, 76], Operations: []\nExploring Operation: 35-1=34, Resulting Numbers: [45, 76, 34]\nGenerated Node #2: [45, 76, 34] from Operation: 35-1=34\nCurrent State: 65:[45, 76, 34], Operations: ['35-1=34']\nExploring Operation: 76-45=31, Resulting Numbers: [34, 31]\nGenerated Node #3: [34, 31] from Operation: 76-45=31\nCurrent State: 65:[34, 31], Operations: ['35-1=34', '76-45=31']\nExploring Operation: 34+31=65, Resulting Numbers: [65]\n65,65 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 12, + 98, + 41, + 65 + ], + "target": 49, + "solution": [ + "12*98=1176", + "65-41=24", + "1176/24=49" + ], + "optimal_path": "Current State: 49:[12, 98, 41, 65], Operations: []\nExploring Operation: 12*98=1176, Resulting Numbers: [41, 65, 1176]\nGenerated Node #2: [41, 65, 1176] from Operation: 12*98=1176\nCurrent State: 49:[41, 65, 1176], Operations: ['12*98=1176']\nExploring Operation: 65-41=24, Resulting Numbers: [1176, 24]\nGenerated Node #3: [1176, 24] from Operation: 65-41=24\nCurrent State: 49:[1176, 24], Operations: ['12*98=1176', '65-41=24']\nExploring Operation: 1176/24=49, Resulting Numbers: [49]\n49,49 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 98, + 29, + 14, + 37 + ], + "target": 46, + "solution": [ + "98-29=69", + "37-14=23", + "69-23=46" + ], + "optimal_path": "Current State: 46:[98, 29, 14, 37], Operations: []\nExploring Operation: 98-29=69, Resulting Numbers: [14, 37, 69]\nGenerated Node #2: [14, 37, 69] from Operation: 98-29=69\nCurrent State: 46:[14, 37, 69], Operations: ['98-29=69']\nExploring Operation: 37-14=23, Resulting Numbers: [69, 23]\nGenerated Node #3: [69, 23] from Operation: 37-14=23\nCurrent State: 46:[69, 23], Operations: ['98-29=69', '37-14=23']\nExploring Operation: 69-23=46, Resulting Numbers: [46]\n46,46 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 24, + 3, + 4, + 96 + ], + "target": 32, + "solution": [ + "24/3=8", + "96/4=24", + "8+24=32" + ], + "optimal_path": "Current State: 32:[24, 3, 4, 96], Operations: []\nExploring Operation: 24/3=8, Resulting Numbers: [4, 96, 8]\nGenerated Node #2: [4, 96, 8] from Operation: 24/3=8\nCurrent State: 32:[4, 96, 8], Operations: ['24/3=8']\nExploring Operation: 96/4=24, Resulting Numbers: [8, 24]\nGenerated Node #3: [8, 24] from Operation: 96/4=24\nCurrent State: 32:[8, 24], Operations: ['24/3=8', '96/4=24']\nExploring Operation: 8+24=32, Resulting Numbers: [32]\n32,32 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 30, + 93, + 26, + 88 + ], + "target": 20, + "solution": [ + "30-26=4", + "93-88=5", + "4*5=20" + ], + "optimal_path": "Current State: 20:[30, 93, 26, 88], Operations: []\nExploring Operation: 30-26=4, Resulting Numbers: [93, 88, 4]\nGenerated Node #2: [93, 88, 4] from Operation: 30-26=4\nCurrent State: 20:[93, 88, 4], Operations: ['30-26=4']\nExploring Operation: 93-88=5, Resulting Numbers: [4, 5]\nGenerated Node #3: [4, 5] from Operation: 93-88=5\nCurrent State: 20:[4, 5], Operations: ['30-26=4', '93-88=5']\nExploring Operation: 4*5=20, Resulting Numbers: [20]\n20,20 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 13, + 51, + 53, + 68 + ], + "target": 83, + "solution": [ + "51-13=38", + "53+68=121", + "121-38=83" + ], + "optimal_path": "Current State: 83:[13, 51, 53, 68], Operations: []\nExploring Operation: 51-13=38, Resulting Numbers: [53, 68, 38]\nGenerated Node #2: [53, 68, 38] from Operation: 51-13=38\nCurrent State: 83:[53, 68, 38], Operations: ['51-13=38']\nExploring Operation: 53+68=121, Resulting Numbers: [38, 121]\nGenerated Node #3: [38, 121] from Operation: 53+68=121\nCurrent State: 83:[38, 121], Operations: ['51-13=38', '53+68=121']\nExploring Operation: 121-38=83, Resulting Numbers: [83]\n83,83 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 86, + 4, + 24, + 92 + ], + "target": 36, + "solution": [ + "92-86=6", + "24/4=6", + "6*6=36" + ], + "optimal_path": "Current State: 36:[86, 4, 24, 92], Operations: []\nExploring Operation: 92-86=6, Resulting Numbers: [4, 24, 6]\nGenerated Node #2: [4, 24, 6] from Operation: 92-86=6\nCurrent State: 36:[4, 24, 6], Operations: ['92-86=6']\nExploring Operation: 24/4=6, Resulting Numbers: [6, 6]\nGenerated Node #3: [6, 6] from Operation: 24/4=6\nCurrent State: 36:[6, 6], Operations: ['92-86=6', '24/4=6']\nExploring Operation: 6*6=36, Resulting Numbers: [36]\n36,36 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 40, + 36, + 20, + 92 + ], + "target": 80, + "solution": [ + "92-20=72", + "40*72=2880", + "2880/36=80" + ], + "optimal_path": "Current State: 80:[40, 36, 20, 92], Operations: []\nExploring Operation: 92-20=72, Resulting Numbers: [40, 36, 72]\nGenerated Node #2: [40, 36, 72] from Operation: 92-20=72\nCurrent State: 80:[40, 36, 72], Operations: ['92-20=72']\nExploring Operation: 40*72=2880, Resulting Numbers: [36, 2880]\nGenerated Node #3: [36, 2880] from Operation: 40*72=2880\nCurrent State: 80:[36, 2880], Operations: ['92-20=72', '40*72=2880']\nExploring Operation: 2880/36=80, Resulting Numbers: [80]\n80,80 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 39, + 39, + 54, + 53 + ], + "target": 78, + "solution": [ + "39+39=78", + "54-53=1", + "78*1=78" + ], + "optimal_path": "Current State: 78:[39, 39, 54, 53], Operations: []\nExploring Operation: 39+39=78, Resulting Numbers: [54, 53, 78]\nGenerated Node #2: [54, 53, 78] from Operation: 39+39=78\nCurrent State: 78:[54, 53, 78], Operations: ['39+39=78']\nExploring Operation: 54-53=1, Resulting Numbers: [78, 1]\nGenerated Node #3: [78, 1] from Operation: 54-53=1\nCurrent State: 78:[78, 1], Operations: ['39+39=78', '54-53=1']\nExploring Operation: 78*1=78, Resulting Numbers: [78]\n78,78 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 21, + 20, + 47, + 30 + ], + "target": 16, + "solution": [ + "21-20=1", + "47-30=17", + "17-1=16" + ], + "optimal_path": "Current State: 16:[21, 20, 47, 30], Operations: []\nExploring Operation: 21-20=1, Resulting Numbers: [47, 30, 1]\nGenerated Node #2: [47, 30, 1] from Operation: 21-20=1\nCurrent State: 16:[47, 30, 1], Operations: ['21-20=1']\nExploring Operation: 47-30=17, Resulting Numbers: [1, 17]\nGenerated Node #3: [1, 17] from Operation: 47-30=17\nCurrent State: 16:[1, 17], Operations: ['21-20=1', '47-30=17']\nExploring Operation: 17-1=16, Resulting Numbers: [16]\n16,16 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 33, + 80, + 32, + 69 + ], + "target": 76, + "solution": [ + "33+80=113", + "69-32=37", + "113-37=76" + ], + "optimal_path": "Current State: 76:[33, 80, 32, 69], Operations: []\nExploring Operation: 33+80=113, Resulting Numbers: [32, 69, 113]\nGenerated Node #2: [32, 69, 113] from Operation: 33+80=113\nCurrent State: 76:[32, 69, 113], Operations: ['33+80=113']\nExploring Operation: 69-32=37, Resulting Numbers: [113, 37]\nGenerated Node #3: [113, 37] from Operation: 69-32=37\nCurrent State: 76:[113, 37], Operations: ['33+80=113', '69-32=37']\nExploring Operation: 113-37=76, Resulting Numbers: [76]\n76,76 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 69, + 63, + 92, + 5 + ], + "target": 89, + "solution": [ + "63*92=5796", + "5796/69=84", + "5+84=89" + ], + "optimal_path": "Current State: 89:[69, 63, 92, 5], Operations: []\nExploring Operation: 63*92=5796, Resulting Numbers: [69, 5, 5796]\nGenerated Node #2: [69, 5, 5796] from Operation: 63*92=5796\nCurrent State: 89:[69, 5, 5796], Operations: ['63*92=5796']\nExploring Operation: 5796/69=84, Resulting Numbers: [5, 84]\nGenerated Node #3: [5, 84] from Operation: 5796/69=84\nCurrent State: 89:[5, 84], Operations: ['63*92=5796', '5796/69=84']\nExploring Operation: 5+84=89, Resulting Numbers: [89]\n89,89 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 76, + 44, + 85, + 95 + ], + "target": 60, + "solution": [ + "76+44=120", + "85+95=180", + "180-120=60" + ], + "optimal_path": "Current State: 60:[76, 44, 85, 95], Operations: []\nExploring Operation: 76+44=120, Resulting Numbers: [85, 95, 120]\nGenerated Node #2: [85, 95, 120] from Operation: 76+44=120\nCurrent State: 60:[85, 95, 120], Operations: ['76+44=120']\nExploring Operation: 85+95=180, Resulting Numbers: [120, 180]\nGenerated Node #3: [120, 180] from Operation: 85+95=180\nCurrent State: 60:[120, 180], Operations: ['76+44=120', '85+95=180']\nExploring Operation: 180-120=60, Resulting Numbers: [60]\n60,60 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 18, + 96, + 14, + 36 + ], + "target": 56, + "solution": [ + "96-18=78", + "36-14=22", + "78-22=56" + ], + "optimal_path": "Current State: 56:[18, 96, 14, 36], Operations: []\nExploring Operation: 96-18=78, Resulting Numbers: [14, 36, 78]\nGenerated Node #2: [14, 36, 78] from Operation: 96-18=78\nCurrent State: 56:[14, 36, 78], Operations: ['96-18=78']\nExploring Operation: 36-14=22, Resulting Numbers: [78, 22]\nGenerated Node #3: [78, 22] from Operation: 36-14=22\nCurrent State: 56:[78, 22], Operations: ['96-18=78', '36-14=22']\nExploring Operation: 78-22=56, Resulting Numbers: [56]\n56,56 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 18, + 6, + 88, + 5 + ], + "target": 96, + "solution": [ + "18/6=3", + "88+5=93", + "3+93=96" + ], + "optimal_path": "Current State: 96:[18, 6, 88, 5], Operations: []\nExploring Operation: 18/6=3, Resulting Numbers: [88, 5, 3]\nGenerated Node #2: [88, 5, 3] from Operation: 18/6=3\nCurrent State: 96:[88, 5, 3], Operations: ['18/6=3']\nExploring Operation: 88+5=93, Resulting Numbers: [3, 93]\nGenerated Node #3: [3, 93] from Operation: 88+5=93\nCurrent State: 96:[3, 93], Operations: ['18/6=3', '88+5=93']\nExploring Operation: 3+93=96, Resulting Numbers: [96]\n96,96 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 2, + 84, + 40, + 16 + ], + "target": 90, + "solution": [ + "84+16=100", + "100/2=50", + "40+50=90" + ], + "optimal_path": "Current State: 90:[2, 84, 40, 16], Operations: []\nExploring Operation: 84+16=100, Resulting Numbers: [2, 40, 100]\nGenerated Node #2: [2, 40, 100] from Operation: 84+16=100\nCurrent State: 90:[2, 40, 100], Operations: ['84+16=100']\nExploring Operation: 100/2=50, Resulting Numbers: [40, 50]\nGenerated Node #3: [40, 50] from Operation: 100/2=50\nCurrent State: 90:[40, 50], Operations: ['84+16=100', '100/2=50']\nExploring Operation: 40+50=90, Resulting Numbers: [90]\n90,90 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 40, + 42, + 85, + 63 + ], + "target": 74, + "solution": [ + "42-40=2", + "85+63=148", + "148/2=74" + ], + "optimal_path": "Current State: 74:[40, 42, 85, 63], Operations: []\nExploring Operation: 42-40=2, Resulting Numbers: [85, 63, 2]\nGenerated Node #2: [85, 63, 2] from Operation: 42-40=2\nCurrent State: 74:[85, 63, 2], Operations: ['42-40=2']\nExploring Operation: 85+63=148, Resulting Numbers: [2, 148]\nGenerated Node #3: [2, 148] from Operation: 85+63=148\nCurrent State: 74:[2, 148], Operations: ['42-40=2', '85+63=148']\nExploring Operation: 148/2=74, Resulting Numbers: [74]\n74,74 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 96, + 4, + 85, + 90 + ], + "target": 95, + "solution": [ + "96+4=100", + "90-85=5", + "100-5=95" + ], + "optimal_path": "Current State: 95:[96, 4, 85, 90], Operations: []\nExploring Operation: 96+4=100, Resulting Numbers: [85, 90, 100]\nGenerated Node #2: [85, 90, 100] from Operation: 96+4=100\nCurrent State: 95:[85, 90, 100], Operations: ['96+4=100']\nExploring Operation: 90-85=5, Resulting Numbers: [100, 5]\nGenerated Node #3: [100, 5] from Operation: 90-85=5\nCurrent State: 95:[100, 5], Operations: ['96+4=100', '90-85=5']\nExploring Operation: 100-5=95, Resulting Numbers: [95]\n95,95 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 90, + 32, + 5, + 23 + ], + "target": 30, + "solution": [ + "90-32=58", + "5+23=28", + "58-28=30" + ], + "optimal_path": "Current State: 30:[90, 32, 5, 23], Operations: []\nExploring Operation: 90-32=58, Resulting Numbers: [5, 23, 58]\nGenerated Node #2: [5, 23, 58] from Operation: 90-32=58\nCurrent State: 30:[5, 23, 58], Operations: ['90-32=58']\nExploring Operation: 5+23=28, Resulting Numbers: [58, 28]\nGenerated Node #3: [58, 28] from Operation: 5+23=28\nCurrent State: 30:[58, 28], Operations: ['90-32=58', '5+23=28']\nExploring Operation: 58-28=30, Resulting Numbers: [30]\n30,30 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 49, + 77, + 11, + 38 + ], + "target": 94, + "solution": [ + "49+38=87", + "77/11=7", + "87+7=94" + ], + "optimal_path": "Current State: 94:[49, 77, 11, 38], Operations: []\nExploring Operation: 49+38=87, Resulting Numbers: [77, 11, 87]\nGenerated Node #2: [77, 11, 87] from Operation: 49+38=87\nCurrent State: 94:[77, 11, 87], Operations: ['49+38=87']\nExploring Operation: 77/11=7, Resulting Numbers: [87, 7]\nGenerated Node #3: [87, 7] from Operation: 77/11=7\nCurrent State: 94:[87, 7], Operations: ['49+38=87', '77/11=7']\nExploring Operation: 87+7=94, Resulting Numbers: [94]\n94,94 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 36, + 31, + 43, + 33 + ], + "target": 98, + "solution": [ + "36-33=3", + "43*3=129", + "129-31=98" + ], + "optimal_path": "Current State: 98:[36, 31, 43, 33], Operations: []\nExploring Operation: 36-33=3, Resulting Numbers: [31, 43, 3]\nGenerated Node #2: [31, 43, 3] from Operation: 36-33=3\nCurrent State: 98:[31, 43, 3], Operations: ['36-33=3']\nExploring Operation: 43*3=129, Resulting Numbers: [31, 129]\nGenerated Node #3: [31, 129] from Operation: 43*3=129\nCurrent State: 98:[31, 129], Operations: ['36-33=3', '43*3=129']\nExploring Operation: 129-31=98, Resulting Numbers: [98]\n98,98 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 28, + 10, + 23, + 17 + ], + "target": 67, + "solution": [ + "28-23=5", + "10*5=50", + "17+50=67" + ], + "optimal_path": "Current State: 67:[28, 10, 23, 17], Operations: []\nExploring Operation: 28-23=5, Resulting Numbers: [10, 17, 5]\nGenerated Node #2: [10, 17, 5] from Operation: 28-23=5\nCurrent State: 67:[10, 17, 5], Operations: ['28-23=5']\nExploring Operation: 10*5=50, Resulting Numbers: [17, 50]\nGenerated Node #3: [17, 50] from Operation: 10*5=50\nCurrent State: 67:[17, 50], Operations: ['28-23=5', '10*5=50']\nExploring Operation: 17+50=67, Resulting Numbers: [67]\n67,67 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 81, + 70, + 49, + 81 + ], + "target": 43, + "solution": [ + "81-70=11", + "81-49=32", + "11+32=43" + ], + "optimal_path": "Current State: 43:[81, 70, 49, 81], Operations: []\nExploring Operation: 81-70=11, Resulting Numbers: [49, 11]\nGenerated Node #2: [49, 11] from Operation: 81-70=11\nCurrent State: 43:[49, 11], Operations: ['81-70=11']\nExploring Operation: 81-49=32, Resulting Numbers: [11, 32]\nGenerated Node #3: [11, 32] from Operation: 81-49=32\nCurrent State: 43:[11, 32], Operations: ['81-70=11', '81-49=32']\nExploring Operation: 11+32=43, Resulting Numbers: [43]\n43,43 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 10, + 3, + 4, + 9 + ], + "target": 46, + "solution": [ + "10*4=40", + "9-3=6", + "40+6=46" + ], + "optimal_path": "Current State: 46:[10, 3, 4, 9], Operations: []\nExploring Operation: 10*4=40, Resulting Numbers: [3, 9, 40]\nGenerated Node #2: [3, 9, 40] from Operation: 10*4=40\nCurrent State: 46:[3, 9, 40], Operations: ['10*4=40']\nExploring Operation: 9-3=6, Resulting Numbers: [40, 6]\nGenerated Node #3: [40, 6] from Operation: 9-3=6\nCurrent State: 46:[40, 6], Operations: ['10*4=40', '9-3=6']\nExploring Operation: 40+6=46, Resulting Numbers: [46]\n46,46 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 55, + 61, + 18, + 6 + ], + "target": 19, + "solution": [ + "61-55=6", + "6/6=1", + "18+1=19" + ], + "optimal_path": "Current State: 19:[55, 61, 18, 6], Operations: []\nExploring Operation: 61-55=6, Resulting Numbers: [18, 6, 6]\nGenerated Node #2: [18, 6, 6] from Operation: 61-55=6\nCurrent State: 19:[18, 6, 6], Operations: ['61-55=6']\nExploring Operation: 6/6=1, Resulting Numbers: [18, 1]\nGenerated Node #3: [18, 1] from Operation: 6/6=1\nCurrent State: 19:[18, 1], Operations: ['61-55=6', '6/6=1']\nExploring Operation: 18+1=19, Resulting Numbers: [19]\n19,19 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 55, + 8, + 15, + 46 + ], + "target": 48, + "solution": [ + "55-15=40", + "46-40=6", + "8*6=48" + ], + "optimal_path": "Current State: 48:[55, 8, 15, 46], Operations: []\nExploring Operation: 55-15=40, Resulting Numbers: [8, 46, 40]\nGenerated Node #2: [8, 46, 40] from Operation: 55-15=40\nCurrent State: 48:[8, 46, 40], Operations: ['55-15=40']\nExploring Operation: 46-40=6, Resulting Numbers: [8, 6]\nGenerated Node #3: [8, 6] from Operation: 46-40=6\nCurrent State: 48:[8, 6], Operations: ['55-15=40', '46-40=6']\nExploring Operation: 8*6=48, Resulting Numbers: [48]\n48,48 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 46, + 88, + 64, + 55 + ], + "target": 15, + "solution": [ + "46+88=134", + "64+55=119", + "134-119=15" + ], + "optimal_path": "Current State: 15:[46, 88, 64, 55], Operations: []\nExploring Operation: 46+88=134, Resulting Numbers: [64, 55, 134]\nGenerated Node #2: [64, 55, 134] from Operation: 46+88=134\nCurrent State: 15:[64, 55, 134], Operations: ['46+88=134']\nExploring Operation: 64+55=119, Resulting Numbers: [134, 119]\nGenerated Node #3: [134, 119] from Operation: 64+55=119\nCurrent State: 15:[134, 119], Operations: ['46+88=134', '64+55=119']\nExploring Operation: 134-119=15, Resulting Numbers: [15]\n15,15 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 26, + 69, + 87, + 34 + ], + "target": 10, + "solution": [ + "69-26=43", + "87-34=53", + "53-43=10" + ], + "optimal_path": "Current State: 10:[26, 69, 87, 34], Operations: []\nExploring Operation: 69-26=43, Resulting Numbers: [87, 34, 43]\nGenerated Node #2: [87, 34, 43] from Operation: 69-26=43\nCurrent State: 10:[87, 34, 43], Operations: ['69-26=43']\nExploring Operation: 87-34=53, Resulting Numbers: [43, 53]\nGenerated Node #3: [43, 53] from Operation: 87-34=53\nCurrent State: 10:[43, 53], Operations: ['69-26=43', '87-34=53']\nExploring Operation: 53-43=10, Resulting Numbers: [10]\n10,10 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 81, + 28, + 6, + 58 + ], + "target": 45, + "solution": [ + "81+28=109", + "6+58=64", + "109-64=45" + ], + "optimal_path": "Current State: 45:[81, 28, 6, 58], Operations: []\nExploring Operation: 81+28=109, Resulting Numbers: [6, 58, 109]\nGenerated Node #2: [6, 58, 109] from Operation: 81+28=109\nCurrent State: 45:[6, 58, 109], Operations: ['81+28=109']\nExploring Operation: 6+58=64, Resulting Numbers: [109, 64]\nGenerated Node #3: [109, 64] from Operation: 6+58=64\nCurrent State: 45:[109, 64], Operations: ['81+28=109', '6+58=64']\nExploring Operation: 109-64=45, Resulting Numbers: [45]\n45,45 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 76, + 5, + 14, + 16 + ], + "target": 56, + "solution": [ + "5*16=80", + "80-76=4", + "14*4=56" + ], + "optimal_path": "Current State: 56:[76, 5, 14, 16], Operations: []\nExploring Operation: 5*16=80, Resulting Numbers: [76, 14, 80]\nGenerated Node #2: [76, 14, 80] from Operation: 5*16=80\nCurrent State: 56:[76, 14, 80], Operations: ['5*16=80']\nExploring Operation: 80-76=4, Resulting Numbers: [14, 4]\nGenerated Node #3: [14, 4] from Operation: 80-76=4\nCurrent State: 56:[14, 4], Operations: ['5*16=80', '80-76=4']\nExploring Operation: 14*4=56, Resulting Numbers: [56]\n56,56 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 5, + 75, + 9, + 95 + ], + "target": 36, + "solution": [ + "95-75=20", + "20/5=4", + "9*4=36" + ], + "optimal_path": "Current State: 36:[5, 75, 9, 95], Operations: []\nExploring Operation: 95-75=20, Resulting Numbers: [5, 9, 20]\nGenerated Node #2: [5, 9, 20] from Operation: 95-75=20\nCurrent State: 36:[5, 9, 20], Operations: ['95-75=20']\nExploring Operation: 20/5=4, Resulting Numbers: [9, 4]\nGenerated Node #3: [9, 4] from Operation: 20/5=4\nCurrent State: 36:[9, 4], Operations: ['95-75=20', '20/5=4']\nExploring Operation: 9*4=36, Resulting Numbers: [36]\n36,36 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 61, + 3, + 98, + 80 + ], + "target": 31, + "solution": [ + "98-61=37", + "3*37=111", + "111-80=31" + ], + "optimal_path": "Current State: 31:[61, 3, 98, 80], Operations: []\nExploring Operation: 98-61=37, Resulting Numbers: [3, 80, 37]\nGenerated Node #2: [3, 80, 37] from Operation: 98-61=37\nCurrent State: 31:[3, 80, 37], Operations: ['98-61=37']\nExploring Operation: 3*37=111, Resulting Numbers: [80, 111]\nGenerated Node #3: [80, 111] from Operation: 3*37=111\nCurrent State: 31:[80, 111], Operations: ['98-61=37', '3*37=111']\nExploring Operation: 111-80=31, Resulting Numbers: [31]\n31,31 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 81, + 73, + 99, + 22 + ], + "target": 85, + "solution": [ + "81-73=8", + "99-22=77", + "8+77=85" + ], + "optimal_path": "Current State: 85:[81, 73, 99, 22], Operations: []\nExploring Operation: 81-73=8, Resulting Numbers: [99, 22, 8]\nGenerated Node #2: [99, 22, 8] from Operation: 81-73=8\nCurrent State: 85:[99, 22, 8], Operations: ['81-73=8']\nExploring Operation: 99-22=77, Resulting Numbers: [8, 77]\nGenerated Node #3: [8, 77] from Operation: 99-22=77\nCurrent State: 85:[8, 77], Operations: ['81-73=8', '99-22=77']\nExploring Operation: 8+77=85, Resulting Numbers: [85]\n85,85 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 98, + 99, + 22, + 77 + ], + "target": 97, + "solution": [ + "99-22=77", + "77/77=1", + "98-1=97" + ], + "optimal_path": "Current State: 97:[98, 99, 22, 77], Operations: []\nExploring Operation: 99-22=77, Resulting Numbers: [98, 77, 77]\nGenerated Node #2: [98, 77, 77] from Operation: 99-22=77\nCurrent State: 97:[98, 77, 77], Operations: ['99-22=77']\nExploring Operation: 77/77=1, Resulting Numbers: [98, 1]\nGenerated Node #3: [98, 1] from Operation: 77/77=1\nCurrent State: 97:[98, 1], Operations: ['99-22=77', '77/77=1']\nExploring Operation: 98-1=97, Resulting Numbers: [97]\n97,97 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 11, + 18, + 70, + 16 + ], + "target": 92, + "solution": [ + "18-16=2", + "11*2=22", + "70+22=92" + ], + "optimal_path": "Current State: 92:[11, 18, 70, 16], Operations: []\nExploring Operation: 18-16=2, Resulting Numbers: [11, 70, 2]\nGenerated Node #2: [11, 70, 2] from Operation: 18-16=2\nCurrent State: 92:[11, 70, 2], Operations: ['18-16=2']\nExploring Operation: 11*2=22, Resulting Numbers: [70, 22]\nGenerated Node #3: [70, 22] from Operation: 11*2=22\nCurrent State: 92:[70, 22], Operations: ['18-16=2', '11*2=22']\nExploring Operation: 70+22=92, Resulting Numbers: [92]\n92,92 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 95, + 49, + 71, + 69 + ], + "target": 48, + "solution": [ + "95-49=46", + "71-69=2", + "46+2=48" + ], + "optimal_path": "Current State: 48:[95, 49, 71, 69], Operations: []\nExploring Operation: 95-49=46, Resulting Numbers: [71, 69, 46]\nGenerated Node #2: [71, 69, 46] from Operation: 95-49=46\nCurrent State: 48:[71, 69, 46], Operations: ['95-49=46']\nExploring Operation: 71-69=2, Resulting Numbers: [46, 2]\nGenerated Node #3: [46, 2] from Operation: 71-69=2\nCurrent State: 48:[46, 2], Operations: ['95-49=46', '71-69=2']\nExploring Operation: 46+2=48, Resulting Numbers: [48]\n48,48 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 14, + 25, + 43, + 2 + ], + "target": 89, + "solution": [ + "14+43=57", + "2*57=114", + "114-25=89" + ], + "optimal_path": "Current State: 89:[14, 25, 43, 2], Operations: []\nExploring Operation: 14+43=57, Resulting Numbers: [25, 2, 57]\nGenerated Node #2: [25, 2, 57] from Operation: 14+43=57\nCurrent State: 89:[25, 2, 57], Operations: ['14+43=57']\nExploring Operation: 2*57=114, Resulting Numbers: [25, 114]\nGenerated Node #3: [25, 114] from Operation: 2*57=114\nCurrent State: 89:[25, 114], Operations: ['14+43=57', '2*57=114']\nExploring Operation: 114-25=89, Resulting Numbers: [89]\n89,89 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 64, + 16, + 44, + 52 + ], + "target": 66, + "solution": [ + "52-44=8", + "16/8=2", + "64+2=66" + ], + "optimal_path": "Current State: 66:[64, 16, 44, 52], Operations: []\nExploring Operation: 52-44=8, Resulting Numbers: [64, 16, 8]\nGenerated Node #2: [64, 16, 8] from Operation: 52-44=8\nCurrent State: 66:[64, 16, 8], Operations: ['52-44=8']\nExploring Operation: 16/8=2, Resulting Numbers: [64, 2]\nGenerated Node #3: [64, 2] from Operation: 16/8=2\nCurrent State: 66:[64, 2], Operations: ['52-44=8', '16/8=2']\nExploring Operation: 64+2=66, Resulting Numbers: [66]\n66,66 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 1, + 29, + 65, + 59 + ], + "target": 94, + "solution": [ + "1+29=30", + "65+59=124", + "124-30=94" + ], + "optimal_path": "Current State: 94:[1, 29, 65, 59], Operations: []\nExploring Operation: 1+29=30, Resulting Numbers: [65, 59, 30]\nGenerated Node #2: [65, 59, 30] from Operation: 1+29=30\nCurrent State: 94:[65, 59, 30], Operations: ['1+29=30']\nExploring Operation: 65+59=124, Resulting Numbers: [30, 124]\nGenerated Node #3: [30, 124] from Operation: 65+59=124\nCurrent State: 94:[30, 124], Operations: ['1+29=30', '65+59=124']\nExploring Operation: 124-30=94, Resulting Numbers: [94]\n94,94 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 29, + 76, + 37, + 2 + ], + "target": 86, + "solution": [ + "76-29=47", + "37+2=39", + "47+39=86" + ], + "optimal_path": "Current State: 86:[29, 76, 37, 2], Operations: []\nExploring Operation: 76-29=47, Resulting Numbers: [37, 2, 47]\nGenerated Node #2: [37, 2, 47] from Operation: 76-29=47\nCurrent State: 86:[37, 2, 47], Operations: ['76-29=47']\nExploring Operation: 37+2=39, Resulting Numbers: [47, 39]\nGenerated Node #3: [47, 39] from Operation: 37+2=39\nCurrent State: 86:[47, 39], Operations: ['76-29=47', '37+2=39']\nExploring Operation: 47+39=86, Resulting Numbers: [86]\n86,86 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 11, + 94, + 13, + 52 + ], + "target": 50, + "solution": [ + "11*52=572", + "572/13=44", + "94-44=50" + ], + "optimal_path": "Current State: 50:[11, 94, 13, 52], Operations: []\nExploring Operation: 11*52=572, Resulting Numbers: [94, 13, 572]\nGenerated Node #2: [94, 13, 572] from Operation: 11*52=572\nCurrent State: 50:[94, 13, 572], Operations: ['11*52=572']\nExploring Operation: 572/13=44, Resulting Numbers: [94, 44]\nGenerated Node #3: [94, 44] from Operation: 572/13=44\nCurrent State: 50:[94, 44], Operations: ['11*52=572', '572/13=44']\nExploring Operation: 94-44=50, Resulting Numbers: [50]\n50,50 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 85, + 86, + 39, + 89 + ], + "target": 49, + "solution": [ + "86-85=1", + "89-39=50", + "50-1=49" + ], + "optimal_path": "Current State: 49:[85, 86, 39, 89], Operations: []\nExploring Operation: 86-85=1, Resulting Numbers: [39, 89, 1]\nGenerated Node #2: [39, 89, 1] from Operation: 86-85=1\nCurrent State: 49:[39, 89, 1], Operations: ['86-85=1']\nExploring Operation: 89-39=50, Resulting Numbers: [1, 50]\nGenerated Node #3: [1, 50] from Operation: 89-39=50\nCurrent State: 49:[1, 50], Operations: ['86-85=1', '89-39=50']\nExploring Operation: 50-1=49, Resulting Numbers: [49]\n49,49 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 33, + 76, + 51, + 3 + ], + "target": 14, + "solution": [ + "33/3=11", + "76-51=25", + "25-11=14" + ], + "optimal_path": "Current State: 14:[33, 76, 51, 3], Operations: []\nExploring Operation: 33/3=11, Resulting Numbers: [76, 51, 11]\nGenerated Node #2: [76, 51, 11] from Operation: 33/3=11\nCurrent State: 14:[76, 51, 11], Operations: ['33/3=11']\nExploring Operation: 76-51=25, Resulting Numbers: [11, 25]\nGenerated Node #3: [11, 25] from Operation: 76-51=25\nCurrent State: 14:[11, 25], Operations: ['33/3=11', '76-51=25']\nExploring Operation: 25-11=14, Resulting Numbers: [14]\n14,14 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 10, + 27, + 64, + 83 + ], + "target": 56, + "solution": [ + "10+27=37", + "83-64=19", + "37+19=56" + ], + "optimal_path": "Current State: 56:[10, 27, 64, 83], Operations: []\nExploring Operation: 10+27=37, Resulting Numbers: [64, 83, 37]\nGenerated Node #2: [64, 83, 37] from Operation: 10+27=37\nCurrent State: 56:[64, 83, 37], Operations: ['10+27=37']\nExploring Operation: 83-64=19, Resulting Numbers: [37, 19]\nGenerated Node #3: [37, 19] from Operation: 83-64=19\nCurrent State: 56:[37, 19], Operations: ['10+27=37', '83-64=19']\nExploring Operation: 37+19=56, Resulting Numbers: [56]\n56,56 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 16, + 84, + 1, + 34 + ], + "target": 35, + "solution": [ + "84-16=68", + "34-1=33", + "68-33=35" + ], + "optimal_path": "Current State: 35:[16, 84, 1, 34], Operations: []\nExploring Operation: 84-16=68, Resulting Numbers: [1, 34, 68]\nGenerated Node #2: [1, 34, 68] from Operation: 84-16=68\nCurrent State: 35:[1, 34, 68], Operations: ['84-16=68']\nExploring Operation: 34-1=33, Resulting Numbers: [68, 33]\nGenerated Node #3: [68, 33] from Operation: 34-1=33\nCurrent State: 35:[68, 33], Operations: ['84-16=68', '34-1=33']\nExploring Operation: 68-33=35, Resulting Numbers: [35]\n35,35 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 7, + 46, + 4, + 35 + ], + "target": 84, + "solution": [ + "7+46=53", + "35-4=31", + "53+31=84" + ], + "optimal_path": "Current State: 84:[7, 46, 4, 35], Operations: []\nExploring Operation: 7+46=53, Resulting Numbers: [4, 35, 53]\nGenerated Node #2: [4, 35, 53] from Operation: 7+46=53\nCurrent State: 84:[4, 35, 53], Operations: ['7+46=53']\nExploring Operation: 35-4=31, Resulting Numbers: [53, 31]\nGenerated Node #3: [53, 31] from Operation: 35-4=31\nCurrent State: 84:[53, 31], Operations: ['7+46=53', '35-4=31']\nExploring Operation: 53+31=84, Resulting Numbers: [84]\n84,84 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 83, + 9, + 18, + 92 + ], + "target": 37, + "solution": [ + "18/9=2", + "92/2=46", + "83-46=37" + ], + "optimal_path": "Current State: 37:[83, 9, 18, 92], Operations: []\nExploring Operation: 18/9=2, Resulting Numbers: [83, 92, 2]\nGenerated Node #2: [83, 92, 2] from Operation: 18/9=2\nCurrent State: 37:[83, 92, 2], Operations: ['18/9=2']\nExploring Operation: 92/2=46, Resulting Numbers: [83, 46]\nGenerated Node #3: [83, 46] from Operation: 92/2=46\nCurrent State: 37:[83, 46], Operations: ['18/9=2', '92/2=46']\nExploring Operation: 83-46=37, Resulting Numbers: [37]\n37,37 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 63, + 70, + 34, + 27 + ], + "target": 54, + "solution": [ + "70-63=7", + "34+27=61", + "61-7=54" + ], + "optimal_path": "Current State: 54:[63, 70, 34, 27], Operations: []\nExploring Operation: 70-63=7, Resulting Numbers: [34, 27, 7]\nGenerated Node #2: [34, 27, 7] from Operation: 70-63=7\nCurrent State: 54:[34, 27, 7], Operations: ['70-63=7']\nExploring Operation: 34+27=61, Resulting Numbers: [7, 61]\nGenerated Node #3: [7, 61] from Operation: 34+27=61\nCurrent State: 54:[7, 61], Operations: ['70-63=7', '34+27=61']\nExploring Operation: 61-7=54, Resulting Numbers: [54]\n54,54 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 3, + 48, + 26, + 21 + ], + "target": 46, + "solution": [ + "3+48=51", + "26-21=5", + "51-5=46" + ], + "optimal_path": "Current State: 46:[3, 48, 26, 21], Operations: []\nExploring Operation: 3+48=51, Resulting Numbers: [26, 21, 51]\nGenerated Node #2: [26, 21, 51] from Operation: 3+48=51\nCurrent State: 46:[26, 21, 51], Operations: ['3+48=51']\nExploring Operation: 26-21=5, Resulting Numbers: [51, 5]\nGenerated Node #3: [51, 5] from Operation: 26-21=5\nCurrent State: 46:[51, 5], Operations: ['3+48=51', '26-21=5']\nExploring Operation: 51-5=46, Resulting Numbers: [46]\n46,46 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 2, + 6, + 19, + 15 + ], + "target": 42, + "solution": [ + "2+6=8", + "19+15=34", + "8+34=42" + ], + "optimal_path": "Current State: 42:[2, 6, 19, 15], Operations: []\nExploring Operation: 2+6=8, Resulting Numbers: [19, 15, 8]\nGenerated Node #2: [19, 15, 8] from Operation: 2+6=8\nCurrent State: 42:[19, 15, 8], Operations: ['2+6=8']\nExploring Operation: 19+15=34, Resulting Numbers: [8, 34]\nGenerated Node #3: [8, 34] from Operation: 19+15=34\nCurrent State: 42:[8, 34], Operations: ['2+6=8', '19+15=34']\nExploring Operation: 8+34=42, Resulting Numbers: [42]\n42,42 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 37, + 82, + 90, + 97 + ], + "target": 68, + "solution": [ + "37+82=119", + "90+97=187", + "187-119=68" + ], + "optimal_path": "Current State: 68:[37, 82, 90, 97], Operations: []\nExploring Operation: 37+82=119, Resulting Numbers: [90, 97, 119]\nGenerated Node #2: [90, 97, 119] from Operation: 37+82=119\nCurrent State: 68:[90, 97, 119], Operations: ['37+82=119']\nExploring Operation: 90+97=187, Resulting Numbers: [119, 187]\nGenerated Node #3: [119, 187] from Operation: 90+97=187\nCurrent State: 68:[119, 187], Operations: ['37+82=119', '90+97=187']\nExploring Operation: 187-119=68, Resulting Numbers: [68]\n68,68 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 36, + 2, + 92, + 86 + ], + "target": 33, + "solution": [ + "92-86=6", + "6/2=3", + "36-3=33" + ], + "optimal_path": "Current State: 33:[36, 2, 92, 86], Operations: []\nExploring Operation: 92-86=6, Resulting Numbers: [36, 2, 6]\nGenerated Node #2: [36, 2, 6] from Operation: 92-86=6\nCurrent State: 33:[36, 2, 6], Operations: ['92-86=6']\nExploring Operation: 6/2=3, Resulting Numbers: [36, 3]\nGenerated Node #3: [36, 3] from Operation: 6/2=3\nCurrent State: 33:[36, 3], Operations: ['92-86=6', '6/2=3']\nExploring Operation: 36-3=33, Resulting Numbers: [33]\n33,33 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 33, + 94, + 37, + 14 + ], + "target": 76, + "solution": [ + "33+94=127", + "37+14=51", + "127-51=76" + ], + "optimal_path": "Current State: 76:[33, 94, 37, 14], Operations: []\nExploring Operation: 33+94=127, Resulting Numbers: [37, 14, 127]\nGenerated Node #2: [37, 14, 127] from Operation: 33+94=127\nCurrent State: 76:[37, 14, 127], Operations: ['33+94=127']\nExploring Operation: 37+14=51, Resulting Numbers: [127, 51]\nGenerated Node #3: [127, 51] from Operation: 37+14=51\nCurrent State: 76:[127, 51], Operations: ['33+94=127', '37+14=51']\nExploring Operation: 127-51=76, Resulting Numbers: [76]\n76,76 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 47, + 56, + 63, + 4 + ], + "target": 58, + "solution": [ + "56-47=9", + "63+4=67", + "67-9=58" + ], + "optimal_path": "Current State: 58:[47, 56, 63, 4], Operations: []\nExploring Operation: 56-47=9, Resulting Numbers: [63, 4, 9]\nGenerated Node #2: [63, 4, 9] from Operation: 56-47=9\nCurrent State: 58:[63, 4, 9], Operations: ['56-47=9']\nExploring Operation: 63+4=67, Resulting Numbers: [9, 67]\nGenerated Node #3: [9, 67] from Operation: 63+4=67\nCurrent State: 58:[9, 67], Operations: ['56-47=9', '63+4=67']\nExploring Operation: 67-9=58, Resulting Numbers: [58]\n58,58 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 64, + 50, + 73, + 18 + ], + "target": 69, + "solution": [ + "64-50=14", + "73-18=55", + "14+55=69" + ], + "optimal_path": "Current State: 69:[64, 50, 73, 18], Operations: []\nExploring Operation: 64-50=14, Resulting Numbers: [73, 18, 14]\nGenerated Node #2: [73, 18, 14] from Operation: 64-50=14\nCurrent State: 69:[73, 18, 14], Operations: ['64-50=14']\nExploring Operation: 73-18=55, Resulting Numbers: [14, 55]\nGenerated Node #3: [14, 55] from Operation: 73-18=55\nCurrent State: 69:[14, 55], Operations: ['64-50=14', '73-18=55']\nExploring Operation: 14+55=69, Resulting Numbers: [69]\n69,69 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 23, + 16, + 96, + 53 + ], + "target": 85, + "solution": [ + "23*96=2208", + "2208/16=138", + "138-53=85" + ], + "optimal_path": "Current State: 85:[23, 16, 96, 53], Operations: []\nExploring Operation: 23*96=2208, Resulting Numbers: [16, 53, 2208]\nGenerated Node #2: [16, 53, 2208] from Operation: 23*96=2208\nCurrent State: 85:[16, 53, 2208], Operations: ['23*96=2208']\nExploring Operation: 2208/16=138, Resulting Numbers: [53, 138]\nGenerated Node #3: [53, 138] from Operation: 2208/16=138\nCurrent State: 85:[53, 138], Operations: ['23*96=2208', '2208/16=138']\nExploring Operation: 138-53=85, Resulting Numbers: [85]\n85,85 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 59, + 29, + 3, + 28 + ], + "target": 31, + "solution": [ + "59-3=56", + "56/28=2", + "29+2=31" + ], + "optimal_path": "Current State: 31:[59, 29, 3, 28], Operations: []\nExploring Operation: 59-3=56, Resulting Numbers: [29, 28, 56]\nGenerated Node #2: [29, 28, 56] from Operation: 59-3=56\nCurrent State: 31:[29, 28, 56], Operations: ['59-3=56']\nExploring Operation: 56/28=2, Resulting Numbers: [29, 2]\nGenerated Node #3: [29, 2] from Operation: 56/28=2\nCurrent State: 31:[29, 2], Operations: ['59-3=56', '56/28=2']\nExploring Operation: 29+2=31, Resulting Numbers: [31]\n31,31 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 39, + 3, + 19, + 13 + ], + "target": 60, + "solution": [ + "39*19=741", + "741/13=57", + "3+57=60" + ], + "optimal_path": "Current State: 60:[39, 3, 19, 13], Operations: []\nExploring Operation: 39*19=741, Resulting Numbers: [3, 13, 741]\nGenerated Node #2: [3, 13, 741] from Operation: 39*19=741\nCurrent State: 60:[3, 13, 741], Operations: ['39*19=741']\nExploring Operation: 741/13=57, Resulting Numbers: [3, 57]\nGenerated Node #3: [3, 57] from Operation: 741/13=57\nCurrent State: 60:[3, 57], Operations: ['39*19=741', '741/13=57']\nExploring Operation: 3+57=60, Resulting Numbers: [60]\n60,60 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 89, + 84, + 76, + 80 + ], + "target": 99, + "solution": [ + "84-76=8", + "80/8=10", + "89+10=99" + ], + "optimal_path": "Current State: 99:[89, 84, 76, 80], Operations: []\nExploring Operation: 84-76=8, Resulting Numbers: [89, 80, 8]\nGenerated Node #2: [89, 80, 8] from Operation: 84-76=8\nCurrent State: 99:[89, 80, 8], Operations: ['84-76=8']\nExploring Operation: 80/8=10, Resulting Numbers: [89, 10]\nGenerated Node #3: [89, 10] from Operation: 80/8=10\nCurrent State: 99:[89, 10], Operations: ['84-76=8', '80/8=10']\nExploring Operation: 89+10=99, Resulting Numbers: [99]\n99,99 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 50, + 25, + 90, + 46 + ], + "target": 61, + "solution": [ + "50+25=75", + "90+46=136", + "136-75=61" + ], + "optimal_path": "Current State: 61:[50, 25, 90, 46], Operations: []\nExploring Operation: 50+25=75, Resulting Numbers: [90, 46, 75]\nGenerated Node #2: [90, 46, 75] from Operation: 50+25=75\nCurrent State: 61:[90, 46, 75], Operations: ['50+25=75']\nExploring Operation: 90+46=136, Resulting Numbers: [75, 136]\nGenerated Node #3: [75, 136] from Operation: 90+46=136\nCurrent State: 61:[75, 136], Operations: ['50+25=75', '90+46=136']\nExploring Operation: 136-75=61, Resulting Numbers: [61]\n61,61 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 19, + 41, + 60, + 20 + ], + "target": 30, + "solution": [ + "41-19=22", + "22-20=2", + "60/2=30" + ], + "optimal_path": "Current State: 30:[19, 41, 60, 20], Operations: []\nExploring Operation: 41-19=22, Resulting Numbers: [60, 20, 22]\nGenerated Node #2: [60, 20, 22] from Operation: 41-19=22\nCurrent State: 30:[60, 20, 22], Operations: ['41-19=22']\nExploring Operation: 22-20=2, Resulting Numbers: [60, 2]\nGenerated Node #3: [60, 2] from Operation: 22-20=2\nCurrent State: 30:[60, 2], Operations: ['41-19=22', '22-20=2']\nExploring Operation: 60/2=30, Resulting Numbers: [30]\n30,30 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 73, + 28, + 3, + 48 + ], + "target": 47, + "solution": [ + "73-48=25", + "3*25=75", + "75-28=47" + ], + "optimal_path": "Current State: 47:[73, 28, 3, 48], Operations: []\nExploring Operation: 73-48=25, Resulting Numbers: [28, 3, 25]\nGenerated Node #2: [28, 3, 25] from Operation: 73-48=25\nCurrent State: 47:[28, 3, 25], Operations: ['73-48=25']\nExploring Operation: 3*25=75, Resulting Numbers: [28, 75]\nGenerated Node #3: [28, 75] from Operation: 3*25=75\nCurrent State: 47:[28, 75], Operations: ['73-48=25', '3*25=75']\nExploring Operation: 75-28=47, Resulting Numbers: [47]\n47,47 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 95, + 97, + 42, + 28 + ], + "target": 35, + "solution": [ + "97-95=2", + "42+28=70", + "70/2=35" + ], + "optimal_path": "Current State: 35:[95, 97, 42, 28], Operations: []\nExploring Operation: 97-95=2, Resulting Numbers: [42, 28, 2]\nGenerated Node #2: [42, 28, 2] from Operation: 97-95=2\nCurrent State: 35:[42, 28, 2], Operations: ['97-95=2']\nExploring Operation: 42+28=70, Resulting Numbers: [2, 70]\nGenerated Node #3: [2, 70] from Operation: 42+28=70\nCurrent State: 35:[2, 70], Operations: ['97-95=2', '42+28=70']\nExploring Operation: 70/2=35, Resulting Numbers: [35]\n35,35 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 9, + 99, + 27, + 63 + ], + "target": 67, + "solution": [ + "9+99=108", + "108/27=4", + "63+4=67" + ], + "optimal_path": "Current State: 67:[9, 99, 27, 63], Operations: []\nExploring Operation: 9+99=108, Resulting Numbers: [27, 63, 108]\nGenerated Node #2: [27, 63, 108] from Operation: 9+99=108\nCurrent State: 67:[27, 63, 108], Operations: ['9+99=108']\nExploring Operation: 108/27=4, Resulting Numbers: [63, 4]\nGenerated Node #3: [63, 4] from Operation: 108/27=4\nCurrent State: 67:[63, 4], Operations: ['9+99=108', '108/27=4']\nExploring Operation: 63+4=67, Resulting Numbers: [67]\n67,67 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 52, + 44, + 75, + 77 + ], + "target": 41, + "solution": [ + "77-52=25", + "75/25=3", + "44-3=41" + ], + "optimal_path": "Current State: 41:[52, 44, 75, 77], Operations: []\nExploring Operation: 77-52=25, Resulting Numbers: [44, 75, 25]\nGenerated Node #2: [44, 75, 25] from Operation: 77-52=25\nCurrent State: 41:[44, 75, 25], Operations: ['77-52=25']\nExploring Operation: 75/25=3, Resulting Numbers: [44, 3]\nGenerated Node #3: [44, 3] from Operation: 75/25=3\nCurrent State: 41:[44, 3], Operations: ['77-52=25', '75/25=3']\nExploring Operation: 44-3=41, Resulting Numbers: [41]\n41,41 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 44, + 13, + 39, + 79 + ], + "target": 17, + "solution": [ + "44+13=57", + "79-39=40", + "57-40=17" + ], + "optimal_path": "Current State: 17:[44, 13, 39, 79], Operations: []\nExploring Operation: 44+13=57, Resulting Numbers: [39, 79, 57]\nGenerated Node #2: [39, 79, 57] from Operation: 44+13=57\nCurrent State: 17:[39, 79, 57], Operations: ['44+13=57']\nExploring Operation: 79-39=40, Resulting Numbers: [57, 40]\nGenerated Node #3: [57, 40] from Operation: 79-39=40\nCurrent State: 17:[57, 40], Operations: ['44+13=57', '79-39=40']\nExploring Operation: 57-40=17, Resulting Numbers: [17]\n17,17 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 59, + 45, + 44, + 52 + ], + "target": 13, + "solution": [ + "59+45=104", + "52-44=8", + "104/8=13" + ], + "optimal_path": "Current State: 13:[59, 45, 44, 52], Operations: []\nExploring Operation: 59+45=104, Resulting Numbers: [44, 52, 104]\nGenerated Node #2: [44, 52, 104] from Operation: 59+45=104\nCurrent State: 13:[44, 52, 104], Operations: ['59+45=104']\nExploring Operation: 52-44=8, Resulting Numbers: [104, 8]\nGenerated Node #3: [104, 8] from Operation: 52-44=8\nCurrent State: 13:[104, 8], Operations: ['59+45=104', '52-44=8']\nExploring Operation: 104/8=13, Resulting Numbers: [13]\n13,13 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 11, + 24, + 70, + 7 + ], + "target": 15, + "solution": [ + "11+24=35", + "70+35=105", + "105/7=15" + ], + "optimal_path": "Current State: 15:[11, 24, 70, 7], Operations: []\nExploring Operation: 11+24=35, Resulting Numbers: [70, 7, 35]\nGenerated Node #2: [70, 7, 35] from Operation: 11+24=35\nCurrent State: 15:[70, 7, 35], Operations: ['11+24=35']\nExploring Operation: 70+35=105, Resulting Numbers: [7, 105]\nGenerated Node #3: [7, 105] from Operation: 70+35=105\nCurrent State: 15:[7, 105], Operations: ['11+24=35', '70+35=105']\nExploring Operation: 105/7=15, Resulting Numbers: [15]\n15,15 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 39, + 28, + 66, + 32 + ], + "target": 62, + "solution": [ + "39-32=7", + "28/7=4", + "66-4=62" + ], + "optimal_path": "Current State: 62:[39, 28, 66, 32], Operations: []\nExploring Operation: 39-32=7, Resulting Numbers: [28, 66, 7]\nGenerated Node #2: [28, 66, 7] from Operation: 39-32=7\nCurrent State: 62:[28, 66, 7], Operations: ['39-32=7']\nExploring Operation: 28/7=4, Resulting Numbers: [66, 4]\nGenerated Node #3: [66, 4] from Operation: 28/7=4\nCurrent State: 62:[66, 4], Operations: ['39-32=7', '28/7=4']\nExploring Operation: 66-4=62, Resulting Numbers: [62]\n62,62 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 28, + 38, + 41, + 64 + ], + "target": 95, + "solution": [ + "38-28=10", + "41+64=105", + "105-10=95" + ], + "optimal_path": "Current State: 95:[28, 38, 41, 64], Operations: []\nExploring Operation: 38-28=10, Resulting Numbers: [41, 64, 10]\nGenerated Node #2: [41, 64, 10] from Operation: 38-28=10\nCurrent State: 95:[41, 64, 10], Operations: ['38-28=10']\nExploring Operation: 41+64=105, Resulting Numbers: [10, 105]\nGenerated Node #3: [10, 105] from Operation: 41+64=105\nCurrent State: 95:[10, 105], Operations: ['38-28=10', '41+64=105']\nExploring Operation: 105-10=95, Resulting Numbers: [95]\n95,95 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 25, + 65, + 61, + 78 + ], + "target": 73, + "solution": [ + "25+65=90", + "78-61=17", + "90-17=73" + ], + "optimal_path": "Current State: 73:[25, 65, 61, 78], Operations: []\nExploring Operation: 25+65=90, Resulting Numbers: [61, 78, 90]\nGenerated Node #2: [61, 78, 90] from Operation: 25+65=90\nCurrent State: 73:[61, 78, 90], Operations: ['25+65=90']\nExploring Operation: 78-61=17, Resulting Numbers: [90, 17]\nGenerated Node #3: [90, 17] from Operation: 78-61=17\nCurrent State: 73:[90, 17], Operations: ['25+65=90', '78-61=17']\nExploring Operation: 90-17=73, Resulting Numbers: [73]\n73,73 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 64, + 97, + 1, + 15 + ], + "target": 18, + "solution": [ + "97-64=33", + "1*15=15", + "33-15=18" + ], + "optimal_path": "Current State: 18:[64, 97, 1, 15], Operations: []\nExploring Operation: 97-64=33, Resulting Numbers: [1, 15, 33]\nGenerated Node #2: [1, 15, 33] from Operation: 97-64=33\nCurrent State: 18:[1, 15, 33], Operations: ['97-64=33']\nExploring Operation: 1*15=15, Resulting Numbers: [33, 15]\nGenerated Node #3: [33, 15] from Operation: 1*15=15\nCurrent State: 18:[33, 15], Operations: ['97-64=33', '1*15=15']\nExploring Operation: 33-15=18, Resulting Numbers: [18]\n18,18 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 57, + 27, + 40, + 87 + ], + "target": 38, + "solution": [ + "57*40=2280", + "87-27=60", + "2280/60=38" + ], + "optimal_path": "Current State: 38:[57, 27, 40, 87], Operations: []\nExploring Operation: 57*40=2280, Resulting Numbers: [27, 87, 2280]\nGenerated Node #2: [27, 87, 2280] from Operation: 57*40=2280\nCurrent State: 38:[27, 87, 2280], Operations: ['57*40=2280']\nExploring Operation: 87-27=60, Resulting Numbers: [2280, 60]\nGenerated Node #3: [2280, 60] from Operation: 87-27=60\nCurrent State: 38:[2280, 60], Operations: ['57*40=2280', '87-27=60']\nExploring Operation: 2280/60=38, Resulting Numbers: [38]\n38,38 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 30, + 74, + 59, + 6 + ], + "target": 39, + "solution": [ + "30+74=104", + "59+6=65", + "104-65=39" + ], + "optimal_path": "Current State: 39:[30, 74, 59, 6], Operations: []\nExploring Operation: 30+74=104, Resulting Numbers: [59, 6, 104]\nGenerated Node #2: [59, 6, 104] from Operation: 30+74=104\nCurrent State: 39:[59, 6, 104], Operations: ['30+74=104']\nExploring Operation: 59+6=65, Resulting Numbers: [104, 65]\nGenerated Node #3: [104, 65] from Operation: 59+6=65\nCurrent State: 39:[104, 65], Operations: ['30+74=104', '59+6=65']\nExploring Operation: 104-65=39, Resulting Numbers: [39]\n39,39 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 10, + 99, + 16, + 17 + ], + "target": 87, + "solution": [ + "10*17=170", + "99-16=83", + "170-83=87" + ], + "optimal_path": "Current State: 87:[10, 99, 16, 17], Operations: []\nExploring Operation: 10*17=170, Resulting Numbers: [99, 16, 170]\nGenerated Node #2: [99, 16, 170] from Operation: 10*17=170\nCurrent State: 87:[99, 16, 170], Operations: ['10*17=170']\nExploring Operation: 99-16=83, Resulting Numbers: [170, 83]\nGenerated Node #3: [170, 83] from Operation: 99-16=83\nCurrent State: 87:[170, 83], Operations: ['10*17=170', '99-16=83']\nExploring Operation: 170-83=87, Resulting Numbers: [87]\n87,87 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 24, + 84, + 83, + 4 + ], + "target": 29, + "solution": [ + "24+84=108", + "83-4=79", + "108-79=29" + ], + "optimal_path": "Current State: 29:[24, 84, 83, 4], Operations: []\nExploring Operation: 24+84=108, Resulting Numbers: [83, 4, 108]\nGenerated Node #2: [83, 4, 108] from Operation: 24+84=108\nCurrent State: 29:[83, 4, 108], Operations: ['24+84=108']\nExploring Operation: 83-4=79, Resulting Numbers: [108, 79]\nGenerated Node #3: [108, 79] from Operation: 83-4=79\nCurrent State: 29:[108, 79], Operations: ['24+84=108', '83-4=79']\nExploring Operation: 108-79=29, Resulting Numbers: [29]\n29,29 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 5, + 32, + 27, + 49 + ], + "target": 84, + "solution": [ + "5*32=160", + "27+49=76", + "160-76=84" + ], + "optimal_path": "Current State: 84:[5, 32, 27, 49], Operations: []\nExploring Operation: 5*32=160, Resulting Numbers: [27, 49, 160]\nGenerated Node #2: [27, 49, 160] from Operation: 5*32=160\nCurrent State: 84:[27, 49, 160], Operations: ['5*32=160']\nExploring Operation: 27+49=76, Resulting Numbers: [160, 76]\nGenerated Node #3: [160, 76] from Operation: 27+49=76\nCurrent State: 84:[160, 76], Operations: ['5*32=160', '27+49=76']\nExploring Operation: 160-76=84, Resulting Numbers: [84]\n84,84 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 32, + 39, + 25, + 38 + ], + "target": 91, + "solution": [ + "39-32=7", + "38-25=13", + "7*13=91" + ], + "optimal_path": "Current State: 91:[32, 39, 25, 38], Operations: []\nExploring Operation: 39-32=7, Resulting Numbers: [25, 38, 7]\nGenerated Node #2: [25, 38, 7] from Operation: 39-32=7\nCurrent State: 91:[25, 38, 7], Operations: ['39-32=7']\nExploring Operation: 38-25=13, Resulting Numbers: [7, 13]\nGenerated Node #3: [7, 13] from Operation: 38-25=13\nCurrent State: 91:[7, 13], Operations: ['39-32=7', '38-25=13']\nExploring Operation: 7*13=91, Resulting Numbers: [91]\n91,91 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 35, + 60, + 48, + 52 + ], + "target": 99, + "solution": [ + "35+60=95", + "52-48=4", + "95+4=99" + ], + "optimal_path": "Current State: 99:[35, 60, 48, 52], Operations: []\nExploring Operation: 35+60=95, Resulting Numbers: [48, 52, 95]\nGenerated Node #2: [48, 52, 95] from Operation: 35+60=95\nCurrent State: 99:[48, 52, 95], Operations: ['35+60=95']\nExploring Operation: 52-48=4, Resulting Numbers: [95, 4]\nGenerated Node #3: [95, 4] from Operation: 52-48=4\nCurrent State: 99:[95, 4], Operations: ['35+60=95', '52-48=4']\nExploring Operation: 95+4=99, Resulting Numbers: [99]\n99,99 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 81, + 39, + 24, + 12 + ], + "target": 10, + "solution": [ + "81+39=120", + "24-12=12", + "120/12=10" + ], + "optimal_path": "Current State: 10:[81, 39, 24, 12], Operations: []\nExploring Operation: 81+39=120, Resulting Numbers: [24, 12, 120]\nGenerated Node #2: [24, 12, 120] from Operation: 81+39=120\nCurrent State: 10:[24, 12, 120], Operations: ['81+39=120']\nExploring Operation: 24-12=12, Resulting Numbers: [120, 12]\nGenerated Node #3: [120, 12] from Operation: 24-12=12\nCurrent State: 10:[120, 12], Operations: ['81+39=120', '24-12=12']\nExploring Operation: 120/12=10, Resulting Numbers: [10]\n10,10 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 25, + 85, + 75, + 47 + ], + "target": 62, + "solution": [ + "85-25=60", + "75+47=122", + "122-60=62" + ], + "optimal_path": "Current State: 62:[25, 85, 75, 47], Operations: []\nExploring Operation: 85-25=60, Resulting Numbers: [75, 47, 60]\nGenerated Node #2: [75, 47, 60] from Operation: 85-25=60\nCurrent State: 62:[75, 47, 60], Operations: ['85-25=60']\nExploring Operation: 75+47=122, Resulting Numbers: [60, 122]\nGenerated Node #3: [60, 122] from Operation: 75+47=122\nCurrent State: 62:[60, 122], Operations: ['85-25=60', '75+47=122']\nExploring Operation: 122-60=62, Resulting Numbers: [62]\n62,62 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 25, + 44, + 77, + 8 + ], + "target": 79, + "solution": [ + "25*8=200", + "44+77=121", + "200-121=79" + ], + "optimal_path": "Current State: 79:[25, 44, 77, 8], Operations: []\nExploring Operation: 25*8=200, Resulting Numbers: [44, 77, 200]\nGenerated Node #2: [44, 77, 200] from Operation: 25*8=200\nCurrent State: 79:[44, 77, 200], Operations: ['25*8=200']\nExploring Operation: 44+77=121, Resulting Numbers: [200, 121]\nGenerated Node #3: [200, 121] from Operation: 44+77=121\nCurrent State: 79:[200, 121], Operations: ['25*8=200', '44+77=121']\nExploring Operation: 200-121=79, Resulting Numbers: [79]\n79,79 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 77, + 33, + 16, + 80 + ], + "target": 39, + "solution": [ + "77-33=44", + "80/16=5", + "44-5=39" + ], + "optimal_path": "Current State: 39:[77, 33, 16, 80], Operations: []\nExploring Operation: 77-33=44, Resulting Numbers: [16, 80, 44]\nGenerated Node #2: [16, 80, 44] from Operation: 77-33=44\nCurrent State: 39:[16, 80, 44], Operations: ['77-33=44']\nExploring Operation: 80/16=5, Resulting Numbers: [44, 5]\nGenerated Node #3: [44, 5] from Operation: 80/16=5\nCurrent State: 39:[44, 5], Operations: ['77-33=44', '80/16=5']\nExploring Operation: 44-5=39, Resulting Numbers: [39]\n39,39 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 19, + 17, + 81, + 20 + ], + "target": 85, + "solution": [ + "19+81=100", + "17*100=1700", + "1700/20=85" + ], + "optimal_path": "Current State: 85:[19, 17, 81, 20], Operations: []\nExploring Operation: 19+81=100, Resulting Numbers: [17, 20, 100]\nGenerated Node #2: [17, 20, 100] from Operation: 19+81=100\nCurrent State: 85:[17, 20, 100], Operations: ['19+81=100']\nExploring Operation: 17*100=1700, Resulting Numbers: [20, 1700]\nGenerated Node #3: [20, 1700] from Operation: 17*100=1700\nCurrent State: 85:[20, 1700], Operations: ['19+81=100', '17*100=1700']\nExploring Operation: 1700/20=85, Resulting Numbers: [85]\n85,85 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 16, + 41, + 48, + 64 + ], + "target": 53, + "solution": [ + "16*48=768", + "768/64=12", + "41+12=53" + ], + "optimal_path": "Current State: 53:[16, 41, 48, 64], Operations: []\nExploring Operation: 16*48=768, Resulting Numbers: [41, 64, 768]\nGenerated Node #2: [41, 64, 768] from Operation: 16*48=768\nCurrent State: 53:[41, 64, 768], Operations: ['16*48=768']\nExploring Operation: 768/64=12, Resulting Numbers: [41, 12]\nGenerated Node #3: [41, 12] from Operation: 768/64=12\nCurrent State: 53:[41, 12], Operations: ['16*48=768', '768/64=12']\nExploring Operation: 41+12=53, Resulting Numbers: [53]\n53,53 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 66, + 4, + 24, + 22 + ], + "target": 50, + "solution": [ + "66-22=44", + "24/4=6", + "44+6=50" + ], + "optimal_path": "Current State: 50:[66, 4, 24, 22], Operations: []\nExploring Operation: 66-22=44, Resulting Numbers: [4, 24, 44]\nGenerated Node #2: [4, 24, 44] from Operation: 66-22=44\nCurrent State: 50:[4, 24, 44], Operations: ['66-22=44']\nExploring Operation: 24/4=6, Resulting Numbers: [44, 6]\nGenerated Node #3: [44, 6] from Operation: 24/4=6\nCurrent State: 50:[44, 6], Operations: ['66-22=44', '24/4=6']\nExploring Operation: 44+6=50, Resulting Numbers: [50]\n50,50 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 48, + 1, + 4, + 30 + ], + "target": 71, + "solution": [ + "48+1=49", + "4*30=120", + "120-49=71" + ], + "optimal_path": "Current State: 71:[48, 1, 4, 30], Operations: []\nExploring Operation: 48+1=49, Resulting Numbers: [4, 30, 49]\nGenerated Node #2: [4, 30, 49] from Operation: 48+1=49\nCurrent State: 71:[4, 30, 49], Operations: ['48+1=49']\nExploring Operation: 4*30=120, Resulting Numbers: [49, 120]\nGenerated Node #3: [49, 120] from Operation: 4*30=120\nCurrent State: 71:[49, 120], Operations: ['48+1=49', '4*30=120']\nExploring Operation: 120-49=71, Resulting Numbers: [71]\n71,71 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 31, + 85, + 83, + 44 + ], + "target": 57, + "solution": [ + "85-83=2", + "44*2=88", + "88-31=57" + ], + "optimal_path": "Current State: 57:[31, 85, 83, 44], Operations: []\nExploring Operation: 85-83=2, Resulting Numbers: [31, 44, 2]\nGenerated Node #2: [31, 44, 2] from Operation: 85-83=2\nCurrent State: 57:[31, 44, 2], Operations: ['85-83=2']\nExploring Operation: 44*2=88, Resulting Numbers: [31, 88]\nGenerated Node #3: [31, 88] from Operation: 44*2=88\nCurrent State: 57:[31, 88], Operations: ['85-83=2', '44*2=88']\nExploring Operation: 88-31=57, Resulting Numbers: [57]\n57,57 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 87, + 88, + 86, + 61 + ], + "target": 13, + "solution": [ + "87-61=26", + "88-86=2", + "26/2=13" + ], + "optimal_path": "Current State: 13:[87, 88, 86, 61], Operations: []\nExploring Operation: 87-61=26, Resulting Numbers: [88, 86, 26]\nGenerated Node #2: [88, 86, 26] from Operation: 87-61=26\nCurrent State: 13:[88, 86, 26], Operations: ['87-61=26']\nExploring Operation: 88-86=2, Resulting Numbers: [26, 2]\nGenerated Node #3: [26, 2] from Operation: 88-86=2\nCurrent State: 13:[26, 2], Operations: ['87-61=26', '88-86=2']\nExploring Operation: 26/2=13, Resulting Numbers: [13]\n13,13 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 4, + 64, + 65, + 48 + ], + "target": 37, + "solution": [ + "64+48=112", + "112/4=28", + "65-28=37" + ], + "optimal_path": "Current State: 37:[4, 64, 65, 48], Operations: []\nExploring Operation: 64+48=112, Resulting Numbers: [4, 65, 112]\nGenerated Node #2: [4, 65, 112] from Operation: 64+48=112\nCurrent State: 37:[4, 65, 112], Operations: ['64+48=112']\nExploring Operation: 112/4=28, Resulting Numbers: [65, 28]\nGenerated Node #3: [65, 28] from Operation: 112/4=28\nCurrent State: 37:[65, 28], Operations: ['64+48=112', '112/4=28']\nExploring Operation: 65-28=37, Resulting Numbers: [37]\n37,37 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 54, + 30, + 73, + 44 + ], + "target": 76, + "solution": [ + "54-44=10", + "30/10=3", + "73+3=76" + ], + "optimal_path": "Current State: 76:[54, 30, 73, 44], Operations: []\nExploring Operation: 54-44=10, Resulting Numbers: [30, 73, 10]\nGenerated Node #2: [30, 73, 10] from Operation: 54-44=10\nCurrent State: 76:[30, 73, 10], Operations: ['54-44=10']\nExploring Operation: 30/10=3, Resulting Numbers: [73, 3]\nGenerated Node #3: [73, 3] from Operation: 30/10=3\nCurrent State: 76:[73, 3], Operations: ['54-44=10', '30/10=3']\nExploring Operation: 73+3=76, Resulting Numbers: [76]\n76,76 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 36, + 96, + 9, + 23 + ], + "target": 39, + "solution": [ + "9+23=32", + "96/32=3", + "36+3=39" + ], + "optimal_path": "Current State: 39:[36, 96, 9, 23], Operations: []\nExploring Operation: 9+23=32, Resulting Numbers: [36, 96, 32]\nGenerated Node #2: [36, 96, 32] from Operation: 9+23=32\nCurrent State: 39:[36, 96, 32], Operations: ['9+23=32']\nExploring Operation: 96/32=3, Resulting Numbers: [36, 3]\nGenerated Node #3: [36, 3] from Operation: 96/32=3\nCurrent State: 39:[36, 3], Operations: ['9+23=32', '96/32=3']\nExploring Operation: 36+3=39, Resulting Numbers: [39]\n39,39 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 8, + 88, + 42, + 55 + ], + "target": 17, + "solution": [ + "88-8=80", + "42+55=97", + "97-80=17" + ], + "optimal_path": "Current State: 17:[8, 88, 42, 55], Operations: []\nExploring Operation: 88-8=80, Resulting Numbers: [42, 55, 80]\nGenerated Node #2: [42, 55, 80] from Operation: 88-8=80\nCurrent State: 17:[42, 55, 80], Operations: ['88-8=80']\nExploring Operation: 42+55=97, Resulting Numbers: [80, 97]\nGenerated Node #3: [80, 97] from Operation: 42+55=97\nCurrent State: 17:[80, 97], Operations: ['88-8=80', '42+55=97']\nExploring Operation: 97-80=17, Resulting Numbers: [17]\n17,17 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 17, + 42, + 26, + 88 + ], + "target": 35, + "solution": [ + "17*88=1496", + "1496-26=1470", + "1470/42=35" + ], + "optimal_path": "Current State: 35:[17, 42, 26, 88], Operations: []\nExploring Operation: 17*88=1496, Resulting Numbers: [42, 26, 1496]\nGenerated Node #2: [42, 26, 1496] from Operation: 17*88=1496\nCurrent State: 35:[42, 26, 1496], Operations: ['17*88=1496']\nExploring Operation: 1496-26=1470, Resulting Numbers: [42, 1470]\nGenerated Node #3: [42, 1470] from Operation: 1496-26=1470\nCurrent State: 35:[42, 1470], Operations: ['17*88=1496', '1496-26=1470']\nExploring Operation: 1470/42=35, Resulting Numbers: [35]\n35,35 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 22, + 80, + 27, + 32 + ], + "target": 80, + "solution": [ + "27-22=5", + "32*5=160", + "160-80=80" + ], + "optimal_path": "Current State: 80:[22, 80, 27, 32], Operations: []\nExploring Operation: 27-22=5, Resulting Numbers: [80, 32, 5]\nGenerated Node #2: [80, 32, 5] from Operation: 27-22=5\nCurrent State: 80:[80, 32, 5], Operations: ['27-22=5']\nExploring Operation: 32*5=160, Resulting Numbers: [80, 160]\nGenerated Node #3: [80, 160] from Operation: 32*5=160\nCurrent State: 80:[80, 160], Operations: ['27-22=5', '32*5=160']\nExploring Operation: 160-80=80, Resulting Numbers: [80]\n80,80 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 15, + 1, + 79, + 15 + ], + "target": 49, + "solution": [ + "15*1=15", + "79-15=64", + "64-15=49" + ], + "optimal_path": "Current State: 49:[15, 1, 79, 15], Operations: []\nExploring Operation: 15*1=15, Resulting Numbers: [79, 15]\nGenerated Node #2: [79, 15] from Operation: 15*1=15\nCurrent State: 49:[79, 15], Operations: ['15*1=15']\nExploring Operation: 79-15=64, Resulting Numbers: [64]\n64,49 equal: Goal Reached\nExploring Operation: 64-15=49, Resulting Numbers: [49]\n49,49 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 59, + 86, + 54, + 55 + ], + "target": 26, + "solution": [ + "86-59=27", + "55-54=1", + "27-1=26" + ], + "optimal_path": "Current State: 26:[59, 86, 54, 55], Operations: []\nExploring Operation: 86-59=27, Resulting Numbers: [54, 55, 27]\nGenerated Node #2: [54, 55, 27] from Operation: 86-59=27\nCurrent State: 26:[54, 55, 27], Operations: ['86-59=27']\nExploring Operation: 55-54=1, Resulting Numbers: [27, 1]\nGenerated Node #3: [27, 1] from Operation: 55-54=1\nCurrent State: 26:[27, 1], Operations: ['86-59=27', '55-54=1']\nExploring Operation: 27-1=26, Resulting Numbers: [26]\n26,26 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 1, + 3, + 67, + 57 + ], + "target": 31, + "solution": [ + "1+3=4", + "67+57=124", + "124/4=31" + ], + "optimal_path": "Current State: 31:[1, 3, 67, 57], Operations: []\nExploring Operation: 1+3=4, Resulting Numbers: [67, 57, 4]\nGenerated Node #2: [67, 57, 4] from Operation: 1+3=4\nCurrent State: 31:[67, 57, 4], Operations: ['1+3=4']\nExploring Operation: 67+57=124, Resulting Numbers: [4, 124]\nGenerated Node #3: [4, 124] from Operation: 67+57=124\nCurrent State: 31:[4, 124], Operations: ['1+3=4', '67+57=124']\nExploring Operation: 124/4=31, Resulting Numbers: [31]\n31,31 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 72, + 98, + 84, + 2 + ], + "target": 38, + "solution": [ + "72*2=144", + "98+84=182", + "182-144=38" + ], + "optimal_path": "Current State: 38:[72, 98, 84, 2], Operations: []\nExploring Operation: 72*2=144, Resulting Numbers: [98, 84, 144]\nGenerated Node #2: [98, 84, 144] from Operation: 72*2=144\nCurrent State: 38:[98, 84, 144], Operations: ['72*2=144']\nExploring Operation: 98+84=182, Resulting Numbers: [144, 182]\nGenerated Node #3: [144, 182] from Operation: 98+84=182\nCurrent State: 38:[144, 182], Operations: ['72*2=144', '98+84=182']\nExploring Operation: 182-144=38, Resulting Numbers: [38]\n38,38 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 11, + 66, + 25, + 3 + ], + "target": 42, + "solution": [ + "11+25=36", + "3*36=108", + "108-66=42" + ], + "optimal_path": "Current State: 42:[11, 66, 25, 3], Operations: []\nExploring Operation: 11+25=36, Resulting Numbers: [66, 3, 36]\nGenerated Node #2: [66, 3, 36] from Operation: 11+25=36\nCurrent State: 42:[66, 3, 36], Operations: ['11+25=36']\nExploring Operation: 3*36=108, Resulting Numbers: [66, 108]\nGenerated Node #3: [66, 108] from Operation: 3*36=108\nCurrent State: 42:[66, 108], Operations: ['11+25=36', '3*36=108']\nExploring Operation: 108-66=42, Resulting Numbers: [42]\n42,42 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 48, + 18, + 23, + 9 + ], + "target": 62, + "solution": [ + "48-18=30", + "23+9=32", + "30+32=62" + ], + "optimal_path": "Current State: 62:[48, 18, 23, 9], Operations: []\nExploring Operation: 48-18=30, Resulting Numbers: [23, 9, 30]\nGenerated Node #2: [23, 9, 30] from Operation: 48-18=30\nCurrent State: 62:[23, 9, 30], Operations: ['48-18=30']\nExploring Operation: 23+9=32, Resulting Numbers: [30, 32]\nGenerated Node #3: [30, 32] from Operation: 23+9=32\nCurrent State: 62:[30, 32], Operations: ['48-18=30', '23+9=32']\nExploring Operation: 30+32=62, Resulting Numbers: [62]\n62,62 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 13, + 78, + 2, + 91 + ], + "target": 73, + "solution": [ + "91/13=7", + "78+2=80", + "80-7=73" + ], + "optimal_path": "Current State: 73:[13, 78, 2, 91], Operations: []\nExploring Operation: 91/13=7, Resulting Numbers: [78, 2, 7]\nGenerated Node #2: [78, 2, 7] from Operation: 91/13=7\nCurrent State: 73:[78, 2, 7], Operations: ['91/13=7']\nExploring Operation: 78+2=80, Resulting Numbers: [7, 80]\nGenerated Node #3: [7, 80] from Operation: 78+2=80\nCurrent State: 73:[7, 80], Operations: ['91/13=7', '78+2=80']\nExploring Operation: 80-7=73, Resulting Numbers: [73]\n73,73 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 22, + 14, + 90, + 31 + ], + "target": 36, + "solution": [ + "31-22=9", + "14*9=126", + "126-90=36" + ], + "optimal_path": "Current State: 36:[22, 14, 90, 31], Operations: []\nExploring Operation: 31-22=9, Resulting Numbers: [14, 90, 9]\nGenerated Node #2: [14, 90, 9] from Operation: 31-22=9\nCurrent State: 36:[14, 90, 9], Operations: ['31-22=9']\nExploring Operation: 14*9=126, Resulting Numbers: [90, 126]\nGenerated Node #3: [90, 126] from Operation: 14*9=126\nCurrent State: 36:[90, 126], Operations: ['31-22=9', '14*9=126']\nExploring Operation: 126-90=36, Resulting Numbers: [36]\n36,36 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 88, + 42, + 46, + 44 + ], + "target": 67, + "solution": [ + "88+46=134", + "44-42=2", + "134/2=67" + ], + "optimal_path": "Current State: 67:[88, 42, 46, 44], Operations: []\nExploring Operation: 88+46=134, Resulting Numbers: [42, 44, 134]\nGenerated Node #2: [42, 44, 134] from Operation: 88+46=134\nCurrent State: 67:[42, 44, 134], Operations: ['88+46=134']\nExploring Operation: 44-42=2, Resulting Numbers: [134, 2]\nGenerated Node #3: [134, 2] from Operation: 44-42=2\nCurrent State: 67:[134, 2], Operations: ['88+46=134', '44-42=2']\nExploring Operation: 134/2=67, Resulting Numbers: [67]\n67,67 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 39, + 65, + 17, + 32 + ], + "target": 89, + "solution": [ + "39+65=104", + "32-17=15", + "104-15=89" + ], + "optimal_path": "Current State: 89:[39, 65, 17, 32], Operations: []\nExploring Operation: 39+65=104, Resulting Numbers: [17, 32, 104]\nGenerated Node #2: [17, 32, 104] from Operation: 39+65=104\nCurrent State: 89:[17, 32, 104], Operations: ['39+65=104']\nExploring Operation: 32-17=15, Resulting Numbers: [104, 15]\nGenerated Node #3: [104, 15] from Operation: 32-17=15\nCurrent State: 89:[104, 15], Operations: ['39+65=104', '32-17=15']\nExploring Operation: 104-15=89, Resulting Numbers: [89]\n89,89 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 87, + 14, + 46, + 8 + ], + "target": 35, + "solution": [ + "87-14=73", + "46-8=38", + "73-38=35" + ], + "optimal_path": "Current State: 35:[87, 14, 46, 8], Operations: []\nExploring Operation: 87-14=73, Resulting Numbers: [46, 8, 73]\nGenerated Node #2: [46, 8, 73] from Operation: 87-14=73\nCurrent State: 35:[46, 8, 73], Operations: ['87-14=73']\nExploring Operation: 46-8=38, Resulting Numbers: [73, 38]\nGenerated Node #3: [73, 38] from Operation: 46-8=38\nCurrent State: 35:[73, 38], Operations: ['87-14=73', '46-8=38']\nExploring Operation: 73-38=35, Resulting Numbers: [35]\n35,35 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 50, + 34, + 88, + 82 + ], + "target": 44, + "solution": [ + "50+34=84", + "84-82=2", + "88/2=44" + ], + "optimal_path": "Current State: 44:[50, 34, 88, 82], Operations: []\nExploring Operation: 50+34=84, Resulting Numbers: [88, 82, 84]\nGenerated Node #2: [88, 82, 84] from Operation: 50+34=84\nCurrent State: 44:[88, 82, 84], Operations: ['50+34=84']\nExploring Operation: 84-82=2, Resulting Numbers: [88, 2]\nGenerated Node #3: [88, 2] from Operation: 84-82=2\nCurrent State: 44:[88, 2], Operations: ['50+34=84', '84-82=2']\nExploring Operation: 88/2=44, Resulting Numbers: [44]\n44,44 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 20, + 11, + 3, + 88 + ], + "target": 84, + "solution": [ + "88/11=8", + "20+8=28", + "3*28=84" + ], + "optimal_path": "Current State: 84:[20, 11, 3, 88], Operations: []\nExploring Operation: 88/11=8, Resulting Numbers: [20, 3, 8]\nGenerated Node #2: [20, 3, 8] from Operation: 88/11=8\nCurrent State: 84:[20, 3, 8], Operations: ['88/11=8']\nExploring Operation: 20+8=28, Resulting Numbers: [3, 28]\nGenerated Node #3: [3, 28] from Operation: 20+8=28\nCurrent State: 84:[3, 28], Operations: ['88/11=8', '20+8=28']\nExploring Operation: 3*28=84, Resulting Numbers: [84]\n84,84 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 89, + 70, + 38, + 59 + ], + "target": 78, + "solution": [ + "89-70=19", + "38+59=97", + "97-19=78" + ], + "optimal_path": "Current State: 78:[89, 70, 38, 59], Operations: []\nExploring Operation: 89-70=19, Resulting Numbers: [38, 59, 19]\nGenerated Node #2: [38, 59, 19] from Operation: 89-70=19\nCurrent State: 78:[38, 59, 19], Operations: ['89-70=19']\nExploring Operation: 38+59=97, Resulting Numbers: [19, 97]\nGenerated Node #3: [19, 97] from Operation: 38+59=97\nCurrent State: 78:[19, 97], Operations: ['89-70=19', '38+59=97']\nExploring Operation: 97-19=78, Resulting Numbers: [78]\n78,78 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 17, + 8, + 86, + 6 + ], + "target": 30, + "solution": [ + "86-8=78", + "78/6=13", + "17+13=30" + ], + "optimal_path": "Current State: 30:[17, 8, 86, 6], Operations: []\nExploring Operation: 86-8=78, Resulting Numbers: [17, 6, 78]\nGenerated Node #2: [17, 6, 78] from Operation: 86-8=78\nCurrent State: 30:[17, 6, 78], Operations: ['86-8=78']\nExploring Operation: 78/6=13, Resulting Numbers: [17, 13]\nGenerated Node #3: [17, 13] from Operation: 78/6=13\nCurrent State: 30:[17, 13], Operations: ['86-8=78', '78/6=13']\nExploring Operation: 17+13=30, Resulting Numbers: [30]\n30,30 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 34, + 22, + 2, + 88 + ], + "target": 19, + "solution": [ + "88/22=4", + "34+4=38", + "38/2=19" + ], + "optimal_path": "Current State: 19:[34, 22, 2, 88], Operations: []\nExploring Operation: 88/22=4, Resulting Numbers: [34, 2, 4]\nGenerated Node #2: [34, 2, 4] from Operation: 88/22=4\nCurrent State: 19:[34, 2, 4], Operations: ['88/22=4']\nExploring Operation: 34+4=38, Resulting Numbers: [2, 38]\nGenerated Node #3: [2, 38] from Operation: 34+4=38\nCurrent State: 19:[2, 38], Operations: ['88/22=4', '34+4=38']\nExploring Operation: 38/2=19, Resulting Numbers: [19]\n19,19 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 10, + 68, + 8, + 6 + ], + "target": 63, + "solution": [ + "8-6=2", + "10/2=5", + "68-5=63" + ], + "optimal_path": "Current State: 63:[10, 68, 8, 6], Operations: []\nExploring Operation: 8-6=2, Resulting Numbers: [10, 68, 2]\nGenerated Node #2: [10, 68, 2] from Operation: 8-6=2\nCurrent State: 63:[10, 68, 2], Operations: ['8-6=2']\nExploring Operation: 10/2=5, Resulting Numbers: [68, 5]\nGenerated Node #3: [68, 5] from Operation: 10/2=5\nCurrent State: 63:[68, 5], Operations: ['8-6=2', '10/2=5']\nExploring Operation: 68-5=63, Resulting Numbers: [63]\n63,63 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 99, + 77, + 78, + 2 + ], + "target": 23, + "solution": [ + "99+78=177", + "77*2=154", + "177-154=23" + ], + "optimal_path": "Current State: 23:[99, 77, 78, 2], Operations: []\nExploring Operation: 99+78=177, Resulting Numbers: [77, 2, 177]\nGenerated Node #2: [77, 2, 177] from Operation: 99+78=177\nCurrent State: 23:[77, 2, 177], Operations: ['99+78=177']\nExploring Operation: 77*2=154, Resulting Numbers: [177, 154]\nGenerated Node #3: [177, 154] from Operation: 77*2=154\nCurrent State: 23:[177, 154], Operations: ['99+78=177', '77*2=154']\nExploring Operation: 177-154=23, Resulting Numbers: [23]\n23,23 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 55, + 99, + 66, + 28 + ], + "target": 18, + "solution": [ + "55-28=27", + "66*27=1782", + "1782/99=18" + ], + "optimal_path": "Current State: 18:[55, 99, 66, 28], Operations: []\nExploring Operation: 55-28=27, Resulting Numbers: [99, 66, 27]\nGenerated Node #2: [99, 66, 27] from Operation: 55-28=27\nCurrent State: 18:[99, 66, 27], Operations: ['55-28=27']\nExploring Operation: 66*27=1782, Resulting Numbers: [99, 1782]\nGenerated Node #3: [99, 1782] from Operation: 66*27=1782\nCurrent State: 18:[99, 1782], Operations: ['55-28=27', '66*27=1782']\nExploring Operation: 1782/99=18, Resulting Numbers: [18]\n18,18 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 79, + 95, + 36, + 99 + ], + "target": 44, + "solution": [ + "95-79=16", + "99*16=1584", + "1584/36=44" + ], + "optimal_path": "Current State: 44:[79, 95, 36, 99], Operations: []\nExploring Operation: 95-79=16, Resulting Numbers: [36, 99, 16]\nGenerated Node #2: [36, 99, 16] from Operation: 95-79=16\nCurrent State: 44:[36, 99, 16], Operations: ['95-79=16']\nExploring Operation: 99*16=1584, Resulting Numbers: [36, 1584]\nGenerated Node #3: [36, 1584] from Operation: 99*16=1584\nCurrent State: 44:[36, 1584], Operations: ['95-79=16', '99*16=1584']\nExploring Operation: 1584/36=44, Resulting Numbers: [44]\n44,44 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 48, + 70, + 64, + 55 + ], + "target": 97, + "solution": [ + "70-48=22", + "64+55=119", + "119-22=97" + ], + "optimal_path": "Current State: 97:[48, 70, 64, 55], Operations: []\nExploring Operation: 70-48=22, Resulting Numbers: [64, 55, 22]\nGenerated Node #2: [64, 55, 22] from Operation: 70-48=22\nCurrent State: 97:[64, 55, 22], Operations: ['70-48=22']\nExploring Operation: 64+55=119, Resulting Numbers: [22, 119]\nGenerated Node #3: [22, 119] from Operation: 64+55=119\nCurrent State: 97:[22, 119], Operations: ['70-48=22', '64+55=119']\nExploring Operation: 119-22=97, Resulting Numbers: [97]\n97,97 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 48, + 63, + 83, + 61 + ], + "target": 60, + "solution": [ + "83+61=144", + "144/48=3", + "63-3=60" + ], + "optimal_path": "Current State: 60:[48, 63, 83, 61], Operations: []\nExploring Operation: 83+61=144, Resulting Numbers: [48, 63, 144]\nGenerated Node #2: [48, 63, 144] from Operation: 83+61=144\nCurrent State: 60:[48, 63, 144], Operations: ['83+61=144']\nExploring Operation: 144/48=3, Resulting Numbers: [63, 3]\nGenerated Node #3: [63, 3] from Operation: 144/48=3\nCurrent State: 60:[63, 3], Operations: ['83+61=144', '144/48=3']\nExploring Operation: 63-3=60, Resulting Numbers: [60]\n60,60 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 43, + 2, + 80, + 70 + ], + "target": 96, + "solution": [ + "43*2=86", + "80-70=10", + "86+10=96" + ], + "optimal_path": "Current State: 96:[43, 2, 80, 70], Operations: []\nExploring Operation: 43*2=86, Resulting Numbers: [80, 70, 86]\nGenerated Node #2: [80, 70, 86] from Operation: 43*2=86\nCurrent State: 96:[80, 70, 86], Operations: ['43*2=86']\nExploring Operation: 80-70=10, Resulting Numbers: [86, 10]\nGenerated Node #3: [86, 10] from Operation: 80-70=10\nCurrent State: 96:[86, 10], Operations: ['43*2=86', '80-70=10']\nExploring Operation: 86+10=96, Resulting Numbers: [96]\n96,96 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 52, + 67, + 51, + 58 + ], + "target": 96, + "solution": [ + "58-52=6", + "67-51=16", + "6*16=96" + ], + "optimal_path": "Current State: 96:[52, 67, 51, 58], Operations: []\nExploring Operation: 58-52=6, Resulting Numbers: [67, 51, 6]\nGenerated Node #2: [67, 51, 6] from Operation: 58-52=6\nCurrent State: 96:[67, 51, 6], Operations: ['58-52=6']\nExploring Operation: 67-51=16, Resulting Numbers: [6, 16]\nGenerated Node #3: [6, 16] from Operation: 67-51=16\nCurrent State: 96:[6, 16], Operations: ['58-52=6', '67-51=16']\nExploring Operation: 6*16=96, Resulting Numbers: [96]\n96,96 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 78, + 61, + 77, + 76 + ], + "target": 69, + "solution": [ + "78-76=2", + "61+77=138", + "138/2=69" + ], + "optimal_path": "Current State: 69:[78, 61, 77, 76], Operations: []\nExploring Operation: 78-76=2, Resulting Numbers: [61, 77, 2]\nGenerated Node #2: [61, 77, 2] from Operation: 78-76=2\nCurrent State: 69:[61, 77, 2], Operations: ['78-76=2']\nExploring Operation: 61+77=138, Resulting Numbers: [2, 138]\nGenerated Node #3: [2, 138] from Operation: 61+77=138\nCurrent State: 69:[2, 138], Operations: ['78-76=2', '61+77=138']\nExploring Operation: 138/2=69, Resulting Numbers: [69]\n69,69 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 68, + 12, + 34, + 8 + ], + "target": 72, + "solution": [ + "68/34=2", + "8-2=6", + "12*6=72" + ], + "optimal_path": "Current State: 72:[68, 12, 34, 8], Operations: []\nExploring Operation: 68/34=2, Resulting Numbers: [12, 8, 2]\nGenerated Node #2: [12, 8, 2] from Operation: 68/34=2\nCurrent State: 72:[12, 8, 2], Operations: ['68/34=2']\nExploring Operation: 8-2=6, Resulting Numbers: [12, 6]\nGenerated Node #3: [12, 6] from Operation: 8-2=6\nCurrent State: 72:[12, 6], Operations: ['68/34=2', '8-2=6']\nExploring Operation: 12*6=72, Resulting Numbers: [72]\n72,72 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 36, + 65, + 40, + 12 + ], + "target": 78, + "solution": [ + "36+12=48", + "65*48=3120", + "3120/40=78" + ], + "optimal_path": "Current State: 78:[36, 65, 40, 12], Operations: []\nExploring Operation: 36+12=48, Resulting Numbers: [65, 40, 48]\nGenerated Node #2: [65, 40, 48] from Operation: 36+12=48\nCurrent State: 78:[65, 40, 48], Operations: ['36+12=48']\nExploring Operation: 65*48=3120, Resulting Numbers: [40, 3120]\nGenerated Node #3: [40, 3120] from Operation: 65*48=3120\nCurrent State: 78:[40, 3120], Operations: ['36+12=48', '65*48=3120']\nExploring Operation: 3120/40=78, Resulting Numbers: [78]\n78,78 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 27, + 2, + 75, + 38 + ], + "target": 35, + "solution": [ + "27-2=25", + "75/25=3", + "38-3=35" + ], + "optimal_path": "Current State: 35:[27, 2, 75, 38], Operations: []\nExploring Operation: 27-2=25, Resulting Numbers: [75, 38, 25]\nGenerated Node #2: [75, 38, 25] from Operation: 27-2=25\nCurrent State: 35:[75, 38, 25], Operations: ['27-2=25']\nExploring Operation: 75/25=3, Resulting Numbers: [38, 3]\nGenerated Node #3: [38, 3] from Operation: 75/25=3\nCurrent State: 35:[38, 3], Operations: ['27-2=25', '75/25=3']\nExploring Operation: 38-3=35, Resulting Numbers: [35]\n35,35 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 7, + 60, + 39, + 80 + ], + "target": 83, + "solution": [ + "60-39=21", + "21/7=3", + "80+3=83" + ], + "optimal_path": "Current State: 83:[7, 60, 39, 80], Operations: []\nExploring Operation: 60-39=21, Resulting Numbers: [7, 80, 21]\nGenerated Node #2: [7, 80, 21] from Operation: 60-39=21\nCurrent State: 83:[7, 80, 21], Operations: ['60-39=21']\nExploring Operation: 21/7=3, Resulting Numbers: [80, 3]\nGenerated Node #3: [80, 3] from Operation: 21/7=3\nCurrent State: 83:[80, 3], Operations: ['60-39=21', '21/7=3']\nExploring Operation: 80+3=83, Resulting Numbers: [83]\n83,83 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 86, + 87, + 50, + 26 + ], + "target": 23, + "solution": [ + "87-86=1", + "50-26=24", + "24-1=23" + ], + "optimal_path": "Current State: 23:[86, 87, 50, 26], Operations: []\nExploring Operation: 87-86=1, Resulting Numbers: [50, 26, 1]\nGenerated Node #2: [50, 26, 1] from Operation: 87-86=1\nCurrent State: 23:[50, 26, 1], Operations: ['87-86=1']\nExploring Operation: 50-26=24, Resulting Numbers: [1, 24]\nGenerated Node #3: [1, 24] from Operation: 50-26=24\nCurrent State: 23:[1, 24], Operations: ['87-86=1', '50-26=24']\nExploring Operation: 24-1=23, Resulting Numbers: [23]\n23,23 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 1, + 24, + 72, + 4 + ], + "target": 43, + "solution": [ + "1+24=25", + "72-4=68", + "68-25=43" + ], + "optimal_path": "Current State: 43:[1, 24, 72, 4], Operations: []\nExploring Operation: 1+24=25, Resulting Numbers: [72, 4, 25]\nGenerated Node #2: [72, 4, 25] from Operation: 1+24=25\nCurrent State: 43:[72, 4, 25], Operations: ['1+24=25']\nExploring Operation: 72-4=68, Resulting Numbers: [25, 68]\nGenerated Node #3: [25, 68] from Operation: 72-4=68\nCurrent State: 43:[25, 68], Operations: ['1+24=25', '72-4=68']\nExploring Operation: 68-25=43, Resulting Numbers: [43]\n43,43 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 78, + 93, + 39, + 86 + ], + "target": 14, + "solution": [ + "78/39=2", + "93-86=7", + "2*7=14" + ], + "optimal_path": "Current State: 14:[78, 93, 39, 86], Operations: []\nExploring Operation: 78/39=2, Resulting Numbers: [93, 86, 2]\nGenerated Node #2: [93, 86, 2] from Operation: 78/39=2\nCurrent State: 14:[93, 86, 2], Operations: ['78/39=2']\nExploring Operation: 93-86=7, Resulting Numbers: [2, 7]\nGenerated Node #3: [2, 7] from Operation: 93-86=7\nCurrent State: 14:[2, 7], Operations: ['78/39=2', '93-86=7']\nExploring Operation: 2*7=14, Resulting Numbers: [14]\n14,14 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 81, + 3, + 99, + 88 + ], + "target": 40, + "solution": [ + "88-81=7", + "99/3=33", + "7+33=40" + ], + "optimal_path": "Current State: 40:[81, 3, 99, 88], Operations: []\nExploring Operation: 88-81=7, Resulting Numbers: [3, 99, 7]\nGenerated Node #2: [3, 99, 7] from Operation: 88-81=7\nCurrent State: 40:[3, 99, 7], Operations: ['88-81=7']\nExploring Operation: 99/3=33, Resulting Numbers: [7, 33]\nGenerated Node #3: [7, 33] from Operation: 99/3=33\nCurrent State: 40:[7, 33], Operations: ['88-81=7', '99/3=33']\nExploring Operation: 7+33=40, Resulting Numbers: [40]\n40,40 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 23, + 4, + 22, + 97 + ], + "target": 13, + "solution": [ + "23+22=45", + "97-45=52", + "52/4=13" + ], + "optimal_path": "Current State: 13:[23, 4, 22, 97], Operations: []\nExploring Operation: 23+22=45, Resulting Numbers: [4, 97, 45]\nGenerated Node #2: [4, 97, 45] from Operation: 23+22=45\nCurrent State: 13:[4, 97, 45], Operations: ['23+22=45']\nExploring Operation: 97-45=52, Resulting Numbers: [4, 52]\nGenerated Node #3: [4, 52] from Operation: 97-45=52\nCurrent State: 13:[4, 52], Operations: ['23+22=45', '97-45=52']\nExploring Operation: 52/4=13, Resulting Numbers: [13]\n13,13 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 7, + 78, + 41, + 30 + ], + "target": 96, + "solution": [ + "7+78=85", + "41-30=11", + "85+11=96" + ], + "optimal_path": "Current State: 96:[7, 78, 41, 30], Operations: []\nExploring Operation: 7+78=85, Resulting Numbers: [41, 30, 85]\nGenerated Node #2: [41, 30, 85] from Operation: 7+78=85\nCurrent State: 96:[41, 30, 85], Operations: ['7+78=85']\nExploring Operation: 41-30=11, Resulting Numbers: [85, 11]\nGenerated Node #3: [85, 11] from Operation: 41-30=11\nCurrent State: 96:[85, 11], Operations: ['7+78=85', '41-30=11']\nExploring Operation: 85+11=96, Resulting Numbers: [96]\n96,96 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 72, + 21, + 88, + 96 + ], + "target": 11, + "solution": [ + "72+96=168", + "21*88=1848", + "1848/168=11" + ], + "optimal_path": "Current State: 11:[72, 21, 88, 96], Operations: []\nExploring Operation: 72+96=168, Resulting Numbers: [21, 88, 168]\nGenerated Node #2: [21, 88, 168] from Operation: 72+96=168\nCurrent State: 11:[21, 88, 168], Operations: ['72+96=168']\nExploring Operation: 21*88=1848, Resulting Numbers: [168, 1848]\nGenerated Node #3: [168, 1848] from Operation: 21*88=1848\nCurrent State: 11:[168, 1848], Operations: ['72+96=168', '21*88=1848']\nExploring Operation: 1848/168=11, Resulting Numbers: [11]\n11,11 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 63, + 22, + 81, + 80 + ], + "target": 85, + "solution": [ + "63+22=85", + "81-80=1", + "85*1=85" + ], + "optimal_path": "Current State: 85:[63, 22, 81, 80], Operations: []\nExploring Operation: 63+22=85, Resulting Numbers: [81, 80, 85]\nGenerated Node #2: [81, 80, 85] from Operation: 63+22=85\nCurrent State: 85:[81, 80, 85], Operations: ['63+22=85']\nExploring Operation: 81-80=1, Resulting Numbers: [85, 1]\nGenerated Node #3: [85, 1] from Operation: 81-80=1\nCurrent State: 85:[85, 1], Operations: ['63+22=85', '81-80=1']\nExploring Operation: 85*1=85, Resulting Numbers: [85]\n85,85 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 84, + 93, + 1, + 42 + ], + "target": 94, + "solution": [ + "84/42=2", + "93-1=92", + "2+92=94" + ], + "optimal_path": "Current State: 94:[84, 93, 1, 42], Operations: []\nExploring Operation: 84/42=2, Resulting Numbers: [93, 1, 2]\nGenerated Node #2: [93, 1, 2] from Operation: 84/42=2\nCurrent State: 94:[93, 1, 2], Operations: ['84/42=2']\nExploring Operation: 93-1=92, Resulting Numbers: [2, 92]\nGenerated Node #3: [2, 92] from Operation: 93-1=92\nCurrent State: 94:[2, 92], Operations: ['84/42=2', '93-1=92']\nExploring Operation: 2+92=94, Resulting Numbers: [94]\n94,94 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 83, + 90, + 22, + 2 + ], + "target": 27, + "solution": [ + "90-83=7", + "22-2=20", + "7+20=27" + ], + "optimal_path": "Current State: 27:[83, 90, 22, 2], Operations: []\nExploring Operation: 90-83=7, Resulting Numbers: [22, 2, 7]\nGenerated Node #2: [22, 2, 7] from Operation: 90-83=7\nCurrent State: 27:[22, 2, 7], Operations: ['90-83=7']\nExploring Operation: 22-2=20, Resulting Numbers: [7, 20]\nGenerated Node #3: [7, 20] from Operation: 22-2=20\nCurrent State: 27:[7, 20], Operations: ['90-83=7', '22-2=20']\nExploring Operation: 7+20=27, Resulting Numbers: [27]\n27,27 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 26, + 8, + 30, + 31 + ], + "target": 24, + "solution": [ + "26+30=56", + "56/8=7", + "31-7=24" + ], + "optimal_path": "Current State: 24:[26, 8, 30, 31], Operations: []\nExploring Operation: 26+30=56, Resulting Numbers: [8, 31, 56]\nGenerated Node #2: [8, 31, 56] from Operation: 26+30=56\nCurrent State: 24:[8, 31, 56], Operations: ['26+30=56']\nExploring Operation: 56/8=7, Resulting Numbers: [31, 7]\nGenerated Node #3: [31, 7] from Operation: 56/8=7\nCurrent State: 24:[31, 7], Operations: ['26+30=56', '56/8=7']\nExploring Operation: 31-7=24, Resulting Numbers: [24]\n24,24 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 51, + 5, + 81, + 23 + ], + "target": 59, + "solution": [ + "51-23=28", + "5*28=140", + "140-81=59" + ], + "optimal_path": "Current State: 59:[51, 5, 81, 23], Operations: []\nExploring Operation: 51-23=28, Resulting Numbers: [5, 81, 28]\nGenerated Node #2: [5, 81, 28] from Operation: 51-23=28\nCurrent State: 59:[5, 81, 28], Operations: ['51-23=28']\nExploring Operation: 5*28=140, Resulting Numbers: [81, 140]\nGenerated Node #3: [81, 140] from Operation: 5*28=140\nCurrent State: 59:[81, 140], Operations: ['51-23=28', '5*28=140']\nExploring Operation: 140-81=59, Resulting Numbers: [59]\n59,59 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 84, + 18, + 15, + 7 + ], + "target": 27, + "solution": [ + "84+15=99", + "18*7=126", + "126-99=27" + ], + "optimal_path": "Current State: 27:[84, 18, 15, 7], Operations: []\nExploring Operation: 84+15=99, Resulting Numbers: [18, 7, 99]\nGenerated Node #2: [18, 7, 99] from Operation: 84+15=99\nCurrent State: 27:[18, 7, 99], Operations: ['84+15=99']\nExploring Operation: 18*7=126, Resulting Numbers: [99, 126]\nGenerated Node #3: [99, 126] from Operation: 18*7=126\nCurrent State: 27:[99, 126], Operations: ['84+15=99', '18*7=126']\nExploring Operation: 126-99=27, Resulting Numbers: [27]\n27,27 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 3, + 27, + 31, + 8 + ], + "target": 63, + "solution": [ + "27-3=24", + "31+8=39", + "24+39=63" + ], + "optimal_path": "Current State: 63:[3, 27, 31, 8], Operations: []\nExploring Operation: 27-3=24, Resulting Numbers: [31, 8, 24]\nGenerated Node #2: [31, 8, 24] from Operation: 27-3=24\nCurrent State: 63:[31, 8, 24], Operations: ['27-3=24']\nExploring Operation: 31+8=39, Resulting Numbers: [24, 39]\nGenerated Node #3: [24, 39] from Operation: 31+8=39\nCurrent State: 63:[24, 39], Operations: ['27-3=24', '31+8=39']\nExploring Operation: 24+39=63, Resulting Numbers: [63]\n63,63 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 60, + 42, + 50, + 12 + ], + "target": 87, + "solution": [ + "60/12=5", + "42+50=92", + "92-5=87" + ], + "optimal_path": "Current State: 87:[60, 42, 50, 12], Operations: []\nExploring Operation: 60/12=5, Resulting Numbers: [42, 50, 5]\nGenerated Node #2: [42, 50, 5] from Operation: 60/12=5\nCurrent State: 87:[42, 50, 5], Operations: ['60/12=5']\nExploring Operation: 42+50=92, Resulting Numbers: [5, 92]\nGenerated Node #3: [5, 92] from Operation: 42+50=92\nCurrent State: 87:[5, 92], Operations: ['60/12=5', '42+50=92']\nExploring Operation: 92-5=87, Resulting Numbers: [87]\n87,87 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 26, + 98, + 32, + 77 + ], + "target": 72, + "solution": [ + "98+32=130", + "130/26=5", + "77-5=72" + ], + "optimal_path": "Current State: 72:[26, 98, 32, 77], Operations: []\nExploring Operation: 98+32=130, Resulting Numbers: [26, 77, 130]\nGenerated Node #2: [26, 77, 130] from Operation: 98+32=130\nCurrent State: 72:[26, 77, 130], Operations: ['98+32=130']\nExploring Operation: 130/26=5, Resulting Numbers: [77, 5]\nGenerated Node #3: [77, 5] from Operation: 130/26=5\nCurrent State: 72:[77, 5], Operations: ['98+32=130', '130/26=5']\nExploring Operation: 77-5=72, Resulting Numbers: [72]\n72,72 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 62, + 34, + 14, + 2 + ], + "target": 59, + "solution": [ + "62+14=76", + "34/2=17", + "76-17=59" + ], + "optimal_path": "Current State: 59:[62, 34, 14, 2], Operations: []\nExploring Operation: 62+14=76, Resulting Numbers: [34, 2, 76]\nGenerated Node #2: [34, 2, 76] from Operation: 62+14=76\nCurrent State: 59:[34, 2, 76], Operations: ['62+14=76']\nExploring Operation: 34/2=17, Resulting Numbers: [76, 17]\nGenerated Node #3: [76, 17] from Operation: 34/2=17\nCurrent State: 59:[76, 17], Operations: ['62+14=76', '34/2=17']\nExploring Operation: 76-17=59, Resulting Numbers: [59]\n59,59 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 90, + 28, + 79, + 69 + ], + "target": 52, + "solution": [ + "90-28=62", + "79-69=10", + "62-10=52" + ], + "optimal_path": "Current State: 52:[90, 28, 79, 69], Operations: []\nExploring Operation: 90-28=62, Resulting Numbers: [79, 69, 62]\nGenerated Node #2: [79, 69, 62] from Operation: 90-28=62\nCurrent State: 52:[79, 69, 62], Operations: ['90-28=62']\nExploring Operation: 79-69=10, Resulting Numbers: [62, 10]\nGenerated Node #3: [62, 10] from Operation: 79-69=10\nCurrent State: 52:[62, 10], Operations: ['90-28=62', '79-69=10']\nExploring Operation: 62-10=52, Resulting Numbers: [52]\n52,52 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 39, + 6, + 37, + 50 + ], + "target": 46, + "solution": [ + "39-6=33", + "50-37=13", + "33+13=46" + ], + "optimal_path": "Current State: 46:[39, 6, 37, 50], Operations: []\nExploring Operation: 39-6=33, Resulting Numbers: [37, 50, 33]\nGenerated Node #2: [37, 50, 33] from Operation: 39-6=33\nCurrent State: 46:[37, 50, 33], Operations: ['39-6=33']\nExploring Operation: 50-37=13, Resulting Numbers: [33, 13]\nGenerated Node #3: [33, 13] from Operation: 50-37=13\nCurrent State: 46:[33, 13], Operations: ['39-6=33', '50-37=13']\nExploring Operation: 33+13=46, Resulting Numbers: [46]\n46,46 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 45, + 61, + 36, + 2 + ], + "target": 43, + "solution": [ + "45-36=9", + "2*9=18", + "61-18=43" + ], + "optimal_path": "Current State: 43:[45, 61, 36, 2], Operations: []\nExploring Operation: 45-36=9, Resulting Numbers: [61, 2, 9]\nGenerated Node #2: [61, 2, 9] from Operation: 45-36=9\nCurrent State: 43:[61, 2, 9], Operations: ['45-36=9']\nExploring Operation: 2*9=18, Resulting Numbers: [61, 18]\nGenerated Node #3: [61, 18] from Operation: 2*9=18\nCurrent State: 43:[61, 18], Operations: ['45-36=9', '2*9=18']\nExploring Operation: 61-18=43, Resulting Numbers: [43]\n43,43 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 35, + 99, + 79, + 24 + ], + "target": 70, + "solution": [ + "35-24=11", + "99/11=9", + "79-9=70" + ], + "optimal_path": "Current State: 70:[35, 99, 79, 24], Operations: []\nExploring Operation: 35-24=11, Resulting Numbers: [99, 79, 11]\nGenerated Node #2: [99, 79, 11] from Operation: 35-24=11\nCurrent State: 70:[99, 79, 11], Operations: ['35-24=11']\nExploring Operation: 99/11=9, Resulting Numbers: [79, 9]\nGenerated Node #3: [79, 9] from Operation: 99/11=9\nCurrent State: 70:[79, 9], Operations: ['35-24=11', '99/11=9']\nExploring Operation: 79-9=70, Resulting Numbers: [70]\n70,70 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 68, + 4, + 99, + 18 + ], + "target": 99, + "solution": [ + "68/4=17", + "18-17=1", + "99*1=99" + ], + "optimal_path": "Current State: 99:[68, 4, 99, 18], Operations: []\nExploring Operation: 68/4=17, Resulting Numbers: [99, 18, 17]\nGenerated Node #2: [99, 18, 17] from Operation: 68/4=17\nCurrent State: 99:[99, 18, 17], Operations: ['68/4=17']\nExploring Operation: 18-17=1, Resulting Numbers: [99, 1]\nGenerated Node #3: [99, 1] from Operation: 18-17=1\nCurrent State: 99:[99, 1], Operations: ['68/4=17', '18-17=1']\nExploring Operation: 99*1=99, Resulting Numbers: [99]\n99,99 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 92, + 4, + 48, + 90 + ], + "target": 42, + "solution": [ + "92+4=96", + "48+90=138", + "138-96=42" + ], + "optimal_path": "Current State: 42:[92, 4, 48, 90], Operations: []\nExploring Operation: 92+4=96, Resulting Numbers: [48, 90, 96]\nGenerated Node #2: [48, 90, 96] from Operation: 92+4=96\nCurrent State: 42:[48, 90, 96], Operations: ['92+4=96']\nExploring Operation: 48+90=138, Resulting Numbers: [96, 138]\nGenerated Node #3: [96, 138] from Operation: 48+90=138\nCurrent State: 42:[96, 138], Operations: ['92+4=96', '48+90=138']\nExploring Operation: 138-96=42, Resulting Numbers: [42]\n42,42 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 41, + 3, + 94, + 90 + ], + "target": 29, + "solution": [ + "94-90=4", + "3*4=12", + "41-12=29" + ], + "optimal_path": "Current State: 29:[41, 3, 94, 90], Operations: []\nExploring Operation: 94-90=4, Resulting Numbers: [41, 3, 4]\nGenerated Node #2: [41, 3, 4] from Operation: 94-90=4\nCurrent State: 29:[41, 3, 4], Operations: ['94-90=4']\nExploring Operation: 3*4=12, Resulting Numbers: [41, 12]\nGenerated Node #3: [41, 12] from Operation: 3*4=12\nCurrent State: 29:[41, 12], Operations: ['94-90=4', '3*4=12']\nExploring Operation: 41-12=29, Resulting Numbers: [29]\n29,29 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 26, + 58, + 52, + 45 + ], + "target": 12, + "solution": [ + "26+58=84", + "52-45=7", + "84/7=12" + ], + "optimal_path": "Current State: 12:[26, 58, 52, 45], Operations: []\nExploring Operation: 26+58=84, Resulting Numbers: [52, 45, 84]\nGenerated Node #2: [52, 45, 84] from Operation: 26+58=84\nCurrent State: 12:[52, 45, 84], Operations: ['26+58=84']\nExploring Operation: 52-45=7, Resulting Numbers: [84, 7]\nGenerated Node #3: [84, 7] from Operation: 52-45=7\nCurrent State: 12:[84, 7], Operations: ['26+58=84', '52-45=7']\nExploring Operation: 84/7=12, Resulting Numbers: [12]\n12,12 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 96, + 23, + 30, + 5 + ], + "target": 77, + "solution": [ + "96-23=73", + "30*5=150", + "150-73=77" + ], + "optimal_path": "Current State: 77:[96, 23, 30, 5], Operations: []\nExploring Operation: 96-23=73, Resulting Numbers: [30, 5, 73]\nGenerated Node #2: [30, 5, 73] from Operation: 96-23=73\nCurrent State: 77:[30, 5, 73], Operations: ['96-23=73']\nExploring Operation: 30*5=150, Resulting Numbers: [73, 150]\nGenerated Node #3: [73, 150] from Operation: 30*5=150\nCurrent State: 77:[73, 150], Operations: ['96-23=73', '30*5=150']\nExploring Operation: 150-73=77, Resulting Numbers: [77]\n77,77 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 3, + 82, + 80, + 72 + ], + "target": 93, + "solution": [ + "3+82=85", + "80-72=8", + "85+8=93" + ], + "optimal_path": "Current State: 93:[3, 82, 80, 72], Operations: []\nExploring Operation: 3+82=85, Resulting Numbers: [80, 72, 85]\nGenerated Node #2: [80, 72, 85] from Operation: 3+82=85\nCurrent State: 93:[80, 72, 85], Operations: ['3+82=85']\nExploring Operation: 80-72=8, Resulting Numbers: [85, 8]\nGenerated Node #3: [85, 8] from Operation: 80-72=8\nCurrent State: 93:[85, 8], Operations: ['3+82=85', '80-72=8']\nExploring Operation: 85+8=93, Resulting Numbers: [93]\n93,93 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 24, + 86, + 31, + 13 + ], + "target": 92, + "solution": [ + "24+86=110", + "31-13=18", + "110-18=92" + ], + "optimal_path": "Current State: 92:[24, 86, 31, 13], Operations: []\nExploring Operation: 24+86=110, Resulting Numbers: [31, 13, 110]\nGenerated Node #2: [31, 13, 110] from Operation: 24+86=110\nCurrent State: 92:[31, 13, 110], Operations: ['24+86=110']\nExploring Operation: 31-13=18, Resulting Numbers: [110, 18]\nGenerated Node #3: [110, 18] from Operation: 31-13=18\nCurrent State: 92:[110, 18], Operations: ['24+86=110', '31-13=18']\nExploring Operation: 110-18=92, Resulting Numbers: [92]\n92,92 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 9, + 53, + 51, + 73 + ], + "target": 55, + "solution": [ + "53-51=2", + "9*2=18", + "73-18=55" + ], + "optimal_path": "Current State: 55:[9, 53, 51, 73], Operations: []\nExploring Operation: 53-51=2, Resulting Numbers: [9, 73, 2]\nGenerated Node #2: [9, 73, 2] from Operation: 53-51=2\nCurrent State: 55:[9, 73, 2], Operations: ['53-51=2']\nExploring Operation: 9*2=18, Resulting Numbers: [73, 18]\nGenerated Node #3: [73, 18] from Operation: 9*2=18\nCurrent State: 55:[73, 18], Operations: ['53-51=2', '9*2=18']\nExploring Operation: 73-18=55, Resulting Numbers: [55]\n55,55 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 44, + 7, + 43, + 97 + ], + "target": 17, + "solution": [ + "44-7=37", + "97-43=54", + "54-37=17" + ], + "optimal_path": "Current State: 17:[44, 7, 43, 97], Operations: []\nExploring Operation: 44-7=37, Resulting Numbers: [43, 97, 37]\nGenerated Node #2: [43, 97, 37] from Operation: 44-7=37\nCurrent State: 17:[43, 97, 37], Operations: ['44-7=37']\nExploring Operation: 97-43=54, Resulting Numbers: [37, 54]\nGenerated Node #3: [37, 54] from Operation: 97-43=54\nCurrent State: 17:[37, 54], Operations: ['44-7=37', '97-43=54']\nExploring Operation: 54-37=17, Resulting Numbers: [17]\n17,17 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 17, + 82, + 23, + 28 + ], + "target": 14, + "solution": [ + "82-17=65", + "23+28=51", + "65-51=14" + ], + "optimal_path": "Current State: 14:[17, 82, 23, 28], Operations: []\nExploring Operation: 82-17=65, Resulting Numbers: [23, 28, 65]\nGenerated Node #2: [23, 28, 65] from Operation: 82-17=65\nCurrent State: 14:[23, 28, 65], Operations: ['82-17=65']\nExploring Operation: 23+28=51, Resulting Numbers: [65, 51]\nGenerated Node #3: [65, 51] from Operation: 23+28=51\nCurrent State: 14:[65, 51], Operations: ['82-17=65', '23+28=51']\nExploring Operation: 65-51=14, Resulting Numbers: [14]\n14,14 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 92, + 52, + 5, + 94 + ], + "target": 42, + "solution": [ + "94-92=2", + "5*2=10", + "52-10=42" + ], + "optimal_path": "Current State: 42:[92, 52, 5, 94], Operations: []\nExploring Operation: 94-92=2, Resulting Numbers: [52, 5, 2]\nGenerated Node #2: [52, 5, 2] from Operation: 94-92=2\nCurrent State: 42:[52, 5, 2], Operations: ['94-92=2']\nExploring Operation: 5*2=10, Resulting Numbers: [52, 10]\nGenerated Node #3: [52, 10] from Operation: 5*2=10\nCurrent State: 42:[52, 10], Operations: ['94-92=2', '5*2=10']\nExploring Operation: 52-10=42, Resulting Numbers: [42]\n42,42 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 26, + 12, + 65, + 35 + ], + "target": 62, + "solution": [ + "26+12=38", + "65+35=100", + "100-38=62" + ], + "optimal_path": "Current State: 62:[26, 12, 65, 35], Operations: []\nExploring Operation: 26+12=38, Resulting Numbers: [65, 35, 38]\nGenerated Node #2: [65, 35, 38] from Operation: 26+12=38\nCurrent State: 62:[65, 35, 38], Operations: ['26+12=38']\nExploring Operation: 65+35=100, Resulting Numbers: [38, 100]\nGenerated Node #3: [38, 100] from Operation: 65+35=100\nCurrent State: 62:[38, 100], Operations: ['26+12=38', '65+35=100']\nExploring Operation: 100-38=62, Resulting Numbers: [62]\n62,62 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 84, + 25, + 1, + 5 + ], + "target": 36, + "solution": [ + "25-1=24", + "5*24=120", + "120-84=36" + ], + "optimal_path": "Current State: 36:[84, 25, 1, 5], Operations: []\nExploring Operation: 25-1=24, Resulting Numbers: [84, 5, 24]\nGenerated Node #2: [84, 5, 24] from Operation: 25-1=24\nCurrent State: 36:[84, 5, 24], Operations: ['25-1=24']\nExploring Operation: 5*24=120, Resulting Numbers: [84, 120]\nGenerated Node #3: [84, 120] from Operation: 5*24=120\nCurrent State: 36:[84, 120], Operations: ['25-1=24', '5*24=120']\nExploring Operation: 120-84=36, Resulting Numbers: [36]\n36,36 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 7, + 21, + 91, + 26 + ], + "target": 98, + "solution": [ + "7+21=28", + "91*28=2548", + "2548/26=98" + ], + "optimal_path": "Current State: 98:[7, 21, 91, 26], Operations: []\nExploring Operation: 7+21=28, Resulting Numbers: [91, 26, 28]\nGenerated Node #2: [91, 26, 28] from Operation: 7+21=28\nCurrent State: 98:[91, 26, 28], Operations: ['7+21=28']\nExploring Operation: 91*28=2548, Resulting Numbers: [26, 2548]\nGenerated Node #3: [26, 2548] from Operation: 91*28=2548\nCurrent State: 98:[26, 2548], Operations: ['7+21=28', '91*28=2548']\nExploring Operation: 2548/26=98, Resulting Numbers: [98]\n98,98 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 29, + 67, + 51, + 29 + ], + "target": 60, + "solution": [ + "67-29=38", + "51-29=22", + "38+22=60" + ], + "optimal_path": "Current State: 60:[29, 67, 51, 29], Operations: []\nExploring Operation: 67-29=38, Resulting Numbers: [51, 38]\nGenerated Node #2: [51, 38] from Operation: 67-29=38\nCurrent State: 60:[51, 38], Operations: ['67-29=38']\nExploring Operation: 51-29=22, Resulting Numbers: [38, 22]\nGenerated Node #3: [38, 22] from Operation: 51-29=22\nCurrent State: 60:[38, 22], Operations: ['67-29=38', '51-29=22']\nExploring Operation: 38+22=60, Resulting Numbers: [60]\n60,60 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 9, + 35, + 55, + 88 + ], + "target": 78, + "solution": [ + "35+55=90", + "90/9=10", + "88-10=78" + ], + "optimal_path": "Current State: 78:[9, 35, 55, 88], Operations: []\nExploring Operation: 35+55=90, Resulting Numbers: [9, 88, 90]\nGenerated Node #2: [9, 88, 90] from Operation: 35+55=90\nCurrent State: 78:[9, 88, 90], Operations: ['35+55=90']\nExploring Operation: 90/9=10, Resulting Numbers: [88, 10]\nGenerated Node #3: [88, 10] from Operation: 90/9=10\nCurrent State: 78:[88, 10], Operations: ['35+55=90', '90/9=10']\nExploring Operation: 88-10=78, Resulting Numbers: [78]\n78,78 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 76, + 86, + 53, + 37 + ], + "target": 19, + "solution": [ + "86-53=33", + "37-33=4", + "76/4=19" + ], + "optimal_path": "Current State: 19:[76, 86, 53, 37], Operations: []\nExploring Operation: 86-53=33, Resulting Numbers: [76, 37, 33]\nGenerated Node #2: [76, 37, 33] from Operation: 86-53=33\nCurrent State: 19:[76, 37, 33], Operations: ['86-53=33']\nExploring Operation: 37-33=4, Resulting Numbers: [76, 4]\nGenerated Node #3: [76, 4] from Operation: 37-33=4\nCurrent State: 19:[76, 4], Operations: ['86-53=33', '37-33=4']\nExploring Operation: 76/4=19, Resulting Numbers: [19]\n19,19 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 30, + 55, + 13, + 12 + ], + "target": 71, + "solution": [ + "30+55=85", + "13*12=156", + "156-85=71" + ], + "optimal_path": "Current State: 71:[30, 55, 13, 12], Operations: []\nExploring Operation: 30+55=85, Resulting Numbers: [13, 12, 85]\nGenerated Node #2: [13, 12, 85] from Operation: 30+55=85\nCurrent State: 71:[13, 12, 85], Operations: ['30+55=85']\nExploring Operation: 13*12=156, Resulting Numbers: [85, 156]\nGenerated Node #3: [85, 156] from Operation: 13*12=156\nCurrent State: 71:[85, 156], Operations: ['30+55=85', '13*12=156']\nExploring Operation: 156-85=71, Resulting Numbers: [71]\n71,71 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 84, + 42, + 10, + 37 + ], + "target": 44, + "solution": [ + "84-10=74", + "74/37=2", + "42+2=44" + ], + "optimal_path": "Current State: 44:[84, 42, 10, 37], Operations: []\nExploring Operation: 84-10=74, Resulting Numbers: [42, 37, 74]\nGenerated Node #2: [42, 37, 74] from Operation: 84-10=74\nCurrent State: 44:[42, 37, 74], Operations: ['84-10=74']\nExploring Operation: 74/37=2, Resulting Numbers: [42, 2]\nGenerated Node #3: [42, 2] from Operation: 74/37=2\nCurrent State: 44:[42, 2], Operations: ['84-10=74', '74/37=2']\nExploring Operation: 42+2=44, Resulting Numbers: [44]\n44,44 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 6, + 38, + 43, + 17 + ], + "target": 79, + "solution": [ + "43-38=5", + "17*5=85", + "85-6=79" + ], + "optimal_path": "Current State: 79:[6, 38, 43, 17], Operations: []\nExploring Operation: 43-38=5, Resulting Numbers: [6, 17, 5]\nGenerated Node #2: [6, 17, 5] from Operation: 43-38=5\nCurrent State: 79:[6, 17, 5], Operations: ['43-38=5']\nExploring Operation: 17*5=85, Resulting Numbers: [6, 85]\nGenerated Node #3: [6, 85] from Operation: 17*5=85\nCurrent State: 79:[6, 85], Operations: ['43-38=5', '17*5=85']\nExploring Operation: 85-6=79, Resulting Numbers: [79]\n79,79 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 51, + 68, + 4, + 83 + ], + "target": 32, + "solution": [ + "51+68=119", + "4+83=87", + "119-87=32" + ], + "optimal_path": "Current State: 32:[51, 68, 4, 83], Operations: []\nExploring Operation: 51+68=119, Resulting Numbers: [4, 83, 119]\nGenerated Node #2: [4, 83, 119] from Operation: 51+68=119\nCurrent State: 32:[4, 83, 119], Operations: ['51+68=119']\nExploring Operation: 4+83=87, Resulting Numbers: [119, 87]\nGenerated Node #3: [119, 87] from Operation: 4+83=87\nCurrent State: 32:[119, 87], Operations: ['51+68=119', '4+83=87']\nExploring Operation: 119-87=32, Resulting Numbers: [32]\n32,32 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 70, + 50, + 56, + 52 + ], + "target": 28, + "solution": [ + "70-56=14", + "52-50=2", + "14*2=28" + ], + "optimal_path": "Current State: 28:[70, 50, 56, 52], Operations: []\nExploring Operation: 70-56=14, Resulting Numbers: [50, 52, 14]\nGenerated Node #2: [50, 52, 14] from Operation: 70-56=14\nCurrent State: 28:[50, 52, 14], Operations: ['70-56=14']\nExploring Operation: 52-50=2, Resulting Numbers: [14, 2]\nGenerated Node #3: [14, 2] from Operation: 52-50=2\nCurrent State: 28:[14, 2], Operations: ['70-56=14', '52-50=2']\nExploring Operation: 14*2=28, Resulting Numbers: [28]\n28,28 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 14, + 74, + 42, + 70 + ], + "target": 24, + "solution": [ + "14+74=88", + "42+70=112", + "112-88=24" + ], + "optimal_path": "Current State: 24:[14, 74, 42, 70], Operations: []\nExploring Operation: 14+74=88, Resulting Numbers: [42, 70, 88]\nGenerated Node #2: [42, 70, 88] from Operation: 14+74=88\nCurrent State: 24:[42, 70, 88], Operations: ['14+74=88']\nExploring Operation: 42+70=112, Resulting Numbers: [88, 112]\nGenerated Node #3: [88, 112] from Operation: 42+70=112\nCurrent State: 24:[88, 112], Operations: ['14+74=88', '42+70=112']\nExploring Operation: 112-88=24, Resulting Numbers: [24]\n24,24 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 76, + 42, + 41, + 92 + ], + "target": 45, + "solution": [ + "76+92=168", + "168/42=4", + "41+4=45" + ], + "optimal_path": "Current State: 45:[76, 42, 41, 92], Operations: []\nExploring Operation: 76+92=168, Resulting Numbers: [42, 41, 168]\nGenerated Node #2: [42, 41, 168] from Operation: 76+92=168\nCurrent State: 45:[42, 41, 168], Operations: ['76+92=168']\nExploring Operation: 168/42=4, Resulting Numbers: [41, 4]\nGenerated Node #3: [41, 4] from Operation: 168/42=4\nCurrent State: 45:[41, 4], Operations: ['76+92=168', '168/42=4']\nExploring Operation: 41+4=45, Resulting Numbers: [45]\n45,45 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 65, + 26, + 37, + 88 + ], + "target": 40, + "solution": [ + "65+26=91", + "88-37=51", + "91-51=40" + ], + "optimal_path": "Current State: 40:[65, 26, 37, 88], Operations: []\nExploring Operation: 65+26=91, Resulting Numbers: [37, 88, 91]\nGenerated Node #2: [37, 88, 91] from Operation: 65+26=91\nCurrent State: 40:[37, 88, 91], Operations: ['65+26=91']\nExploring Operation: 88-37=51, Resulting Numbers: [91, 51]\nGenerated Node #3: [91, 51] from Operation: 88-37=51\nCurrent State: 40:[91, 51], Operations: ['65+26=91', '88-37=51']\nExploring Operation: 91-51=40, Resulting Numbers: [40]\n40,40 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 74, + 32, + 17, + 81 + ], + "target": 87, + "solution": [ + "81-74=7", + "17*7=119", + "119-32=87" + ], + "optimal_path": "Current State: 87:[74, 32, 17, 81], Operations: []\nExploring Operation: 81-74=7, Resulting Numbers: [32, 17, 7]\nGenerated Node #2: [32, 17, 7] from Operation: 81-74=7\nCurrent State: 87:[32, 17, 7], Operations: ['81-74=7']\nExploring Operation: 17*7=119, Resulting Numbers: [32, 119]\nGenerated Node #3: [32, 119] from Operation: 17*7=119\nCurrent State: 87:[32, 119], Operations: ['81-74=7', '17*7=119']\nExploring Operation: 119-32=87, Resulting Numbers: [87]\n87,87 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 18, + 47, + 7, + 69 + ], + "target": 72, + "solution": [ + "47+7=54", + "54/18=3", + "69+3=72" + ], + "optimal_path": "Current State: 72:[18, 47, 7, 69], Operations: []\nExploring Operation: 47+7=54, Resulting Numbers: [18, 69, 54]\nGenerated Node #2: [18, 69, 54] from Operation: 47+7=54\nCurrent State: 72:[18, 69, 54], Operations: ['47+7=54']\nExploring Operation: 54/18=3, Resulting Numbers: [69, 3]\nGenerated Node #3: [69, 3] from Operation: 54/18=3\nCurrent State: 72:[69, 3], Operations: ['47+7=54', '54/18=3']\nExploring Operation: 69+3=72, Resulting Numbers: [72]\n72,72 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 76, + 39, + 1, + 87 + ], + "target": 49, + "solution": [ + "76-39=37", + "87-1=86", + "86-37=49" + ], + "optimal_path": "Current State: 49:[76, 39, 1, 87], Operations: []\nExploring Operation: 76-39=37, Resulting Numbers: [1, 87, 37]\nGenerated Node #2: [1, 87, 37] from Operation: 76-39=37\nCurrent State: 49:[1, 87, 37], Operations: ['76-39=37']\nExploring Operation: 87-1=86, Resulting Numbers: [37, 86]\nGenerated Node #3: [37, 86] from Operation: 87-1=86\nCurrent State: 49:[37, 86], Operations: ['76-39=37', '87-1=86']\nExploring Operation: 86-37=49, Resulting Numbers: [49]\n49,49 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 7, + 5, + 53, + 3 + ], + "target": 59, + "solution": [ + "7-5=2", + "3*2=6", + "53+6=59" + ], + "optimal_path": "Current State: 59:[7, 5, 53, 3], Operations: []\nExploring Operation: 7-5=2, Resulting Numbers: [53, 3, 2]\nGenerated Node #2: [53, 3, 2] from Operation: 7-5=2\nCurrent State: 59:[53, 3, 2], Operations: ['7-5=2']\nExploring Operation: 3*2=6, Resulting Numbers: [53, 6]\nGenerated Node #3: [53, 6] from Operation: 3*2=6\nCurrent State: 59:[53, 6], Operations: ['7-5=2', '3*2=6']\nExploring Operation: 53+6=59, Resulting Numbers: [59]\n59,59 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 4, + 54, + 13, + 61 + ], + "target": 66, + "solution": [ + "61-13=48", + "48/4=12", + "54+12=66" + ], + "optimal_path": "Current State: 66:[4, 54, 13, 61], Operations: []\nExploring Operation: 61-13=48, Resulting Numbers: [4, 54, 48]\nGenerated Node #2: [4, 54, 48] from Operation: 61-13=48\nCurrent State: 66:[4, 54, 48], Operations: ['61-13=48']\nExploring Operation: 48/4=12, Resulting Numbers: [54, 12]\nGenerated Node #3: [54, 12] from Operation: 48/4=12\nCurrent State: 66:[54, 12], Operations: ['61-13=48', '48/4=12']\nExploring Operation: 54+12=66, Resulting Numbers: [66]\n66,66 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 59, + 13, + 98, + 50 + ], + "target": 94, + "solution": [ + "59-13=46", + "98-50=48", + "46+48=94" + ], + "optimal_path": "Current State: 94:[59, 13, 98, 50], Operations: []\nExploring Operation: 59-13=46, Resulting Numbers: [98, 50, 46]\nGenerated Node #2: [98, 50, 46] from Operation: 59-13=46\nCurrent State: 94:[98, 50, 46], Operations: ['59-13=46']\nExploring Operation: 98-50=48, Resulting Numbers: [46, 48]\nGenerated Node #3: [46, 48] from Operation: 98-50=48\nCurrent State: 94:[46, 48], Operations: ['59-13=46', '98-50=48']\nExploring Operation: 46+48=94, Resulting Numbers: [94]\n94,94 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 61, + 16, + 15, + 62 + ], + "target": 32, + "solution": [ + "61-16=45", + "15+62=77", + "77-45=32" + ], + "optimal_path": "Current State: 32:[61, 16, 15, 62], Operations: []\nExploring Operation: 61-16=45, Resulting Numbers: [15, 62, 45]\nGenerated Node #2: [15, 62, 45] from Operation: 61-16=45\nCurrent State: 32:[15, 62, 45], Operations: ['61-16=45']\nExploring Operation: 15+62=77, Resulting Numbers: [45, 77]\nGenerated Node #3: [45, 77] from Operation: 15+62=77\nCurrent State: 32:[45, 77], Operations: ['61-16=45', '15+62=77']\nExploring Operation: 77-45=32, Resulting Numbers: [32]\n32,32 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 43, + 94, + 72, + 66 + ], + "target": 45, + "solution": [ + "94-43=51", + "72-66=6", + "51-6=45" + ], + "optimal_path": "Current State: 45:[43, 94, 72, 66], Operations: []\nExploring Operation: 94-43=51, Resulting Numbers: [72, 66, 51]\nGenerated Node #2: [72, 66, 51] from Operation: 94-43=51\nCurrent State: 45:[72, 66, 51], Operations: ['94-43=51']\nExploring Operation: 72-66=6, Resulting Numbers: [51, 6]\nGenerated Node #3: [51, 6] from Operation: 72-66=6\nCurrent State: 45:[51, 6], Operations: ['94-43=51', '72-66=6']\nExploring Operation: 51-6=45, Resulting Numbers: [45]\n45,45 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 12, + 14, + 26, + 98 + ], + "target": 31, + "solution": [ + "12+26=38", + "98/14=7", + "38-7=31" + ], + "optimal_path": "Current State: 31:[12, 14, 26, 98], Operations: []\nExploring Operation: 12+26=38, Resulting Numbers: [14, 98, 38]\nGenerated Node #2: [14, 98, 38] from Operation: 12+26=38\nCurrent State: 31:[14, 98, 38], Operations: ['12+26=38']\nExploring Operation: 98/14=7, Resulting Numbers: [38, 7]\nGenerated Node #3: [38, 7] from Operation: 98/14=7\nCurrent State: 31:[38, 7], Operations: ['12+26=38', '98/14=7']\nExploring Operation: 38-7=31, Resulting Numbers: [31]\n31,31 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 33, + 84, + 36, + 13 + ], + "target": 90, + "solution": [ + "33*84=2772", + "2772/36=77", + "13+77=90" + ], + "optimal_path": "Current State: 90:[33, 84, 36, 13], Operations: []\nExploring Operation: 33*84=2772, Resulting Numbers: [36, 13, 2772]\nGenerated Node #2: [36, 13, 2772] from Operation: 33*84=2772\nCurrent State: 90:[36, 13, 2772], Operations: ['33*84=2772']\nExploring Operation: 2772/36=77, Resulting Numbers: [13, 77]\nGenerated Node #3: [13, 77] from Operation: 2772/36=77\nCurrent State: 90:[13, 77], Operations: ['33*84=2772', '2772/36=77']\nExploring Operation: 13+77=90, Resulting Numbers: [90]\n90,90 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 95, + 97, + 39, + 68 + ], + "target": 85, + "solution": [ + "95+97=192", + "39+68=107", + "192-107=85" + ], + "optimal_path": "Current State: 85:[95, 97, 39, 68], Operations: []\nExploring Operation: 95+97=192, Resulting Numbers: [39, 68, 192]\nGenerated Node #2: [39, 68, 192] from Operation: 95+97=192\nCurrent State: 85:[39, 68, 192], Operations: ['95+97=192']\nExploring Operation: 39+68=107, Resulting Numbers: [192, 107]\nGenerated Node #3: [192, 107] from Operation: 39+68=107\nCurrent State: 85:[192, 107], Operations: ['95+97=192', '39+68=107']\nExploring Operation: 192-107=85, Resulting Numbers: [85]\n85,85 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 48, + 81, + 99, + 49 + ], + "target": 19, + "solution": [ + "48+81=129", + "99+49=148", + "148-129=19" + ], + "optimal_path": "Current State: 19:[48, 81, 99, 49], Operations: []\nExploring Operation: 48+81=129, Resulting Numbers: [99, 49, 129]\nGenerated Node #2: [99, 49, 129] from Operation: 48+81=129\nCurrent State: 19:[99, 49, 129], Operations: ['48+81=129']\nExploring Operation: 99+49=148, Resulting Numbers: [129, 148]\nGenerated Node #3: [129, 148] from Operation: 99+49=148\nCurrent State: 19:[129, 148], Operations: ['48+81=129', '99+49=148']\nExploring Operation: 148-129=19, Resulting Numbers: [19]\n19,19 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 18, + 7, + 67, + 38 + ], + "target": 75, + "solution": [ + "18+38=56", + "56/7=8", + "67+8=75" + ], + "optimal_path": "Current State: 75:[18, 7, 67, 38], Operations: []\nExploring Operation: 18+38=56, Resulting Numbers: [7, 67, 56]\nGenerated Node #2: [7, 67, 56] from Operation: 18+38=56\nCurrent State: 75:[7, 67, 56], Operations: ['18+38=56']\nExploring Operation: 56/7=8, Resulting Numbers: [67, 8]\nGenerated Node #3: [67, 8] from Operation: 56/7=8\nCurrent State: 75:[67, 8], Operations: ['18+38=56', '56/7=8']\nExploring Operation: 67+8=75, Resulting Numbers: [75]\n75,75 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 76, + 33, + 20, + 34 + ], + "target": 96, + "solution": [ + "76+20=96", + "34-33=1", + "96*1=96" + ], + "optimal_path": "Current State: 96:[76, 33, 20, 34], Operations: []\nExploring Operation: 76+20=96, Resulting Numbers: [33, 34, 96]\nGenerated Node #2: [33, 34, 96] from Operation: 76+20=96\nCurrent State: 96:[33, 34, 96], Operations: ['76+20=96']\nExploring Operation: 34-33=1, Resulting Numbers: [96, 1]\nGenerated Node #3: [96, 1] from Operation: 34-33=1\nCurrent State: 96:[96, 1], Operations: ['76+20=96', '34-33=1']\nExploring Operation: 96*1=96, Resulting Numbers: [96]\n96,96 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 88, + 70, + 82, + 48 + ], + "target": 92, + "solution": [ + "82-70=12", + "48/12=4", + "88+4=92" + ], + "optimal_path": "Current State: 92:[88, 70, 82, 48], Operations: []\nExploring Operation: 82-70=12, Resulting Numbers: [88, 48, 12]\nGenerated Node #2: [88, 48, 12] from Operation: 82-70=12\nCurrent State: 92:[88, 48, 12], Operations: ['82-70=12']\nExploring Operation: 48/12=4, Resulting Numbers: [88, 4]\nGenerated Node #3: [88, 4] from Operation: 48/12=4\nCurrent State: 92:[88, 4], Operations: ['82-70=12', '48/12=4']\nExploring Operation: 88+4=92, Resulting Numbers: [92]\n92,92 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 77, + 96, + 87, + 79 + ], + "target": 78, + "solution": [ + "79-77=2", + "87*2=174", + "174-96=78" + ], + "optimal_path": "Current State: 78:[77, 96, 87, 79], Operations: []\nExploring Operation: 79-77=2, Resulting Numbers: [96, 87, 2]\nGenerated Node #2: [96, 87, 2] from Operation: 79-77=2\nCurrent State: 78:[96, 87, 2], Operations: ['79-77=2']\nExploring Operation: 87*2=174, Resulting Numbers: [96, 174]\nGenerated Node #3: [96, 174] from Operation: 87*2=174\nCurrent State: 78:[96, 174], Operations: ['79-77=2', '87*2=174']\nExploring Operation: 174-96=78, Resulting Numbers: [78]\n78,78 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 42, + 4, + 72, + 58 + ], + "target": 97, + "solution": [ + "42+58=100", + "100/4=25", + "72+25=97" + ], + "optimal_path": "Current State: 97:[42, 4, 72, 58], Operations: []\nExploring Operation: 42+58=100, Resulting Numbers: [4, 72, 100]\nGenerated Node #2: [4, 72, 100] from Operation: 42+58=100\nCurrent State: 97:[4, 72, 100], Operations: ['42+58=100']\nExploring Operation: 100/4=25, Resulting Numbers: [72, 25]\nGenerated Node #3: [72, 25] from Operation: 100/4=25\nCurrent State: 97:[72, 25], Operations: ['42+58=100', '100/4=25']\nExploring Operation: 72+25=97, Resulting Numbers: [97]\n97,97 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 21, + 79, + 35, + 3 + ], + "target": 47, + "solution": [ + "79-21=58", + "35*3=105", + "105-58=47" + ], + "optimal_path": "Current State: 47:[21, 79, 35, 3], Operations: []\nExploring Operation: 79-21=58, Resulting Numbers: [35, 3, 58]\nGenerated Node #2: [35, 3, 58] from Operation: 79-21=58\nCurrent State: 47:[35, 3, 58], Operations: ['79-21=58']\nExploring Operation: 35*3=105, Resulting Numbers: [58, 105]\nGenerated Node #3: [58, 105] from Operation: 35*3=105\nCurrent State: 47:[58, 105], Operations: ['79-21=58', '35*3=105']\nExploring Operation: 105-58=47, Resulting Numbers: [47]\n47,47 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 69, + 12, + 40, + 97 + ], + "target": 56, + "solution": [ + "69+12=81", + "40+97=137", + "137-81=56" + ], + "optimal_path": "Current State: 56:[69, 12, 40, 97], Operations: []\nExploring Operation: 69+12=81, Resulting Numbers: [40, 97, 81]\nGenerated Node #2: [40, 97, 81] from Operation: 69+12=81\nCurrent State: 56:[40, 97, 81], Operations: ['69+12=81']\nExploring Operation: 40+97=137, Resulting Numbers: [81, 137]\nGenerated Node #3: [81, 137] from Operation: 40+97=137\nCurrent State: 56:[81, 137], Operations: ['69+12=81', '40+97=137']\nExploring Operation: 137-81=56, Resulting Numbers: [56]\n56,56 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 49, + 25, + 35, + 85 + ], + "target": 25, + "solution": [ + "49+35=84", + "85-84=1", + "25*1=25" + ], + "optimal_path": "Current State: 25:[49, 25, 35, 85], Operations: []\nExploring Operation: 49+35=84, Resulting Numbers: [25, 85, 84]\nGenerated Node #2: [25, 85, 84] from Operation: 49+35=84\nCurrent State: 25:[25, 85, 84], Operations: ['49+35=84']\nExploring Operation: 85-84=1, Resulting Numbers: [25, 1]\nGenerated Node #3: [25, 1] from Operation: 85-84=1\nCurrent State: 25:[25, 1], Operations: ['49+35=84', '85-84=1']\nExploring Operation: 25*1=25, Resulting Numbers: [25]\n25,25 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 18, + 37, + 11, + 16 + ], + "target": 46, + "solution": [ + "37-18=19", + "11+16=27", + "19+27=46" + ], + "optimal_path": "Current State: 46:[18, 37, 11, 16], Operations: []\nExploring Operation: 37-18=19, Resulting Numbers: [11, 16, 19]\nGenerated Node #2: [11, 16, 19] from Operation: 37-18=19\nCurrent State: 46:[11, 16, 19], Operations: ['37-18=19']\nExploring Operation: 11+16=27, Resulting Numbers: [19, 27]\nGenerated Node #3: [19, 27] from Operation: 11+16=27\nCurrent State: 46:[19, 27], Operations: ['37-18=19', '11+16=27']\nExploring Operation: 19+27=46, Resulting Numbers: [46]\n46,46 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 26, + 69, + 9, + 49 + ], + "target": 83, + "solution": [ + "69-26=43", + "49-9=40", + "43+40=83" + ], + "optimal_path": "Current State: 83:[26, 69, 9, 49], Operations: []\nExploring Operation: 69-26=43, Resulting Numbers: [9, 49, 43]\nGenerated Node #2: [9, 49, 43] from Operation: 69-26=43\nCurrent State: 83:[9, 49, 43], Operations: ['69-26=43']\nExploring Operation: 49-9=40, Resulting Numbers: [43, 40]\nGenerated Node #3: [43, 40] from Operation: 49-9=40\nCurrent State: 83:[43, 40], Operations: ['69-26=43', '49-9=40']\nExploring Operation: 43+40=83, Resulting Numbers: [83]\n83,83 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 18, + 14, + 22, + 10 + ], + "target": 28, + "solution": [ + "18-14=4", + "22+10=32", + "32-4=28" + ], + "optimal_path": "Current State: 28:[18, 14, 22, 10], Operations: []\nExploring Operation: 18-14=4, Resulting Numbers: [22, 10, 4]\nGenerated Node #2: [22, 10, 4] from Operation: 18-14=4\nCurrent State: 28:[22, 10, 4], Operations: ['18-14=4']\nExploring Operation: 22+10=32, Resulting Numbers: [4, 32]\nGenerated Node #3: [4, 32] from Operation: 22+10=32\nCurrent State: 28:[4, 32], Operations: ['18-14=4', '22+10=32']\nExploring Operation: 32-4=28, Resulting Numbers: [28]\n28,28 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 79, + 18, + 4, + 70 + ], + "target": 66, + "solution": [ + "70-18=52", + "52/4=13", + "79-13=66" + ], + "optimal_path": "Current State: 66:[79, 18, 4, 70], Operations: []\nExploring Operation: 70-18=52, Resulting Numbers: [79, 4, 52]\nGenerated Node #2: [79, 4, 52] from Operation: 70-18=52\nCurrent State: 66:[79, 4, 52], Operations: ['70-18=52']\nExploring Operation: 52/4=13, Resulting Numbers: [79, 13]\nGenerated Node #3: [79, 13] from Operation: 52/4=13\nCurrent State: 66:[79, 13], Operations: ['70-18=52', '52/4=13']\nExploring Operation: 79-13=66, Resulting Numbers: [66]\n66,66 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 66, + 31, + 7, + 25 + ], + "target": 70, + "solution": [ + "66-31=35", + "35-25=10", + "7*10=70" + ], + "optimal_path": "Current State: 70:[66, 31, 7, 25], Operations: []\nExploring Operation: 66-31=35, Resulting Numbers: [7, 25, 35]\nGenerated Node #2: [7, 25, 35] from Operation: 66-31=35\nCurrent State: 70:[7, 25, 35], Operations: ['66-31=35']\nExploring Operation: 35-25=10, Resulting Numbers: [7, 10]\nGenerated Node #3: [7, 10] from Operation: 35-25=10\nCurrent State: 70:[7, 10], Operations: ['66-31=35', '35-25=10']\nExploring Operation: 7*10=70, Resulting Numbers: [70]\n70,70 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 27, + 61, + 50, + 17 + ], + "target": 100, + "solution": [ + "61-27=34", + "50*34=1700", + "1700/17=100" + ], + "optimal_path": "Current State: 100:[27, 61, 50, 17], Operations: []\nExploring Operation: 61-27=34, Resulting Numbers: [50, 17, 34]\nGenerated Node #2: [50, 17, 34] from Operation: 61-27=34\nCurrent State: 100:[50, 17, 34], Operations: ['61-27=34']\nExploring Operation: 50*34=1700, Resulting Numbers: [17, 1700]\nGenerated Node #3: [17, 1700] from Operation: 50*34=1700\nCurrent State: 100:[17, 1700], Operations: ['61-27=34', '50*34=1700']\nExploring Operation: 1700/17=100, Resulting Numbers: [100]\n100,100 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 4, + 44, + 54, + 10 + ], + "target": 33, + "solution": [ + "44/4=11", + "54-10=44", + "44-11=33" + ], + "optimal_path": "Current State: 33:[4, 44, 54, 10], Operations: []\nExploring Operation: 44/4=11, Resulting Numbers: [54, 10, 11]\nGenerated Node #2: [54, 10, 11] from Operation: 44/4=11\nCurrent State: 33:[54, 10, 11], Operations: ['44/4=11']\nExploring Operation: 54-10=44, Resulting Numbers: [11, 44]\nGenerated Node #3: [11, 44] from Operation: 54-10=44\nCurrent State: 33:[11, 44], Operations: ['44/4=11', '54-10=44']\nExploring Operation: 44-11=33, Resulting Numbers: [33]\n33,33 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 73, + 15, + 11, + 79 + ], + "target": 14, + "solution": [ + "73*15=1095", + "11+1095=1106", + "1106/79=14" + ], + "optimal_path": "Current State: 14:[73, 15, 11, 79], Operations: []\nExploring Operation: 73*15=1095, Resulting Numbers: [11, 79, 1095]\nGenerated Node #2: [11, 79, 1095] from Operation: 73*15=1095\nCurrent State: 14:[11, 79, 1095], Operations: ['73*15=1095']\nExploring Operation: 11+1095=1106, Resulting Numbers: [79, 1106]\nGenerated Node #3: [79, 1106] from Operation: 11+1095=1106\nCurrent State: 14:[79, 1106], Operations: ['73*15=1095', '11+1095=1106']\nExploring Operation: 1106/79=14, Resulting Numbers: [14]\n14,14 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 4, + 5, + 52, + 55 + ], + "target": 28, + "solution": [ + "5+52=57", + "55+57=112", + "112/4=28" + ], + "optimal_path": "Current State: 28:[4, 5, 52, 55], Operations: []\nExploring Operation: 5+52=57, Resulting Numbers: [4, 55, 57]\nGenerated Node #2: [4, 55, 57] from Operation: 5+52=57\nCurrent State: 28:[4, 55, 57], Operations: ['5+52=57']\nExploring Operation: 55+57=112, Resulting Numbers: [4, 112]\nGenerated Node #3: [4, 112] from Operation: 55+57=112\nCurrent State: 28:[4, 112], Operations: ['5+52=57', '55+57=112']\nExploring Operation: 112/4=28, Resulting Numbers: [28]\n28,28 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 45, + 95, + 70, + 84 + ], + "target": 82, + "solution": [ + "45+95=140", + "140/70=2", + "84-2=82" + ], + "optimal_path": "Current State: 82:[45, 95, 70, 84], Operations: []\nExploring Operation: 45+95=140, Resulting Numbers: [70, 84, 140]\nGenerated Node #2: [70, 84, 140] from Operation: 45+95=140\nCurrent State: 82:[70, 84, 140], Operations: ['45+95=140']\nExploring Operation: 140/70=2, Resulting Numbers: [84, 2]\nGenerated Node #3: [84, 2] from Operation: 140/70=2\nCurrent State: 82:[84, 2], Operations: ['45+95=140', '140/70=2']\nExploring Operation: 84-2=82, Resulting Numbers: [82]\n82,82 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 36, + 37, + 9, + 43 + ], + "target": 52, + "solution": [ + "37-36=1", + "9+43=52", + "1*52=52" + ], + "optimal_path": "Current State: 52:[36, 37, 9, 43], Operations: []\nExploring Operation: 37-36=1, Resulting Numbers: [9, 43, 1]\nGenerated Node #2: [9, 43, 1] from Operation: 37-36=1\nCurrent State: 52:[9, 43, 1], Operations: ['37-36=1']\nExploring Operation: 9+43=52, Resulting Numbers: [1, 52]\nGenerated Node #3: [1, 52] from Operation: 9+43=52\nCurrent State: 52:[1, 52], Operations: ['37-36=1', '9+43=52']\nExploring Operation: 1*52=52, Resulting Numbers: [52]\n52,52 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 54, + 67, + 31, + 64 + ], + "target": 96, + "solution": [ + "54*64=3456", + "67-31=36", + "3456/36=96" + ], + "optimal_path": "Current State: 96:[54, 67, 31, 64], Operations: []\nExploring Operation: 54*64=3456, Resulting Numbers: [67, 31, 3456]\nGenerated Node #2: [67, 31, 3456] from Operation: 54*64=3456\nCurrent State: 96:[67, 31, 3456], Operations: ['54*64=3456']\nExploring Operation: 67-31=36, Resulting Numbers: [3456, 36]\nGenerated Node #3: [3456, 36] from Operation: 67-31=36\nCurrent State: 96:[3456, 36], Operations: ['54*64=3456', '67-31=36']\nExploring Operation: 3456/36=96, Resulting Numbers: [96]\n96,96 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 16, + 47, + 72, + 22 + ], + "target": 43, + "solution": [ + "16+72=88", + "88/22=4", + "47-4=43" + ], + "optimal_path": "Current State: 43:[16, 47, 72, 22], Operations: []\nExploring Operation: 16+72=88, Resulting Numbers: [47, 22, 88]\nGenerated Node #2: [47, 22, 88] from Operation: 16+72=88\nCurrent State: 43:[47, 22, 88], Operations: ['16+72=88']\nExploring Operation: 88/22=4, Resulting Numbers: [47, 4]\nGenerated Node #3: [47, 4] from Operation: 88/22=4\nCurrent State: 43:[47, 4], Operations: ['16+72=88', '88/22=4']\nExploring Operation: 47-4=43, Resulting Numbers: [43]\n43,43 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 3, + 58, + 22, + 10 + ], + "target": 38, + "solution": [ + "58-10=48", + "48/3=16", + "22+16=38" + ], + "optimal_path": "Current State: 38:[3, 58, 22, 10], Operations: []\nExploring Operation: 58-10=48, Resulting Numbers: [3, 22, 48]\nGenerated Node #2: [3, 22, 48] from Operation: 58-10=48\nCurrent State: 38:[3, 22, 48], Operations: ['58-10=48']\nExploring Operation: 48/3=16, Resulting Numbers: [22, 16]\nGenerated Node #3: [22, 16] from Operation: 48/3=16\nCurrent State: 38:[22, 16], Operations: ['58-10=48', '48/3=16']\nExploring Operation: 22+16=38, Resulting Numbers: [38]\n38,38 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 79, + 32, + 42, + 54 + ], + "target": 82, + "solution": [ + "42+54=96", + "96/32=3", + "79+3=82" + ], + "optimal_path": "Current State: 82:[79, 32, 42, 54], Operations: []\nExploring Operation: 42+54=96, Resulting Numbers: [79, 32, 96]\nGenerated Node #2: [79, 32, 96] from Operation: 42+54=96\nCurrent State: 82:[79, 32, 96], Operations: ['42+54=96']\nExploring Operation: 96/32=3, Resulting Numbers: [79, 3]\nGenerated Node #3: [79, 3] from Operation: 96/32=3\nCurrent State: 82:[79, 3], Operations: ['42+54=96', '96/32=3']\nExploring Operation: 79+3=82, Resulting Numbers: [82]\n82,82 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 1, + 78, + 4, + 68 + ], + "target": 62, + "solution": [ + "1+78=79", + "68/4=17", + "79-17=62" + ], + "optimal_path": "Current State: 62:[1, 78, 4, 68], Operations: []\nExploring Operation: 1+78=79, Resulting Numbers: [4, 68, 79]\nGenerated Node #2: [4, 68, 79] from Operation: 1+78=79\nCurrent State: 62:[4, 68, 79], Operations: ['1+78=79']\nExploring Operation: 68/4=17, Resulting Numbers: [79, 17]\nGenerated Node #3: [79, 17] from Operation: 68/4=17\nCurrent State: 62:[79, 17], Operations: ['1+78=79', '68/4=17']\nExploring Operation: 79-17=62, Resulting Numbers: [62]\n62,62 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 74, + 27, + 94, + 25 + ], + "target": 40, + "solution": [ + "94-74=20", + "27-25=2", + "20*2=40" + ], + "optimal_path": "Current State: 40:[74, 27, 94, 25], Operations: []\nExploring Operation: 94-74=20, Resulting Numbers: [27, 25, 20]\nGenerated Node #2: [27, 25, 20] from Operation: 94-74=20\nCurrent State: 40:[27, 25, 20], Operations: ['94-74=20']\nExploring Operation: 27-25=2, Resulting Numbers: [20, 2]\nGenerated Node #3: [20, 2] from Operation: 27-25=2\nCurrent State: 40:[20, 2], Operations: ['94-74=20', '27-25=2']\nExploring Operation: 20*2=40, Resulting Numbers: [40]\n40,40 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 72, + 12, + 94, + 19 + ], + "target": 29, + "solution": [ + "72+12=84", + "94+19=113", + "113-84=29" + ], + "optimal_path": "Current State: 29:[72, 12, 94, 19], Operations: []\nExploring Operation: 72+12=84, Resulting Numbers: [94, 19, 84]\nGenerated Node #2: [94, 19, 84] from Operation: 72+12=84\nCurrent State: 29:[94, 19, 84], Operations: ['72+12=84']\nExploring Operation: 94+19=113, Resulting Numbers: [84, 113]\nGenerated Node #3: [84, 113] from Operation: 94+19=113\nCurrent State: 29:[84, 113], Operations: ['72+12=84', '94+19=113']\nExploring Operation: 113-84=29, Resulting Numbers: [29]\n29,29 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 50, + 64, + 33, + 38 + ], + "target": 74, + "solution": [ + "38-33=5", + "50/5=10", + "64+10=74" + ], + "optimal_path": "Current State: 74:[50, 64, 33, 38], Operations: []\nExploring Operation: 38-33=5, Resulting Numbers: [50, 64, 5]\nGenerated Node #2: [50, 64, 5] from Operation: 38-33=5\nCurrent State: 74:[50, 64, 5], Operations: ['38-33=5']\nExploring Operation: 50/5=10, Resulting Numbers: [64, 10]\nGenerated Node #3: [64, 10] from Operation: 50/5=10\nCurrent State: 74:[64, 10], Operations: ['38-33=5', '50/5=10']\nExploring Operation: 64+10=74, Resulting Numbers: [74]\n74,74 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 69, + 14, + 91, + 72 + ], + "target": 36, + "solution": [ + "69-14=55", + "91-72=19", + "55-19=36" + ], + "optimal_path": "Current State: 36:[69, 14, 91, 72], Operations: []\nExploring Operation: 69-14=55, Resulting Numbers: [91, 72, 55]\nGenerated Node #2: [91, 72, 55] from Operation: 69-14=55\nCurrent State: 36:[91, 72, 55], Operations: ['69-14=55']\nExploring Operation: 91-72=19, Resulting Numbers: [55, 19]\nGenerated Node #3: [55, 19] from Operation: 91-72=19\nCurrent State: 36:[55, 19], Operations: ['69-14=55', '91-72=19']\nExploring Operation: 55-19=36, Resulting Numbers: [36]\n36,36 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 56, + 3, + 8, + 85 + ], + "target": 64, + "solution": [ + "56*3=168", + "168/8=21", + "85-21=64" + ], + "optimal_path": "Current State: 64:[56, 3, 8, 85], Operations: []\nExploring Operation: 56*3=168, Resulting Numbers: [8, 85, 168]\nGenerated Node #2: [8, 85, 168] from Operation: 56*3=168\nCurrent State: 64:[8, 85, 168], Operations: ['56*3=168']\nExploring Operation: 168/8=21, Resulting Numbers: [85, 21]\nGenerated Node #3: [85, 21] from Operation: 168/8=21\nCurrent State: 64:[85, 21], Operations: ['56*3=168', '168/8=21']\nExploring Operation: 85-21=64, Resulting Numbers: [64]\n64,64 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 7, + 22, + 20, + 1 + ], + "target": 34, + "solution": [ + "22-7=15", + "20-1=19", + "15+19=34" + ], + "optimal_path": "Current State: 34:[7, 22, 20, 1], Operations: []\nExploring Operation: 22-7=15, Resulting Numbers: [20, 1, 15]\nGenerated Node #2: [20, 1, 15] from Operation: 22-7=15\nCurrent State: 34:[20, 1, 15], Operations: ['22-7=15']\nExploring Operation: 20-1=19, Resulting Numbers: [15, 19]\nGenerated Node #3: [15, 19] from Operation: 20-1=19\nCurrent State: 34:[15, 19], Operations: ['22-7=15', '20-1=19']\nExploring Operation: 15+19=34, Resulting Numbers: [34]\n34,34 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 2, + 76, + 5, + 78 + ], + "target": 22, + "solution": [ + "2+5=7", + "76+78=154", + "154/7=22" + ], + "optimal_path": "Current State: 22:[2, 76, 5, 78], Operations: []\nExploring Operation: 2+5=7, Resulting Numbers: [76, 78, 7]\nGenerated Node #2: [76, 78, 7] from Operation: 2+5=7\nCurrent State: 22:[76, 78, 7], Operations: ['2+5=7']\nExploring Operation: 76+78=154, Resulting Numbers: [7, 154]\nGenerated Node #3: [7, 154] from Operation: 76+78=154\nCurrent State: 22:[7, 154], Operations: ['2+5=7', '76+78=154']\nExploring Operation: 154/7=22, Resulting Numbers: [22]\n22,22 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 84, + 70, + 53, + 46 + ], + "target": 74, + "solution": [ + "53-46=7", + "70/7=10", + "84-10=74" + ], + "optimal_path": "Current State: 74:[84, 70, 53, 46], Operations: []\nExploring Operation: 53-46=7, Resulting Numbers: [84, 70, 7]\nGenerated Node #2: [84, 70, 7] from Operation: 53-46=7\nCurrent State: 74:[84, 70, 7], Operations: ['53-46=7']\nExploring Operation: 70/7=10, Resulting Numbers: [84, 10]\nGenerated Node #3: [84, 10] from Operation: 70/7=10\nCurrent State: 74:[84, 10], Operations: ['53-46=7', '70/7=10']\nExploring Operation: 84-10=74, Resulting Numbers: [74]\n74,74 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 20, + 22, + 44, + 47 + ], + "target": 50, + "solution": [ + "22-20=2", + "47*2=94", + "94-44=50" + ], + "optimal_path": "Current State: 50:[20, 22, 44, 47], Operations: []\nExploring Operation: 22-20=2, Resulting Numbers: [44, 47, 2]\nGenerated Node #2: [44, 47, 2] from Operation: 22-20=2\nCurrent State: 50:[44, 47, 2], Operations: ['22-20=2']\nExploring Operation: 47*2=94, Resulting Numbers: [44, 94]\nGenerated Node #3: [44, 94] from Operation: 47*2=94\nCurrent State: 50:[44, 94], Operations: ['22-20=2', '47*2=94']\nExploring Operation: 94-44=50, Resulting Numbers: [50]\n50,50 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 2, + 90, + 39, + 48 + ], + "target": 75, + "solution": [ + "48/2=24", + "90-39=51", + "24+51=75" + ], + "optimal_path": "Current State: 75:[2, 90, 39, 48], Operations: []\nExploring Operation: 48/2=24, Resulting Numbers: [90, 39, 24]\nGenerated Node #2: [90, 39, 24] from Operation: 48/2=24\nCurrent State: 75:[90, 39, 24], Operations: ['48/2=24']\nExploring Operation: 90-39=51, Resulting Numbers: [24, 51]\nGenerated Node #3: [24, 51] from Operation: 90-39=51\nCurrent State: 75:[24, 51], Operations: ['48/2=24', '90-39=51']\nExploring Operation: 24+51=75, Resulting Numbers: [75]\n75,75 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 70, + 38, + 43, + 36 + ], + "target": 47, + "solution": [ + "70-38=32", + "43+36=79", + "79-32=47" + ], + "optimal_path": "Current State: 47:[70, 38, 43, 36], Operations: []\nExploring Operation: 70-38=32, Resulting Numbers: [43, 36, 32]\nGenerated Node #2: [43, 36, 32] from Operation: 70-38=32\nCurrent State: 47:[43, 36, 32], Operations: ['70-38=32']\nExploring Operation: 43+36=79, Resulting Numbers: [32, 79]\nGenerated Node #3: [32, 79] from Operation: 43+36=79\nCurrent State: 47:[32, 79], Operations: ['70-38=32', '43+36=79']\nExploring Operation: 79-32=47, Resulting Numbers: [47]\n47,47 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 10, + 12, + 56, + 79 + ], + "target": 21, + "solution": [ + "12-10=2", + "79-56=23", + "23-2=21" + ], + "optimal_path": "Current State: 21:[10, 12, 56, 79], Operations: []\nExploring Operation: 12-10=2, Resulting Numbers: [56, 79, 2]\nGenerated Node #2: [56, 79, 2] from Operation: 12-10=2\nCurrent State: 21:[56, 79, 2], Operations: ['12-10=2']\nExploring Operation: 79-56=23, Resulting Numbers: [2, 23]\nGenerated Node #3: [2, 23] from Operation: 79-56=23\nCurrent State: 21:[2, 23], Operations: ['12-10=2', '79-56=23']\nExploring Operation: 23-2=21, Resulting Numbers: [21]\n21,21 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 75, + 22, + 72, + 52 + ], + "target": 77, + "solution": [ + "75+22=97", + "72-52=20", + "97-20=77" + ], + "optimal_path": "Current State: 77:[75, 22, 72, 52], Operations: []\nExploring Operation: 75+22=97, Resulting Numbers: [72, 52, 97]\nGenerated Node #2: [72, 52, 97] from Operation: 75+22=97\nCurrent State: 77:[72, 52, 97], Operations: ['75+22=97']\nExploring Operation: 72-52=20, Resulting Numbers: [97, 20]\nGenerated Node #3: [97, 20] from Operation: 72-52=20\nCurrent State: 77:[97, 20], Operations: ['75+22=97', '72-52=20']\nExploring Operation: 97-20=77, Resulting Numbers: [77]\n77,77 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 37, + 91, + 6, + 12 + ], + "target": 48, + "solution": [ + "91-37=54", + "12-6=6", + "54-6=48" + ], + "optimal_path": "Current State: 48:[37, 91, 6, 12], Operations: []\nExploring Operation: 91-37=54, Resulting Numbers: [6, 12, 54]\nGenerated Node #2: [6, 12, 54] from Operation: 91-37=54\nCurrent State: 48:[6, 12, 54], Operations: ['91-37=54']\nExploring Operation: 12-6=6, Resulting Numbers: [54, 6]\nGenerated Node #3: [54, 6] from Operation: 12-6=6\nCurrent State: 48:[54, 6], Operations: ['91-37=54', '12-6=6']\nExploring Operation: 54-6=48, Resulting Numbers: [48]\n48,48 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 63, + 25, + 23, + 63 + ], + "target": 78, + "solution": [ + "63-25=38", + "63-23=40", + "38+40=78" + ], + "optimal_path": "Current State: 78:[63, 25, 23, 63], Operations: []\nExploring Operation: 63-25=38, Resulting Numbers: [23, 38]\nGenerated Node #2: [23, 38] from Operation: 63-25=38\nCurrent State: 78:[23, 38], Operations: ['63-25=38']\nExploring Operation: 63-23=40, Resulting Numbers: [38, 40]\nGenerated Node #3: [38, 40] from Operation: 63-23=40\nCurrent State: 78:[38, 40], Operations: ['63-25=38', '63-23=40']\nExploring Operation: 38+40=78, Resulting Numbers: [78]\n78,78 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 19, + 15, + 10, + 60 + ], + "target": 16, + "solution": [ + "19+15=34", + "60-10=50", + "50-34=16" + ], + "optimal_path": "Current State: 16:[19, 15, 10, 60], Operations: []\nExploring Operation: 19+15=34, Resulting Numbers: [10, 60, 34]\nGenerated Node #2: [10, 60, 34] from Operation: 19+15=34\nCurrent State: 16:[10, 60, 34], Operations: ['19+15=34']\nExploring Operation: 60-10=50, Resulting Numbers: [34, 50]\nGenerated Node #3: [34, 50] from Operation: 60-10=50\nCurrent State: 16:[34, 50], Operations: ['19+15=34', '60-10=50']\nExploring Operation: 50-34=16, Resulting Numbers: [16]\n16,16 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 28, + 12, + 78, + 14 + ], + "target": 10, + "solution": [ + "28+78=106", + "14+106=120", + "120/12=10" + ], + "optimal_path": "Current State: 10:[28, 12, 78, 14], Operations: []\nExploring Operation: 28+78=106, Resulting Numbers: [12, 14, 106]\nGenerated Node #2: [12, 14, 106] from Operation: 28+78=106\nCurrent State: 10:[12, 14, 106], Operations: ['28+78=106']\nExploring Operation: 14+106=120, Resulting Numbers: [12, 120]\nGenerated Node #3: [12, 120] from Operation: 14+106=120\nCurrent State: 10:[12, 120], Operations: ['28+78=106', '14+106=120']\nExploring Operation: 120/12=10, Resulting Numbers: [10]\n10,10 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 94, + 33, + 62, + 34 + ], + "target": 33, + "solution": [ + "94-33=61", + "62-34=28", + "61-28=33" + ], + "optimal_path": "Current State: 33:[94, 33, 62, 34], Operations: []\nExploring Operation: 94-33=61, Resulting Numbers: [62, 34, 61]\nGenerated Node #2: [62, 34, 61] from Operation: 94-33=61\nCurrent State: 33:[62, 34, 61], Operations: ['94-33=61']\nExploring Operation: 62-34=28, Resulting Numbers: [61, 28]\nGenerated Node #3: [61, 28] from Operation: 62-34=28\nCurrent State: 33:[61, 28], Operations: ['94-33=61', '62-34=28']\nExploring Operation: 61-28=33, Resulting Numbers: [33]\n33,33 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 32, + 64, + 81, + 56 + ], + "target": 53, + "solution": [ + "64/32=2", + "56/2=28", + "81-28=53" + ], + "optimal_path": "Current State: 53:[32, 64, 81, 56], Operations: []\nExploring Operation: 64/32=2, Resulting Numbers: [81, 56, 2]\nGenerated Node #2: [81, 56, 2] from Operation: 64/32=2\nCurrent State: 53:[81, 56, 2], Operations: ['64/32=2']\nExploring Operation: 56/2=28, Resulting Numbers: [81, 28]\nGenerated Node #3: [81, 28] from Operation: 56/2=28\nCurrent State: 53:[81, 28], Operations: ['64/32=2', '56/2=28']\nExploring Operation: 81-28=53, Resulting Numbers: [53]\n53,53 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 26, + 42, + 7, + 28 + ], + "target": 13, + "solution": [ + "26*7=182", + "42-28=14", + "182/14=13" + ], + "optimal_path": "Current State: 13:[26, 42, 7, 28], Operations: []\nExploring Operation: 26*7=182, Resulting Numbers: [42, 28, 182]\nGenerated Node #2: [42, 28, 182] from Operation: 26*7=182\nCurrent State: 13:[42, 28, 182], Operations: ['26*7=182']\nExploring Operation: 42-28=14, Resulting Numbers: [182, 14]\nGenerated Node #3: [182, 14] from Operation: 42-28=14\nCurrent State: 13:[182, 14], Operations: ['26*7=182', '42-28=14']\nExploring Operation: 182/14=13, Resulting Numbers: [13]\n13,13 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 24, + 53, + 75, + 6 + ], + "target": 18, + "solution": [ + "24/6=4", + "75-53=22", + "22-4=18" + ], + "optimal_path": "Current State: 18:[24, 53, 75, 6], Operations: []\nExploring Operation: 24/6=4, Resulting Numbers: [53, 75, 4]\nGenerated Node #2: [53, 75, 4] from Operation: 24/6=4\nCurrent State: 18:[53, 75, 4], Operations: ['24/6=4']\nExploring Operation: 75-53=22, Resulting Numbers: [4, 22]\nGenerated Node #3: [4, 22] from Operation: 75-53=22\nCurrent State: 18:[4, 22], Operations: ['24/6=4', '75-53=22']\nExploring Operation: 22-4=18, Resulting Numbers: [18]\n18,18 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 5, + 37, + 35, + 8 + ], + "target": 59, + "solution": [ + "37-5=32", + "35-8=27", + "32+27=59" + ], + "optimal_path": "Current State: 59:[5, 37, 35, 8], Operations: []\nExploring Operation: 37-5=32, Resulting Numbers: [35, 8, 32]\nGenerated Node #2: [35, 8, 32] from Operation: 37-5=32\nCurrent State: 59:[35, 8, 32], Operations: ['37-5=32']\nExploring Operation: 35-8=27, Resulting Numbers: [32, 27]\nGenerated Node #3: [32, 27] from Operation: 35-8=27\nCurrent State: 59:[32, 27], Operations: ['37-5=32', '35-8=27']\nExploring Operation: 32+27=59, Resulting Numbers: [59]\n59,59 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 96, + 33, + 95, + 75 + ], + "target": 100, + "solution": [ + "33+95=128", + "75*128=9600", + "9600/96=100" + ], + "optimal_path": "Current State: 100:[96, 33, 95, 75], Operations: []\nExploring Operation: 33+95=128, Resulting Numbers: [96, 75, 128]\nGenerated Node #2: [96, 75, 128] from Operation: 33+95=128\nCurrent State: 100:[96, 75, 128], Operations: ['33+95=128']\nExploring Operation: 75*128=9600, Resulting Numbers: [96, 9600]\nGenerated Node #3: [96, 9600] from Operation: 75*128=9600\nCurrent State: 100:[96, 9600], Operations: ['33+95=128', '75*128=9600']\nExploring Operation: 9600/96=100, Resulting Numbers: [100]\n100,100 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 88, + 39, + 35, + 3 + ], + "target": 11, + "solution": [ + "88-39=49", + "35+3=38", + "49-38=11" + ], + "optimal_path": "Current State: 11:[88, 39, 35, 3], Operations: []\nExploring Operation: 88-39=49, Resulting Numbers: [35, 3, 49]\nGenerated Node #2: [35, 3, 49] from Operation: 88-39=49\nCurrent State: 11:[35, 3, 49], Operations: ['88-39=49']\nExploring Operation: 35+3=38, Resulting Numbers: [49, 38]\nGenerated Node #3: [49, 38] from Operation: 35+3=38\nCurrent State: 11:[49, 38], Operations: ['88-39=49', '35+3=38']\nExploring Operation: 49-38=11, Resulting Numbers: [11]\n11,11 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 83, + 75, + 20, + 62 + ], + "target": 11, + "solution": [ + "83+75=158", + "62+158=220", + "220/20=11" + ], + "optimal_path": "Current State: 11:[83, 75, 20, 62], Operations: []\nExploring Operation: 83+75=158, Resulting Numbers: [20, 62, 158]\nGenerated Node #2: [20, 62, 158] from Operation: 83+75=158\nCurrent State: 11:[20, 62, 158], Operations: ['83+75=158']\nExploring Operation: 62+158=220, Resulting Numbers: [20, 220]\nGenerated Node #3: [20, 220] from Operation: 62+158=220\nCurrent State: 11:[20, 220], Operations: ['83+75=158', '62+158=220']\nExploring Operation: 220/20=11, Resulting Numbers: [11]\n11,11 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 43, + 33, + 89, + 14 + ], + "target": 27, + "solution": [ + "43+33=76", + "89+14=103", + "103-76=27" + ], + "optimal_path": "Current State: 27:[43, 33, 89, 14], Operations: []\nExploring Operation: 43+33=76, Resulting Numbers: [89, 14, 76]\nGenerated Node #2: [89, 14, 76] from Operation: 43+33=76\nCurrent State: 27:[89, 14, 76], Operations: ['43+33=76']\nExploring Operation: 89+14=103, Resulting Numbers: [76, 103]\nGenerated Node #3: [76, 103] from Operation: 89+14=103\nCurrent State: 27:[76, 103], Operations: ['43+33=76', '89+14=103']\nExploring Operation: 103-76=27, Resulting Numbers: [27]\n27,27 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 94, + 26, + 28, + 38 + ], + "target": 24, + "solution": [ + "94-38=56", + "56/28=2", + "26-2=24" + ], + "optimal_path": "Current State: 24:[94, 26, 28, 38], Operations: []\nExploring Operation: 94-38=56, Resulting Numbers: [26, 28, 56]\nGenerated Node #2: [26, 28, 56] from Operation: 94-38=56\nCurrent State: 24:[26, 28, 56], Operations: ['94-38=56']\nExploring Operation: 56/28=2, Resulting Numbers: [26, 2]\nGenerated Node #3: [26, 2] from Operation: 56/28=2\nCurrent State: 24:[26, 2], Operations: ['94-38=56', '56/28=2']\nExploring Operation: 26-2=24, Resulting Numbers: [24]\n24,24 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 34, + 98, + 9, + 23 + ], + "target": 41, + "solution": [ + "23-9=14", + "98/14=7", + "34+7=41" + ], + "optimal_path": "Current State: 41:[34, 98, 9, 23], Operations: []\nExploring Operation: 23-9=14, Resulting Numbers: [34, 98, 14]\nGenerated Node #2: [34, 98, 14] from Operation: 23-9=14\nCurrent State: 41:[34, 98, 14], Operations: ['23-9=14']\nExploring Operation: 98/14=7, Resulting Numbers: [34, 7]\nGenerated Node #3: [34, 7] from Operation: 98/14=7\nCurrent State: 41:[34, 7], Operations: ['23-9=14', '98/14=7']\nExploring Operation: 34+7=41, Resulting Numbers: [41]\n41,41 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 48, + 15, + 40, + 59 + ], + "target": 77, + "solution": [ + "48*15=720", + "720/40=18", + "59+18=77" + ], + "optimal_path": "Current State: 77:[48, 15, 40, 59], Operations: []\nExploring Operation: 48*15=720, Resulting Numbers: [40, 59, 720]\nGenerated Node #2: [40, 59, 720] from Operation: 48*15=720\nCurrent State: 77:[40, 59, 720], Operations: ['48*15=720']\nExploring Operation: 720/40=18, Resulting Numbers: [59, 18]\nGenerated Node #3: [59, 18] from Operation: 720/40=18\nCurrent State: 77:[59, 18], Operations: ['48*15=720', '720/40=18']\nExploring Operation: 59+18=77, Resulting Numbers: [77]\n77,77 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 28, + 40, + 32, + 49 + ], + "target": 51, + "solution": [ + "28+40=68", + "49-32=17", + "68-17=51" + ], + "optimal_path": "Current State: 51:[28, 40, 32, 49], Operations: []\nExploring Operation: 28+40=68, Resulting Numbers: [32, 49, 68]\nGenerated Node #2: [32, 49, 68] from Operation: 28+40=68\nCurrent State: 51:[32, 49, 68], Operations: ['28+40=68']\nExploring Operation: 49-32=17, Resulting Numbers: [68, 17]\nGenerated Node #3: [68, 17] from Operation: 49-32=17\nCurrent State: 51:[68, 17], Operations: ['28+40=68', '49-32=17']\nExploring Operation: 68-17=51, Resulting Numbers: [51]\n51,51 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 3, + 32, + 53, + 62 + ], + "target": 38, + "solution": [ + "32-3=29", + "62-53=9", + "29+9=38" + ], + "optimal_path": "Current State: 38:[3, 32, 53, 62], Operations: []\nExploring Operation: 32-3=29, Resulting Numbers: [53, 62, 29]\nGenerated Node #2: [53, 62, 29] from Operation: 32-3=29\nCurrent State: 38:[53, 62, 29], Operations: ['32-3=29']\nExploring Operation: 62-53=9, Resulting Numbers: [29, 9]\nGenerated Node #3: [29, 9] from Operation: 62-53=9\nCurrent State: 38:[29, 9], Operations: ['32-3=29', '62-53=9']\nExploring Operation: 29+9=38, Resulting Numbers: [38]\n38,38 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 44, + 5, + 45, + 85 + ], + "target": 91, + "solution": [ + "44-5=39", + "45+85=130", + "130-39=91" + ], + "optimal_path": "Current State: 91:[44, 5, 45, 85], Operations: []\nExploring Operation: 44-5=39, Resulting Numbers: [45, 85, 39]\nGenerated Node #2: [45, 85, 39] from Operation: 44-5=39\nCurrent State: 91:[45, 85, 39], Operations: ['44-5=39']\nExploring Operation: 45+85=130, Resulting Numbers: [39, 130]\nGenerated Node #3: [39, 130] from Operation: 45+85=130\nCurrent State: 91:[39, 130], Operations: ['44-5=39', '45+85=130']\nExploring Operation: 130-39=91, Resulting Numbers: [91]\n91,91 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 7, + 92, + 75, + 83 + ], + "target": 73, + "solution": [ + "92-7=85", + "75+83=158", + "158-85=73" + ], + "optimal_path": "Current State: 73:[7, 92, 75, 83], Operations: []\nExploring Operation: 92-7=85, Resulting Numbers: [75, 83, 85]\nGenerated Node #2: [75, 83, 85] from Operation: 92-7=85\nCurrent State: 73:[75, 83, 85], Operations: ['92-7=85']\nExploring Operation: 75+83=158, Resulting Numbers: [85, 158]\nGenerated Node #3: [85, 158] from Operation: 75+83=158\nCurrent State: 73:[85, 158], Operations: ['92-7=85', '75+83=158']\nExploring Operation: 158-85=73, Resulting Numbers: [73]\n73,73 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 9, + 52, + 96, + 4 + ], + "target": 67, + "solution": [ + "52-9=43", + "96/4=24", + "43+24=67" + ], + "optimal_path": "Current State: 67:[9, 52, 96, 4], Operations: []\nExploring Operation: 52-9=43, Resulting Numbers: [96, 4, 43]\nGenerated Node #2: [96, 4, 43] from Operation: 52-9=43\nCurrent State: 67:[96, 4, 43], Operations: ['52-9=43']\nExploring Operation: 96/4=24, Resulting Numbers: [43, 24]\nGenerated Node #3: [43, 24] from Operation: 96/4=24\nCurrent State: 67:[43, 24], Operations: ['52-9=43', '96/4=24']\nExploring Operation: 43+24=67, Resulting Numbers: [67]\n67,67 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 3, + 53, + 19, + 62 + ], + "target": 58, + "solution": [ + "3*19=57", + "53+62=115", + "115-57=58" + ], + "optimal_path": "Current State: 58:[3, 53, 19, 62], Operations: []\nExploring Operation: 3*19=57, Resulting Numbers: [53, 62, 57]\nGenerated Node #2: [53, 62, 57] from Operation: 3*19=57\nCurrent State: 58:[53, 62, 57], Operations: ['3*19=57']\nExploring Operation: 53+62=115, Resulting Numbers: [57, 115]\nGenerated Node #3: [57, 115] from Operation: 53+62=115\nCurrent State: 58:[57, 115], Operations: ['3*19=57', '53+62=115']\nExploring Operation: 115-57=58, Resulting Numbers: [58]\n58,58 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 80, + 90, + 4, + 6 + ], + "target": 17, + "solution": [ + "80+90=170", + "4+6=10", + "170/10=17" + ], + "optimal_path": "Current State: 17:[80, 90, 4, 6], Operations: []\nExploring Operation: 80+90=170, Resulting Numbers: [4, 6, 170]\nGenerated Node #2: [4, 6, 170] from Operation: 80+90=170\nCurrent State: 17:[4, 6, 170], Operations: ['80+90=170']\nExploring Operation: 4+6=10, Resulting Numbers: [170, 10]\nGenerated Node #3: [170, 10] from Operation: 4+6=10\nCurrent State: 17:[170, 10], Operations: ['80+90=170', '4+6=10']\nExploring Operation: 170/10=17, Resulting Numbers: [17]\n17,17 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 39, + 51, + 64, + 24 + ], + "target": 32, + "solution": [ + "51-39=12", + "64*12=768", + "768/24=32" + ], + "optimal_path": "Current State: 32:[39, 51, 64, 24], Operations: []\nExploring Operation: 51-39=12, Resulting Numbers: [64, 24, 12]\nGenerated Node #2: [64, 24, 12] from Operation: 51-39=12\nCurrent State: 32:[64, 24, 12], Operations: ['51-39=12']\nExploring Operation: 64*12=768, Resulting Numbers: [24, 768]\nGenerated Node #3: [24, 768] from Operation: 64*12=768\nCurrent State: 32:[24, 768], Operations: ['51-39=12', '64*12=768']\nExploring Operation: 768/24=32, Resulting Numbers: [32]\n32,32 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 7, + 15, + 26, + 23 + ], + "target": 53, + "solution": [ + "15*23=345", + "26+345=371", + "371/7=53" + ], + "optimal_path": "Current State: 53:[7, 15, 26, 23], Operations: []\nExploring Operation: 15*23=345, Resulting Numbers: [7, 26, 345]\nGenerated Node #2: [7, 26, 345] from Operation: 15*23=345\nCurrent State: 53:[7, 26, 345], Operations: ['15*23=345']\nExploring Operation: 26+345=371, Resulting Numbers: [7, 371]\nGenerated Node #3: [7, 371] from Operation: 26+345=371\nCurrent State: 53:[7, 371], Operations: ['15*23=345', '26+345=371']\nExploring Operation: 371/7=53, Resulting Numbers: [53]\n53,53 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 95, + 61, + 66, + 41 + ], + "target": 73, + "solution": [ + "95-61=34", + "66+41=107", + "107-34=73" + ], + "optimal_path": "Current State: 73:[95, 61, 66, 41], Operations: []\nExploring Operation: 95-61=34, Resulting Numbers: [66, 41, 34]\nGenerated Node #2: [66, 41, 34] from Operation: 95-61=34\nCurrent State: 73:[66, 41, 34], Operations: ['95-61=34']\nExploring Operation: 66+41=107, Resulting Numbers: [34, 107]\nGenerated Node #3: [34, 107] from Operation: 66+41=107\nCurrent State: 73:[34, 107], Operations: ['95-61=34', '66+41=107']\nExploring Operation: 107-34=73, Resulting Numbers: [73]\n73,73 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 14, + 6, + 4, + 28 + ], + "target": 74, + "solution": [ + "28-6=22", + "4*22=88", + "88-14=74" + ], + "optimal_path": "Current State: 74:[14, 6, 4, 28], Operations: []\nExploring Operation: 28-6=22, Resulting Numbers: [14, 4, 22]\nGenerated Node #2: [14, 4, 22] from Operation: 28-6=22\nCurrent State: 74:[14, 4, 22], Operations: ['28-6=22']\nExploring Operation: 4*22=88, Resulting Numbers: [14, 88]\nGenerated Node #3: [14, 88] from Operation: 4*22=88\nCurrent State: 74:[14, 88], Operations: ['28-6=22', '4*22=88']\nExploring Operation: 88-14=74, Resulting Numbers: [74]\n74,74 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 36, + 1, + 4, + 54 + ], + "target": 21, + "solution": [ + "36+1=37", + "4+54=58", + "58-37=21" + ], + "optimal_path": "Current State: 21:[36, 1, 4, 54], Operations: []\nExploring Operation: 36+1=37, Resulting Numbers: [4, 54, 37]\nGenerated Node #2: [4, 54, 37] from Operation: 36+1=37\nCurrent State: 21:[4, 54, 37], Operations: ['36+1=37']\nExploring Operation: 4+54=58, Resulting Numbers: [37, 58]\nGenerated Node #3: [37, 58] from Operation: 4+54=58\nCurrent State: 21:[37, 58], Operations: ['36+1=37', '4+54=58']\nExploring Operation: 58-37=21, Resulting Numbers: [21]\n21,21 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 4, + 36, + 21, + 32 + ], + "target": 22, + "solution": [ + "36-4=32", + "32/32=1", + "21+1=22" + ], + "optimal_path": "Current State: 22:[4, 36, 21, 32], Operations: []\nExploring Operation: 36-4=32, Resulting Numbers: [21, 32, 32]\nGenerated Node #2: [21, 32, 32] from Operation: 36-4=32\nCurrent State: 22:[21, 32, 32], Operations: ['36-4=32']\nExploring Operation: 32/32=1, Resulting Numbers: [21, 1]\nGenerated Node #3: [21, 1] from Operation: 32/32=1\nCurrent State: 22:[21, 1], Operations: ['36-4=32', '32/32=1']\nExploring Operation: 21+1=22, Resulting Numbers: [22]\n22,22 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 92, + 15, + 91, + 81 + ], + "target": 66, + "solution": [ + "92-91=1", + "81-15=66", + "1*66=66" + ], + "optimal_path": "Current State: 66:[92, 15, 91, 81], Operations: []\nExploring Operation: 92-91=1, Resulting Numbers: [15, 81, 1]\nGenerated Node #2: [15, 81, 1] from Operation: 92-91=1\nCurrent State: 66:[15, 81, 1], Operations: ['92-91=1']\nExploring Operation: 81-15=66, Resulting Numbers: [1, 66]\nGenerated Node #3: [1, 66] from Operation: 81-15=66\nCurrent State: 66:[1, 66], Operations: ['92-91=1', '81-15=66']\nExploring Operation: 1*66=66, Resulting Numbers: [66]\n66,66 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 41, + 36, + 9, + 1 + ], + "target": 46, + "solution": [ + "41-36=5", + "9*5=45", + "1+45=46" + ], + "optimal_path": "Current State: 46:[41, 36, 9, 1], Operations: []\nExploring Operation: 41-36=5, Resulting Numbers: [9, 1, 5]\nGenerated Node #2: [9, 1, 5] from Operation: 41-36=5\nCurrent State: 46:[9, 1, 5], Operations: ['41-36=5']\nExploring Operation: 9*5=45, Resulting Numbers: [1, 45]\nGenerated Node #3: [1, 45] from Operation: 9*5=45\nCurrent State: 46:[1, 45], Operations: ['41-36=5', '9*5=45']\nExploring Operation: 1+45=46, Resulting Numbers: [46]\n46,46 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 89, + 34, + 91, + 58 + ], + "target": 10, + "solution": [ + "91-89=2", + "34*2=68", + "68-58=10" + ], + "optimal_path": "Current State: 10:[89, 34, 91, 58], Operations: []\nExploring Operation: 91-89=2, Resulting Numbers: [34, 58, 2]\nGenerated Node #2: [34, 58, 2] from Operation: 91-89=2\nCurrent State: 10:[34, 58, 2], Operations: ['91-89=2']\nExploring Operation: 34*2=68, Resulting Numbers: [58, 68]\nGenerated Node #3: [58, 68] from Operation: 34*2=68\nCurrent State: 10:[58, 68], Operations: ['91-89=2', '34*2=68']\nExploring Operation: 68-58=10, Resulting Numbers: [10]\n10,10 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 85, + 43, + 42, + 28 + ], + "target": 29, + "solution": [ + "85-43=42", + "42/42=1", + "28+1=29" + ], + "optimal_path": "Current State: 29:[85, 43, 42, 28], Operations: []\nExploring Operation: 85-43=42, Resulting Numbers: [42, 28, 42]\nGenerated Node #2: [42, 28, 42] from Operation: 85-43=42\nCurrent State: 29:[42, 28, 42], Operations: ['85-43=42']\nExploring Operation: 42/42=1, Resulting Numbers: [28, 1]\nGenerated Node #3: [28, 1] from Operation: 42/42=1\nCurrent State: 29:[28, 1], Operations: ['85-43=42', '42/42=1']\nExploring Operation: 28+1=29, Resulting Numbers: [29]\n29,29 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 53, + 78, + 36, + 16 + ], + "target": 45, + "solution": [ + "78-53=25", + "36-16=20", + "25+20=45" + ], + "optimal_path": "Current State: 45:[53, 78, 36, 16], Operations: []\nExploring Operation: 78-53=25, Resulting Numbers: [36, 16, 25]\nGenerated Node #2: [36, 16, 25] from Operation: 78-53=25\nCurrent State: 45:[36, 16, 25], Operations: ['78-53=25']\nExploring Operation: 36-16=20, Resulting Numbers: [25, 20]\nGenerated Node #3: [25, 20] from Operation: 36-16=20\nCurrent State: 45:[25, 20], Operations: ['78-53=25', '36-16=20']\nExploring Operation: 25+20=45, Resulting Numbers: [45]\n45,45 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 54, + 54, + 62, + 26 + ], + "target": 37, + "solution": [ + "54/54=1", + "62-26=36", + "1+36=37" + ], + "optimal_path": "Current State: 37:[54, 54, 62, 26], Operations: []\nExploring Operation: 54/54=1, Resulting Numbers: [62, 26, 1]\nGenerated Node #2: [62, 26, 1] from Operation: 54/54=1\nCurrent State: 37:[62, 26, 1], Operations: ['54/54=1']\nExploring Operation: 62-26=36, Resulting Numbers: [1, 36]\nGenerated Node #3: [1, 36] from Operation: 62-26=36\nCurrent State: 37:[1, 36], Operations: ['54/54=1', '62-26=36']\nExploring Operation: 1+36=37, Resulting Numbers: [37]\n37,37 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 75, + 4, + 58, + 60 + ], + "target": 39, + "solution": [ + "75+4=79", + "58+60=118", + "118-79=39" + ], + "optimal_path": "Current State: 39:[75, 4, 58, 60], Operations: []\nExploring Operation: 75+4=79, Resulting Numbers: [58, 60, 79]\nGenerated Node #2: [58, 60, 79] from Operation: 75+4=79\nCurrent State: 39:[58, 60, 79], Operations: ['75+4=79']\nExploring Operation: 58+60=118, Resulting Numbers: [79, 118]\nGenerated Node #3: [79, 118] from Operation: 58+60=118\nCurrent State: 39:[79, 118], Operations: ['75+4=79', '58+60=118']\nExploring Operation: 118-79=39, Resulting Numbers: [39]\n39,39 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 45, + 74, + 96, + 49 + ], + "target": 72, + "solution": [ + "45+74=119", + "96-49=47", + "119-47=72" + ], + "optimal_path": "Current State: 72:[45, 74, 96, 49], Operations: []\nExploring Operation: 45+74=119, Resulting Numbers: [96, 49, 119]\nGenerated Node #2: [96, 49, 119] from Operation: 45+74=119\nCurrent State: 72:[96, 49, 119], Operations: ['45+74=119']\nExploring Operation: 96-49=47, Resulting Numbers: [119, 47]\nGenerated Node #3: [119, 47] from Operation: 96-49=47\nCurrent State: 72:[119, 47], Operations: ['45+74=119', '96-49=47']\nExploring Operation: 119-47=72, Resulting Numbers: [72]\n72,72 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 26, + 49, + 62, + 40 + ], + "target": 27, + "solution": [ + "26+49=75", + "62+40=102", + "102-75=27" + ], + "optimal_path": "Current State: 55:[7, 26, 31, 24], Operations: []\nExploring Operation: 26-24=2, Resulting Numbers: [7, 31, 2]\nGenerated Node #2: [7, 31, 2] from Operation: 26-24=2\nCurrent State: 55:[7, 31, 2], Operations: ['26-24=2']\nExploring Operation: 31*2=62, Resulting Numbers: [7, 62]\nGenerated Node #3: [7, 62] from Operation: 31*2=62\nCurrent State: 55:[7, 62], Operations: ['26-24=2', '31*2=62']\nExploring Operation: 62-7=55, Resulting Numbers: [55]\n55,55 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 95, + 29, + 76, + 15 + ], + "target": 63, + "solution": [ + "95+29=124", + "76-15=61", + "124-61=63" + ], + "optimal_path": "Current State: 63:[95, 29, 76, 15], Operations: []\nExploring Operation: 95+29=124, Resulting Numbers: [76, 15, 124]\nGenerated Node #2: [76, 15, 124] from Operation: 95+29=124\nCurrent State: 63:[76, 15, 124], Operations: ['95+29=124']\nExploring Operation: 76-15=61, Resulting Numbers: [124, 61]\nGenerated Node #3: [124, 61] from Operation: 76-15=61\nCurrent State: 63:[124, 61], Operations: ['95+29=124', '76-15=61']\nExploring Operation: 124-61=63, Resulting Numbers: [63]\n63,63 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 17, + 53, + 49, + 4 + ], + "target": 52, + "solution": [ + "53-17=36", + "49-36=13", + "4*13=52" + ], + "optimal_path": "Current State: 52:[17, 53, 49, 4], Operations: []\nExploring Operation: 53-17=36, Resulting Numbers: [49, 4, 36]\nGenerated Node #2: [49, 4, 36] from Operation: 53-17=36\nCurrent State: 52:[49, 4, 36], Operations: ['53-17=36']\nExploring Operation: 49-36=13, Resulting Numbers: [4, 13]\nGenerated Node #3: [4, 13] from Operation: 49-36=13\nCurrent State: 52:[4, 13], Operations: ['53-17=36', '49-36=13']\nExploring Operation: 4*13=52, Resulting Numbers: [52]\n52,52 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 73, + 84, + 94, + 45 + ], + "target": 41, + "solution": [ + "94-73=21", + "84/21=4", + "45-4=41" + ], + "optimal_path": "Current State: 41:[73, 84, 94, 45], Operations: []\nExploring Operation: 94-73=21, Resulting Numbers: [84, 45, 21]\nGenerated Node #2: [84, 45, 21] from Operation: 94-73=21\nCurrent State: 41:[84, 45, 21], Operations: ['94-73=21']\nExploring Operation: 84/21=4, Resulting Numbers: [45, 4]\nGenerated Node #3: [45, 4] from Operation: 84/21=4\nCurrent State: 41:[45, 4], Operations: ['94-73=21', '84/21=4']\nExploring Operation: 45-4=41, Resulting Numbers: [41]\n41,41 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 7, + 65, + 12, + 16 + ], + "target": 93, + "solution": [ + "16-12=4", + "7*4=28", + "65+28=93" + ], + "optimal_path": "Current State: 93:[7, 65, 12, 16], Operations: []\nExploring Operation: 16-12=4, Resulting Numbers: [7, 65, 4]\nGenerated Node #2: [7, 65, 4] from Operation: 16-12=4\nCurrent State: 93:[7, 65, 4], Operations: ['16-12=4']\nExploring Operation: 7*4=28, Resulting Numbers: [65, 28]\nGenerated Node #3: [65, 28] from Operation: 7*4=28\nCurrent State: 93:[65, 28], Operations: ['16-12=4', '7*4=28']\nExploring Operation: 65+28=93, Resulting Numbers: [93]\n93,93 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 95, + 55, + 98, + 81 + ], + "target": 48, + "solution": [ + "95-81=14", + "98/14=7", + "55-7=48" + ], + "optimal_path": "Current State: 48:[95, 55, 98, 81], Operations: []\nExploring Operation: 95-81=14, Resulting Numbers: [55, 98, 14]\nGenerated Node #2: [55, 98, 14] from Operation: 95-81=14\nCurrent State: 48:[55, 98, 14], Operations: ['95-81=14']\nExploring Operation: 98/14=7, Resulting Numbers: [55, 7]\nGenerated Node #3: [55, 7] from Operation: 98/14=7\nCurrent State: 48:[55, 7], Operations: ['95-81=14', '98/14=7']\nExploring Operation: 55-7=48, Resulting Numbers: [48]\n48,48 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 83, + 9, + 76, + 28 + ], + "target": 30, + "solution": [ + "83-9=74", + "76+28=104", + "104-74=30" + ], + "optimal_path": "Current State: 30:[83, 9, 76, 28], Operations: []\nExploring Operation: 83-9=74, Resulting Numbers: [76, 28, 74]\nGenerated Node #2: [76, 28, 74] from Operation: 83-9=74\nCurrent State: 30:[76, 28, 74], Operations: ['83-9=74']\nExploring Operation: 76+28=104, Resulting Numbers: [74, 104]\nGenerated Node #3: [74, 104] from Operation: 76+28=104\nCurrent State: 30:[74, 104], Operations: ['83-9=74', '76+28=104']\nExploring Operation: 104-74=30, Resulting Numbers: [30]\n30,30 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 81, + 75, + 27, + 61 + ], + "target": 94, + "solution": [ + "81-75=6", + "27+61=88", + "6+88=94" + ], + "optimal_path": "Current State: 94:[81, 75, 27, 61], Operations: []\nExploring Operation: 81-75=6, Resulting Numbers: [27, 61, 6]\nGenerated Node #2: [27, 61, 6] from Operation: 81-75=6\nCurrent State: 94:[27, 61, 6], Operations: ['81-75=6']\nExploring Operation: 27+61=88, Resulting Numbers: [6, 88]\nGenerated Node #3: [6, 88] from Operation: 27+61=88\nCurrent State: 94:[6, 88], Operations: ['81-75=6', '27+61=88']\nExploring Operation: 6+88=94, Resulting Numbers: [94]\n94,94 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 73, + 62, + 30, + 74 + ], + "target": 93, + "solution": [ + "73-62=11", + "30+74=104", + "104-11=93" + ], + "optimal_path": "Current State: 93:[73, 62, 30, 74], Operations: []\nExploring Operation: 73-62=11, Resulting Numbers: [30, 74, 11]\nGenerated Node #2: [30, 74, 11] from Operation: 73-62=11\nCurrent State: 93:[30, 74, 11], Operations: ['73-62=11']\nExploring Operation: 30+74=104, Resulting Numbers: [11, 104]\nGenerated Node #3: [11, 104] from Operation: 30+74=104\nCurrent State: 93:[11, 104], Operations: ['73-62=11', '30+74=104']\nExploring Operation: 104-11=93, Resulting Numbers: [93]\n93,93 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 58, + 32, + 6, + 14 + ], + "target": 65, + "solution": [ + "32*14=448", + "448-58=390", + "390/6=65" + ], + "optimal_path": "Current State: 65:[58, 32, 6, 14], Operations: []\nExploring Operation: 32*14=448, Resulting Numbers: [58, 6, 448]\nGenerated Node #2: [58, 6, 448] from Operation: 32*14=448\nCurrent State: 65:[58, 6, 448], Operations: ['32*14=448']\nExploring Operation: 448-58=390, Resulting Numbers: [6, 390]\nGenerated Node #3: [6, 390] from Operation: 448-58=390\nCurrent State: 65:[6, 390], Operations: ['32*14=448', '448-58=390']\nExploring Operation: 390/6=65, Resulting Numbers: [65]\n65,65 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 94, + 2, + 68, + 70 + ], + "target": 22, + "solution": [ + "94+68=162", + "2*70=140", + "162-140=22" + ], + "optimal_path": "Current State: 22:[94, 2, 68, 70], Operations: []\nExploring Operation: 94+68=162, Resulting Numbers: [2, 70, 162]\nGenerated Node #2: [2, 70, 162] from Operation: 94+68=162\nCurrent State: 22:[2, 70, 162], Operations: ['94+68=162']\nExploring Operation: 2*70=140, Resulting Numbers: [162, 140]\nGenerated Node #3: [162, 140] from Operation: 2*70=140\nCurrent State: 22:[162, 140], Operations: ['94+68=162', '2*70=140']\nExploring Operation: 162-140=22, Resulting Numbers: [22]\n22,22 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 40, + 97, + 87, + 68 + ], + "target": 38, + "solution": [ + "97-40=57", + "87-68=19", + "57-19=38" + ], + "optimal_path": "Current State: 38:[40, 97, 87, 68], Operations: []\nExploring Operation: 97-40=57, Resulting Numbers: [87, 68, 57]\nGenerated Node #2: [87, 68, 57] from Operation: 97-40=57\nCurrent State: 38:[87, 68, 57], Operations: ['97-40=57']\nExploring Operation: 87-68=19, Resulting Numbers: [57, 19]\nGenerated Node #3: [57, 19] from Operation: 87-68=19\nCurrent State: 38:[57, 19], Operations: ['97-40=57', '87-68=19']\nExploring Operation: 57-19=38, Resulting Numbers: [38]\n38,38 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 50, + 58, + 30, + 59 + ], + "target": 25, + "solution": [ + "59-30=29", + "50*29=1450", + "1450/58=25" + ], + "optimal_path": "Current State: 25:[50, 58, 30, 59], Operations: []\nExploring Operation: 59-30=29, Resulting Numbers: [50, 58, 29]\nGenerated Node #2: [50, 58, 29] from Operation: 59-30=29\nCurrent State: 25:[50, 58, 29], Operations: ['59-30=29']\nExploring Operation: 50*29=1450, Resulting Numbers: [58, 1450]\nGenerated Node #3: [58, 1450] from Operation: 50*29=1450\nCurrent State: 25:[58, 1450], Operations: ['59-30=29', '50*29=1450']\nExploring Operation: 1450/58=25, Resulting Numbers: [25]\n25,25 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 72, + 67, + 63, + 20 + ], + "target": 37, + "solution": [ + "72-67=5", + "20*5=100", + "100-63=37" + ], + "optimal_path": "Current State: 37:[72, 67, 63, 20], Operations: []\nExploring Operation: 72-67=5, Resulting Numbers: [63, 20, 5]\nGenerated Node #2: [63, 20, 5] from Operation: 72-67=5\nCurrent State: 37:[63, 20, 5], Operations: ['72-67=5']\nExploring Operation: 20*5=100, Resulting Numbers: [63, 100]\nGenerated Node #3: [63, 100] from Operation: 20*5=100\nCurrent State: 37:[63, 100], Operations: ['72-67=5', '20*5=100']\nExploring Operation: 100-63=37, Resulting Numbers: [37]\n37,37 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 93, + 2, + 23, + 3 + ], + "target": 15, + "solution": [ + "93/3=31", + "2*23=46", + "46-31=15" + ], + "optimal_path": "Current State: 15:[93, 2, 23, 3], Operations: []\nExploring Operation: 93/3=31, Resulting Numbers: [2, 23, 31]\nGenerated Node #2: [2, 23, 31] from Operation: 93/3=31\nCurrent State: 15:[2, 23, 31], Operations: ['93/3=31']\nExploring Operation: 2*23=46, Resulting Numbers: [31, 46]\nGenerated Node #3: [31, 46] from Operation: 2*23=46\nCurrent State: 15:[31, 46], Operations: ['93/3=31', '2*23=46']\nExploring Operation: 46-31=15, Resulting Numbers: [15]\n15,15 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 60, + 76, + 19, + 61 + ], + "target": 64, + "solution": [ + "76-60=16", + "19+61=80", + "80-16=64" + ], + "optimal_path": "Current State: 64:[60, 76, 19, 61], Operations: []\nExploring Operation: 76-60=16, Resulting Numbers: [19, 61, 16]\nGenerated Node #2: [19, 61, 16] from Operation: 76-60=16\nCurrent State: 64:[19, 61, 16], Operations: ['76-60=16']\nExploring Operation: 19+61=80, Resulting Numbers: [16, 80]\nGenerated Node #3: [16, 80] from Operation: 19+61=80\nCurrent State: 64:[16, 80], Operations: ['76-60=16', '19+61=80']\nExploring Operation: 80-16=64, Resulting Numbers: [64]\n64,64 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 57, + 15, + 3, + 34 + ], + "target": 10, + "solution": [ + "57+15=72", + "72/3=24", + "34-24=10" + ], + "optimal_path": "Current State: 10:[57, 15, 3, 34], Operations: []\nExploring Operation: 57+15=72, Resulting Numbers: [3, 34, 72]\nGenerated Node #2: [3, 34, 72] from Operation: 57+15=72\nCurrent State: 10:[3, 34, 72], Operations: ['57+15=72']\nExploring Operation: 72/3=24, Resulting Numbers: [34, 24]\nGenerated Node #3: [34, 24] from Operation: 72/3=24\nCurrent State: 10:[34, 24], Operations: ['57+15=72', '72/3=24']\nExploring Operation: 34-24=10, Resulting Numbers: [10]\n10,10 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 8, + 2, + 2, + 58 + ], + "target": 63, + "solution": [ + "8+2=10", + "10/2=5", + "58+5=63" + ], + "optimal_path": "Current State: 63:[8, 2, 2, 58], Operations: []\nExploring Operation: 8+2=10, Resulting Numbers: [58, 10]\nGenerated Node #2: [58, 10] from Operation: 8+2=10\nCurrent State: 63:[58, 10], Operations: ['8+2=10']\nExploring Operation: 10/2=5, Resulting Numbers: [58, 5]\nGenerated Node #3: [58, 5] from Operation: 10/2=5\nCurrent State: 63:[58, 5], Operations: ['8+2=10', '10/2=5']\nExploring Operation: 58+5=63, Resulting Numbers: [63]\n63,63 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 61, + 64, + 29, + 62 + ], + "target": 11, + "solution": [ + "64-61=3", + "62-29=33", + "33/3=11" + ], + "optimal_path": "Current State: 11:[61, 64, 29, 62], Operations: []\nExploring Operation: 64-61=3, Resulting Numbers: [29, 62, 3]\nGenerated Node #2: [29, 62, 3] from Operation: 64-61=3\nCurrent State: 11:[29, 62, 3], Operations: ['64-61=3']\nExploring Operation: 62-29=33, Resulting Numbers: [3, 33]\nGenerated Node #3: [3, 33] from Operation: 62-29=33\nCurrent State: 11:[3, 33], Operations: ['64-61=3', '62-29=33']\nExploring Operation: 33/3=11, Resulting Numbers: [11]\n11,11 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 73, + 92, + 69, + 70 + ], + "target": 20, + "solution": [ + "92-73=19", + "70-69=1", + "19+1=20" + ], + "optimal_path": "Current State: 20:[73, 92, 69, 70], Operations: []\nExploring Operation: 92-73=19, Resulting Numbers: [69, 70, 19]\nGenerated Node #2: [69, 70, 19] from Operation: 92-73=19\nCurrent State: 20:[69, 70, 19], Operations: ['92-73=19']\nExploring Operation: 70-69=1, Resulting Numbers: [19, 1]\nGenerated Node #3: [19, 1] from Operation: 70-69=1\nCurrent State: 20:[19, 1], Operations: ['92-73=19', '70-69=1']\nExploring Operation: 19+1=20, Resulting Numbers: [20]\n20,20 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 14, + 51, + 56, + 7 + ], + "target": 35, + "solution": [ + "14-7=7", + "56-51=5", + "7*5=35" + ], + "optimal_path": "Current State: 35:[14, 51, 56, 7], Operations: []\nExploring Operation: 14-7=7, Resulting Numbers: [51, 56, 7]\nGenerated Node #2: [51, 56, 7] from Operation: 14-7=7\nCurrent State: 35:[51, 56, 7], Operations: ['14-7=7']\nExploring Operation: 56-51=5, Resulting Numbers: [7, 5]\nGenerated Node #3: [7, 5] from Operation: 56-51=5\nCurrent State: 35:[7, 5], Operations: ['14-7=7', '56-51=5']\nExploring Operation: 7*5=35, Resulting Numbers: [35]\n35,35 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 32, + 57, + 69, + 5 + ], + "target": 99, + "solution": [ + "57-32=25", + "69+5=74", + "25+74=99" + ], + "optimal_path": "Current State: 99:[32, 57, 69, 5], Operations: []\nExploring Operation: 57-32=25, Resulting Numbers: [69, 5, 25]\nGenerated Node #2: [69, 5, 25] from Operation: 57-32=25\nCurrent State: 99:[69, 5, 25], Operations: ['57-32=25']\nExploring Operation: 69+5=74, Resulting Numbers: [25, 74]\nGenerated Node #3: [25, 74] from Operation: 69+5=74\nCurrent State: 99:[25, 74], Operations: ['57-32=25', '69+5=74']\nExploring Operation: 25+74=99, Resulting Numbers: [99]\n99,99 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 28, + 95, + 94, + 79 + ], + "target": 82, + "solution": [ + "95-28=67", + "94-79=15", + "67+15=82" + ], + "optimal_path": "Current State: 82:[28, 95, 94, 79], Operations: []\nExploring Operation: 95-28=67, Resulting Numbers: [94, 79, 67]\nGenerated Node #2: [94, 79, 67] from Operation: 95-28=67\nCurrent State: 82:[94, 79, 67], Operations: ['95-28=67']\nExploring Operation: 94-79=15, Resulting Numbers: [67, 15]\nGenerated Node #3: [67, 15] from Operation: 94-79=15\nCurrent State: 82:[67, 15], Operations: ['95-28=67', '94-79=15']\nExploring Operation: 67+15=82, Resulting Numbers: [82]\n82,82 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 77, + 83, + 89, + 14 + ], + "target": 33, + "solution": [ + "89-83=6", + "77*6=462", + "462/14=33" + ], + "optimal_path": "Current State: 33:[77, 83, 89, 14], Operations: []\nExploring Operation: 89-83=6, Resulting Numbers: [77, 14, 6]\nGenerated Node #2: [77, 14, 6] from Operation: 89-83=6\nCurrent State: 33:[77, 14, 6], Operations: ['89-83=6']\nExploring Operation: 77*6=462, Resulting Numbers: [14, 462]\nGenerated Node #3: [14, 462] from Operation: 77*6=462\nCurrent State: 33:[14, 462], Operations: ['89-83=6', '77*6=462']\nExploring Operation: 462/14=33, Resulting Numbers: [33]\n33,33 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 17, + 79, + 2, + 87 + ], + "target": 18, + "solution": [ + "17+79=96", + "96-87=9", + "2*9=18" + ], + "optimal_path": "Current State: 18:[17, 79, 2, 87], Operations: []\nExploring Operation: 17+79=96, Resulting Numbers: [2, 87, 96]\nGenerated Node #2: [2, 87, 96] from Operation: 17+79=96\nCurrent State: 18:[2, 87, 96], Operations: ['17+79=96']\nExploring Operation: 96-87=9, Resulting Numbers: [2, 9]\nGenerated Node #3: [2, 9] from Operation: 96-87=9\nCurrent State: 18:[2, 9], Operations: ['17+79=96', '96-87=9']\nExploring Operation: 2*9=18, Resulting Numbers: [18]\n18,18 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 22, + 62, + 35, + 76 + ], + "target": 27, + "solution": [ + "22+62=84", + "35+76=111", + "111-84=27" + ], + "optimal_path": "Current State: 27:[22, 62, 35, 76], Operations: []\nExploring Operation: 22+62=84, Resulting Numbers: [35, 76, 84]\nGenerated Node #2: [35, 76, 84] from Operation: 22+62=84\nCurrent State: 27:[35, 76, 84], Operations: ['22+62=84']\nExploring Operation: 35+76=111, Resulting Numbers: [84, 111]\nGenerated Node #3: [84, 111] from Operation: 35+76=111\nCurrent State: 27:[84, 111], Operations: ['22+62=84', '35+76=111']\nExploring Operation: 111-84=27, Resulting Numbers: [27]\n27,27 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 31, + 34, + 34, + 67 + ], + "target": 97, + "solution": [ + "31+67=98", + "34/34=1", + "98-1=97" + ], + "optimal_path": "Current State: 97:[31, 34, 34, 67], Operations: []\nExploring Operation: 31+67=98, Resulting Numbers: [34, 34, 98]\nGenerated Node #2: [34, 34, 98] from Operation: 31+67=98\nCurrent State: 97:[34, 34, 98], Operations: ['31+67=98']\nExploring Operation: 34/34=1, Resulting Numbers: [98, 1]\nGenerated Node #3: [98, 1] from Operation: 34/34=1\nCurrent State: 97:[98, 1], Operations: ['31+67=98', '34/34=1']\nExploring Operation: 98-1=97, Resulting Numbers: [97]\n97,97 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 75, + 66, + 64, + 17 + ], + "target": 72, + "solution": [ + "75-66=9", + "64+17=81", + "81-9=72" + ], + "optimal_path": "Current State: 72:[75, 66, 64, 17], Operations: []\nExploring Operation: 75-66=9, Resulting Numbers: [64, 17, 9]\nGenerated Node #2: [64, 17, 9] from Operation: 75-66=9\nCurrent State: 72:[64, 17, 9], Operations: ['75-66=9']\nExploring Operation: 64+17=81, Resulting Numbers: [9, 81]\nGenerated Node #3: [9, 81] from Operation: 64+17=81\nCurrent State: 72:[9, 81], Operations: ['75-66=9', '64+17=81']\nExploring Operation: 81-9=72, Resulting Numbers: [72]\n72,72 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 96, + 26, + 43, + 59 + ], + "target": 41, + "solution": [ + "96*26=2496", + "43*59=2537", + "2537-2496=41" + ], + "optimal_path": "Current State: 41:[96, 26, 43, 59], Operations: []\nExploring Operation: 96*26=2496, Resulting Numbers: [43, 59, 2496]\nGenerated Node #2: [43, 59, 2496] from Operation: 96*26=2496\nCurrent State: 41:[43, 59, 2496], Operations: ['96*26=2496']\nExploring Operation: 43*59=2537, Resulting Numbers: [2496, 2537]\nGenerated Node #3: [2496, 2537] from Operation: 43*59=2537\nCurrent State: 41:[2496, 2537], Operations: ['96*26=2496', '43*59=2537']\nExploring Operation: 2537-2496=41, Resulting Numbers: [41]\n41,41 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 54, + 45, + 90, + 85 + ], + "target": 78, + "solution": [ + "45+85=130", + "54*130=7020", + "7020/90=78" + ], + "optimal_path": "Current State: 78:[54, 45, 90, 85], Operations: []\nExploring Operation: 45+85=130, Resulting Numbers: [54, 90, 130]\nGenerated Node #2: [54, 90, 130] from Operation: 45+85=130\nCurrent State: 78:[54, 90, 130], Operations: ['45+85=130']\nExploring Operation: 54*130=7020, Resulting Numbers: [90, 7020]\nGenerated Node #3: [90, 7020] from Operation: 54*130=7020\nCurrent State: 78:[90, 7020], Operations: ['45+85=130', '54*130=7020']\nExploring Operation: 7020/90=78, Resulting Numbers: [78]\n78,78 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 62, + 20, + 13, + 21 + ], + "target": 85, + "solution": [ + "20-13=7", + "21*7=147", + "147-62=85" + ], + "optimal_path": "Current State: 85:[62, 20, 13, 21], Operations: []\nExploring Operation: 20-13=7, Resulting Numbers: [62, 21, 7]\nGenerated Node #2: [62, 21, 7] from Operation: 20-13=7\nCurrent State: 85:[62, 21, 7], Operations: ['20-13=7']\nExploring Operation: 21*7=147, Resulting Numbers: [62, 147]\nGenerated Node #3: [62, 147] from Operation: 21*7=147\nCurrent State: 85:[62, 147], Operations: ['20-13=7', '21*7=147']\nExploring Operation: 147-62=85, Resulting Numbers: [85]\n85,85 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 28, + 21, + 7, + 79 + ], + "target": 25, + "solution": [ + "28/7=4", + "21+79=100", + "100/4=25" + ], + "optimal_path": "Current State: 25:[28, 21, 7, 79], Operations: []\nExploring Operation: 28/7=4, Resulting Numbers: [21, 79, 4]\nGenerated Node #2: [21, 79, 4] from Operation: 28/7=4\nCurrent State: 25:[21, 79, 4], Operations: ['28/7=4']\nExploring Operation: 21+79=100, Resulting Numbers: [4, 100]\nGenerated Node #3: [4, 100] from Operation: 21+79=100\nCurrent State: 25:[4, 100], Operations: ['28/7=4', '21+79=100']\nExploring Operation: 100/4=25, Resulting Numbers: [25]\n25,25 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 80, + 55, + 82, + 54 + ], + "target": 78, + "solution": [ + "82-55=27", + "54/27=2", + "80-2=78" + ], + "optimal_path": "Current State: 78:[80, 55, 82, 54], Operations: []\nExploring Operation: 82-55=27, Resulting Numbers: [80, 54, 27]\nGenerated Node #2: [80, 54, 27] from Operation: 82-55=27\nCurrent State: 78:[80, 54, 27], Operations: ['82-55=27']\nExploring Operation: 54/27=2, Resulting Numbers: [80, 2]\nGenerated Node #3: [80, 2] from Operation: 54/27=2\nCurrent State: 78:[80, 2], Operations: ['82-55=27', '54/27=2']\nExploring Operation: 80-2=78, Resulting Numbers: [78]\n78,78 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 66, + 7, + 10, + 7 + ], + "target": 42, + "solution": [ + "66-7=59", + "10+7=17", + "59-17=42" + ], + "optimal_path": "Current State: 42:[66, 7, 10, 7], Operations: []\nExploring Operation: 66-7=59, Resulting Numbers: [10, 59]\nGenerated Node #2: [10, 59] from Operation: 66-7=59\nCurrent State: 42:[10, 59], Operations: ['66-7=59']\nExploring Operation: 10+7=17, Resulting Numbers: [59, 17]\nGenerated Node #3: [59, 17] from Operation: 10+7=17\nCurrent State: 42:[59, 17], Operations: ['66-7=59', '10+7=17']\nExploring Operation: 59-17=42, Resulting Numbers: [42]\n42,42 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 54, + 36, + 33, + 33 + ], + "target": 45, + "solution": [ + "36-33=3", + "33*3=99", + "99-54=45" + ], + "optimal_path": "Current State: 45:[54, 36, 33, 33], Operations: []\nExploring Operation: 36-33=3, Resulting Numbers: [54, 3]\nGenerated Node #2: [54, 3] from Operation: 36-33=3\nCurrent State: 45:[54, 3], Operations: ['36-33=3']\nExploring Operation: 33*3=99, Resulting Numbers: [54, 99]\nGenerated Node #3: [54, 99] from Operation: 33*3=99\nCurrent State: 45:[54, 99], Operations: ['36-33=3', '33*3=99']\nExploring Operation: 99-54=45, Resulting Numbers: [45]\n45,45 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 57, + 63, + 22, + 46 + ], + "target": 65, + "solution": [ + "57-46=11", + "22/11=2", + "63+2=65" + ], + "optimal_path": "Current State: 65:[57, 63, 22, 46], Operations: []\nExploring Operation: 57-46=11, Resulting Numbers: [63, 22, 11]\nGenerated Node #2: [63, 22, 11] from Operation: 57-46=11\nCurrent State: 65:[63, 22, 11], Operations: ['57-46=11']\nExploring Operation: 22/11=2, Resulting Numbers: [63, 2]\nGenerated Node #3: [63, 2] from Operation: 22/11=2\nCurrent State: 65:[63, 2], Operations: ['57-46=11', '22/11=2']\nExploring Operation: 63+2=65, Resulting Numbers: [65]\n65,65 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 35, + 17, + 18, + 50 + ], + "target": 15, + "solution": [ + "50-35=15", + "18-17=1", + "15*1=15" + ], + "optimal_path": "Current State: 15:[35, 17, 18, 50], Operations: []\nExploring Operation: 50-35=15, Resulting Numbers: [17, 18, 15]\nGenerated Node #2: [17, 18, 15] from Operation: 50-35=15\nCurrent State: 15:[17, 18, 15], Operations: ['50-35=15']\nExploring Operation: 18-17=1, Resulting Numbers: [15, 1]\nGenerated Node #3: [15, 1] from Operation: 18-17=1\nCurrent State: 15:[15, 1], Operations: ['50-35=15', '18-17=1']\nExploring Operation: 15*1=15, Resulting Numbers: [15]\n15,15 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 69, + 4, + 67, + 28 + ], + "target": 87, + "solution": [ + "67-28=39", + "4*39=156", + "156-69=87" + ], + "optimal_path": "Current State: 87:[69, 4, 67, 28], Operations: []\nExploring Operation: 67-28=39, Resulting Numbers: [69, 4, 39]\nGenerated Node #2: [69, 4, 39] from Operation: 67-28=39\nCurrent State: 87:[69, 4, 39], Operations: ['67-28=39']\nExploring Operation: 4*39=156, Resulting Numbers: [69, 156]\nGenerated Node #3: [69, 156] from Operation: 4*39=156\nCurrent State: 87:[69, 156], Operations: ['67-28=39', '4*39=156']\nExploring Operation: 156-69=87, Resulting Numbers: [87]\n87,87 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 83, + 87, + 3, + 87 + ], + "target": 25, + "solution": [ + "87-83=4", + "87/3=29", + "29-4=25" + ], + "optimal_path": "Current State: 25:[83, 87, 3, 87], Operations: []\nExploring Operation: 87-83=4, Resulting Numbers: [3, 4]\nGenerated Node #2: [3, 4] from Operation: 87-83=4\nCurrent State: 25:[3, 4], Operations: ['87-83=4']\nExploring Operation: 87/3=29, Resulting Numbers: [4, 29]\nGenerated Node #3: [4, 29] from Operation: 87/3=29\nCurrent State: 25:[4, 29], Operations: ['87-83=4', '87/3=29']\nExploring Operation: 29-4=25, Resulting Numbers: [25]\n25,25 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 36, + 65, + 88, + 54 + ], + "target": 63, + "solution": [ + "65-36=29", + "88-54=34", + "29+34=63" + ], + "optimal_path": "Current State: 63:[36, 65, 88, 54], Operations: []\nExploring Operation: 65-36=29, Resulting Numbers: [88, 54, 29]\nGenerated Node #2: [88, 54, 29] from Operation: 65-36=29\nCurrent State: 63:[88, 54, 29], Operations: ['65-36=29']\nExploring Operation: 88-54=34, Resulting Numbers: [29, 34]\nGenerated Node #3: [29, 34] from Operation: 88-54=34\nCurrent State: 63:[29, 34], Operations: ['65-36=29', '88-54=34']\nExploring Operation: 29+34=63, Resulting Numbers: [63]\n63,63 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 78, + 95, + 71, + 65 + ], + "target": 23, + "solution": [ + "95-78=17", + "71-65=6", + "17+6=23" + ], + "optimal_path": "Current State: 23:[78, 95, 71, 65], Operations: []\nExploring Operation: 95-78=17, Resulting Numbers: [71, 65, 17]\nGenerated Node #2: [71, 65, 17] from Operation: 95-78=17\nCurrent State: 23:[71, 65, 17], Operations: ['95-78=17']\nExploring Operation: 71-65=6, Resulting Numbers: [17, 6]\nGenerated Node #3: [17, 6] from Operation: 71-65=6\nCurrent State: 23:[17, 6], Operations: ['95-78=17', '71-65=6']\nExploring Operation: 17+6=23, Resulting Numbers: [23]\n23,23 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 67, + 1, + 62, + 78 + ], + "target": 13, + "solution": [ + "67+1=68", + "68-62=6", + "78/6=13" + ], + "optimal_path": "Current State: 13:[67, 1, 62, 78], Operations: []\nExploring Operation: 67+1=68, Resulting Numbers: [62, 78, 68]\nGenerated Node #2: [62, 78, 68] from Operation: 67+1=68\nCurrent State: 13:[62, 78, 68], Operations: ['67+1=68']\nExploring Operation: 68-62=6, Resulting Numbers: [78, 6]\nGenerated Node #3: [78, 6] from Operation: 68-62=6\nCurrent State: 13:[78, 6], Operations: ['67+1=68', '68-62=6']\nExploring Operation: 78/6=13, Resulting Numbers: [13]\n13,13 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 36, + 52, + 34, + 85 + ], + "target": 59, + "solution": [ + "36-34=2", + "52/2=26", + "85-26=59" + ], + "optimal_path": "Current State: 59:[36, 52, 34, 85], Operations: []\nExploring Operation: 36-34=2, Resulting Numbers: [52, 85, 2]\nGenerated Node #2: [52, 85, 2] from Operation: 36-34=2\nCurrent State: 59:[52, 85, 2], Operations: ['36-34=2']\nExploring Operation: 52/2=26, Resulting Numbers: [85, 26]\nGenerated Node #3: [85, 26] from Operation: 52/2=26\nCurrent State: 59:[85, 26], Operations: ['36-34=2', '52/2=26']\nExploring Operation: 85-26=59, Resulting Numbers: [59]\n59,59 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 85, + 13, + 8, + 13 + ], + "target": 67, + "solution": [ + "85-13=72", + "13-8=5", + "72-5=67" + ], + "optimal_path": "Current State: 67:[85, 13, 8, 13], Operations: []\nExploring Operation: 85-13=72, Resulting Numbers: [8, 72]\nGenerated Node #2: [8, 72] from Operation: 85-13=72\nCurrent State: 67:[8, 72], Operations: ['85-13=72']\nExploring Operation: 13-8=5, Resulting Numbers: [72, 5]\nGenerated Node #3: [72, 5] from Operation: 13-8=5\nCurrent State: 67:[72, 5], Operations: ['85-13=72', '13-8=5']\nExploring Operation: 72-5=67, Resulting Numbers: [67]\n67,67 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 81, + 36, + 62, + 49 + ], + "target": 58, + "solution": [ + "81-36=45", + "62-49=13", + "45+13=58" + ], + "optimal_path": "Current State: 58:[81, 36, 62, 49], Operations: []\nExploring Operation: 81-36=45, Resulting Numbers: [62, 49, 45]\nGenerated Node #2: [62, 49, 45] from Operation: 81-36=45\nCurrent State: 58:[62, 49, 45], Operations: ['81-36=45']\nExploring Operation: 62-49=13, Resulting Numbers: [45, 13]\nGenerated Node #3: [45, 13] from Operation: 62-49=13\nCurrent State: 58:[45, 13], Operations: ['81-36=45', '62-49=13']\nExploring Operation: 45+13=58, Resulting Numbers: [58]\n58,58 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 80, + 91, + 14, + 28 + ], + "target": 13, + "solution": [ + "91-80=11", + "28/14=2", + "11+2=13" + ], + "optimal_path": "Current State: 13:[80, 91, 14, 28], Operations: []\nExploring Operation: 91-80=11, Resulting Numbers: [14, 28, 11]\nGenerated Node #2: [14, 28, 11] from Operation: 91-80=11\nCurrent State: 13:[14, 28, 11], Operations: ['91-80=11']\nExploring Operation: 28/14=2, Resulting Numbers: [11, 2]\nGenerated Node #3: [11, 2] from Operation: 28/14=2\nCurrent State: 13:[11, 2], Operations: ['91-80=11', '28/14=2']\nExploring Operation: 11+2=13, Resulting Numbers: [13]\n13,13 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 9, + 14, + 6, + 28 + ], + "target": 45, + "solution": [ + "9+14=23", + "28-6=22", + "23+22=45" + ], + "optimal_path": "Current State: 45:[9, 14, 6, 28], Operations: []\nExploring Operation: 9+14=23, Resulting Numbers: [6, 28, 23]\nGenerated Node #2: [6, 28, 23] from Operation: 9+14=23\nCurrent State: 45:[6, 28, 23], Operations: ['9+14=23']\nExploring Operation: 28-6=22, Resulting Numbers: [23, 22]\nGenerated Node #3: [23, 22] from Operation: 28-6=22\nCurrent State: 45:[23, 22], Operations: ['9+14=23', '28-6=22']\nExploring Operation: 23+22=45, Resulting Numbers: [45]\n45,45 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 74, + 15, + 70, + 35 + ], + "target": 57, + "solution": [ + "74-15=59", + "70/35=2", + "59-2=57" + ], + "optimal_path": "Current State: 57:[74, 15, 70, 35], Operations: []\nExploring Operation: 74-15=59, Resulting Numbers: [70, 35, 59]\nGenerated Node #2: [70, 35, 59] from Operation: 74-15=59\nCurrent State: 57:[70, 35, 59], Operations: ['74-15=59']\nExploring Operation: 70/35=2, Resulting Numbers: [59, 2]\nGenerated Node #3: [59, 2] from Operation: 70/35=2\nCurrent State: 57:[59, 2], Operations: ['74-15=59', '70/35=2']\nExploring Operation: 59-2=57, Resulting Numbers: [57]\n57,57 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 47, + 75, + 3, + 68 + ], + "target": 99, + "solution": [ + "75-47=28", + "3+68=71", + "28+71=99" + ], + "optimal_path": "Current State: 99:[47, 75, 3, 68], Operations: []\nExploring Operation: 75-47=28, Resulting Numbers: [3, 68, 28]\nGenerated Node #2: [3, 68, 28] from Operation: 75-47=28\nCurrent State: 99:[3, 68, 28], Operations: ['75-47=28']\nExploring Operation: 3+68=71, Resulting Numbers: [28, 71]\nGenerated Node #3: [28, 71] from Operation: 3+68=71\nCurrent State: 99:[28, 71], Operations: ['75-47=28', '3+68=71']\nExploring Operation: 28+71=99, Resulting Numbers: [99]\n99,99 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 69, + 88, + 34, + 91 + ], + "target": 33, + "solution": [ + "91-88=3", + "34*3=102", + "102-69=33" + ], + "optimal_path": "Current State: 33:[69, 88, 34, 91], Operations: []\nExploring Operation: 91-88=3, Resulting Numbers: [69, 34, 3]\nGenerated Node #2: [69, 34, 3] from Operation: 91-88=3\nCurrent State: 33:[69, 34, 3], Operations: ['91-88=3']\nExploring Operation: 34*3=102, Resulting Numbers: [69, 102]\nGenerated Node #3: [69, 102] from Operation: 34*3=102\nCurrent State: 33:[69, 102], Operations: ['91-88=3', '34*3=102']\nExploring Operation: 102-69=33, Resulting Numbers: [33]\n33,33 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 99, + 45, + 61, + 64 + ], + "target": 78, + "solution": [ + "64-61=3", + "99/3=33", + "45+33=78" + ], + "optimal_path": "Current State: 78:[99, 45, 61, 64], Operations: []\nExploring Operation: 64-61=3, Resulting Numbers: [99, 45, 3]\nGenerated Node #2: [99, 45, 3] from Operation: 64-61=3\nCurrent State: 78:[99, 45, 3], Operations: ['64-61=3']\nExploring Operation: 99/3=33, Resulting Numbers: [45, 33]\nGenerated Node #3: [45, 33] from Operation: 99/3=33\nCurrent State: 78:[45, 33], Operations: ['64-61=3', '99/3=33']\nExploring Operation: 45+33=78, Resulting Numbers: [78]\n78,78 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 27, + 32, + 59, + 25 + ], + "target": 54, + "solution": [ + "32-27=5", + "25/5=5", + "59-5=54" + ], + "optimal_path": "Current State: 54:[27, 32, 59, 25], Operations: []\nExploring Operation: 32-27=5, Resulting Numbers: [59, 25, 5]\nGenerated Node #2: [59, 25, 5] from Operation: 32-27=5\nCurrent State: 54:[59, 25, 5], Operations: ['32-27=5']\nExploring Operation: 25/5=5, Resulting Numbers: [59, 5]\nGenerated Node #3: [59, 5] from Operation: 25/5=5\nCurrent State: 54:[59, 5], Operations: ['32-27=5', '25/5=5']\nExploring Operation: 59-5=54, Resulting Numbers: [54]\n54,54 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 13, + 65, + 14, + 84 + ], + "target": 75, + "solution": [ + "65/13=5", + "84-14=70", + "5+70=75" + ], + "optimal_path": "Current State: 75:[13, 65, 14, 84], Operations: []\nExploring Operation: 65/13=5, Resulting Numbers: [14, 84, 5]\nGenerated Node #2: [14, 84, 5] from Operation: 65/13=5\nCurrent State: 75:[14, 84, 5], Operations: ['65/13=5']\nExploring Operation: 84-14=70, Resulting Numbers: [5, 70]\nGenerated Node #3: [5, 70] from Operation: 84-14=70\nCurrent State: 75:[5, 70], Operations: ['65/13=5', '84-14=70']\nExploring Operation: 5+70=75, Resulting Numbers: [75]\n75,75 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 24, + 39, + 15, + 14 + ], + "target": 40, + "solution": [ + "39-14=25", + "24*25=600", + "600/15=40" + ], + "optimal_path": "Current State: 40:[24, 39, 15, 14], Operations: []\nExploring Operation: 39-14=25, Resulting Numbers: [24, 15, 25]\nGenerated Node #2: [24, 15, 25] from Operation: 39-14=25\nCurrent State: 40:[24, 15, 25], Operations: ['39-14=25']\nExploring Operation: 24*25=600, Resulting Numbers: [15, 600]\nGenerated Node #3: [15, 600] from Operation: 24*25=600\nCurrent State: 40:[15, 600], Operations: ['39-14=25', '24*25=600']\nExploring Operation: 600/15=40, Resulting Numbers: [40]\n40,40 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 7, + 57, + 25, + 98 + ], + "target": 46, + "solution": [ + "98/7=14", + "57-25=32", + "14+32=46" + ], + "optimal_path": "Current State: 46:[7, 57, 25, 98], Operations: []\nExploring Operation: 98/7=14, Resulting Numbers: [57, 25, 14]\nGenerated Node #2: [57, 25, 14] from Operation: 98/7=14\nCurrent State: 46:[57, 25, 14], Operations: ['98/7=14']\nExploring Operation: 57-25=32, Resulting Numbers: [14, 32]\nGenerated Node #3: [14, 32] from Operation: 57-25=32\nCurrent State: 46:[14, 32], Operations: ['98/7=14', '57-25=32']\nExploring Operation: 14+32=46, Resulting Numbers: [46]\n46,46 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 90, + 2, + 29, + 8 + ], + "target": 45, + "solution": [ + "90-29=61", + "2*8=16", + "61-16=45" + ], + "optimal_path": "Current State: 45:[90, 2, 29, 8], Operations: []\nExploring Operation: 90-29=61, Resulting Numbers: [2, 8, 61]\nGenerated Node #2: [2, 8, 61] from Operation: 90-29=61\nCurrent State: 45:[2, 8, 61], Operations: ['90-29=61']\nExploring Operation: 2*8=16, Resulting Numbers: [61, 16]\nGenerated Node #3: [61, 16] from Operation: 2*8=16\nCurrent State: 45:[61, 16], Operations: ['90-29=61', '2*8=16']\nExploring Operation: 61-16=45, Resulting Numbers: [45]\n45,45 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 42, + 87, + 82, + 2 + ], + "target": 89, + "solution": [ + "42*2=84", + "87-82=5", + "84+5=89" + ], + "optimal_path": "Current State: 89:[42, 87, 82, 2], Operations: []\nExploring Operation: 42*2=84, Resulting Numbers: [87, 82, 84]\nGenerated Node #2: [87, 82, 84] from Operation: 42*2=84\nCurrent State: 89:[87, 82, 84], Operations: ['42*2=84']\nExploring Operation: 87-82=5, Resulting Numbers: [84, 5]\nGenerated Node #3: [84, 5] from Operation: 87-82=5\nCurrent State: 89:[84, 5], Operations: ['42*2=84', '87-82=5']\nExploring Operation: 84+5=89, Resulting Numbers: [89]\n89,89 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 18, + 80, + 68, + 9 + ], + "target": 28, + "solution": [ + "18/9=2", + "80/2=40", + "68-40=28" + ], + "optimal_path": "Current State: 28:[18, 80, 68, 9], Operations: []\nExploring Operation: 18/9=2, Resulting Numbers: [80, 68, 2]\nGenerated Node #2: [80, 68, 2] from Operation: 18/9=2\nCurrent State: 28:[80, 68, 2], Operations: ['18/9=2']\nExploring Operation: 80/2=40, Resulting Numbers: [68, 40]\nGenerated Node #3: [68, 40] from Operation: 80/2=40\nCurrent State: 28:[68, 40], Operations: ['18/9=2', '80/2=40']\nExploring Operation: 68-40=28, Resulting Numbers: [28]\n28,28 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 2, + 46, + 6, + 44 + ], + "target": 14, + "solution": [ + "2*6=12", + "46-44=2", + "12+2=14" + ], + "optimal_path": "Current State: 14:[2, 46, 6, 44], Operations: []\nExploring Operation: 2*6=12, Resulting Numbers: [46, 44, 12]\nGenerated Node #2: [46, 44, 12] from Operation: 2*6=12\nCurrent State: 14:[46, 44, 12], Operations: ['2*6=12']\nExploring Operation: 46-44=2, Resulting Numbers: [12, 2]\nGenerated Node #3: [12, 2] from Operation: 46-44=2\nCurrent State: 14:[12, 2], Operations: ['2*6=12', '46-44=2']\nExploring Operation: 12+2=14, Resulting Numbers: [14]\n14,14 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 46, + 3, + 73, + 68 + ], + "target": 59, + "solution": [ + "73-46=27", + "27/3=9", + "68-9=59" + ], + "optimal_path": "Current State: 59:[46, 3, 73, 68], Operations: []\nExploring Operation: 73-46=27, Resulting Numbers: [3, 68, 27]\nGenerated Node #2: [3, 68, 27] from Operation: 73-46=27\nCurrent State: 59:[3, 68, 27], Operations: ['73-46=27']\nExploring Operation: 27/3=9, Resulting Numbers: [68, 9]\nGenerated Node #3: [68, 9] from Operation: 27/3=9\nCurrent State: 59:[68, 9], Operations: ['73-46=27', '27/3=9']\nExploring Operation: 68-9=59, Resulting Numbers: [59]\n59,59 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 89, + 68, + 59, + 16 + ], + "target": 96, + "solution": [ + "89-68=21", + "59+16=75", + "21+75=96" + ], + "optimal_path": "Current State: 96:[89, 68, 59, 16], Operations: []\nExploring Operation: 89-68=21, Resulting Numbers: [59, 16, 21]\nGenerated Node #2: [59, 16, 21] from Operation: 89-68=21\nCurrent State: 96:[59, 16, 21], Operations: ['89-68=21']\nExploring Operation: 59+16=75, Resulting Numbers: [21, 75]\nGenerated Node #3: [21, 75] from Operation: 59+16=75\nCurrent State: 96:[21, 75], Operations: ['89-68=21', '59+16=75']\nExploring Operation: 21+75=96, Resulting Numbers: [96]\n96,96 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 14, + 87, + 85, + 88 + ], + "target": 81, + "solution": [ + "87-85=2", + "14/2=7", + "88-7=81" + ], + "optimal_path": "Current State: 81:[14, 87, 85, 88], Operations: []\nExploring Operation: 87-85=2, Resulting Numbers: [14, 88, 2]\nGenerated Node #2: [14, 88, 2] from Operation: 87-85=2\nCurrent State: 81:[14, 88, 2], Operations: ['87-85=2']\nExploring Operation: 14/2=7, Resulting Numbers: [88, 7]\nGenerated Node #3: [88, 7] from Operation: 14/2=7\nCurrent State: 81:[88, 7], Operations: ['87-85=2', '14/2=7']\nExploring Operation: 88-7=81, Resulting Numbers: [81]\n81,81 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 44, + 26, + 63, + 82 + ], + "target": 89, + "solution": [ + "44+26=70", + "82-63=19", + "70+19=89" + ], + "optimal_path": "Current State: 89:[44, 26, 63, 82], Operations: []\nExploring Operation: 44+26=70, Resulting Numbers: [63, 82, 70]\nGenerated Node #2: [63, 82, 70] from Operation: 44+26=70\nCurrent State: 89:[63, 82, 70], Operations: ['44+26=70']\nExploring Operation: 82-63=19, Resulting Numbers: [70, 19]\nGenerated Node #3: [70, 19] from Operation: 82-63=19\nCurrent State: 89:[70, 19], Operations: ['44+26=70', '82-63=19']\nExploring Operation: 70+19=89, Resulting Numbers: [89]\n89,89 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 57, + 36, + 64, + 95 + ], + "target": 66, + "solution": [ + "57+36=93", + "64+95=159", + "159-93=66" + ], + "optimal_path": "Current State: 66:[57, 36, 64, 95], Operations: []\nExploring Operation: 57+36=93, Resulting Numbers: [64, 95, 93]\nGenerated Node #2: [64, 95, 93] from Operation: 57+36=93\nCurrent State: 66:[64, 95, 93], Operations: ['57+36=93']\nExploring Operation: 64+95=159, Resulting Numbers: [93, 159]\nGenerated Node #3: [93, 159] from Operation: 64+95=159\nCurrent State: 66:[93, 159], Operations: ['57+36=93', '64+95=159']\nExploring Operation: 159-93=66, Resulting Numbers: [66]\n66,66 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 27, + 69, + 62, + 93 + ], + "target": 96, + "solution": [ + "69-62=7", + "27*7=189", + "189-93=96" + ], + "optimal_path": "Current State: 96:[27, 69, 62, 93], Operations: []\nExploring Operation: 69-62=7, Resulting Numbers: [27, 93, 7]\nGenerated Node #2: [27, 93, 7] from Operation: 69-62=7\nCurrent State: 96:[27, 93, 7], Operations: ['69-62=7']\nExploring Operation: 27*7=189, Resulting Numbers: [93, 189]\nGenerated Node #3: [93, 189] from Operation: 27*7=189\nCurrent State: 96:[93, 189], Operations: ['69-62=7', '27*7=189']\nExploring Operation: 189-93=96, Resulting Numbers: [96]\n96,96 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 8, + 69, + 40, + 33 + ], + "target": 70, + "solution": [ + "8+69=77", + "40-33=7", + "77-7=70" + ], + "optimal_path": "Current State: 70:[8, 69, 40, 33], Operations: []\nExploring Operation: 8+69=77, Resulting Numbers: [40, 33, 77]\nGenerated Node #2: [40, 33, 77] from Operation: 8+69=77\nCurrent State: 70:[40, 33, 77], Operations: ['8+69=77']\nExploring Operation: 40-33=7, Resulting Numbers: [77, 7]\nGenerated Node #3: [77, 7] from Operation: 40-33=7\nCurrent State: 70:[77, 7], Operations: ['8+69=77', '40-33=7']\nExploring Operation: 77-7=70, Resulting Numbers: [70]\n70,70 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 10, + 27, + 7, + 63 + ], + "target": 26, + "solution": [ + "27-10=17", + "63/7=9", + "17+9=26" + ], + "optimal_path": "Current State: 26:[10, 27, 7, 63], Operations: []\nExploring Operation: 27-10=17, Resulting Numbers: [7, 63, 17]\nGenerated Node #2: [7, 63, 17] from Operation: 27-10=17\nCurrent State: 26:[7, 63, 17], Operations: ['27-10=17']\nExploring Operation: 63/7=9, Resulting Numbers: [17, 9]\nGenerated Node #3: [17, 9] from Operation: 63/7=9\nCurrent State: 26:[17, 9], Operations: ['27-10=17', '63/7=9']\nExploring Operation: 17+9=26, Resulting Numbers: [26]\n26,26 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 55, + 13, + 48, + 29 + ], + "target": 49, + "solution": [ + "55+13=68", + "48-29=19", + "68-19=49" + ], + "optimal_path": "Current State: 49:[55, 13, 48, 29], Operations: []\nExploring Operation: 55+13=68, Resulting Numbers: [48, 29, 68]\nGenerated Node #2: [48, 29, 68] from Operation: 55+13=68\nCurrent State: 49:[48, 29, 68], Operations: ['55+13=68']\nExploring Operation: 48-29=19, Resulting Numbers: [68, 19]\nGenerated Node #3: [68, 19] from Operation: 48-29=19\nCurrent State: 49:[68, 19], Operations: ['55+13=68', '48-29=19']\nExploring Operation: 68-19=49, Resulting Numbers: [49]\n49,49 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 8, + 95, + 92, + 37 + ], + "target": 13, + "solution": [ + "95-92=3", + "8*3=24", + "37-24=13" + ], + "optimal_path": "Current State: 13:[8, 95, 92, 37], Operations: []\nExploring Operation: 95-92=3, Resulting Numbers: [8, 37, 3]\nGenerated Node #2: [8, 37, 3] from Operation: 95-92=3\nCurrent State: 13:[8, 37, 3], Operations: ['95-92=3']\nExploring Operation: 8*3=24, Resulting Numbers: [37, 24]\nGenerated Node #3: [37, 24] from Operation: 8*3=24\nCurrent State: 13:[37, 24], Operations: ['95-92=3', '8*3=24']\nExploring Operation: 37-24=13, Resulting Numbers: [13]\n13,13 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 47, + 64, + 66, + 99 + ], + "target": 49, + "solution": [ + "64*99=6336", + "6336/66=96", + "96-47=49" + ], + "optimal_path": "Current State: 49:[47, 64, 66, 99], Operations: []\nExploring Operation: 64*99=6336, Resulting Numbers: [47, 66, 6336]\nGenerated Node #2: [47, 66, 6336] from Operation: 64*99=6336\nCurrent State: 49:[47, 66, 6336], Operations: ['64*99=6336']\nExploring Operation: 6336/66=96, Resulting Numbers: [47, 96]\nGenerated Node #3: [47, 96] from Operation: 6336/66=96\nCurrent State: 49:[47, 96], Operations: ['64*99=6336', '6336/66=96']\nExploring Operation: 96-47=49, Resulting Numbers: [49]\n49,49 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 91, + 28, + 26, + 30 + ], + "target": 89, + "solution": [ + "26+30=56", + "56/28=2", + "91-2=89" + ], + "optimal_path": "Current State: 89:[91, 28, 26, 30], Operations: []\nExploring Operation: 26+30=56, Resulting Numbers: [91, 28, 56]\nGenerated Node #2: [91, 28, 56] from Operation: 26+30=56\nCurrent State: 89:[91, 28, 56], Operations: ['26+30=56']\nExploring Operation: 56/28=2, Resulting Numbers: [91, 2]\nGenerated Node #3: [91, 2] from Operation: 56/28=2\nCurrent State: 89:[91, 2], Operations: ['26+30=56', '56/28=2']\nExploring Operation: 91-2=89, Resulting Numbers: [89]\n89,89 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 3, + 34, + 51, + 12 + ], + "target": 100, + "solution": [ + "3+34=37", + "51+12=63", + "37+63=100" + ], + "optimal_path": "Current State: 100:[3, 34, 51, 12], Operations: []\nExploring Operation: 3+34=37, Resulting Numbers: [51, 12, 37]\nGenerated Node #2: [51, 12, 37] from Operation: 3+34=37\nCurrent State: 100:[51, 12, 37], Operations: ['3+34=37']\nExploring Operation: 51+12=63, Resulting Numbers: [37, 63]\nGenerated Node #3: [37, 63] from Operation: 51+12=63\nCurrent State: 100:[37, 63], Operations: ['3+34=37', '51+12=63']\nExploring Operation: 37+63=100, Resulting Numbers: [100]\n100,100 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 58, + 44, + 93, + 95 + ], + "target": 51, + "solution": [ + "58+44=102", + "95-93=2", + "102/2=51" + ], + "optimal_path": "Current State: 51:[58, 44, 93, 95], Operations: []\nExploring Operation: 58+44=102, Resulting Numbers: [93, 95, 102]\nGenerated Node #2: [93, 95, 102] from Operation: 58+44=102\nCurrent State: 51:[93, 95, 102], Operations: ['58+44=102']\nExploring Operation: 95-93=2, Resulting Numbers: [102, 2]\nGenerated Node #3: [102, 2] from Operation: 95-93=2\nCurrent State: 51:[102, 2], Operations: ['58+44=102', '95-93=2']\nExploring Operation: 102/2=51, Resulting Numbers: [51]\n51,51 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 50, + 44, + 54, + 20 + ], + "target": 40, + "solution": [ + "50-44=6", + "54-20=34", + "6+34=40" + ], + "optimal_path": "Current State: 40:[50, 44, 54, 20], Operations: []\nExploring Operation: 50-44=6, Resulting Numbers: [54, 20, 6]\nGenerated Node #2: [54, 20, 6] from Operation: 50-44=6\nCurrent State: 40:[54, 20, 6], Operations: ['50-44=6']\nExploring Operation: 54-20=34, Resulting Numbers: [6, 34]\nGenerated Node #3: [6, 34] from Operation: 54-20=34\nCurrent State: 40:[6, 34], Operations: ['50-44=6', '54-20=34']\nExploring Operation: 6+34=40, Resulting Numbers: [40]\n40,40 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 80, + 40, + 66, + 72 + ], + "target": 18, + "solution": [ + "80+40=120", + "66+72=138", + "138-120=18" + ], + "optimal_path": "Current State: 18:[80, 40, 66, 72], Operations: []\nExploring Operation: 80+40=120, Resulting Numbers: [66, 72, 120]\nGenerated Node #2: [66, 72, 120] from Operation: 80+40=120\nCurrent State: 18:[66, 72, 120], Operations: ['80+40=120']\nExploring Operation: 66+72=138, Resulting Numbers: [120, 138]\nGenerated Node #3: [120, 138] from Operation: 66+72=138\nCurrent State: 18:[120, 138], Operations: ['80+40=120', '66+72=138']\nExploring Operation: 138-120=18, Resulting Numbers: [18]\n18,18 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 93, + 51, + 23, + 21 + ], + "target": 44, + "solution": [ + "93-51=42", + "23-21=2", + "42+2=44" + ], + "optimal_path": "Current State: 44:[93, 51, 23, 21], Operations: []\nExploring Operation: 93-51=42, Resulting Numbers: [23, 21, 42]\nGenerated Node #2: [23, 21, 42] from Operation: 93-51=42\nCurrent State: 44:[23, 21, 42], Operations: ['93-51=42']\nExploring Operation: 23-21=2, Resulting Numbers: [42, 2]\nGenerated Node #3: [42, 2] from Operation: 23-21=2\nCurrent State: 44:[42, 2], Operations: ['93-51=42', '23-21=2']\nExploring Operation: 42+2=44, Resulting Numbers: [44]\n44,44 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 17, + 10, + 13, + 26 + ], + "target": 54, + "solution": [ + "17+10=27", + "26/13=2", + "27*2=54" + ], + "optimal_path": "Current State: 54:[17, 10, 13, 26], Operations: []\nExploring Operation: 17+10=27, Resulting Numbers: [13, 26, 27]\nGenerated Node #2: [13, 26, 27] from Operation: 17+10=27\nCurrent State: 54:[13, 26, 27], Operations: ['17+10=27']\nExploring Operation: 26/13=2, Resulting Numbers: [27, 2]\nGenerated Node #3: [27, 2] from Operation: 26/13=2\nCurrent State: 54:[27, 2], Operations: ['17+10=27', '26/13=2']\nExploring Operation: 27*2=54, Resulting Numbers: [54]\n54,54 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 91, + 6, + 74, + 72 + ], + "target": 94, + "solution": [ + "74-72=2", + "6/2=3", + "91+3=94" + ], + "optimal_path": "Current State: 94:[91, 6, 74, 72], Operations: []\nExploring Operation: 74-72=2, Resulting Numbers: [91, 6, 2]\nGenerated Node #2: [91, 6, 2] from Operation: 74-72=2\nCurrent State: 94:[91, 6, 2], Operations: ['74-72=2']\nExploring Operation: 6/2=3, Resulting Numbers: [91, 3]\nGenerated Node #3: [91, 3] from Operation: 6/2=3\nCurrent State: 94:[91, 3], Operations: ['74-72=2', '6/2=3']\nExploring Operation: 91+3=94, Resulting Numbers: [94]\n94,94 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 2, + 67, + 27, + 20 + ], + "target": 67, + "solution": [ + "67+27=94", + "94/2=47", + "20+47=67" + ], + "optimal_path": "Current State: 67:[2, 67, 27, 20], Operations: []\nExploring Operation: 67+27=94, Resulting Numbers: [2, 20, 94]\nGenerated Node #2: [2, 20, 94] from Operation: 67+27=94\nCurrent State: 67:[2, 20, 94], Operations: ['67+27=94']\nExploring Operation: 94/2=47, Resulting Numbers: [20, 47]\nGenerated Node #3: [20, 47] from Operation: 94/2=47\nCurrent State: 67:[20, 47], Operations: ['67+27=94', '94/2=47']\nExploring Operation: 20+47=67, Resulting Numbers: [67]\n67,67 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 16, + 24, + 65, + 69 + ], + "target": 44, + "solution": [ + "16+24=40", + "69-65=4", + "40+4=44" + ], + "optimal_path": "Current State: 44:[16, 24, 65, 69], Operations: []\nExploring Operation: 16+24=40, Resulting Numbers: [65, 69, 40]\nGenerated Node #2: [65, 69, 40] from Operation: 16+24=40\nCurrent State: 44:[65, 69, 40], Operations: ['16+24=40']\nExploring Operation: 69-65=4, Resulting Numbers: [40, 4]\nGenerated Node #3: [40, 4] from Operation: 69-65=4\nCurrent State: 44:[40, 4], Operations: ['16+24=40', '69-65=4']\nExploring Operation: 40+4=44, Resulting Numbers: [44]\n44,44 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 41, + 27, + 88, + 2 + ], + "target": 75, + "solution": [ + "41+88=129", + "27*2=54", + "129-54=75" + ], + "optimal_path": "Current State: 75:[41, 27, 88, 2], Operations: []\nExploring Operation: 41+88=129, Resulting Numbers: [27, 2, 129]\nGenerated Node #2: [27, 2, 129] from Operation: 41+88=129\nCurrent State: 75:[27, 2, 129], Operations: ['41+88=129']\nExploring Operation: 27*2=54, Resulting Numbers: [129, 54]\nGenerated Node #3: [129, 54] from Operation: 27*2=54\nCurrent State: 75:[129, 54], Operations: ['41+88=129', '27*2=54']\nExploring Operation: 129-54=75, Resulting Numbers: [75]\n75,75 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 52, + 93, + 62, + 43 + ], + "target": 64, + "solution": [ + "93-52=41", + "62+43=105", + "105-41=64" + ], + "optimal_path": "Current State: 64:[52, 93, 62, 43], Operations: []\nExploring Operation: 93-52=41, Resulting Numbers: [62, 43, 41]\nGenerated Node #2: [62, 43, 41] from Operation: 93-52=41\nCurrent State: 64:[62, 43, 41], Operations: ['93-52=41']\nExploring Operation: 62+43=105, Resulting Numbers: [41, 105]\nGenerated Node #3: [41, 105] from Operation: 62+43=105\nCurrent State: 64:[41, 105], Operations: ['93-52=41', '62+43=105']\nExploring Operation: 105-41=64, Resulting Numbers: [64]\n64,64 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 80, + 2, + 43, + 83 + ], + "target": 77, + "solution": [ + "80+83=163", + "2*43=86", + "163-86=77" + ], + "optimal_path": "Current State: 77:[80, 2, 43, 83], Operations: []\nExploring Operation: 80+83=163, Resulting Numbers: [2, 43, 163]\nGenerated Node #2: [2, 43, 163] from Operation: 80+83=163\nCurrent State: 77:[2, 43, 163], Operations: ['80+83=163']\nExploring Operation: 2*43=86, Resulting Numbers: [163, 86]\nGenerated Node #3: [163, 86] from Operation: 2*43=86\nCurrent State: 77:[163, 86], Operations: ['80+83=163', '2*43=86']\nExploring Operation: 163-86=77, Resulting Numbers: [77]\n77,77 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 6, + 36, + 71, + 66 + ], + "target": 36, + "solution": [ + "71-6=65", + "66-65=1", + "36*1=36" + ], + "optimal_path": "Current State: 36:[6, 36, 71, 66], Operations: []\nExploring Operation: 71-6=65, Resulting Numbers: [36, 66, 65]\nGenerated Node #2: [36, 66, 65] from Operation: 71-6=65\nCurrent State: 36:[36, 66, 65], Operations: ['71-6=65']\nExploring Operation: 66-65=1, Resulting Numbers: [36, 1]\nGenerated Node #3: [36, 1] from Operation: 66-65=1\nCurrent State: 36:[36, 1], Operations: ['71-6=65', '66-65=1']\nExploring Operation: 36*1=36, Resulting Numbers: [36]\n36,36 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 36, + 23, + 90, + 38 + ], + "target": 42, + "solution": [ + "38-23=15", + "90/15=6", + "36+6=42" + ], + "optimal_path": "Current State: 42:[36, 23, 90, 38], Operations: []\nExploring Operation: 38-23=15, Resulting Numbers: [36, 90, 15]\nGenerated Node #2: [36, 90, 15] from Operation: 38-23=15\nCurrent State: 42:[36, 90, 15], Operations: ['38-23=15']\nExploring Operation: 90/15=6, Resulting Numbers: [36, 6]\nGenerated Node #3: [36, 6] from Operation: 90/15=6\nCurrent State: 42:[36, 6], Operations: ['38-23=15', '90/15=6']\nExploring Operation: 36+6=42, Resulting Numbers: [42]\n42,42 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 3, + 21, + 36, + 30 + ], + "target": 11, + "solution": [ + "21+36=57", + "57/3=19", + "30-19=11" + ], + "optimal_path": "Current State: 11:[3, 21, 36, 30], Operations: []\nExploring Operation: 21+36=57, Resulting Numbers: [3, 30, 57]\nGenerated Node #2: [3, 30, 57] from Operation: 21+36=57\nCurrent State: 11:[3, 30, 57], Operations: ['21+36=57']\nExploring Operation: 57/3=19, Resulting Numbers: [30, 19]\nGenerated Node #3: [30, 19] from Operation: 57/3=19\nCurrent State: 11:[30, 19], Operations: ['21+36=57', '57/3=19']\nExploring Operation: 30-19=11, Resulting Numbers: [11]\n11,11 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 41, + 55, + 9, + 21 + ], + "target": 84, + "solution": [ + "41+55=96", + "21-9=12", + "96-12=84" + ], + "optimal_path": "Current State: 84:[41, 55, 9, 21], Operations: []\nExploring Operation: 41+55=96, Resulting Numbers: [9, 21, 96]\nGenerated Node #2: [9, 21, 96] from Operation: 41+55=96\nCurrent State: 84:[9, 21, 96], Operations: ['41+55=96']\nExploring Operation: 21-9=12, Resulting Numbers: [96, 12]\nGenerated Node #3: [96, 12] from Operation: 21-9=12\nCurrent State: 84:[96, 12], Operations: ['41+55=96', '21-9=12']\nExploring Operation: 96-12=84, Resulting Numbers: [84]\n84,84 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 3, + 83, + 65, + 56 + ], + "target": 86, + "solution": [ + "65-56=9", + "9/3=3", + "83+3=86" + ], + "optimal_path": "Current State: 86:[3, 83, 65, 56], Operations: []\nExploring Operation: 65-56=9, Resulting Numbers: [3, 83, 9]\nGenerated Node #2: [3, 83, 9] from Operation: 65-56=9\nCurrent State: 86:[3, 83, 9], Operations: ['65-56=9']\nExploring Operation: 9/3=3, Resulting Numbers: [83, 3]\nGenerated Node #3: [83, 3] from Operation: 9/3=3\nCurrent State: 86:[83, 3], Operations: ['65-56=9', '9/3=3']\nExploring Operation: 83+3=86, Resulting Numbers: [86]\n86,86 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 46, + 83, + 20, + 11 + ], + "target": 91, + "solution": [ + "46+83=129", + "20*11=220", + "220-129=91" + ], + "optimal_path": "Current State: 91:[46, 83, 20, 11], Operations: []\nExploring Operation: 46+83=129, Resulting Numbers: [20, 11, 129]\nGenerated Node #2: [20, 11, 129] from Operation: 46+83=129\nCurrent State: 91:[20, 11, 129], Operations: ['46+83=129']\nExploring Operation: 20*11=220, Resulting Numbers: [129, 220]\nGenerated Node #3: [129, 220] from Operation: 20*11=220\nCurrent State: 91:[129, 220], Operations: ['46+83=129', '20*11=220']\nExploring Operation: 220-129=91, Resulting Numbers: [91]\n91,91 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 40, + 96, + 39, + 35 + ], + "target": 99, + "solution": [ + "40-35=5", + "39*5=195", + "195-96=99" + ], + "optimal_path": "Current State: 99:[40, 96, 39, 35], Operations: []\nExploring Operation: 40-35=5, Resulting Numbers: [96, 39, 5]\nGenerated Node #2: [96, 39, 5] from Operation: 40-35=5\nCurrent State: 99:[96, 39, 5], Operations: ['40-35=5']\nExploring Operation: 39*5=195, Resulting Numbers: [96, 195]\nGenerated Node #3: [96, 195] from Operation: 39*5=195\nCurrent State: 99:[96, 195], Operations: ['40-35=5', '39*5=195']\nExploring Operation: 195-96=99, Resulting Numbers: [99]\n99,99 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 92, + 46, + 24, + 19 + ], + "target": 86, + "solution": [ + "92/46=2", + "24+19=43", + "2*43=86" + ], + "optimal_path": "Current State: 86:[92, 46, 24, 19], Operations: []\nExploring Operation: 92/46=2, Resulting Numbers: [24, 19, 2]\nGenerated Node #2: [24, 19, 2] from Operation: 92/46=2\nCurrent State: 86:[24, 19, 2], Operations: ['92/46=2']\nExploring Operation: 24+19=43, Resulting Numbers: [2, 43]\nGenerated Node #3: [2, 43] from Operation: 24+19=43\nCurrent State: 86:[2, 43], Operations: ['92/46=2', '24+19=43']\nExploring Operation: 2*43=86, Resulting Numbers: [86]\n86,86 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 32, + 24, + 59, + 64 + ], + "target": 67, + "solution": [ + "32+24=56", + "59+64=123", + "123-56=67" + ], + "optimal_path": "Current State: 67:[32, 24, 59, 64], Operations: []\nExploring Operation: 32+24=56, Resulting Numbers: [59, 64, 56]\nGenerated Node #2: [59, 64, 56] from Operation: 32+24=56\nCurrent State: 67:[59, 64, 56], Operations: ['32+24=56']\nExploring Operation: 59+64=123, Resulting Numbers: [56, 123]\nGenerated Node #3: [56, 123] from Operation: 59+64=123\nCurrent State: 67:[56, 123], Operations: ['32+24=56', '59+64=123']\nExploring Operation: 123-56=67, Resulting Numbers: [67]\n67,67 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 95, + 93, + 36, + 98 + ], + "target": 85, + "solution": [ + "95-93=2", + "98/2=49", + "36+49=85" + ], + "optimal_path": "Current State: 85:[95, 93, 36, 98], Operations: []\nExploring Operation: 95-93=2, Resulting Numbers: [36, 98, 2]\nGenerated Node #2: [36, 98, 2] from Operation: 95-93=2\nCurrent State: 85:[36, 98, 2], Operations: ['95-93=2']\nExploring Operation: 98/2=49, Resulting Numbers: [36, 49]\nGenerated Node #3: [36, 49] from Operation: 98/2=49\nCurrent State: 85:[36, 49], Operations: ['95-93=2', '98/2=49']\nExploring Operation: 36+49=85, Resulting Numbers: [85]\n85,85 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 97, + 99, + 38, + 48 + ], + "target": 12, + "solution": [ + "99-97=2", + "48-38=10", + "2+10=12" + ], + "optimal_path": "Current State: 12:[97, 99, 38, 48], Operations: []\nExploring Operation: 99-97=2, Resulting Numbers: [38, 48, 2]\nGenerated Node #2: [38, 48, 2] from Operation: 99-97=2\nCurrent State: 12:[38, 48, 2], Operations: ['99-97=2']\nExploring Operation: 48-38=10, Resulting Numbers: [2, 10]\nGenerated Node #3: [2, 10] from Operation: 48-38=10\nCurrent State: 12:[2, 10], Operations: ['99-97=2', '48-38=10']\nExploring Operation: 2+10=12, Resulting Numbers: [12]\n12,12 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 55, + 11, + 95, + 4 + ], + "target": 46, + "solution": [ + "95+4=99", + "99/11=9", + "55-9=46" + ], + "optimal_path": "Current State: 46:[55, 11, 95, 4], Operations: []\nExploring Operation: 95+4=99, Resulting Numbers: [55, 11, 99]\nGenerated Node #2: [55, 11, 99] from Operation: 95+4=99\nCurrent State: 46:[55, 11, 99], Operations: ['95+4=99']\nExploring Operation: 99/11=9, Resulting Numbers: [55, 9]\nGenerated Node #3: [55, 9] from Operation: 99/11=9\nCurrent State: 46:[55, 9], Operations: ['95+4=99', '99/11=9']\nExploring Operation: 55-9=46, Resulting Numbers: [46]\n46,46 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 40, + 61, + 56, + 58 + ], + "target": 48, + "solution": [ + "56-40=16", + "61-58=3", + "16*3=48" + ], + "optimal_path": "Current State: 48:[40, 61, 56, 58], Operations: []\nExploring Operation: 56-40=16, Resulting Numbers: [61, 58, 16]\nGenerated Node #2: [61, 58, 16] from Operation: 56-40=16\nCurrent State: 48:[61, 58, 16], Operations: ['56-40=16']\nExploring Operation: 61-58=3, Resulting Numbers: [16, 3]\nGenerated Node #3: [16, 3] from Operation: 61-58=3\nCurrent State: 48:[16, 3], Operations: ['56-40=16', '61-58=3']\nExploring Operation: 16*3=48, Resulting Numbers: [48]\n48,48 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 31, + 32, + 21, + 38 + ], + "target": 95, + "solution": [ + "38-32=6", + "21*6=126", + "126-31=95" + ], + "optimal_path": "Current State: 95:[31, 32, 21, 38], Operations: []\nExploring Operation: 38-32=6, Resulting Numbers: [31, 21, 6]\nGenerated Node #2: [31, 21, 6] from Operation: 38-32=6\nCurrent State: 95:[31, 21, 6], Operations: ['38-32=6']\nExploring Operation: 21*6=126, Resulting Numbers: [31, 126]\nGenerated Node #3: [31, 126] from Operation: 21*6=126\nCurrent State: 95:[31, 126], Operations: ['38-32=6', '21*6=126']\nExploring Operation: 126-31=95, Resulting Numbers: [95]\n95,95 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 13, + 62, + 49, + 65 + ], + "target": 66, + "solution": [ + "62-13=49", + "49/49=1", + "65+1=66" + ], + "optimal_path": "Current State: 66:[13, 62, 49, 65], Operations: []\nExploring Operation: 62-13=49, Resulting Numbers: [49, 65, 49]\nGenerated Node #2: [49, 65, 49] from Operation: 62-13=49\nCurrent State: 66:[49, 65, 49], Operations: ['62-13=49']\nExploring Operation: 49/49=1, Resulting Numbers: [65, 1]\nGenerated Node #3: [65, 1] from Operation: 49/49=1\nCurrent State: 66:[65, 1], Operations: ['62-13=49', '49/49=1']\nExploring Operation: 65+1=66, Resulting Numbers: [66]\n66,66 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 74, + 21, + 20, + 56 + ], + "target": 89, + "solution": [ + "74-21=53", + "56-20=36", + "53+36=89" + ], + "optimal_path": "Current State: 89:[74, 21, 20, 56], Operations: []\nExploring Operation: 74-21=53, Resulting Numbers: [20, 56, 53]\nGenerated Node #2: [20, 56, 53] from Operation: 74-21=53\nCurrent State: 89:[20, 56, 53], Operations: ['74-21=53']\nExploring Operation: 56-20=36, Resulting Numbers: [53, 36]\nGenerated Node #3: [53, 36] from Operation: 56-20=36\nCurrent State: 89:[53, 36], Operations: ['74-21=53', '56-20=36']\nExploring Operation: 53+36=89, Resulting Numbers: [89]\n89,89 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 77, + 56, + 62, + 52 + ], + "target": 31, + "solution": [ + "77-56=21", + "62-52=10", + "21+10=31" + ], + "optimal_path": "Current State: 31:[77, 56, 62, 52], Operations: []\nExploring Operation: 77-56=21, Resulting Numbers: [62, 52, 21]\nGenerated Node #2: [62, 52, 21] from Operation: 77-56=21\nCurrent State: 31:[62, 52, 21], Operations: ['77-56=21']\nExploring Operation: 62-52=10, Resulting Numbers: [21, 10]\nGenerated Node #3: [21, 10] from Operation: 62-52=10\nCurrent State: 31:[21, 10], Operations: ['77-56=21', '62-52=10']\nExploring Operation: 21+10=31, Resulting Numbers: [31]\n31,31 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 4, + 90, + 90, + 15 + ], + "target": 80, + "solution": [ + "90-4=86", + "90/15=6", + "86-6=80" + ], + "optimal_path": "Current State: 80:[4, 90, 90, 15], Operations: []\nExploring Operation: 90-4=86, Resulting Numbers: [15, 86]\nGenerated Node #2: [15, 86] from Operation: 90-4=86\nCurrent State: 80:[15, 86], Operations: ['90-4=86']\nExploring Operation: 90/15=6, Resulting Numbers: [86, 6]\nGenerated Node #3: [86, 6] from Operation: 90/15=6\nCurrent State: 80:[86, 6], Operations: ['90-4=86', '90/15=6']\nExploring Operation: 86-6=80, Resulting Numbers: [80]\n80,80 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 88, + 67, + 3, + 66 + ], + "target": 85, + "solution": [ + "88-3=85", + "67-66=1", + "85*1=85" + ], + "optimal_path": "Current State: 85:[88, 67, 3, 66], Operations: []\nExploring Operation: 88-3=85, Resulting Numbers: [67, 66, 85]\nGenerated Node #2: [67, 66, 85] from Operation: 88-3=85\nCurrent State: 85:[67, 66, 85], Operations: ['88-3=85']\nExploring Operation: 67-66=1, Resulting Numbers: [85, 1]\nGenerated Node #3: [85, 1] from Operation: 67-66=1\nCurrent State: 85:[85, 1], Operations: ['88-3=85', '67-66=1']\nExploring Operation: 85*1=85, Resulting Numbers: [85]\n85,85 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 10, + 57, + 66, + 69 + ], + "target": 92, + "solution": [ + "10+66=76", + "69*76=5244", + "5244/57=92" + ], + "optimal_path": "Current State: 92:[10, 57, 66, 69], Operations: []\nExploring Operation: 10+66=76, Resulting Numbers: [57, 69, 76]\nGenerated Node #2: [57, 69, 76] from Operation: 10+66=76\nCurrent State: 92:[57, 69, 76], Operations: ['10+66=76']\nExploring Operation: 69*76=5244, Resulting Numbers: [57, 5244]\nGenerated Node #3: [57, 5244] from Operation: 69*76=5244\nCurrent State: 92:[57, 5244], Operations: ['10+66=76', '69*76=5244']\nExploring Operation: 5244/57=92, Resulting Numbers: [92]\n92,92 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 44, + 33, + 15, + 13 + ], + "target": 52, + "solution": [ + "44-33=11", + "15-11=4", + "13*4=52" + ], + "optimal_path": "Current State: 52:[44, 33, 15, 13], Operations: []\nExploring Operation: 44-33=11, Resulting Numbers: [15, 13, 11]\nGenerated Node #2: [15, 13, 11] from Operation: 44-33=11\nCurrent State: 52:[15, 13, 11], Operations: ['44-33=11']\nExploring Operation: 15-11=4, Resulting Numbers: [13, 4]\nGenerated Node #3: [13, 4] from Operation: 15-11=4\nCurrent State: 52:[13, 4], Operations: ['44-33=11', '15-11=4']\nExploring Operation: 13*4=52, Resulting Numbers: [52]\n52,52 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 60, + 48, + 2, + 55 + ], + "target": 55, + "solution": [ + "60+48=108", + "55-2=53", + "108-53=55" + ], + "optimal_path": "Current State: 55:[60, 48, 2, 55], Operations: []\nExploring Operation: 60+48=108, Resulting Numbers: [2, 55, 108]\nGenerated Node #2: [2, 55, 108] from Operation: 60+48=108\nCurrent State: 55:[2, 55, 108], Operations: ['60+48=108']\nExploring Operation: 55-2=53, Resulting Numbers: [108, 53]\nGenerated Node #3: [108, 53] from Operation: 55-2=53\nCurrent State: 55:[108, 53], Operations: ['60+48=108', '55-2=53']\nExploring Operation: 108-53=55, Resulting Numbers: [55]\n55,55 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 54, + 49, + 41, + 88 + ], + "target": 56, + "solution": [ + "54+49=103", + "88-41=47", + "103-47=56" + ], + "optimal_path": "Current State: 56:[54, 49, 41, 88], Operations: []\nExploring Operation: 54+49=103, Resulting Numbers: [41, 88, 103]\nGenerated Node #2: [41, 88, 103] from Operation: 54+49=103\nCurrent State: 56:[41, 88, 103], Operations: ['54+49=103']\nExploring Operation: 88-41=47, Resulting Numbers: [103, 47]\nGenerated Node #3: [103, 47] from Operation: 88-41=47\nCurrent State: 56:[103, 47], Operations: ['54+49=103', '88-41=47']\nExploring Operation: 103-47=56, Resulting Numbers: [56]\n56,56 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 2, + 77, + 95, + 14 + ], + "target": 23, + "solution": [ + "95-77=18", + "18/2=9", + "14+9=23" + ], + "optimal_path": "Current State: 23:[2, 77, 95, 14], Operations: []\nExploring Operation: 95-77=18, Resulting Numbers: [2, 14, 18]\nGenerated Node #2: [2, 14, 18] from Operation: 95-77=18\nCurrent State: 23:[2, 14, 18], Operations: ['95-77=18']\nExploring Operation: 18/2=9, Resulting Numbers: [14, 9]\nGenerated Node #3: [14, 9] from Operation: 18/2=9\nCurrent State: 23:[14, 9], Operations: ['95-77=18', '18/2=9']\nExploring Operation: 14+9=23, Resulting Numbers: [23]\n23,23 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 15, + 1, + 90, + 59 + ], + "target": 53, + "solution": [ + "15*1=15", + "90/15=6", + "59-6=53" + ], + "optimal_path": "Current State: 53:[15, 1, 90, 59], Operations: []\nExploring Operation: 15*1=15, Resulting Numbers: [90, 59, 15]\nGenerated Node #2: [90, 59, 15] from Operation: 15*1=15\nCurrent State: 53:[90, 59, 15], Operations: ['15*1=15']\nExploring Operation: 90/15=6, Resulting Numbers: [59, 6]\nGenerated Node #3: [59, 6] from Operation: 90/15=6\nCurrent State: 53:[59, 6], Operations: ['15*1=15', '90/15=6']\nExploring Operation: 59-6=53, Resulting Numbers: [53]\n53,53 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 7, + 11, + 41, + 60 + ], + "target": 48, + "solution": [ + "60-11=49", + "49/7=7", + "41+7=48" + ], + "optimal_path": "Current State: 48:[7, 11, 41, 60], Operations: []\nExploring Operation: 60-11=49, Resulting Numbers: [7, 41, 49]\nGenerated Node #2: [7, 41, 49] from Operation: 60-11=49\nCurrent State: 48:[7, 41, 49], Operations: ['60-11=49']\nExploring Operation: 49/7=7, Resulting Numbers: [41, 7]\nGenerated Node #3: [41, 7] from Operation: 49/7=7\nCurrent State: 48:[41, 7], Operations: ['60-11=49', '49/7=7']\nExploring Operation: 41+7=48, Resulting Numbers: [48]\n48,48 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 37, + 56, + 5, + 45 + ], + "target": 28, + "solution": [ + "56-37=19", + "45/5=9", + "19+9=28" + ], + "optimal_path": "Current State: 28:[37, 56, 5, 45], Operations: []\nExploring Operation: 56-37=19, Resulting Numbers: [5, 45, 19]\nGenerated Node #2: [5, 45, 19] from Operation: 56-37=19\nCurrent State: 28:[5, 45, 19], Operations: ['56-37=19']\nExploring Operation: 45/5=9, Resulting Numbers: [19, 9]\nGenerated Node #3: [19, 9] from Operation: 45/5=9\nCurrent State: 28:[19, 9], Operations: ['56-37=19', '45/5=9']\nExploring Operation: 19+9=28, Resulting Numbers: [28]\n28,28 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 92, + 4, + 7, + 73 + ], + "target": 15, + "solution": [ + "92+73=165", + "4+7=11", + "165/11=15" + ], + "optimal_path": "Current State: 15:[92, 4, 7, 73], Operations: []\nExploring Operation: 92+73=165, Resulting Numbers: [4, 7, 165]\nGenerated Node #2: [4, 7, 165] from Operation: 92+73=165\nCurrent State: 15:[4, 7, 165], Operations: ['92+73=165']\nExploring Operation: 4+7=11, Resulting Numbers: [165, 11]\nGenerated Node #3: [165, 11] from Operation: 4+7=11\nCurrent State: 15:[165, 11], Operations: ['92+73=165', '4+7=11']\nExploring Operation: 165/11=15, Resulting Numbers: [15]\n15,15 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 27, + 3, + 67, + 31 + ], + "target": 60, + "solution": [ + "27-3=24", + "67-31=36", + "24+36=60" + ], + "optimal_path": "Current State: 60:[27, 3, 67, 31], Operations: []\nExploring Operation: 27-3=24, Resulting Numbers: [67, 31, 24]\nGenerated Node #2: [67, 31, 24] from Operation: 27-3=24\nCurrent State: 60:[67, 31, 24], Operations: ['27-3=24']\nExploring Operation: 67-31=36, Resulting Numbers: [24, 36]\nGenerated Node #3: [24, 36] from Operation: 67-31=36\nCurrent State: 60:[24, 36], Operations: ['27-3=24', '67-31=36']\nExploring Operation: 24+36=60, Resulting Numbers: [60]\n60,60 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 63, + 8, + 90, + 7 + ], + "target": 27, + "solution": [ + "90-63=27", + "8-7=1", + "27*1=27" + ], + "optimal_path": "Current State: 27:[63, 8, 90, 7], Operations: []\nExploring Operation: 90-63=27, Resulting Numbers: [8, 7, 27]\nGenerated Node #2: [8, 7, 27] from Operation: 90-63=27\nCurrent State: 27:[8, 7, 27], Operations: ['90-63=27']\nExploring Operation: 8-7=1, Resulting Numbers: [27, 1]\nGenerated Node #3: [27, 1] from Operation: 8-7=1\nCurrent State: 27:[27, 1], Operations: ['90-63=27', '8-7=1']\nExploring Operation: 27*1=27, Resulting Numbers: [27]\n27,27 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 65, + 18, + 36, + 72 + ], + "target": 47, + "solution": [ + "65+18=83", + "72-36=36", + "83-36=47" + ], + "optimal_path": "Current State: 47:[65, 18, 36, 72], Operations: []\nExploring Operation: 65+18=83, Resulting Numbers: [36, 72, 83]\nGenerated Node #2: [36, 72, 83] from Operation: 65+18=83\nCurrent State: 47:[36, 72, 83], Operations: ['65+18=83']\nExploring Operation: 72-36=36, Resulting Numbers: [83, 36]\nGenerated Node #3: [83, 36] from Operation: 72-36=36\nCurrent State: 47:[83, 36], Operations: ['65+18=83', '72-36=36']\nExploring Operation: 83-36=47, Resulting Numbers: [47]\n47,47 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 85, + 13, + 6, + 89 + ], + "target": 11, + "solution": [ + "85-13=72", + "89-6=83", + "83-72=11" + ], + "optimal_path": "Current State: 11:[85, 13, 6, 89], Operations: []\nExploring Operation: 85-13=72, Resulting Numbers: [6, 89, 72]\nGenerated Node #2: [6, 89, 72] from Operation: 85-13=72\nCurrent State: 11:[6, 89, 72], Operations: ['85-13=72']\nExploring Operation: 89-6=83, Resulting Numbers: [72, 83]\nGenerated Node #3: [72, 83] from Operation: 89-6=83\nCurrent State: 11:[72, 83], Operations: ['85-13=72', '89-6=83']\nExploring Operation: 83-72=11, Resulting Numbers: [11]\n11,11 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 24, + 51, + 3, + 46 + ], + "target": 23, + "solution": [ + "24*46=1104", + "51-3=48", + "1104/48=23" + ], + "optimal_path": "Current State: 23:[24, 51, 3, 46], Operations: []\nExploring Operation: 24*46=1104, Resulting Numbers: [51, 3, 1104]\nGenerated Node #2: [51, 3, 1104] from Operation: 24*46=1104\nCurrent State: 23:[51, 3, 1104], Operations: ['24*46=1104']\nExploring Operation: 51-3=48, Resulting Numbers: [1104, 48]\nGenerated Node #3: [1104, 48] from Operation: 51-3=48\nCurrent State: 23:[1104, 48], Operations: ['24*46=1104', '51-3=48']\nExploring Operation: 1104/48=23, Resulting Numbers: [23]\n23,23 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 76, + 28, + 75, + 41 + ], + "target": 60, + "solution": [ + "76-41=35", + "28*75=2100", + "2100/35=60" + ], + "optimal_path": "Current State: 60:[76, 28, 75, 41], Operations: []\nExploring Operation: 76-41=35, Resulting Numbers: [28, 75, 35]\nGenerated Node #2: [28, 75, 35] from Operation: 76-41=35\nCurrent State: 60:[28, 75, 35], Operations: ['76-41=35']\nExploring Operation: 28*75=2100, Resulting Numbers: [35, 2100]\nGenerated Node #3: [35, 2100] from Operation: 28*75=2100\nCurrent State: 60:[35, 2100], Operations: ['76-41=35', '28*75=2100']\nExploring Operation: 2100/35=60, Resulting Numbers: [60]\n60,60 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 97, + 17, + 39, + 13 + ], + "target": 21, + "solution": [ + "97+39=136", + "136/17=8", + "13+8=21" + ], + "optimal_path": "Current State: 21:[97, 17, 39, 13], Operations: []\nExploring Operation: 97+39=136, Resulting Numbers: [17, 13, 136]\nGenerated Node #2: [17, 13, 136] from Operation: 97+39=136\nCurrent State: 21:[17, 13, 136], Operations: ['97+39=136']\nExploring Operation: 136/17=8, Resulting Numbers: [13, 8]\nGenerated Node #3: [13, 8] from Operation: 136/17=8\nCurrent State: 21:[13, 8], Operations: ['97+39=136', '136/17=8']\nExploring Operation: 13+8=21, Resulting Numbers: [21]\n21,21 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 12, + 36, + 5, + 58 + ], + "target": 77, + "solution": [ + "36-12=24", + "58-5=53", + "24+53=77" + ], + "optimal_path": "Current State: 77:[12, 36, 5, 58], Operations: []\nExploring Operation: 36-12=24, Resulting Numbers: [5, 58, 24]\nGenerated Node #2: [5, 58, 24] from Operation: 36-12=24\nCurrent State: 77:[5, 58, 24], Operations: ['36-12=24']\nExploring Operation: 58-5=53, Resulting Numbers: [24, 53]\nGenerated Node #3: [24, 53] from Operation: 58-5=53\nCurrent State: 77:[24, 53], Operations: ['36-12=24', '58-5=53']\nExploring Operation: 24+53=77, Resulting Numbers: [77]\n77,77 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 72, + 70, + 6, + 76 + ], + "target": 79, + "solution": [ + "72-70=2", + "6/2=3", + "76+3=79" + ], + "optimal_path": "Current State: 79:[72, 70, 6, 76], Operations: []\nExploring Operation: 72-70=2, Resulting Numbers: [6, 76, 2]\nGenerated Node #2: [6, 76, 2] from Operation: 72-70=2\nCurrent State: 79:[6, 76, 2], Operations: ['72-70=2']\nExploring Operation: 6/2=3, Resulting Numbers: [76, 3]\nGenerated Node #3: [76, 3] from Operation: 6/2=3\nCurrent State: 79:[76, 3], Operations: ['72-70=2', '6/2=3']\nExploring Operation: 76+3=79, Resulting Numbers: [79]\n79,79 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 45, + 3, + 75, + 79 + ], + "target": 45, + "solution": [ + "3+75=78", + "79-78=1", + "45*1=45" + ], + "optimal_path": "Current State: 45:[45, 3, 75, 79], Operations: []\nExploring Operation: 3+75=78, Resulting Numbers: [45, 79, 78]\nGenerated Node #2: [45, 79, 78] from Operation: 3+75=78\nCurrent State: 45:[45, 79, 78], Operations: ['3+75=78']\nExploring Operation: 79-78=1, Resulting Numbers: [45, 1]\nGenerated Node #3: [45, 1] from Operation: 79-78=1\nCurrent State: 45:[45, 1], Operations: ['3+75=78', '79-78=1']\nExploring Operation: 45*1=45, Resulting Numbers: [45]\n45,45 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 24, + 46, + 33, + 99 + ], + "target": 19, + "solution": [ + "46-24=22", + "99/33=3", + "22-3=19" + ], + "optimal_path": "Current State: 19:[24, 46, 33, 99], Operations: []\nExploring Operation: 46-24=22, Resulting Numbers: [33, 99, 22]\nGenerated Node #2: [33, 99, 22] from Operation: 46-24=22\nCurrent State: 19:[33, 99, 22], Operations: ['46-24=22']\nExploring Operation: 99/33=3, Resulting Numbers: [22, 3]\nGenerated Node #3: [22, 3] from Operation: 99/33=3\nCurrent State: 19:[22, 3], Operations: ['46-24=22', '99/33=3']\nExploring Operation: 22-3=19, Resulting Numbers: [19]\n19,19 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 21, + 51, + 24, + 57 + ], + "target": 60, + "solution": [ + "21+51=72", + "72/24=3", + "57+3=60" + ], + "optimal_path": "Current State: 60:[21, 51, 24, 57], Operations: []\nExploring Operation: 21+51=72, Resulting Numbers: [24, 57, 72]\nGenerated Node #2: [24, 57, 72] from Operation: 21+51=72\nCurrent State: 60:[24, 57, 72], Operations: ['21+51=72']\nExploring Operation: 72/24=3, Resulting Numbers: [57, 3]\nGenerated Node #3: [57, 3] from Operation: 72/24=3\nCurrent State: 60:[57, 3], Operations: ['21+51=72', '72/24=3']\nExploring Operation: 57+3=60, Resulting Numbers: [60]\n60,60 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 52, + 80, + 62, + 1 + ], + "target": 69, + "solution": [ + "52+80=132", + "62+1=63", + "132-63=69" + ], + "optimal_path": "Current State: 69:[52, 80, 62, 1], Operations: []\nExploring Operation: 52+80=132, Resulting Numbers: [62, 1, 132]\nGenerated Node #2: [62, 1, 132] from Operation: 52+80=132\nCurrent State: 69:[62, 1, 132], Operations: ['52+80=132']\nExploring Operation: 62+1=63, Resulting Numbers: [132, 63]\nGenerated Node #3: [132, 63] from Operation: 62+1=63\nCurrent State: 69:[132, 63], Operations: ['52+80=132', '62+1=63']\nExploring Operation: 132-63=69, Resulting Numbers: [69]\n69,69 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 26, + 31, + 93, + 28 + ], + "target": 51, + "solution": [ + "26+28=54", + "93/31=3", + "54-3=51" + ], + "optimal_path": "Current State: 51:[26, 31, 93, 28], Operations: []\nExploring Operation: 26+28=54, Resulting Numbers: [31, 93, 54]\nGenerated Node #2: [31, 93, 54] from Operation: 26+28=54\nCurrent State: 51:[31, 93, 54], Operations: ['26+28=54']\nExploring Operation: 93/31=3, Resulting Numbers: [54, 3]\nGenerated Node #3: [54, 3] from Operation: 93/31=3\nCurrent State: 51:[54, 3], Operations: ['26+28=54', '93/31=3']\nExploring Operation: 54-3=51, Resulting Numbers: [51]\n51,51 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 89, + 41, + 13, + 26 + ], + "target": 87, + "solution": [ + "89-41=48", + "13+26=39", + "48+39=87" + ], + "optimal_path": "Current State: 87:[89, 41, 13, 26], Operations: []\nExploring Operation: 89-41=48, Resulting Numbers: [13, 26, 48]\nGenerated Node #2: [13, 26, 48] from Operation: 89-41=48\nCurrent State: 87:[13, 26, 48], Operations: ['89-41=48']\nExploring Operation: 13+26=39, Resulting Numbers: [48, 39]\nGenerated Node #3: [48, 39] from Operation: 13+26=39\nCurrent State: 87:[48, 39], Operations: ['89-41=48', '13+26=39']\nExploring Operation: 48+39=87, Resulting Numbers: [87]\n87,87 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 49, + 3, + 61, + 81 + ], + "target": 45, + "solution": [ + "61-49=12", + "3*12=36", + "81-36=45" + ], + "optimal_path": "Current State: 45:[49, 3, 61, 81], Operations: []\nExploring Operation: 61-49=12, Resulting Numbers: [3, 81, 12]\nGenerated Node #2: [3, 81, 12] from Operation: 61-49=12\nCurrent State: 45:[3, 81, 12], Operations: ['61-49=12']\nExploring Operation: 3*12=36, Resulting Numbers: [81, 36]\nGenerated Node #3: [81, 36] from Operation: 3*12=36\nCurrent State: 45:[81, 36], Operations: ['61-49=12', '3*12=36']\nExploring Operation: 81-36=45, Resulting Numbers: [45]\n45,45 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 2, + 33, + 13, + 26 + ], + "target": 68, + "solution": [ + "2*33=66", + "26/13=2", + "66+2=68" + ], + "optimal_path": "Current State: 68:[2, 33, 13, 26], Operations: []\nExploring Operation: 2*33=66, Resulting Numbers: [13, 26, 66]\nGenerated Node #2: [13, 26, 66] from Operation: 2*33=66\nCurrent State: 68:[13, 26, 66], Operations: ['2*33=66']\nExploring Operation: 26/13=2, Resulting Numbers: [66, 2]\nGenerated Node #3: [66, 2] from Operation: 26/13=2\nCurrent State: 68:[66, 2], Operations: ['2*33=66', '26/13=2']\nExploring Operation: 66+2=68, Resulting Numbers: [68]\n68,68 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 10, + 27, + 98, + 13 + ], + "target": 42, + "solution": [ + "27-13=14", + "10*14=140", + "140-98=42" + ], + "optimal_path": "Current State: 42:[10, 27, 98, 13], Operations: []\nExploring Operation: 27-13=14, Resulting Numbers: [10, 98, 14]\nGenerated Node #2: [10, 98, 14] from Operation: 27-13=14\nCurrent State: 42:[10, 98, 14], Operations: ['27-13=14']\nExploring Operation: 10*14=140, Resulting Numbers: [98, 140]\nGenerated Node #3: [98, 140] from Operation: 10*14=140\nCurrent State: 42:[98, 140], Operations: ['27-13=14', '10*14=140']\nExploring Operation: 140-98=42, Resulting Numbers: [42]\n42,42 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 46, + 21, + 41, + 17 + ], + "target": 88, + "solution": [ + "46-41=5", + "21*5=105", + "105-17=88" + ], + "optimal_path": "Current State: 88:[46, 21, 41, 17], Operations: []\nExploring Operation: 46-41=5, Resulting Numbers: [21, 17, 5]\nGenerated Node #2: [21, 17, 5] from Operation: 46-41=5\nCurrent State: 88:[21, 17, 5], Operations: ['46-41=5']\nExploring Operation: 21*5=105, Resulting Numbers: [17, 105]\nGenerated Node #3: [17, 105] from Operation: 21*5=105\nCurrent State: 88:[17, 105], Operations: ['46-41=5', '21*5=105']\nExploring Operation: 105-17=88, Resulting Numbers: [88]\n88,88 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 85, + 93, + 48, + 92 + ], + "target": 98, + "solution": [ + "93-85=8", + "48/8=6", + "92+6=98" + ], + "optimal_path": "Current State: 98:[85, 93, 48, 92], Operations: []\nExploring Operation: 93-85=8, Resulting Numbers: [48, 92, 8]\nGenerated Node #2: [48, 92, 8] from Operation: 93-85=8\nCurrent State: 98:[48, 92, 8], Operations: ['93-85=8']\nExploring Operation: 48/8=6, Resulting Numbers: [92, 6]\nGenerated Node #3: [92, 6] from Operation: 48/8=6\nCurrent State: 98:[92, 6], Operations: ['93-85=8', '48/8=6']\nExploring Operation: 92+6=98, Resulting Numbers: [98]\n98,98 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 6, + 74, + 80, + 40 + ], + "target": 61, + "solution": [ + "74+40=114", + "114/6=19", + "80-19=61" + ], + "optimal_path": "Current State: 61:[6, 74, 80, 40], Operations: []\nExploring Operation: 74+40=114, Resulting Numbers: [6, 80, 114]\nGenerated Node #2: [6, 80, 114] from Operation: 74+40=114\nCurrent State: 61:[6, 80, 114], Operations: ['74+40=114']\nExploring Operation: 114/6=19, Resulting Numbers: [80, 19]\nGenerated Node #3: [80, 19] from Operation: 114/6=19\nCurrent State: 61:[80, 19], Operations: ['74+40=114', '114/6=19']\nExploring Operation: 80-19=61, Resulting Numbers: [61]\n61,61 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 31, + 54, + 13, + 14 + ], + "target": 17, + "solution": [ + "31-13=18", + "54/18=3", + "14+3=17" + ], + "optimal_path": "Current State: 17:[31, 54, 13, 14], Operations: []\nExploring Operation: 31-13=18, Resulting Numbers: [54, 14, 18]\nGenerated Node #2: [54, 14, 18] from Operation: 31-13=18\nCurrent State: 17:[54, 14, 18], Operations: ['31-13=18']\nExploring Operation: 54/18=3, Resulting Numbers: [14, 3]\nGenerated Node #3: [14, 3] from Operation: 54/18=3\nCurrent State: 17:[14, 3], Operations: ['31-13=18', '54/18=3']\nExploring Operation: 14+3=17, Resulting Numbers: [17]\n17,17 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 33, + 68, + 16, + 22 + ], + "target": 63, + "solution": [ + "33+68=101", + "16+22=38", + "101-38=63" + ], + "optimal_path": "Current State: 63:[33, 68, 16, 22], Operations: []\nExploring Operation: 33+68=101, Resulting Numbers: [16, 22, 101]\nGenerated Node #2: [16, 22, 101] from Operation: 33+68=101\nCurrent State: 63:[16, 22, 101], Operations: ['33+68=101']\nExploring Operation: 16+22=38, Resulting Numbers: [101, 38]\nGenerated Node #3: [101, 38] from Operation: 16+22=38\nCurrent State: 63:[101, 38], Operations: ['33+68=101', '16+22=38']\nExploring Operation: 101-38=63, Resulting Numbers: [63]\n63,63 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 5, + 18, + 55, + 29 + ], + "target": 97, + "solution": [ + "18-5=13", + "55+29=84", + "13+84=97" + ], + "optimal_path": "Current State: 97:[5, 18, 55, 29], Operations: []\nExploring Operation: 18-5=13, Resulting Numbers: [55, 29, 13]\nGenerated Node #2: [55, 29, 13] from Operation: 18-5=13\nCurrent State: 97:[55, 29, 13], Operations: ['18-5=13']\nExploring Operation: 55+29=84, Resulting Numbers: [13, 84]\nGenerated Node #3: [13, 84] from Operation: 55+29=84\nCurrent State: 97:[13, 84], Operations: ['18-5=13', '55+29=84']\nExploring Operation: 13+84=97, Resulting Numbers: [97]\n97,97 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 7, + 43, + 14, + 6 + ], + "target": 20, + "solution": [ + "43-7=36", + "36/6=6", + "14+6=20" + ], + "optimal_path": "Current State: 20:[7, 43, 14, 6], Operations: []\nExploring Operation: 43-7=36, Resulting Numbers: [14, 6, 36]\nGenerated Node #2: [14, 6, 36] from Operation: 43-7=36\nCurrent State: 20:[14, 6, 36], Operations: ['43-7=36']\nExploring Operation: 36/6=6, Resulting Numbers: [14, 6]\nGenerated Node #3: [14, 6] from Operation: 36/6=6\nCurrent State: 20:[14, 6], Operations: ['43-7=36', '36/6=6']\nExploring Operation: 14+6=20, Resulting Numbers: [20]\n20,20 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 78, + 18, + 64, + 25 + ], + "target": 100, + "solution": [ + "78-18=60", + "64-60=4", + "25*4=100" + ], + "optimal_path": "Current State: 100:[78, 18, 64, 25], Operations: []\nExploring Operation: 78-18=60, Resulting Numbers: [64, 25, 60]\nGenerated Node #2: [64, 25, 60] from Operation: 78-18=60\nCurrent State: 100:[64, 25, 60], Operations: ['78-18=60']\nExploring Operation: 64-60=4, Resulting Numbers: [25, 4]\nGenerated Node #3: [25, 4] from Operation: 64-60=4\nCurrent State: 100:[25, 4], Operations: ['78-18=60', '64-60=4']\nExploring Operation: 25*4=100, Resulting Numbers: [100]\n100,100 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 41, + 80, + 5, + 4 + ], + "target": 79, + "solution": [ + "41*4=164", + "80+5=85", + "164-85=79" + ], + "optimal_path": "Current State: 79:[41, 80, 5, 4], Operations: []\nExploring Operation: 41*4=164, Resulting Numbers: [80, 5, 164]\nGenerated Node #2: [80, 5, 164] from Operation: 41*4=164\nCurrent State: 79:[80, 5, 164], Operations: ['41*4=164']\nExploring Operation: 80+5=85, Resulting Numbers: [164, 85]\nGenerated Node #3: [164, 85] from Operation: 80+5=85\nCurrent State: 79:[164, 85], Operations: ['41*4=164', '80+5=85']\nExploring Operation: 164-85=79, Resulting Numbers: [79]\n79,79 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 67, + 6, + 55, + 78 + ], + "target": 71, + "solution": [ + "78-55=23", + "6*23=138", + "138-67=71" + ], + "optimal_path": "Current State: 71:[67, 6, 55, 78], Operations: []\nExploring Operation: 78-55=23, Resulting Numbers: [67, 6, 23]\nGenerated Node #2: [67, 6, 23] from Operation: 78-55=23\nCurrent State: 71:[67, 6, 23], Operations: ['78-55=23']\nExploring Operation: 6*23=138, Resulting Numbers: [67, 138]\nGenerated Node #3: [67, 138] from Operation: 6*23=138\nCurrent State: 71:[67, 138], Operations: ['78-55=23', '6*23=138']\nExploring Operation: 138-67=71, Resulting Numbers: [71]\n71,71 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 85, + 20, + 49, + 60 + ], + "target": 28, + "solution": [ + "85+20=105", + "49*60=2940", + "2940/105=28" + ], + "optimal_path": "Current State: 28:[85, 20, 49, 60], Operations: []\nExploring Operation: 85+20=105, Resulting Numbers: [49, 60, 105]\nGenerated Node #2: [49, 60, 105] from Operation: 85+20=105\nCurrent State: 28:[49, 60, 105], Operations: ['85+20=105']\nExploring Operation: 49*60=2940, Resulting Numbers: [105, 2940]\nGenerated Node #3: [105, 2940] from Operation: 49*60=2940\nCurrent State: 28:[105, 2940], Operations: ['85+20=105', '49*60=2940']\nExploring Operation: 2940/105=28, Resulting Numbers: [28]\n28,28 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 47, + 22, + 35, + 20 + ], + "target": 30, + "solution": [ + "47-22=25", + "35+20=55", + "55-25=30" + ], + "optimal_path": "Current State: 30:[47, 22, 35, 20], Operations: []\nExploring Operation: 47-22=25, Resulting Numbers: [35, 20, 25]\nGenerated Node #2: [35, 20, 25] from Operation: 47-22=25\nCurrent State: 30:[35, 20, 25], Operations: ['47-22=25']\nExploring Operation: 35+20=55, Resulting Numbers: [25, 55]\nGenerated Node #3: [25, 55] from Operation: 35+20=55\nCurrent State: 30:[25, 55], Operations: ['47-22=25', '35+20=55']\nExploring Operation: 55-25=30, Resulting Numbers: [30]\n30,30 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 32, + 51, + 21, + 9 + ], + "target": 40, + "solution": [ + "51+21=72", + "72/9=8", + "32+8=40" + ], + "optimal_path": "Current State: 40:[32, 51, 21, 9], Operations: []\nExploring Operation: 51+21=72, Resulting Numbers: [32, 9, 72]\nGenerated Node #2: [32, 9, 72] from Operation: 51+21=72\nCurrent State: 40:[32, 9, 72], Operations: ['51+21=72']\nExploring Operation: 72/9=8, Resulting Numbers: [32, 8]\nGenerated Node #3: [32, 8] from Operation: 72/9=8\nCurrent State: 40:[32, 8], Operations: ['51+21=72', '72/9=8']\nExploring Operation: 32+8=40, Resulting Numbers: [40]\n40,40 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 54, + 48, + 44, + 90 + ], + "target": 59, + "solution": [ + "54-48=6", + "90/6=15", + "44+15=59" + ], + "optimal_path": "Current State: 59:[54, 48, 44, 90], Operations: []\nExploring Operation: 54-48=6, Resulting Numbers: [44, 90, 6]\nGenerated Node #2: [44, 90, 6] from Operation: 54-48=6\nCurrent State: 59:[44, 90, 6], Operations: ['54-48=6']\nExploring Operation: 90/6=15, Resulting Numbers: [44, 15]\nGenerated Node #3: [44, 15] from Operation: 90/6=15\nCurrent State: 59:[44, 15], Operations: ['54-48=6', '90/6=15']\nExploring Operation: 44+15=59, Resulting Numbers: [59]\n59,59 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 2, + 22, + 12, + 68 + ], + "target": 70, + "solution": [ + "2+22=24", + "24/12=2", + "68+2=70" + ], + "optimal_path": "Current State: 70:[2, 22, 12, 68], Operations: []\nExploring Operation: 2+22=24, Resulting Numbers: [12, 68, 24]\nGenerated Node #2: [12, 68, 24] from Operation: 2+22=24\nCurrent State: 70:[12, 68, 24], Operations: ['2+22=24']\nExploring Operation: 24/12=2, Resulting Numbers: [68, 2]\nGenerated Node #3: [68, 2] from Operation: 24/12=2\nCurrent State: 70:[68, 2], Operations: ['2+22=24', '24/12=2']\nExploring Operation: 68+2=70, Resulting Numbers: [70]\n70,70 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 21, + 38, + 7, + 7 + ], + "target": 59, + "solution": [ + "21+38=59", + "7-7=0", + "59+0=59" + ], + "optimal_path": "Current State: 59:[21, 38, 7, 7], Operations: []\nExploring Operation: 21+38=59, Resulting Numbers: [7, 7, 59]\nGenerated Node #2: [7, 7, 59] from Operation: 21+38=59\nCurrent State: 59:[7, 7, 59], Operations: ['21+38=59']\nExploring Operation: 7-7=0, Resulting Numbers: [59, 0]\nGenerated Node #3: [59, 0] from Operation: 7-7=0\nCurrent State: 59:[59, 0], Operations: ['21+38=59', '7-7=0']\nExploring Operation: 59+0=59, Resulting Numbers: [59]\n59,59 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 15, + 12, + 49, + 8 + ], + "target": 83, + "solution": [ + "15*8=120", + "49-12=37", + "120-37=83" + ], + "optimal_path": "Current State: 83:[15, 12, 49, 8], Operations: []\nExploring Operation: 15*8=120, Resulting Numbers: [12, 49, 120]\nGenerated Node #2: [12, 49, 120] from Operation: 15*8=120\nCurrent State: 83:[12, 49, 120], Operations: ['15*8=120']\nExploring Operation: 49-12=37, Resulting Numbers: [120, 37]\nGenerated Node #3: [120, 37] from Operation: 49-12=37\nCurrent State: 83:[120, 37], Operations: ['15*8=120', '49-12=37']\nExploring Operation: 120-37=83, Resulting Numbers: [83]\n83,83 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 95, + 29, + 25, + 60 + ], + "target": 39, + "solution": [ + "95+29=124", + "25+60=85", + "124-85=39" + ], + "optimal_path": "Current State: 39:[95, 29, 25, 60], Operations: []\nExploring Operation: 95+29=124, Resulting Numbers: [25, 60, 124]\nGenerated Node #2: [25, 60, 124] from Operation: 95+29=124\nCurrent State: 39:[25, 60, 124], Operations: ['95+29=124']\nExploring Operation: 25+60=85, Resulting Numbers: [124, 85]\nGenerated Node #3: [124, 85] from Operation: 25+60=85\nCurrent State: 39:[124, 85], Operations: ['95+29=124', '25+60=85']\nExploring Operation: 124-85=39, Resulting Numbers: [39]\n39,39 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 4, + 63, + 57, + 23 + ], + "target": 13, + "solution": [ + "4+63=67", + "57+23=80", + "80-67=13" + ], + "optimal_path": "Current State: 13:[4, 63, 57, 23], Operations: []\nExploring Operation: 4+63=67, Resulting Numbers: [57, 23, 67]\nGenerated Node #2: [57, 23, 67] from Operation: 4+63=67\nCurrent State: 13:[57, 23, 67], Operations: ['4+63=67']\nExploring Operation: 57+23=80, Resulting Numbers: [67, 80]\nGenerated Node #3: [67, 80] from Operation: 57+23=80\nCurrent State: 13:[67, 80], Operations: ['4+63=67', '57+23=80']\nExploring Operation: 80-67=13, Resulting Numbers: [13]\n13,13 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 66, + 11, + 64, + 18 + ], + "target": 47, + "solution": [ + "66-64=2", + "18*2=36", + "11+36=47" + ], + "optimal_path": "Current State: 47:[66, 11, 64, 18], Operations: []\nExploring Operation: 66-64=2, Resulting Numbers: [11, 18, 2]\nGenerated Node #2: [11, 18, 2] from Operation: 66-64=2\nCurrent State: 47:[11, 18, 2], Operations: ['66-64=2']\nExploring Operation: 18*2=36, Resulting Numbers: [11, 36]\nGenerated Node #3: [11, 36] from Operation: 18*2=36\nCurrent State: 47:[11, 36], Operations: ['66-64=2', '18*2=36']\nExploring Operation: 11+36=47, Resulting Numbers: [47]\n47,47 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 60, + 20, + 35, + 87 + ], + "target": 55, + "solution": [ + "60/20=3", + "87-35=52", + "3+52=55" + ], + "optimal_path": "Current State: 55:[60, 20, 35, 87], Operations: []\nExploring Operation: 60/20=3, Resulting Numbers: [35, 87, 3]\nGenerated Node #2: [35, 87, 3] from Operation: 60/20=3\nCurrent State: 55:[35, 87, 3], Operations: ['60/20=3']\nExploring Operation: 87-35=52, Resulting Numbers: [3, 52]\nGenerated Node #3: [3, 52] from Operation: 87-35=52\nCurrent State: 55:[3, 52], Operations: ['60/20=3', '87-35=52']\nExploring Operation: 3+52=55, Resulting Numbers: [55]\n55,55 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 12, + 90, + 15, + 5 + ], + "target": 26, + "solution": [ + "90-12=78", + "15/5=3", + "78/3=26" + ], + "optimal_path": "Current State: 26:[12, 90, 15, 5], Operations: []\nExploring Operation: 90-12=78, Resulting Numbers: [15, 5, 78]\nGenerated Node #2: [15, 5, 78] from Operation: 90-12=78\nCurrent State: 26:[15, 5, 78], Operations: ['90-12=78']\nExploring Operation: 15/5=3, Resulting Numbers: [78, 3]\nGenerated Node #3: [78, 3] from Operation: 15/5=3\nCurrent State: 26:[78, 3], Operations: ['90-12=78', '15/5=3']\nExploring Operation: 78/3=26, Resulting Numbers: [26]\n26,26 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 23, + 17, + 21, + 36 + ], + "target": 14, + "solution": [ + "21-17=4", + "36/4=9", + "23-9=14" + ], + "optimal_path": "Current State: 14:[23, 17, 21, 36], Operations: []\nExploring Operation: 21-17=4, Resulting Numbers: [23, 36, 4]\nGenerated Node #2: [23, 36, 4] from Operation: 21-17=4\nCurrent State: 14:[23, 36, 4], Operations: ['21-17=4']\nExploring Operation: 36/4=9, Resulting Numbers: [23, 9]\nGenerated Node #3: [23, 9] from Operation: 36/4=9\nCurrent State: 14:[23, 9], Operations: ['21-17=4', '36/4=9']\nExploring Operation: 23-9=14, Resulting Numbers: [14]\n14,14 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 31, + 11, + 20, + 42 + ], + "target": 22, + "solution": [ + "20+42=62", + "62/31=2", + "11*2=22" + ], + "optimal_path": "Current State: 22:[31, 11, 20, 42], Operations: []\nExploring Operation: 20+42=62, Resulting Numbers: [31, 11, 62]\nGenerated Node #2: [31, 11, 62] from Operation: 20+42=62\nCurrent State: 22:[31, 11, 62], Operations: ['20+42=62']\nExploring Operation: 62/31=2, Resulting Numbers: [11, 2]\nGenerated Node #3: [11, 2] from Operation: 62/31=2\nCurrent State: 22:[11, 2], Operations: ['20+42=62', '62/31=2']\nExploring Operation: 11*2=22, Resulting Numbers: [22]\n22,22 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 2, + 33, + 32, + 37 + ], + "target": 16, + "solution": [ + "2+33=35", + "37-35=2", + "32/2=16" + ], + "optimal_path": "Current State: 16:[2, 33, 32, 37], Operations: []\nExploring Operation: 2+33=35, Resulting Numbers: [32, 37, 35]\nGenerated Node #2: [32, 37, 35] from Operation: 2+33=35\nCurrent State: 16:[32, 37, 35], Operations: ['2+33=35']\nExploring Operation: 37-35=2, Resulting Numbers: [32, 2]\nGenerated Node #3: [32, 2] from Operation: 37-35=2\nCurrent State: 16:[32, 2], Operations: ['2+33=35', '37-35=2']\nExploring Operation: 32/2=16, Resulting Numbers: [16]\n16,16 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 58, + 48, + 78, + 5 + ], + "target": 93, + "solution": [ + "58-48=10", + "78+5=83", + "10+83=93" + ], + "optimal_path": "Current State: 93:[58, 48, 78, 5], Operations: []\nExploring Operation: 58-48=10, Resulting Numbers: [78, 5, 10]\nGenerated Node #2: [78, 5, 10] from Operation: 58-48=10\nCurrent State: 93:[78, 5, 10], Operations: ['58-48=10']\nExploring Operation: 78+5=83, Resulting Numbers: [10, 83]\nGenerated Node #3: [10, 83] from Operation: 78+5=83\nCurrent State: 93:[10, 83], Operations: ['58-48=10', '78+5=83']\nExploring Operation: 10+83=93, Resulting Numbers: [93]\n93,93 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 10, + 44, + 9, + 53 + ], + "target": 81, + "solution": [ + "10*9=90", + "53-44=9", + "90-9=81" + ], + "optimal_path": "Current State: 81:[10, 44, 9, 53], Operations: []\nExploring Operation: 10*9=90, Resulting Numbers: [44, 53, 90]\nGenerated Node #2: [44, 53, 90] from Operation: 10*9=90\nCurrent State: 81:[44, 53, 90], Operations: ['10*9=90']\nExploring Operation: 53-44=9, Resulting Numbers: [90, 9]\nGenerated Node #3: [90, 9] from Operation: 53-44=9\nCurrent State: 81:[90, 9], Operations: ['10*9=90', '53-44=9']\nExploring Operation: 90-9=81, Resulting Numbers: [81]\n81,81 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 13, + 4, + 21, + 28 + ], + "target": 32, + "solution": [ + "13+4=17", + "21+28=49", + "49-17=32" + ], + "optimal_path": "Current State: 32:[13, 4, 21, 28], Operations: []\nExploring Operation: 13+4=17, Resulting Numbers: [21, 28, 17]\nGenerated Node #2: [21, 28, 17] from Operation: 13+4=17\nCurrent State: 32:[21, 28, 17], Operations: ['13+4=17']\nExploring Operation: 21+28=49, Resulting Numbers: [17, 49]\nGenerated Node #3: [17, 49] from Operation: 21+28=49\nCurrent State: 32:[17, 49], Operations: ['13+4=17', '21+28=49']\nExploring Operation: 49-17=32, Resulting Numbers: [32]\n32,32 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 71, + 62, + 15, + 75 + ], + "target": 81, + "solution": [ + "71-62=9", + "15+75=90", + "90-9=81" + ], + "optimal_path": "Current State: 81:[71, 62, 15, 75], Operations: []\nExploring Operation: 71-62=9, Resulting Numbers: [15, 75, 9]\nGenerated Node #2: [15, 75, 9] from Operation: 71-62=9\nCurrent State: 81:[15, 75, 9], Operations: ['71-62=9']\nExploring Operation: 15+75=90, Resulting Numbers: [9, 90]\nGenerated Node #3: [9, 90] from Operation: 15+75=90\nCurrent State: 81:[9, 90], Operations: ['71-62=9', '15+75=90']\nExploring Operation: 90-9=81, Resulting Numbers: [81]\n81,81 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 66, + 50, + 41, + 52 + ], + "target": 91, + "solution": [ + "52-50=2", + "66*2=132", + "132-41=91" + ], + "optimal_path": "Current State: 91:[66, 50, 41, 52], Operations: []\nExploring Operation: 52-50=2, Resulting Numbers: [66, 41, 2]\nGenerated Node #2: [66, 41, 2] from Operation: 52-50=2\nCurrent State: 91:[66, 41, 2], Operations: ['52-50=2']\nExploring Operation: 66*2=132, Resulting Numbers: [41, 132]\nGenerated Node #3: [41, 132] from Operation: 66*2=132\nCurrent State: 91:[41, 132], Operations: ['52-50=2', '66*2=132']\nExploring Operation: 132-41=91, Resulting Numbers: [91]\n91,91 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 37, + 51, + 50, + 96 + ], + "target": 60, + "solution": [ + "51-37=14", + "96-50=46", + "14+46=60" + ], + "optimal_path": "Current State: 60:[37, 51, 50, 96], Operations: []\nExploring Operation: 51-37=14, Resulting Numbers: [50, 96, 14]\nGenerated Node #2: [50, 96, 14] from Operation: 51-37=14\nCurrent State: 60:[50, 96, 14], Operations: ['51-37=14']\nExploring Operation: 96-50=46, Resulting Numbers: [14, 46]\nGenerated Node #3: [14, 46] from Operation: 96-50=46\nCurrent State: 60:[14, 46], Operations: ['51-37=14', '96-50=46']\nExploring Operation: 14+46=60, Resulting Numbers: [60]\n60,60 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 19, + 3, + 57, + 67 + ], + "target": 73, + "solution": [ + "57/19=3", + "3+67=70", + "3+70=73" + ], + "optimal_path": "Current State: 73:[19, 3, 57, 67], Operations: []\nExploring Operation: 57/19=3, Resulting Numbers: [3, 67, 3]\nGenerated Node #2: [3, 67, 3] from Operation: 57/19=3\nCurrent State: 73:[3, 67, 3], Operations: ['57/19=3']\nExploring Operation: 3+67=70, Resulting Numbers: [70]\n70,73 equal: Goal Reached\nExploring Operation: 3+70=73, Resulting Numbers: [73]\n73,73 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 43, + 96, + 72, + 51 + ], + "target": 84, + "solution": [ + "51-43=8", + "96/8=12", + "72+12=84" + ], + "optimal_path": "Current State: 84:[43, 96, 72, 51], Operations: []\nExploring Operation: 51-43=8, Resulting Numbers: [96, 72, 8]\nGenerated Node #2: [96, 72, 8] from Operation: 51-43=8\nCurrent State: 84:[96, 72, 8], Operations: ['51-43=8']\nExploring Operation: 96/8=12, Resulting Numbers: [72, 12]\nGenerated Node #3: [72, 12] from Operation: 96/8=12\nCurrent State: 84:[72, 12], Operations: ['51-43=8', '96/8=12']\nExploring Operation: 72+12=84, Resulting Numbers: [84]\n84,84 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 65, + 60, + 67, + 19 + ], + "target": 77, + "solution": [ + "65+60=125", + "67-19=48", + "125-48=77" + ], + "optimal_path": "Current State: 77:[65, 60, 67, 19], Operations: []\nExploring Operation: 65+60=125, Resulting Numbers: [67, 19, 125]\nGenerated Node #2: [67, 19, 125] from Operation: 65+60=125\nCurrent State: 77:[67, 19, 125], Operations: ['65+60=125']\nExploring Operation: 67-19=48, Resulting Numbers: [125, 48]\nGenerated Node #3: [125, 48] from Operation: 67-19=48\nCurrent State: 77:[125, 48], Operations: ['65+60=125', '67-19=48']\nExploring Operation: 125-48=77, Resulting Numbers: [77]\n77,77 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 46, + 56, + 1, + 94 + ], + "target": 54, + "solution": [ + "46+1=47", + "94/47=2", + "56-2=54" + ], + "optimal_path": "Current State: 54:[46, 56, 1, 94], Operations: []\nExploring Operation: 46+1=47, Resulting Numbers: [56, 94, 47]\nGenerated Node #2: [56, 94, 47] from Operation: 46+1=47\nCurrent State: 54:[56, 94, 47], Operations: ['46+1=47']\nExploring Operation: 94/47=2, Resulting Numbers: [56, 2]\nGenerated Node #3: [56, 2] from Operation: 94/47=2\nCurrent State: 54:[56, 2], Operations: ['46+1=47', '94/47=2']\nExploring Operation: 56-2=54, Resulting Numbers: [54]\n54,54 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 55, + 93, + 29, + 94 + ], + "target": 26, + "solution": [ + "55-29=26", + "94-93=1", + "26*1=26" + ], + "optimal_path": "Current State: 26:[55, 93, 29, 94], Operations: []\nExploring Operation: 55-29=26, Resulting Numbers: [93, 94, 26]\nGenerated Node #2: [93, 94, 26] from Operation: 55-29=26\nCurrent State: 26:[93, 94, 26], Operations: ['55-29=26']\nExploring Operation: 94-93=1, Resulting Numbers: [26, 1]\nGenerated Node #3: [26, 1] from Operation: 94-93=1\nCurrent State: 26:[26, 1], Operations: ['55-29=26', '94-93=1']\nExploring Operation: 26*1=26, Resulting Numbers: [26]\n26,26 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 90, + 87, + 38, + 15 + ], + "target": 56, + "solution": [ + "90-87=3", + "38+15=53", + "3+53=56" + ], + "optimal_path": "Current State: 56:[90, 87, 38, 15], Operations: []\nExploring Operation: 90-87=3, Resulting Numbers: [38, 15, 3]\nGenerated Node #2: [38, 15, 3] from Operation: 90-87=3\nCurrent State: 56:[38, 15, 3], Operations: ['90-87=3']\nExploring Operation: 38+15=53, Resulting Numbers: [3, 53]\nGenerated Node #3: [3, 53] from Operation: 38+15=53\nCurrent State: 56:[3, 53], Operations: ['90-87=3', '38+15=53']\nExploring Operation: 3+53=56, Resulting Numbers: [56]\n56,56 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 74, + 31, + 64, + 82 + ], + "target": 41, + "solution": [ + "74+31=105", + "64+82=146", + "146-105=41" + ], + "optimal_path": "Current State: 41:[74, 31, 64, 82], Operations: []\nExploring Operation: 74+31=105, Resulting Numbers: [64, 82, 105]\nGenerated Node #2: [64, 82, 105] from Operation: 74+31=105\nCurrent State: 41:[64, 82, 105], Operations: ['74+31=105']\nExploring Operation: 64+82=146, Resulting Numbers: [105, 146]\nGenerated Node #3: [105, 146] from Operation: 64+82=146\nCurrent State: 41:[105, 146], Operations: ['74+31=105', '64+82=146']\nExploring Operation: 146-105=41, Resulting Numbers: [41]\n41,41 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 68, + 12, + 64, + 56 + ], + "target": 80, + "solution": [ + "68-56=12", + "12*12=144", + "144-64=80" + ], + "optimal_path": "Current State: 80:[68, 12, 64, 56], Operations: []\nExploring Operation: 68-56=12, Resulting Numbers: [12, 64, 12]\nGenerated Node #2: [12, 64, 12] from Operation: 68-56=12\nCurrent State: 80:[12, 64, 12], Operations: ['68-56=12']\nExploring Operation: 12*12=144, Resulting Numbers: [64, 144]\nGenerated Node #3: [64, 144] from Operation: 12*12=144\nCurrent State: 80:[64, 144], Operations: ['68-56=12', '12*12=144']\nExploring Operation: 144-64=80, Resulting Numbers: [80]\n80,80 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 32, + 46, + 26, + 57 + ], + "target": 69, + "solution": [ + "46-32=14", + "26+57=83", + "83-14=69" + ], + "optimal_path": "Current State: 69:[32, 46, 26, 57], Operations: []\nExploring Operation: 46-32=14, Resulting Numbers: [26, 57, 14]\nGenerated Node #2: [26, 57, 14] from Operation: 46-32=14\nCurrent State: 69:[26, 57, 14], Operations: ['46-32=14']\nExploring Operation: 26+57=83, Resulting Numbers: [14, 83]\nGenerated Node #3: [14, 83] from Operation: 26+57=83\nCurrent State: 69:[14, 83], Operations: ['46-32=14', '26+57=83']\nExploring Operation: 83-14=69, Resulting Numbers: [69]\n69,69 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 11, + 24, + 56, + 20 + ], + "target": 32, + "solution": [ + "11+24=35", + "56*20=1120", + "1120/35=32" + ], + "optimal_path": "Current State: 32:[11, 24, 56, 20], Operations: []\nExploring Operation: 11+24=35, Resulting Numbers: [56, 20, 35]\nGenerated Node #2: [56, 20, 35] from Operation: 11+24=35\nCurrent State: 32:[56, 20, 35], Operations: ['11+24=35']\nExploring Operation: 56*20=1120, Resulting Numbers: [35, 1120]\nGenerated Node #3: [35, 1120] from Operation: 56*20=1120\nCurrent State: 32:[35, 1120], Operations: ['11+24=35', '56*20=1120']\nExploring Operation: 1120/35=32, Resulting Numbers: [32]\n32,32 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 54, + 4, + 88, + 62 + ], + "target": 76, + "solution": [ + "54-4=50", + "88-62=26", + "50+26=76" + ], + "optimal_path": "Current State: 76:[54, 4, 88, 62], Operations: []\nExploring Operation: 54-4=50, Resulting Numbers: [88, 62, 50]\nGenerated Node #2: [88, 62, 50] from Operation: 54-4=50\nCurrent State: 76:[88, 62, 50], Operations: ['54-4=50']\nExploring Operation: 88-62=26, Resulting Numbers: [50, 26]\nGenerated Node #3: [50, 26] from Operation: 88-62=26\nCurrent State: 76:[50, 26], Operations: ['54-4=50', '88-62=26']\nExploring Operation: 50+26=76, Resulting Numbers: [76]\n76,76 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 54, + 35, + 7, + 59 + ], + "target": 70, + "solution": [ + "54+7=61", + "61-59=2", + "35*2=70" + ], + "optimal_path": "Current State: 70:[54, 35, 7, 59], Operations: []\nExploring Operation: 54+7=61, Resulting Numbers: [35, 59, 61]\nGenerated Node #2: [35, 59, 61] from Operation: 54+7=61\nCurrent State: 70:[35, 59, 61], Operations: ['54+7=61']\nExploring Operation: 61-59=2, Resulting Numbers: [35, 2]\nGenerated Node #3: [35, 2] from Operation: 61-59=2\nCurrent State: 70:[35, 2], Operations: ['54+7=61', '61-59=2']\nExploring Operation: 35*2=70, Resulting Numbers: [70]\n70,70 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 29, + 29, + 11, + 73 + ], + "target": 33, + "solution": [ + "73-29=44", + "44/11=4", + "29+4=33" + ], + "optimal_path": "Current State: 33:[29, 29, 11, 73], Operations: []\nExploring Operation: 73-29=44, Resulting Numbers: [11, 44]\nGenerated Node #2: [11, 44] from Operation: 73-29=44\nCurrent State: 33:[11, 44], Operations: ['73-29=44']\nExploring Operation: 44/11=4, Resulting Numbers: [4]\n4,33 equal: Goal Reached\nExploring Operation: 29+4=33, Resulting Numbers: [33]\n33,33 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 22, + 25, + 18, + 3 + ], + "target": 63, + "solution": [ + "25-22=3", + "18+3=21", + "3*21=63" + ], + "optimal_path": "Current State: 63:[22, 25, 18, 3], Operations: []\nExploring Operation: 25-22=3, Resulting Numbers: [18, 3, 3]\nGenerated Node #2: [18, 3, 3] from Operation: 25-22=3\nCurrent State: 63:[18, 3, 3], Operations: ['25-22=3']\nExploring Operation: 18+3=21, Resulting Numbers: [21]\n21,63 equal: Goal Reached\nExploring Operation: 3*21=63, Resulting Numbers: [63]\n63,63 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 57, + 7, + 39, + 64 + ], + "target": 53, + "solution": [ + "57-7=50", + "39+64=103", + "103-50=53" + ], + "optimal_path": "Current State: 53:[57, 7, 39, 64], Operations: []\nExploring Operation: 57-7=50, Resulting Numbers: [39, 64, 50]\nGenerated Node #2: [39, 64, 50] from Operation: 57-7=50\nCurrent State: 53:[39, 64, 50], Operations: ['57-7=50']\nExploring Operation: 39+64=103, Resulting Numbers: [50, 103]\nGenerated Node #3: [50, 103] from Operation: 39+64=103\nCurrent State: 53:[50, 103], Operations: ['57-7=50', '39+64=103']\nExploring Operation: 103-50=53, Resulting Numbers: [53]\n53,53 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 54, + 39, + 85, + 56 + ], + "target": 48, + "solution": [ + "54+39=93", + "85+56=141", + "141-93=48" + ], + "optimal_path": "Current State: 48:[54, 39, 85, 56], Operations: []\nExploring Operation: 54+39=93, Resulting Numbers: [85, 56, 93]\nGenerated Node #2: [85, 56, 93] from Operation: 54+39=93\nCurrent State: 48:[85, 56, 93], Operations: ['54+39=93']\nExploring Operation: 85+56=141, Resulting Numbers: [93, 141]\nGenerated Node #3: [93, 141] from Operation: 85+56=141\nCurrent State: 48:[93, 141], Operations: ['54+39=93', '85+56=141']\nExploring Operation: 141-93=48, Resulting Numbers: [48]\n48,48 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 9, + 7, + 13, + 5 + ], + "target": 25, + "solution": [ + "9*5=45", + "7+13=20", + "45-20=25" + ], + "optimal_path": "Current State: 25:[9, 7, 13, 5], Operations: []\nExploring Operation: 9*5=45, Resulting Numbers: [7, 13, 45]\nGenerated Node #2: [7, 13, 45] from Operation: 9*5=45\nCurrent State: 25:[7, 13, 45], Operations: ['9*5=45']\nExploring Operation: 7+13=20, Resulting Numbers: [45, 20]\nGenerated Node #3: [45, 20] from Operation: 7+13=20\nCurrent State: 25:[45, 20], Operations: ['9*5=45', '7+13=20']\nExploring Operation: 45-20=25, Resulting Numbers: [25]\n25,25 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 19, + 5, + 5, + 77 + ], + "target": 20, + "solution": [ + "5*77=385", + "385-5=380", + "380/19=20" + ], + "optimal_path": "Current State: 20:[19, 5, 5, 77], Operations: []\nExploring Operation: 5*77=385, Resulting Numbers: [19, 385]\nGenerated Node #2: [19, 385] from Operation: 5*77=385\nCurrent State: 20:[19, 385], Operations: ['5*77=385']\nExploring Operation: 385-5=380, Resulting Numbers: [19, 380]\nGenerated Node #3: [19, 380] from Operation: 385-5=380\nCurrent State: 20:[19, 380], Operations: ['5*77=385', '385-5=380']\nExploring Operation: 380/19=20, Resulting Numbers: [20]\n20,20 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 76, + 70, + 23, + 47 + ], + "target": 76, + "solution": [ + "76+70=146", + "23+47=70", + "146-70=76" + ], + "optimal_path": "Current State: 76:[76, 70, 23, 47], Operations: []\nExploring Operation: 76+70=146, Resulting Numbers: [23, 47, 146]\nGenerated Node #2: [23, 47, 146] from Operation: 76+70=146\nCurrent State: 76:[23, 47, 146], Operations: ['76+70=146']\nExploring Operation: 23+47=70, Resulting Numbers: [146, 70]\nGenerated Node #3: [146, 70] from Operation: 23+47=70\nCurrent State: 76:[146, 70], Operations: ['76+70=146', '23+47=70']\nExploring Operation: 146-70=76, Resulting Numbers: [76]\n76,76 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 89, + 58, + 3, + 72 + ], + "target": 38, + "solution": [ + "89-58=31", + "72-3=69", + "69-31=38" + ], + "optimal_path": "Current State: 38:[89, 58, 3, 72], Operations: []\nExploring Operation: 89-58=31, Resulting Numbers: [3, 72, 31]\nGenerated Node #2: [3, 72, 31] from Operation: 89-58=31\nCurrent State: 38:[3, 72, 31], Operations: ['89-58=31']\nExploring Operation: 72-3=69, Resulting Numbers: [31, 69]\nGenerated Node #3: [31, 69] from Operation: 72-3=69\nCurrent State: 38:[31, 69], Operations: ['89-58=31', '72-3=69']\nExploring Operation: 69-31=38, Resulting Numbers: [38]\n38,38 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 71, + 40, + 36, + 41 + ], + "target": 34, + "solution": [ + "71+40=111", + "36+41=77", + "111-77=34" + ], + "optimal_path": "Current State: 34:[71, 40, 36, 41], Operations: []\nExploring Operation: 71+40=111, Resulting Numbers: [36, 41, 111]\nGenerated Node #2: [36, 41, 111] from Operation: 71+40=111\nCurrent State: 34:[36, 41, 111], Operations: ['71+40=111']\nExploring Operation: 36+41=77, Resulting Numbers: [111, 77]\nGenerated Node #3: [111, 77] from Operation: 36+41=77\nCurrent State: 34:[111, 77], Operations: ['71+40=111', '36+41=77']\nExploring Operation: 111-77=34, Resulting Numbers: [34]\n34,34 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 68, + 70, + 44, + 66 + ], + "target": 28, + "solution": [ + "68+70=138", + "44+66=110", + "138-110=28" + ], + "optimal_path": "Current State: 28:[68, 70, 44, 66], Operations: []\nExploring Operation: 68+70=138, Resulting Numbers: [44, 66, 138]\nGenerated Node #2: [44, 66, 138] from Operation: 68+70=138\nCurrent State: 28:[44, 66, 138], Operations: ['68+70=138']\nExploring Operation: 44+66=110, Resulting Numbers: [138, 110]\nGenerated Node #3: [138, 110] from Operation: 44+66=110\nCurrent State: 28:[138, 110], Operations: ['68+70=138', '44+66=110']\nExploring Operation: 138-110=28, Resulting Numbers: [28]\n28,28 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 8, + 17, + 30, + 38 + ], + "target": 77, + "solution": [ + "17-8=9", + "30+38=68", + "9+68=77" + ], + "optimal_path": "Current State: 77:[8, 17, 30, 38], Operations: []\nExploring Operation: 17-8=9, Resulting Numbers: [30, 38, 9]\nGenerated Node #2: [30, 38, 9] from Operation: 17-8=9\nCurrent State: 77:[30, 38, 9], Operations: ['17-8=9']\nExploring Operation: 30+38=68, Resulting Numbers: [9, 68]\nGenerated Node #3: [9, 68] from Operation: 30+38=68\nCurrent State: 77:[9, 68], Operations: ['17-8=9', '30+38=68']\nExploring Operation: 9+68=77, Resulting Numbers: [77]\n77,77 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 76, + 3, + 4, + 28 + ], + "target": 92, + "solution": [ + "76*4=304", + "304-28=276", + "276/3=92" + ], + "optimal_path": "Current State: 92:[76, 3, 4, 28], Operations: []\nExploring Operation: 76*4=304, Resulting Numbers: [3, 28, 304]\nGenerated Node #2: [3, 28, 304] from Operation: 76*4=304\nCurrent State: 92:[3, 28, 304], Operations: ['76*4=304']\nExploring Operation: 304-28=276, Resulting Numbers: [3, 276]\nGenerated Node #3: [3, 276] from Operation: 304-28=276\nCurrent State: 92:[3, 276], Operations: ['76*4=304', '304-28=276']\nExploring Operation: 276/3=92, Resulting Numbers: [92]\n92,92 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 18, + 96, + 78, + 24 + ], + "target": 25, + "solution": [ + "96-18=78", + "78/78=1", + "24+1=25" + ], + "optimal_path": "Current State: 25:[18, 96, 78, 24], Operations: []\nExploring Operation: 96-18=78, Resulting Numbers: [78, 24, 78]\nGenerated Node #2: [78, 24, 78] from Operation: 96-18=78\nCurrent State: 25:[78, 24, 78], Operations: ['96-18=78']\nExploring Operation: 78/78=1, Resulting Numbers: [24, 1]\nGenerated Node #3: [24, 1] from Operation: 78/78=1\nCurrent State: 25:[24, 1], Operations: ['96-18=78', '78/78=1']\nExploring Operation: 24+1=25, Resulting Numbers: [25]\n25,25 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 7, + 19, + 90, + 18 + ], + "target": 84, + "solution": [ + "19-7=12", + "90-18=72", + "12+72=84" + ], + "optimal_path": "Current State: 84:[7, 19, 90, 18], Operations: []\nExploring Operation: 19-7=12, Resulting Numbers: [90, 18, 12]\nGenerated Node #2: [90, 18, 12] from Operation: 19-7=12\nCurrent State: 84:[90, 18, 12], Operations: ['19-7=12']\nExploring Operation: 90-18=72, Resulting Numbers: [12, 72]\nGenerated Node #3: [12, 72] from Operation: 90-18=72\nCurrent State: 84:[12, 72], Operations: ['19-7=12', '90-18=72']\nExploring Operation: 12+72=84, Resulting Numbers: [84]\n84,84 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 54, + 2, + 65, + 15 + ], + "target": 79, + "solution": [ + "65-15=50", + "50/2=25", + "54+25=79" + ], + "optimal_path": "Current State: 79:[54, 2, 65, 15], Operations: []\nExploring Operation: 65-15=50, Resulting Numbers: [54, 2, 50]\nGenerated Node #2: [54, 2, 50] from Operation: 65-15=50\nCurrent State: 79:[54, 2, 50], Operations: ['65-15=50']\nExploring Operation: 50/2=25, Resulting Numbers: [54, 25]\nGenerated Node #3: [54, 25] from Operation: 50/2=25\nCurrent State: 79:[54, 25], Operations: ['65-15=50', '50/2=25']\nExploring Operation: 54+25=79, Resulting Numbers: [79]\n79,79 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 45, + 72, + 64, + 33 + ], + "target": 96, + "solution": [ + "45-33=12", + "72-64=8", + "12*8=96" + ], + "optimal_path": "Current State: 96:[45, 72, 64, 33], Operations: []\nExploring Operation: 45-33=12, Resulting Numbers: [72, 64, 12]\nGenerated Node #2: [72, 64, 12] from Operation: 45-33=12\nCurrent State: 96:[72, 64, 12], Operations: ['45-33=12']\nExploring Operation: 72-64=8, Resulting Numbers: [12, 8]\nGenerated Node #3: [12, 8] from Operation: 72-64=8\nCurrent State: 96:[12, 8], Operations: ['45-33=12', '72-64=8']\nExploring Operation: 12*8=96, Resulting Numbers: [96]\n96,96 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 87, + 95, + 60, + 96 + ], + "target": 48, + "solution": [ + "95-87=8", + "96/8=12", + "60-12=48" + ], + "optimal_path": "Current State: 48:[87, 95, 60, 96], Operations: []\nExploring Operation: 95-87=8, Resulting Numbers: [60, 96, 8]\nGenerated Node #2: [60, 96, 8] from Operation: 95-87=8\nCurrent State: 48:[60, 96, 8], Operations: ['95-87=8']\nExploring Operation: 96/8=12, Resulting Numbers: [60, 12]\nGenerated Node #3: [60, 12] from Operation: 96/8=12\nCurrent State: 48:[60, 12], Operations: ['95-87=8', '96/8=12']\nExploring Operation: 60-12=48, Resulting Numbers: [48]\n48,48 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 87, + 27, + 3, + 32 + ], + "target": 34, + "solution": [ + "87/3=29", + "32-27=5", + "29+5=34" + ], + "optimal_path": "Current State: 34:[87, 27, 3, 32], Operations: []\nExploring Operation: 87/3=29, Resulting Numbers: [27, 32, 29]\nGenerated Node #2: [27, 32, 29] from Operation: 87/3=29\nCurrent State: 34:[27, 32, 29], Operations: ['87/3=29']\nExploring Operation: 32-27=5, Resulting Numbers: [29, 5]\nGenerated Node #3: [29, 5] from Operation: 32-27=5\nCurrent State: 34:[29, 5], Operations: ['87/3=29', '32-27=5']\nExploring Operation: 29+5=34, Resulting Numbers: [34]\n34,34 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 85, + 37, + 39, + 3 + ], + "target": 55, + "solution": [ + "85-37=48", + "48/3=16", + "39+16=55" + ], + "optimal_path": "Current State: 55:[85, 37, 39, 3], Operations: []\nExploring Operation: 85-37=48, Resulting Numbers: [39, 3, 48]\nGenerated Node #2: [39, 3, 48] from Operation: 85-37=48\nCurrent State: 55:[39, 3, 48], Operations: ['85-37=48']\nExploring Operation: 48/3=16, Resulting Numbers: [39, 16]\nGenerated Node #3: [39, 16] from Operation: 48/3=16\nCurrent State: 55:[39, 16], Operations: ['85-37=48', '48/3=16']\nExploring Operation: 39+16=55, Resulting Numbers: [55]\n55,55 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 6, + 56, + 72, + 47 + ], + "target": 91, + "solution": [ + "72/6=12", + "56+47=103", + "103-12=91" + ], + "optimal_path": "Current State: 91:[6, 56, 72, 47], Operations: []\nExploring Operation: 72/6=12, Resulting Numbers: [56, 47, 12]\nGenerated Node #2: [56, 47, 12] from Operation: 72/6=12\nCurrent State: 91:[56, 47, 12], Operations: ['72/6=12']\nExploring Operation: 56+47=103, Resulting Numbers: [12, 103]\nGenerated Node #3: [12, 103] from Operation: 56+47=103\nCurrent State: 91:[12, 103], Operations: ['72/6=12', '56+47=103']\nExploring Operation: 103-12=91, Resulting Numbers: [91]\n91,91 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 51, + 26, + 78, + 8 + ], + "target": 61, + "solution": [ + "51-26=25", + "78+8=86", + "86-25=61" + ], + "optimal_path": "Current State: 61:[51, 26, 78, 8], Operations: []\nExploring Operation: 51-26=25, Resulting Numbers: [78, 8, 25]\nGenerated Node #2: [78, 8, 25] from Operation: 51-26=25\nCurrent State: 61:[78, 8, 25], Operations: ['51-26=25']\nExploring Operation: 78+8=86, Resulting Numbers: [25, 86]\nGenerated Node #3: [25, 86] from Operation: 78+8=86\nCurrent State: 61:[25, 86], Operations: ['51-26=25', '78+8=86']\nExploring Operation: 86-25=61, Resulting Numbers: [61]\n61,61 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 60, + 84, + 78, + 90 + ], + "target": 89, + "solution": [ + "78-60=18", + "90/18=5", + "84+5=89" + ], + "optimal_path": "Current State: 89:[60, 84, 78, 90], Operations: []\nExploring Operation: 78-60=18, Resulting Numbers: [84, 90, 18]\nGenerated Node #2: [84, 90, 18] from Operation: 78-60=18\nCurrent State: 89:[84, 90, 18], Operations: ['78-60=18']\nExploring Operation: 90/18=5, Resulting Numbers: [84, 5]\nGenerated Node #3: [84, 5] from Operation: 90/18=5\nCurrent State: 89:[84, 5], Operations: ['78-60=18', '90/18=5']\nExploring Operation: 84+5=89, Resulting Numbers: [89]\n89,89 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 30, + 72, + 69, + 44 + ], + "target": 60, + "solution": [ + "69-44=25", + "72*25=1800", + "1800/30=60" + ], + "optimal_path": "Current State: 60:[30, 72, 69, 44], Operations: []\nExploring Operation: 69-44=25, Resulting Numbers: [30, 72, 25]\nGenerated Node #2: [30, 72, 25] from Operation: 69-44=25\nCurrent State: 60:[30, 72, 25], Operations: ['69-44=25']\nExploring Operation: 72*25=1800, Resulting Numbers: [30, 1800]\nGenerated Node #3: [30, 1800] from Operation: 72*25=1800\nCurrent State: 60:[30, 1800], Operations: ['69-44=25', '72*25=1800']\nExploring Operation: 1800/30=60, Resulting Numbers: [60]\n60,60 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 30, + 60, + 40, + 18 + ], + "target": 49, + "solution": [ + "60/30=2", + "18/2=9", + "40+9=49" + ], + "optimal_path": "Current State: 49:[30, 60, 40, 18], Operations: []\nExploring Operation: 60/30=2, Resulting Numbers: [40, 18, 2]\nGenerated Node #2: [40, 18, 2] from Operation: 60/30=2\nCurrent State: 49:[40, 18, 2], Operations: ['60/30=2']\nExploring Operation: 18/2=9, Resulting Numbers: [40, 9]\nGenerated Node #3: [40, 9] from Operation: 18/2=9\nCurrent State: 49:[40, 9], Operations: ['60/30=2', '18/2=9']\nExploring Operation: 40+9=49, Resulting Numbers: [49]\n49,49 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 21, + 73, + 23, + 22 + ], + "target": 97, + "solution": [ + "73-21=52", + "23+22=45", + "52+45=97" + ], + "optimal_path": "Current State: 97:[21, 73, 23, 22], Operations: []\nExploring Operation: 73-21=52, Resulting Numbers: [23, 22, 52]\nGenerated Node #2: [23, 22, 52] from Operation: 73-21=52\nCurrent State: 97:[23, 22, 52], Operations: ['73-21=52']\nExploring Operation: 23+22=45, Resulting Numbers: [52, 45]\nGenerated Node #3: [52, 45] from Operation: 23+22=45\nCurrent State: 97:[52, 45], Operations: ['73-21=52', '23+22=45']\nExploring Operation: 52+45=97, Resulting Numbers: [97]\n97,97 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 60, + 51, + 5, + 68 + ], + "target": 40, + "solution": [ + "60*51=3060", + "3060/68=45", + "45-5=40" + ], + "optimal_path": "Current State: 40:[60, 51, 5, 68], Operations: []\nExploring Operation: 60*51=3060, Resulting Numbers: [5, 68, 3060]\nGenerated Node #2: [5, 68, 3060] from Operation: 60*51=3060\nCurrent State: 40:[5, 68, 3060], Operations: ['60*51=3060']\nExploring Operation: 3060/68=45, Resulting Numbers: [5, 45]\nGenerated Node #3: [5, 45] from Operation: 3060/68=45\nCurrent State: 40:[5, 45], Operations: ['60*51=3060', '3060/68=45']\nExploring Operation: 45-5=40, Resulting Numbers: [40]\n40,40 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 5, + 34, + 21, + 90 + ], + "target": 82, + "solution": [ + "34-5=29", + "21+90=111", + "111-29=82" + ], + "optimal_path": "Current State: 82:[5, 34, 21, 90], Operations: []\nExploring Operation: 34-5=29, Resulting Numbers: [21, 90, 29]\nGenerated Node #2: [21, 90, 29] from Operation: 34-5=29\nCurrent State: 82:[21, 90, 29], Operations: ['34-5=29']\nExploring Operation: 21+90=111, Resulting Numbers: [29, 111]\nGenerated Node #3: [29, 111] from Operation: 21+90=111\nCurrent State: 82:[29, 111], Operations: ['34-5=29', '21+90=111']\nExploring Operation: 111-29=82, Resulting Numbers: [82]\n82,82 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 93, + 91, + 27, + 15 + ], + "target": 44, + "solution": [ + "93-91=2", + "27+15=42", + "2+42=44" + ], + "optimal_path": "Current State: 44:[93, 91, 27, 15], Operations: []\nExploring Operation: 93-91=2, Resulting Numbers: [27, 15, 2]\nGenerated Node #2: [27, 15, 2] from Operation: 93-91=2\nCurrent State: 44:[27, 15, 2], Operations: ['93-91=2']\nExploring Operation: 27+15=42, Resulting Numbers: [2, 42]\nGenerated Node #3: [2, 42] from Operation: 27+15=42\nCurrent State: 44:[2, 42], Operations: ['93-91=2', '27+15=42']\nExploring Operation: 2+42=44, Resulting Numbers: [44]\n44,44 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 32, + 86, + 11, + 19 + ], + "target": 24, + "solution": [ + "86-32=54", + "11+19=30", + "54-30=24" + ], + "optimal_path": "Current State: 24:[32, 86, 11, 19], Operations: []\nExploring Operation: 86-32=54, Resulting Numbers: [11, 19, 54]\nGenerated Node #2: [11, 19, 54] from Operation: 86-32=54\nCurrent State: 24:[11, 19, 54], Operations: ['86-32=54']\nExploring Operation: 11+19=30, Resulting Numbers: [54, 30]\nGenerated Node #3: [54, 30] from Operation: 11+19=30\nCurrent State: 24:[54, 30], Operations: ['86-32=54', '11+19=30']\nExploring Operation: 54-30=24, Resulting Numbers: [24]\n24,24 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 1, + 20, + 45, + 86 + ], + "target": 62, + "solution": [ + "1+20=21", + "86-45=41", + "21+41=62" + ], + "optimal_path": "Current State: 62:[1, 20, 45, 86], Operations: []\nExploring Operation: 1+20=21, Resulting Numbers: [45, 86, 21]\nGenerated Node #2: [45, 86, 21] from Operation: 1+20=21\nCurrent State: 62:[45, 86, 21], Operations: ['1+20=21']\nExploring Operation: 86-45=41, Resulting Numbers: [21, 41]\nGenerated Node #3: [21, 41] from Operation: 86-45=41\nCurrent State: 62:[21, 41], Operations: ['1+20=21', '86-45=41']\nExploring Operation: 21+41=62, Resulting Numbers: [62]\n62,62 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 29, + 55, + 5, + 63 + ], + "target": 67, + "solution": [ + "55-29=26", + "5*26=130", + "130-63=67" + ], + "optimal_path": "Current State: 67:[29, 55, 5, 63], Operations: []\nExploring Operation: 55-29=26, Resulting Numbers: [5, 63, 26]\nGenerated Node #2: [5, 63, 26] from Operation: 55-29=26\nCurrent State: 67:[5, 63, 26], Operations: ['55-29=26']\nExploring Operation: 5*26=130, Resulting Numbers: [63, 130]\nGenerated Node #3: [63, 130] from Operation: 5*26=130\nCurrent State: 67:[63, 130], Operations: ['55-29=26', '5*26=130']\nExploring Operation: 130-63=67, Resulting Numbers: [67]\n67,67 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 42, + 13, + 93, + 60 + ], + "target": 88, + "solution": [ + "42+13=55", + "93-60=33", + "55+33=88" + ], + "optimal_path": "Current State: 88:[42, 13, 93, 60], Operations: []\nExploring Operation: 42+13=55, Resulting Numbers: [93, 60, 55]\nGenerated Node #2: [93, 60, 55] from Operation: 42+13=55\nCurrent State: 88:[93, 60, 55], Operations: ['42+13=55']\nExploring Operation: 93-60=33, Resulting Numbers: [55, 33]\nGenerated Node #3: [55, 33] from Operation: 93-60=33\nCurrent State: 88:[55, 33], Operations: ['42+13=55', '93-60=33']\nExploring Operation: 55+33=88, Resulting Numbers: [88]\n88,88 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 93, + 54, + 29, + 92 + ], + "target": 82, + "solution": [ + "93-54=39", + "29+92=121", + "121-39=82" + ], + "optimal_path": "Current State: 82:[93, 54, 29, 92], Operations: []\nExploring Operation: 93-54=39, Resulting Numbers: [29, 92, 39]\nGenerated Node #2: [29, 92, 39] from Operation: 93-54=39\nCurrent State: 82:[29, 92, 39], Operations: ['93-54=39']\nExploring Operation: 29+92=121, Resulting Numbers: [39, 121]\nGenerated Node #3: [39, 121] from Operation: 29+92=121\nCurrent State: 82:[39, 121], Operations: ['93-54=39', '29+92=121']\nExploring Operation: 121-39=82, Resulting Numbers: [82]\n82,82 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 49, + 55, + 83, + 38 + ], + "target": 59, + "solution": [ + "49+55=104", + "83-38=45", + "104-45=59" + ], + "optimal_path": "Current State: 59:[49, 55, 83, 38], Operations: []\nExploring Operation: 49+55=104, Resulting Numbers: [83, 38, 104]\nGenerated Node #2: [83, 38, 104] from Operation: 49+55=104\nCurrent State: 59:[83, 38, 104], Operations: ['49+55=104']\nExploring Operation: 83-38=45, Resulting Numbers: [104, 45]\nGenerated Node #3: [104, 45] from Operation: 83-38=45\nCurrent State: 59:[104, 45], Operations: ['49+55=104', '83-38=45']\nExploring Operation: 104-45=59, Resulting Numbers: [59]\n59,59 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 1, + 11, + 5, + 26 + ], + "target": 34, + "solution": [ + "1+11=12", + "5*12=60", + "60-26=34" + ], + "optimal_path": "Current State: 34:[1, 11, 5, 26], Operations: []\nExploring Operation: 1+11=12, Resulting Numbers: [5, 26, 12]\nGenerated Node #2: [5, 26, 12] from Operation: 1+11=12\nCurrent State: 34:[5, 26, 12], Operations: ['1+11=12']\nExploring Operation: 5*12=60, Resulting Numbers: [26, 60]\nGenerated Node #3: [26, 60] from Operation: 5*12=60\nCurrent State: 34:[26, 60], Operations: ['1+11=12', '5*12=60']\nExploring Operation: 60-26=34, Resulting Numbers: [34]\n34,34 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 58, + 12, + 26, + 62 + ], + "target": 56, + "solution": [ + "62-58=4", + "26-12=14", + "4*14=56" + ], + "optimal_path": "Current State: 56:[58, 12, 26, 62], Operations: []\nExploring Operation: 62-58=4, Resulting Numbers: [12, 26, 4]\nGenerated Node #2: [12, 26, 4] from Operation: 62-58=4\nCurrent State: 56:[12, 26, 4], Operations: ['62-58=4']\nExploring Operation: 26-12=14, Resulting Numbers: [4, 14]\nGenerated Node #3: [4, 14] from Operation: 26-12=14\nCurrent State: 56:[4, 14], Operations: ['62-58=4', '26-12=14']\nExploring Operation: 4*14=56, Resulting Numbers: [56]\n56,56 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 23, + 41, + 46, + 69 + ], + "target": 61, + "solution": [ + "41*69=2829", + "2829-23=2806", + "2806/46=61" + ], + "optimal_path": "Current State: 61:[23, 41, 46, 69], Operations: []\nExploring Operation: 41*69=2829, Resulting Numbers: [23, 46, 2829]\nGenerated Node #2: [23, 46, 2829] from Operation: 41*69=2829\nCurrent State: 61:[23, 46, 2829], Operations: ['41*69=2829']\nExploring Operation: 2829-23=2806, Resulting Numbers: [46, 2806]\nGenerated Node #3: [46, 2806] from Operation: 2829-23=2806\nCurrent State: 61:[46, 2806], Operations: ['41*69=2829', '2829-23=2806']\nExploring Operation: 2806/46=61, Resulting Numbers: [61]\n61,61 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 57, + 50, + 3, + 42 + ], + "target": 79, + "solution": [ + "57*3=171", + "50+42=92", + "171-92=79" + ], + "optimal_path": "Current State: 79:[57, 50, 3, 42], Operations: []\nExploring Operation: 57*3=171, Resulting Numbers: [50, 42, 171]\nGenerated Node #2: [50, 42, 171] from Operation: 57*3=171\nCurrent State: 79:[50, 42, 171], Operations: ['57*3=171']\nExploring Operation: 50+42=92, Resulting Numbers: [171, 92]\nGenerated Node #3: [171, 92] from Operation: 50+42=92\nCurrent State: 79:[171, 92], Operations: ['57*3=171', '50+42=92']\nExploring Operation: 171-92=79, Resulting Numbers: [79]\n79,79 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 74, + 30, + 69, + 74 + ], + "target": 68, + "solution": [ + "74-69=5", + "30/5=6", + "74-6=68" + ], + "optimal_path": "Current State: 68:[74, 30, 69, 74], Operations: []\nExploring Operation: 74-69=5, Resulting Numbers: [30, 5]\nGenerated Node #2: [30, 5] from Operation: 74-69=5\nCurrent State: 68:[30, 5], Operations: ['74-69=5']\nExploring Operation: 30/5=6, Resulting Numbers: [6]\n6,68 equal: Goal Reached\nExploring Operation: 74-6=68, Resulting Numbers: [68]\n68,68 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 53, + 70, + 72, + 8 + ], + "target": 59, + "solution": [ + "53+70=123", + "72-8=64", + "123-64=59" + ], + "optimal_path": "Current State: 59:[53, 70, 72, 8], Operations: []\nExploring Operation: 53+70=123, Resulting Numbers: [72, 8, 123]\nGenerated Node #2: [72, 8, 123] from Operation: 53+70=123\nCurrent State: 59:[72, 8, 123], Operations: ['53+70=123']\nExploring Operation: 72-8=64, Resulting Numbers: [123, 64]\nGenerated Node #3: [123, 64] from Operation: 72-8=64\nCurrent State: 59:[123, 64], Operations: ['53+70=123', '72-8=64']\nExploring Operation: 123-64=59, Resulting Numbers: [59]\n59,59 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 77, + 1, + 23, + 12 + ], + "target": 41, + "solution": [ + "77-1=76", + "23+12=35", + "76-35=41" + ], + "optimal_path": "Current State: 41:[77, 1, 23, 12], Operations: []\nExploring Operation: 77-1=76, Resulting Numbers: [23, 12, 76]\nGenerated Node #2: [23, 12, 76] from Operation: 77-1=76\nCurrent State: 41:[23, 12, 76], Operations: ['77-1=76']\nExploring Operation: 23+12=35, Resulting Numbers: [76, 35]\nGenerated Node #3: [76, 35] from Operation: 23+12=35\nCurrent State: 41:[76, 35], Operations: ['77-1=76', '23+12=35']\nExploring Operation: 76-35=41, Resulting Numbers: [41]\n41,41 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 3, + 54, + 6, + 13 + ], + "target": 19, + "solution": [ + "3+6=9", + "54/9=6", + "13+6=19" + ], + "optimal_path": "Current State: 19:[3, 54, 6, 13], Operations: []\nExploring Operation: 3+6=9, Resulting Numbers: [54, 13, 9]\nGenerated Node #2: [54, 13, 9] from Operation: 3+6=9\nCurrent State: 19:[54, 13, 9], Operations: ['3+6=9']\nExploring Operation: 54/9=6, Resulting Numbers: [13, 6]\nGenerated Node #3: [13, 6] from Operation: 54/9=6\nCurrent State: 19:[13, 6], Operations: ['3+6=9', '54/9=6']\nExploring Operation: 13+6=19, Resulting Numbers: [19]\n19,19 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 99, + 19, + 92, + 13 + ], + "target": 42, + "solution": [ + "99-92=7", + "19-13=6", + "7*6=42" + ], + "optimal_path": "Current State: 42:[99, 19, 92, 13], Operations: []\nExploring Operation: 99-92=7, Resulting Numbers: [19, 13, 7]\nGenerated Node #2: [19, 13, 7] from Operation: 99-92=7\nCurrent State: 42:[19, 13, 7], Operations: ['99-92=7']\nExploring Operation: 19-13=6, Resulting Numbers: [7, 6]\nGenerated Node #3: [7, 6] from Operation: 19-13=6\nCurrent State: 42:[7, 6], Operations: ['99-92=7', '19-13=6']\nExploring Operation: 7*6=42, Resulting Numbers: [42]\n42,42 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 24, + 20, + 10, + 18 + ], + "target": 52, + "solution": [ + "24+20=44", + "18-10=8", + "44+8=52" + ], + "optimal_path": "Current State: 52:[24, 20, 10, 18], Operations: []\nExploring Operation: 24+20=44, Resulting Numbers: [10, 18, 44]\nGenerated Node #2: [10, 18, 44] from Operation: 24+20=44\nCurrent State: 52:[10, 18, 44], Operations: ['24+20=44']\nExploring Operation: 18-10=8, Resulting Numbers: [44, 8]\nGenerated Node #3: [44, 8] from Operation: 18-10=8\nCurrent State: 52:[44, 8], Operations: ['24+20=44', '18-10=8']\nExploring Operation: 44+8=52, Resulting Numbers: [52]\n52,52 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 63, + 59, + 63, + 17 + ], + "target": 75, + "solution": [ + "63/63=1", + "59+17=76", + "76-1=75" + ], + "optimal_path": "Current State: 75:[63, 59, 63, 17], Operations: []\nExploring Operation: 63/63=1, Resulting Numbers: [59, 17, 1]\nGenerated Node #2: [59, 17, 1] from Operation: 63/63=1\nCurrent State: 75:[59, 17, 1], Operations: ['63/63=1']\nExploring Operation: 59+17=76, Resulting Numbers: [1, 76]\nGenerated Node #3: [1, 76] from Operation: 59+17=76\nCurrent State: 75:[1, 76], Operations: ['63/63=1', '59+17=76']\nExploring Operation: 76-1=75, Resulting Numbers: [75]\n75,75 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 50, + 94, + 32, + 40 + ], + "target": 54, + "solution": [ + "50*32=1600", + "1600/40=40", + "94-40=54" + ], + "optimal_path": "Current State: 54:[50, 94, 32, 40], Operations: []\nExploring Operation: 50*32=1600, Resulting Numbers: [94, 40, 1600]\nGenerated Node #2: [94, 40, 1600] from Operation: 50*32=1600\nCurrent State: 54:[94, 40, 1600], Operations: ['50*32=1600']\nExploring Operation: 1600/40=40, Resulting Numbers: [94, 40]\nGenerated Node #3: [94, 40] from Operation: 1600/40=40\nCurrent State: 54:[94, 40], Operations: ['50*32=1600', '1600/40=40']\nExploring Operation: 94-40=54, Resulting Numbers: [54]\n54,54 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 3, + 47, + 31, + 27 + ], + "target": 11, + "solution": [ + "47-3=44", + "31-27=4", + "44/4=11" + ], + "optimal_path": "Current State: 11:[3, 47, 31, 27], Operations: []\nExploring Operation: 47-3=44, Resulting Numbers: [31, 27, 44]\nGenerated Node #2: [31, 27, 44] from Operation: 47-3=44\nCurrent State: 11:[31, 27, 44], Operations: ['47-3=44']\nExploring Operation: 31-27=4, Resulting Numbers: [44, 4]\nGenerated Node #3: [44, 4] from Operation: 31-27=4\nCurrent State: 11:[44, 4], Operations: ['47-3=44', '31-27=4']\nExploring Operation: 44/4=11, Resulting Numbers: [11]\n11,11 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 14, + 84, + 98, + 14 + ], + "target": 14, + "solution": [ + "14+84=98", + "98+14=112", + "112-98=14" + ], + "optimal_path": "Current State: 14:[14, 84, 98, 14], Operations: []\nExploring Operation: 14+84=98, Resulting Numbers: [98, 98]\nGenerated Node #2: [98, 98] from Operation: 14+84=98\nCurrent State: 14:[98, 98], Operations: ['14+84=98']\nExploring Operation: 98+14=112, Resulting Numbers: [112]\n112,14 equal: Goal Reached\nExploring Operation: 112-98=14, Resulting Numbers: [14]\n14,14 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 36, + 96, + 56, + 78 + ], + "target": 58, + "solution": [ + "96-78=18", + "36/18=2", + "56+2=58" + ], + "optimal_path": "Current State: 58:[36, 96, 56, 78], Operations: []\nExploring Operation: 96-78=18, Resulting Numbers: [36, 56, 18]\nGenerated Node #2: [36, 56, 18] from Operation: 96-78=18\nCurrent State: 58:[36, 56, 18], Operations: ['96-78=18']\nExploring Operation: 36/18=2, Resulting Numbers: [56, 2]\nGenerated Node #3: [56, 2] from Operation: 36/18=2\nCurrent State: 58:[56, 2], Operations: ['96-78=18', '36/18=2']\nExploring Operation: 56+2=58, Resulting Numbers: [58]\n58,58 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 40, + 3, + 91, + 61 + ], + "target": 44, + "solution": [ + "91-40=51", + "51/3=17", + "61-17=44" + ], + "optimal_path": "Current State: 44:[40, 3, 91, 61], Operations: []\nExploring Operation: 91-40=51, Resulting Numbers: [3, 61, 51]\nGenerated Node #2: [3, 61, 51] from Operation: 91-40=51\nCurrent State: 44:[3, 61, 51], Operations: ['91-40=51']\nExploring Operation: 51/3=17, Resulting Numbers: [61, 17]\nGenerated Node #3: [61, 17] from Operation: 51/3=17\nCurrent State: 44:[61, 17], Operations: ['91-40=51', '51/3=17']\nExploring Operation: 61-17=44, Resulting Numbers: [44]\n44,44 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 91, + 41, + 73, + 74 + ], + "target": 50, + "solution": [ + "91-41=50", + "74-73=1", + "50*1=50" + ], + "optimal_path": "Current State: 50:[91, 41, 73, 74], Operations: []\nExploring Operation: 91-41=50, Resulting Numbers: [73, 74, 50]\nGenerated Node #2: [73, 74, 50] from Operation: 91-41=50\nCurrent State: 50:[73, 74, 50], Operations: ['91-41=50']\nExploring Operation: 74-73=1, Resulting Numbers: [50, 1]\nGenerated Node #3: [50, 1] from Operation: 74-73=1\nCurrent State: 50:[50, 1], Operations: ['91-41=50', '74-73=1']\nExploring Operation: 50*1=50, Resulting Numbers: [50]\n50,50 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 18, + 32, + 92, + 21 + ], + "target": 99, + "solution": [ + "32-18=14", + "92+21=113", + "113-14=99" + ], + "optimal_path": "Current State: 99:[18, 32, 92, 21], Operations: []\nExploring Operation: 32-18=14, Resulting Numbers: [92, 21, 14]\nGenerated Node #2: [92, 21, 14] from Operation: 32-18=14\nCurrent State: 99:[92, 21, 14], Operations: ['32-18=14']\nExploring Operation: 92+21=113, Resulting Numbers: [14, 113]\nGenerated Node #3: [14, 113] from Operation: 92+21=113\nCurrent State: 99:[14, 113], Operations: ['32-18=14', '92+21=113']\nExploring Operation: 113-14=99, Resulting Numbers: [99]\n99,99 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 18, + 27, + 17, + 84 + ], + "target": 76, + "solution": [ + "27-18=9", + "84-17=67", + "9+67=76" + ], + "optimal_path": "Current State: 76:[18, 27, 17, 84], Operations: []\nExploring Operation: 27-18=9, Resulting Numbers: [17, 84, 9]\nGenerated Node #2: [17, 84, 9] from Operation: 27-18=9\nCurrent State: 76:[17, 84, 9], Operations: ['27-18=9']\nExploring Operation: 84-17=67, Resulting Numbers: [9, 67]\nGenerated Node #3: [9, 67] from Operation: 84-17=67\nCurrent State: 76:[9, 67], Operations: ['27-18=9', '84-17=67']\nExploring Operation: 9+67=76, Resulting Numbers: [76]\n76,76 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 32, + 3, + 98, + 42 + ], + "target": 84, + "solution": [ + "32*3=96", + "98-96=2", + "42*2=84" + ], + "optimal_path": "Current State: 84:[32, 3, 98, 42], Operations: []\nExploring Operation: 32*3=96, Resulting Numbers: [98, 42, 96]\nGenerated Node #2: [98, 42, 96] from Operation: 32*3=96\nCurrent State: 84:[98, 42, 96], Operations: ['32*3=96']\nExploring Operation: 98-96=2, Resulting Numbers: [42, 2]\nGenerated Node #3: [42, 2] from Operation: 98-96=2\nCurrent State: 84:[42, 2], Operations: ['32*3=96', '98-96=2']\nExploring Operation: 42*2=84, Resulting Numbers: [84]\n84,84 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 59, + 58, + 34, + 5 + ], + "target": 29, + "solution": [ + "59-58=1", + "34-5=29", + "1*29=29" + ], + "optimal_path": "Current State: 29:[59, 58, 34, 5], Operations: []\nExploring Operation: 59-58=1, Resulting Numbers: [34, 5, 1]\nGenerated Node #2: [34, 5, 1] from Operation: 59-58=1\nCurrent State: 29:[34, 5, 1], Operations: ['59-58=1']\nExploring Operation: 34-5=29, Resulting Numbers: [1, 29]\nGenerated Node #3: [1, 29] from Operation: 34-5=29\nCurrent State: 29:[1, 29], Operations: ['59-58=1', '34-5=29']\nExploring Operation: 1*29=29, Resulting Numbers: [29]\n29,29 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 79, + 69, + 94, + 92 + ], + "target": 59, + "solution": [ + "94-92=2", + "69*2=138", + "138-79=59" + ], + "optimal_path": "Current State: 59:[79, 69, 94, 92], Operations: []\nExploring Operation: 94-92=2, Resulting Numbers: [79, 69, 2]\nGenerated Node #2: [79, 69, 2] from Operation: 94-92=2\nCurrent State: 59:[79, 69, 2], Operations: ['94-92=2']\nExploring Operation: 69*2=138, Resulting Numbers: [79, 138]\nGenerated Node #3: [79, 138] from Operation: 69*2=138\nCurrent State: 59:[79, 138], Operations: ['94-92=2', '69*2=138']\nExploring Operation: 138-79=59, Resulting Numbers: [59]\n59,59 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 60, + 65, + 16, + 40 + ], + "target": 89, + "solution": [ + "60*16=960", + "960/40=24", + "65+24=89" + ], + "optimal_path": "Current State: 89:[60, 65, 16, 40], Operations: []\nExploring Operation: 60*16=960, Resulting Numbers: [65, 40, 960]\nGenerated Node #2: [65, 40, 960] from Operation: 60*16=960\nCurrent State: 89:[65, 40, 960], Operations: ['60*16=960']\nExploring Operation: 960/40=24, Resulting Numbers: [65, 24]\nGenerated Node #3: [65, 24] from Operation: 960/40=24\nCurrent State: 89:[65, 24], Operations: ['60*16=960', '960/40=24']\nExploring Operation: 65+24=89, Resulting Numbers: [89]\n89,89 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 62, + 72, + 86, + 8 + ], + "target": 100, + "solution": [ + "72*86=6192", + "8+6192=6200", + "6200/62=100" + ], + "optimal_path": "Current State: 100:[62, 72, 86, 8], Operations: []\nExploring Operation: 72*86=6192, Resulting Numbers: [62, 8, 6192]\nGenerated Node #2: [62, 8, 6192] from Operation: 72*86=6192\nCurrent State: 100:[62, 8, 6192], Operations: ['72*86=6192']\nExploring Operation: 8+6192=6200, Resulting Numbers: [62, 6200]\nGenerated Node #3: [62, 6200] from Operation: 8+6192=6200\nCurrent State: 100:[62, 6200], Operations: ['72*86=6192', '8+6192=6200']\nExploring Operation: 6200/62=100, Resulting Numbers: [100]\n100,100 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 96, + 75, + 43, + 11 + ], + "target": 75, + "solution": [ + "96-75=21", + "43+11=54", + "21+54=75" + ], + "optimal_path": "Current State: 75:[96, 75, 43, 11], Operations: []\nExploring Operation: 96-75=21, Resulting Numbers: [43, 11, 21]\nGenerated Node #2: [43, 11, 21] from Operation: 96-75=21\nCurrent State: 75:[43, 11, 21], Operations: ['96-75=21']\nExploring Operation: 43+11=54, Resulting Numbers: [21, 54]\nGenerated Node #3: [21, 54] from Operation: 43+11=54\nCurrent State: 75:[21, 54], Operations: ['96-75=21', '43+11=54']\nExploring Operation: 21+54=75, Resulting Numbers: [75]\n75,75 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 13, + 28, + 30, + 42 + ], + "target": 27, + "solution": [ + "28-13=15", + "42-30=12", + "15+12=27" + ], + "optimal_path": "Current State: 27:[13, 28, 30, 42], Operations: []\nExploring Operation: 28-13=15, Resulting Numbers: [30, 42, 15]\nGenerated Node #2: [30, 42, 15] from Operation: 28-13=15\nCurrent State: 27:[30, 42, 15], Operations: ['28-13=15']\nExploring Operation: 42-30=12, Resulting Numbers: [15, 12]\nGenerated Node #3: [15, 12] from Operation: 42-30=12\nCurrent State: 27:[15, 12], Operations: ['28-13=15', '42-30=12']\nExploring Operation: 15+12=27, Resulting Numbers: [27]\n27,27 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 45, + 50, + 26, + 86 + ], + "target": 14, + "solution": [ + "45*50=2250", + "26*86=2236", + "2250-2236=14" + ], + "optimal_path": "Current State: 14:[45, 50, 26, 86], Operations: []\nExploring Operation: 45*50=2250, Resulting Numbers: [26, 86, 2250]\nGenerated Node #2: [26, 86, 2250] from Operation: 45*50=2250\nCurrent State: 14:[26, 86, 2250], Operations: ['45*50=2250']\nExploring Operation: 26*86=2236, Resulting Numbers: [2250, 2236]\nGenerated Node #3: [2250, 2236] from Operation: 26*86=2236\nCurrent State: 14:[2250, 2236], Operations: ['45*50=2250', '26*86=2236']\nExploring Operation: 2250-2236=14, Resulting Numbers: [14]\n14,14 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 35, + 3, + 68, + 63 + ], + "target": 70, + "solution": [ + "68-3=65", + "65-63=2", + "35*2=70" + ], + "optimal_path": "Current State: 70:[35, 3, 68, 63], Operations: []\nExploring Operation: 68-3=65, Resulting Numbers: [35, 63, 65]\nGenerated Node #2: [35, 63, 65] from Operation: 68-3=65\nCurrent State: 70:[35, 63, 65], Operations: ['68-3=65']\nExploring Operation: 65-63=2, Resulting Numbers: [35, 2]\nGenerated Node #3: [35, 2] from Operation: 65-63=2\nCurrent State: 70:[35, 2], Operations: ['68-3=65', '65-63=2']\nExploring Operation: 35*2=70, Resulting Numbers: [70]\n70,70 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 25, + 90, + 31, + 2 + ], + "target": 62, + "solution": [ + "25+31=56", + "56/2=28", + "90-28=62" + ], + "optimal_path": "Current State: 62:[25, 90, 31, 2], Operations: []\nExploring Operation: 25+31=56, Resulting Numbers: [90, 2, 56]\nGenerated Node #2: [90, 2, 56] from Operation: 25+31=56\nCurrent State: 62:[90, 2, 56], Operations: ['25+31=56']\nExploring Operation: 56/2=28, Resulting Numbers: [90, 28]\nGenerated Node #3: [90, 28] from Operation: 56/2=28\nCurrent State: 62:[90, 28], Operations: ['25+31=56', '56/2=28']\nExploring Operation: 90-28=62, Resulting Numbers: [62]\n62,62 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 4, + 70, + 2, + 22 + ], + "target": 30, + "solution": [ + "4+70=74", + "2*22=44", + "74-44=30" + ], + "optimal_path": "Current State: 30:[4, 70, 2, 22], Operations: []\nExploring Operation: 4+70=74, Resulting Numbers: [2, 22, 74]\nGenerated Node #2: [2, 22, 74] from Operation: 4+70=74\nCurrent State: 30:[2, 22, 74], Operations: ['4+70=74']\nExploring Operation: 2*22=44, Resulting Numbers: [74, 44]\nGenerated Node #3: [74, 44] from Operation: 2*22=44\nCurrent State: 30:[74, 44], Operations: ['4+70=74', '2*22=44']\nExploring Operation: 74-44=30, Resulting Numbers: [30]\n30,30 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 32, + 9, + 38, + 11 + ], + "target": 45, + "solution": [ + "38-32=6", + "11-6=5", + "9*5=45" + ], + "optimal_path": "Current State: 45:[32, 9, 38, 11], Operations: []\nExploring Operation: 38-32=6, Resulting Numbers: [9, 11, 6]\nGenerated Node #2: [9, 11, 6] from Operation: 38-32=6\nCurrent State: 45:[9, 11, 6], Operations: ['38-32=6']\nExploring Operation: 11-6=5, Resulting Numbers: [9, 5]\nGenerated Node #3: [9, 5] from Operation: 11-6=5\nCurrent State: 45:[9, 5], Operations: ['38-32=6', '11-6=5']\nExploring Operation: 9*5=45, Resulting Numbers: [45]\n45,45 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 80, + 44, + 30, + 16 + ], + "target": 22, + "solution": [ + "80-44=36", + "30-16=14", + "36-14=22" + ], + "optimal_path": "Current State: 22:[80, 44, 30, 16], Operations: []\nExploring Operation: 80-44=36, Resulting Numbers: [30, 16, 36]\nGenerated Node #2: [30, 16, 36] from Operation: 80-44=36\nCurrent State: 22:[30, 16, 36], Operations: ['80-44=36']\nExploring Operation: 30-16=14, Resulting Numbers: [36, 14]\nGenerated Node #3: [36, 14] from Operation: 30-16=14\nCurrent State: 22:[36, 14], Operations: ['80-44=36', '30-16=14']\nExploring Operation: 36-14=22, Resulting Numbers: [22]\n22,22 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 64, + 78, + 65, + 36 + ], + "target": 87, + "solution": [ + "78-64=14", + "65+36=101", + "101-14=87" + ], + "optimal_path": "Current State: 87:[64, 78, 65, 36], Operations: []\nExploring Operation: 78-64=14, Resulting Numbers: [65, 36, 14]\nGenerated Node #2: [65, 36, 14] from Operation: 78-64=14\nCurrent State: 87:[65, 36, 14], Operations: ['78-64=14']\nExploring Operation: 65+36=101, Resulting Numbers: [14, 101]\nGenerated Node #3: [14, 101] from Operation: 65+36=101\nCurrent State: 87:[14, 101], Operations: ['78-64=14', '65+36=101']\nExploring Operation: 101-14=87, Resulting Numbers: [87]\n87,87 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 5, + 3, + 1, + 54 + ], + "target": 52, + "solution": [ + "5-3=2", + "1*54=54", + "54-2=52" + ], + "optimal_path": "Current State: 52:[5, 3, 1, 54], Operations: []\nExploring Operation: 5-3=2, Resulting Numbers: [1, 54, 2]\nGenerated Node #2: [1, 54, 2] from Operation: 5-3=2\nCurrent State: 52:[1, 54, 2], Operations: ['5-3=2']\nExploring Operation: 1*54=54, Resulting Numbers: [2, 54]\nGenerated Node #3: [2, 54] from Operation: 1*54=54\nCurrent State: 52:[2, 54], Operations: ['5-3=2', '1*54=54']\nExploring Operation: 54-2=52, Resulting Numbers: [52]\n52,52 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 38, + 36, + 42, + 47 + ], + "target": 97, + "solution": [ + "42-38=4", + "36*4=144", + "144-47=97" + ], + "optimal_path": "Current State: 97:[38, 36, 42, 47], Operations: []\nExploring Operation: 42-38=4, Resulting Numbers: [36, 47, 4]\nGenerated Node #2: [36, 47, 4] from Operation: 42-38=4\nCurrent State: 97:[36, 47, 4], Operations: ['42-38=4']\nExploring Operation: 36*4=144, Resulting Numbers: [47, 144]\nGenerated Node #3: [47, 144] from Operation: 36*4=144\nCurrent State: 97:[47, 144], Operations: ['42-38=4', '36*4=144']\nExploring Operation: 144-47=97, Resulting Numbers: [97]\n97,97 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 39, + 28, + 76, + 9 + ], + "target": 23, + "solution": [ + "39-28=11", + "9*11=99", + "99-76=23" + ], + "optimal_path": "Current State: 23:[39, 28, 76, 9], Operations: []\nExploring Operation: 39-28=11, Resulting Numbers: [76, 9, 11]\nGenerated Node #2: [76, 9, 11] from Operation: 39-28=11\nCurrent State: 23:[76, 9, 11], Operations: ['39-28=11']\nExploring Operation: 9*11=99, Resulting Numbers: [76, 99]\nGenerated Node #3: [76, 99] from Operation: 9*11=99\nCurrent State: 23:[76, 99], Operations: ['39-28=11', '9*11=99']\nExploring Operation: 99-76=23, Resulting Numbers: [23]\n23,23 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 5, + 84, + 14, + 73 + ], + "target": 99, + "solution": [ + "14-5=9", + "84-73=11", + "9*11=99" + ], + "optimal_path": "Current State: 99:[5, 84, 14, 73], Operations: []\nExploring Operation: 14-5=9, Resulting Numbers: [84, 73, 9]\nGenerated Node #2: [84, 73, 9] from Operation: 14-5=9\nCurrent State: 99:[84, 73, 9], Operations: ['14-5=9']\nExploring Operation: 84-73=11, Resulting Numbers: [9, 11]\nGenerated Node #3: [9, 11] from Operation: 84-73=11\nCurrent State: 99:[9, 11], Operations: ['14-5=9', '84-73=11']\nExploring Operation: 9*11=99, Resulting Numbers: [99]\n99,99 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 2, + 79, + 45, + 21 + ], + "target": 31, + "solution": [ + "45-21=24", + "2*24=48", + "79-48=31" + ], + "optimal_path": "Current State: 31:[2, 79, 45, 21], Operations: []\nExploring Operation: 45-21=24, Resulting Numbers: [2, 79, 24]\nGenerated Node #2: [2, 79, 24] from Operation: 45-21=24\nCurrent State: 31:[2, 79, 24], Operations: ['45-21=24']\nExploring Operation: 2*24=48, Resulting Numbers: [79, 48]\nGenerated Node #3: [79, 48] from Operation: 2*24=48\nCurrent State: 31:[79, 48], Operations: ['45-21=24', '2*24=48']\nExploring Operation: 79-48=31, Resulting Numbers: [31]\n31,31 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 33, + 26, + 8, + 16 + ], + "target": 14, + "solution": [ + "33-26=7", + "16/8=2", + "7*2=14" + ], + "optimal_path": "Current State: 14:[33, 26, 8, 16], Operations: []\nExploring Operation: 33-26=7, Resulting Numbers: [8, 16, 7]\nGenerated Node #2: [8, 16, 7] from Operation: 33-26=7\nCurrent State: 14:[8, 16, 7], Operations: ['33-26=7']\nExploring Operation: 16/8=2, Resulting Numbers: [7, 2]\nGenerated Node #3: [7, 2] from Operation: 16/8=2\nCurrent State: 14:[7, 2], Operations: ['33-26=7', '16/8=2']\nExploring Operation: 7*2=14, Resulting Numbers: [14]\n14,14 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 53, + 73, + 5, + 26 + ], + "target": 11, + "solution": [ + "73-53=20", + "5+26=31", + "31-20=11" + ], + "optimal_path": "Current State: 11:[53, 73, 5, 26], Operations: []\nExploring Operation: 73-53=20, Resulting Numbers: [5, 26, 20]\nGenerated Node #2: [5, 26, 20] from Operation: 73-53=20\nCurrent State: 11:[5, 26, 20], Operations: ['73-53=20']\nExploring Operation: 5+26=31, Resulting Numbers: [20, 31]\nGenerated Node #3: [20, 31] from Operation: 5+26=31\nCurrent State: 11:[20, 31], Operations: ['73-53=20', '5+26=31']\nExploring Operation: 31-20=11, Resulting Numbers: [11]\n11,11 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 59, + 3, + 86, + 61 + ], + "target": 38, + "solution": [ + "59+86=145", + "3*61=183", + "183-145=38" + ], + "optimal_path": "Current State: 38:[59, 3, 86, 61], Operations: []\nExploring Operation: 59+86=145, Resulting Numbers: [3, 61, 145]\nGenerated Node #2: [3, 61, 145] from Operation: 59+86=145\nCurrent State: 38:[3, 61, 145], Operations: ['59+86=145']\nExploring Operation: 3*61=183, Resulting Numbers: [145, 183]\nGenerated Node #3: [145, 183] from Operation: 3*61=183\nCurrent State: 38:[145, 183], Operations: ['59+86=145', '3*61=183']\nExploring Operation: 183-145=38, Resulting Numbers: [38]\n38,38 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 75, + 73, + 90, + 48 + ], + "target": 10, + "solution": [ + "75+73=148", + "90+48=138", + "148-138=10" + ], + "optimal_path": "Current State: 10:[75, 73, 90, 48], Operations: []\nExploring Operation: 75+73=148, Resulting Numbers: [90, 48, 148]\nGenerated Node #2: [90, 48, 148] from Operation: 75+73=148\nCurrent State: 10:[90, 48, 148], Operations: ['75+73=148']\nExploring Operation: 90+48=138, Resulting Numbers: [148, 138]\nGenerated Node #3: [148, 138] from Operation: 90+48=138\nCurrent State: 10:[148, 138], Operations: ['75+73=148', '90+48=138']\nExploring Operation: 148-138=10, Resulting Numbers: [10]\n10,10 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 47, + 70, + 30, + 14 + ], + "target": 41, + "solution": [ + "70/14=5", + "30/5=6", + "47-6=41" + ], + "optimal_path": "Current State: 41:[47, 70, 30, 14], Operations: []\nExploring Operation: 70/14=5, Resulting Numbers: [47, 30, 5]\nGenerated Node #2: [47, 30, 5] from Operation: 70/14=5\nCurrent State: 41:[47, 30, 5], Operations: ['70/14=5']\nExploring Operation: 30/5=6, Resulting Numbers: [47, 6]\nGenerated Node #3: [47, 6] from Operation: 30/5=6\nCurrent State: 41:[47, 6], Operations: ['70/14=5', '30/5=6']\nExploring Operation: 47-6=41, Resulting Numbers: [41]\n41,41 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 8, + 44, + 33, + 44 + ], + "target": 41, + "solution": [ + "8+44=52", + "44-33=11", + "52-11=41" + ], + "optimal_path": "Current State: 41:[8, 44, 33, 44], Operations: []\nExploring Operation: 8+44=52, Resulting Numbers: [33, 52]\nGenerated Node #2: [33, 52] from Operation: 8+44=52\nCurrent State: 41:[33, 52], Operations: ['8+44=52']\nExploring Operation: 44-33=11, Resulting Numbers: [52, 11]\nGenerated Node #3: [52, 11] from Operation: 44-33=11\nCurrent State: 41:[52, 11], Operations: ['8+44=52', '44-33=11']\nExploring Operation: 52-11=41, Resulting Numbers: [41]\n41,41 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 37, + 80, + 98, + 75 + ], + "target": 27, + "solution": [ + "37+98=135", + "80-75=5", + "135/5=27" + ], + "optimal_path": "Current State: 27:[37, 80, 98, 75], Operations: []\nExploring Operation: 37+98=135, Resulting Numbers: [80, 75, 135]\nGenerated Node #2: [80, 75, 135] from Operation: 37+98=135\nCurrent State: 27:[80, 75, 135], Operations: ['37+98=135']\nExploring Operation: 80-75=5, Resulting Numbers: [135, 5]\nGenerated Node #3: [135, 5] from Operation: 80-75=5\nCurrent State: 27:[135, 5], Operations: ['37+98=135', '80-75=5']\nExploring Operation: 135/5=27, Resulting Numbers: [27]\n27,27 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 39, + 19, + 40, + 79 + ], + "target": 99, + "solution": [ + "39-19=20", + "40+79=119", + "119-20=99" + ], + "optimal_path": "Current State: 99:[39, 19, 40, 79], Operations: []\nExploring Operation: 39-19=20, Resulting Numbers: [40, 79, 20]\nGenerated Node #2: [40, 79, 20] from Operation: 39-19=20\nCurrent State: 99:[40, 79, 20], Operations: ['39-19=20']\nExploring Operation: 40+79=119, Resulting Numbers: [20, 119]\nGenerated Node #3: [20, 119] from Operation: 40+79=119\nCurrent State: 99:[20, 119], Operations: ['39-19=20', '40+79=119']\nExploring Operation: 119-20=99, Resulting Numbers: [99]\n99,99 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 57, + 76, + 78, + 44 + ], + "target": 35, + "solution": [ + "78-76=2", + "44/2=22", + "57-22=35" + ], + "optimal_path": "Current State: 35:[57, 76, 78, 44], Operations: []\nExploring Operation: 78-76=2, Resulting Numbers: [57, 44, 2]\nGenerated Node #2: [57, 44, 2] from Operation: 78-76=2\nCurrent State: 35:[57, 44, 2], Operations: ['78-76=2']\nExploring Operation: 44/2=22, Resulting Numbers: [57, 22]\nGenerated Node #3: [57, 22] from Operation: 44/2=22\nCurrent State: 35:[57, 22], Operations: ['78-76=2', '44/2=22']\nExploring Operation: 57-22=35, Resulting Numbers: [35]\n35,35 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 24, + 5, + 2, + 57 + ], + "target": 74, + "solution": [ + "24-5=19", + "57-2=55", + "19+55=74" + ], + "optimal_path": "Current State: 74:[24, 5, 2, 57], Operations: []\nExploring Operation: 24-5=19, Resulting Numbers: [2, 57, 19]\nGenerated Node #2: [2, 57, 19] from Operation: 24-5=19\nCurrent State: 74:[2, 57, 19], Operations: ['24-5=19']\nExploring Operation: 57-2=55, Resulting Numbers: [19, 55]\nGenerated Node #3: [19, 55] from Operation: 57-2=55\nCurrent State: 74:[19, 55], Operations: ['24-5=19', '57-2=55']\nExploring Operation: 19+55=74, Resulting Numbers: [74]\n74,74 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 30, + 45, + 87, + 40 + ], + "target": 62, + "solution": [ + "45-30=15", + "87-40=47", + "15+47=62" + ], + "optimal_path": "Current State: 62:[30, 45, 87, 40], Operations: []\nExploring Operation: 45-30=15, Resulting Numbers: [87, 40, 15]\nGenerated Node #2: [87, 40, 15] from Operation: 45-30=15\nCurrent State: 62:[87, 40, 15], Operations: ['45-30=15']\nExploring Operation: 87-40=47, Resulting Numbers: [15, 47]\nGenerated Node #3: [15, 47] from Operation: 87-40=47\nCurrent State: 62:[15, 47], Operations: ['45-30=15', '87-40=47']\nExploring Operation: 15+47=62, Resulting Numbers: [62]\n62,62 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 24, + 61, + 82, + 3 + ], + "target": 17, + "solution": [ + "82-61=21", + "21/3=7", + "24-7=17" + ], + "optimal_path": "Current State: 17:[24, 61, 82, 3], Operations: []\nExploring Operation: 82-61=21, Resulting Numbers: [24, 3, 21]\nGenerated Node #2: [24, 3, 21] from Operation: 82-61=21\nCurrent State: 17:[24, 3, 21], Operations: ['82-61=21']\nExploring Operation: 21/3=7, Resulting Numbers: [24, 7]\nGenerated Node #3: [24, 7] from Operation: 21/3=7\nCurrent State: 17:[24, 7], Operations: ['82-61=21', '21/3=7']\nExploring Operation: 24-7=17, Resulting Numbers: [17]\n17,17 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 52, + 42, + 8, + 39 + ], + "target": 57, + "solution": [ + "52-42=10", + "8+39=47", + "10+47=57" + ], + "optimal_path": "Current State: 57:[52, 42, 8, 39], Operations: []\nExploring Operation: 52-42=10, Resulting Numbers: [8, 39, 10]\nGenerated Node #2: [8, 39, 10] from Operation: 52-42=10\nCurrent State: 57:[8, 39, 10], Operations: ['52-42=10']\nExploring Operation: 8+39=47, Resulting Numbers: [10, 47]\nGenerated Node #3: [10, 47] from Operation: 8+39=47\nCurrent State: 57:[10, 47], Operations: ['52-42=10', '8+39=47']\nExploring Operation: 10+47=57, Resulting Numbers: [57]\n57,57 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 42, + 17, + 67, + 9 + ], + "target": 51, + "solution": [ + "42-17=25", + "67+9=76", + "76-25=51" + ], + "optimal_path": "Current State: 51:[42, 17, 67, 9], Operations: []\nExploring Operation: 42-17=25, Resulting Numbers: [67, 9, 25]\nGenerated Node #2: [67, 9, 25] from Operation: 42-17=25\nCurrent State: 51:[67, 9, 25], Operations: ['42-17=25']\nExploring Operation: 67+9=76, Resulting Numbers: [25, 76]\nGenerated Node #3: [25, 76] from Operation: 67+9=76\nCurrent State: 51:[25, 76], Operations: ['42-17=25', '67+9=76']\nExploring Operation: 76-25=51, Resulting Numbers: [51]\n51,51 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 59, + 44, + 55, + 69 + ], + "target": 29, + "solution": [ + "59-44=15", + "69-55=14", + "15+14=29" + ], + "optimal_path": "Current State: 29:[59, 44, 55, 69], Operations: []\nExploring Operation: 59-44=15, Resulting Numbers: [55, 69, 15]\nGenerated Node #2: [55, 69, 15] from Operation: 59-44=15\nCurrent State: 29:[55, 69, 15], Operations: ['59-44=15']\nExploring Operation: 69-55=14, Resulting Numbers: [15, 14]\nGenerated Node #3: [15, 14] from Operation: 69-55=14\nCurrent State: 29:[15, 14], Operations: ['59-44=15', '69-55=14']\nExploring Operation: 15+14=29, Resulting Numbers: [29]\n29,29 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 83, + 73, + 93, + 7 + ], + "target": 56, + "solution": [ + "83+73=156", + "93+7=100", + "156-100=56" + ], + "optimal_path": "Current State: 56:[83, 73, 93, 7], Operations: []\nExploring Operation: 83+73=156, Resulting Numbers: [93, 7, 156]\nGenerated Node #2: [93, 7, 156] from Operation: 83+73=156\nCurrent State: 56:[93, 7, 156], Operations: ['83+73=156']\nExploring Operation: 93+7=100, Resulting Numbers: [156, 100]\nGenerated Node #3: [156, 100] from Operation: 93+7=100\nCurrent State: 56:[156, 100], Operations: ['83+73=156', '93+7=100']\nExploring Operation: 156-100=56, Resulting Numbers: [56]\n56,56 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 45, + 12, + 56, + 39 + ], + "target": 93, + "solution": [ + "56-45=11", + "12*11=132", + "132-39=93" + ], + "optimal_path": "Current State: 93:[45, 12, 56, 39], Operations: []\nExploring Operation: 56-45=11, Resulting Numbers: [12, 39, 11]\nGenerated Node #2: [12, 39, 11] from Operation: 56-45=11\nCurrent State: 93:[12, 39, 11], Operations: ['56-45=11']\nExploring Operation: 12*11=132, Resulting Numbers: [39, 132]\nGenerated Node #3: [39, 132] from Operation: 12*11=132\nCurrent State: 93:[39, 132], Operations: ['56-45=11', '12*11=132']\nExploring Operation: 132-39=93, Resulting Numbers: [93]\n93,93 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 8, + 90, + 80, + 36 + ], + "target": 45, + "solution": [ + "8*90=720", + "720/80=9", + "36+9=45" + ], + "optimal_path": "Current State: 45:[8, 90, 80, 36], Operations: []\nExploring Operation: 8*90=720, Resulting Numbers: [80, 36, 720]\nGenerated Node #2: [80, 36, 720] from Operation: 8*90=720\nCurrent State: 45:[80, 36, 720], Operations: ['8*90=720']\nExploring Operation: 720/80=9, Resulting Numbers: [36, 9]\nGenerated Node #3: [36, 9] from Operation: 720/80=9\nCurrent State: 45:[36, 9], Operations: ['8*90=720', '720/80=9']\nExploring Operation: 36+9=45, Resulting Numbers: [45]\n45,45 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 4, + 19, + 72, + 81 + ], + "target": 55, + "solution": [ + "81-72=9", + "4*9=36", + "19+36=55" + ], + "optimal_path": "Current State: 55:[4, 19, 72, 81], Operations: []\nExploring Operation: 81-72=9, Resulting Numbers: [4, 19, 9]\nGenerated Node #2: [4, 19, 9] from Operation: 81-72=9\nCurrent State: 55:[4, 19, 9], Operations: ['81-72=9']\nExploring Operation: 4*9=36, Resulting Numbers: [19, 36]\nGenerated Node #3: [19, 36] from Operation: 4*9=36\nCurrent State: 55:[19, 36], Operations: ['81-72=9', '4*9=36']\nExploring Operation: 19+36=55, Resulting Numbers: [55]\n55,55 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 68, + 98, + 95, + 97 + ], + "target": 83, + "solution": [ + "68+98=166", + "97-95=2", + "166/2=83" + ], + "optimal_path": "Current State: 83:[68, 98, 95, 97], Operations: []\nExploring Operation: 68+98=166, Resulting Numbers: [95, 97, 166]\nGenerated Node #2: [95, 97, 166] from Operation: 68+98=166\nCurrent State: 83:[95, 97, 166], Operations: ['68+98=166']\nExploring Operation: 97-95=2, Resulting Numbers: [166, 2]\nGenerated Node #3: [166, 2] from Operation: 97-95=2\nCurrent State: 83:[166, 2], Operations: ['68+98=166', '97-95=2']\nExploring Operation: 166/2=83, Resulting Numbers: [83]\n83,83 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 11, + 92, + 56, + 17 + ], + "target": 90, + "solution": [ + "11+17=28", + "56/28=2", + "92-2=90" + ], + "optimal_path": "Current State: 90:[11, 92, 56, 17], Operations: []\nExploring Operation: 11+17=28, Resulting Numbers: [92, 56, 28]\nGenerated Node #2: [92, 56, 28] from Operation: 11+17=28\nCurrent State: 90:[92, 56, 28], Operations: ['11+17=28']\nExploring Operation: 56/28=2, Resulting Numbers: [92, 2]\nGenerated Node #3: [92, 2] from Operation: 56/28=2\nCurrent State: 90:[92, 2], Operations: ['11+17=28', '56/28=2']\nExploring Operation: 92-2=90, Resulting Numbers: [90]\n90,90 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 22, + 20, + 60, + 16 + ], + "target": 18, + "solution": [ + "22-16=6", + "60/20=3", + "6*3=18" + ], + "optimal_path": "Current State: 18:[22, 20, 60, 16], Operations: []\nExploring Operation: 22-16=6, Resulting Numbers: [20, 60, 6]\nGenerated Node #2: [20, 60, 6] from Operation: 22-16=6\nCurrent State: 18:[20, 60, 6], Operations: ['22-16=6']\nExploring Operation: 60/20=3, Resulting Numbers: [6, 3]\nGenerated Node #3: [6, 3] from Operation: 60/20=3\nCurrent State: 18:[6, 3], Operations: ['22-16=6', '60/20=3']\nExploring Operation: 6*3=18, Resulting Numbers: [18]\n18,18 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 49, + 21, + 4, + 55 + ], + "target": 48, + "solution": [ + "49-21=28", + "28/4=7", + "55-7=48" + ], + "optimal_path": "Current State: 48:[49, 21, 4, 55], Operations: []\nExploring Operation: 49-21=28, Resulting Numbers: [4, 55, 28]\nGenerated Node #2: [4, 55, 28] from Operation: 49-21=28\nCurrent State: 48:[4, 55, 28], Operations: ['49-21=28']\nExploring Operation: 28/4=7, Resulting Numbers: [55, 7]\nGenerated Node #3: [55, 7] from Operation: 28/4=7\nCurrent State: 48:[55, 7], Operations: ['49-21=28', '28/4=7']\nExploring Operation: 55-7=48, Resulting Numbers: [48]\n48,48 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 1, + 60, + 31, + 20 + ], + "target": 49, + "solution": [ + "1*60=60", + "31-20=11", + "60-11=49" + ], + "optimal_path": "Current State: 49:[1, 60, 31, 20], Operations: []\nExploring Operation: 1*60=60, Resulting Numbers: [31, 20, 60]\nGenerated Node #2: [31, 20, 60] from Operation: 1*60=60\nCurrent State: 49:[31, 20, 60], Operations: ['1*60=60']\nExploring Operation: 31-20=11, Resulting Numbers: [60, 11]\nGenerated Node #3: [60, 11] from Operation: 31-20=11\nCurrent State: 49:[60, 11], Operations: ['1*60=60', '31-20=11']\nExploring Operation: 60-11=49, Resulting Numbers: [49]\n49,49 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 31, + 6, + 37, + 89 + ], + "target": 17, + "solution": [ + "31+89=120", + "120/6=20", + "37-20=17" + ], + "optimal_path": "Current State: 17:[31, 6, 37, 89], Operations: []\nExploring Operation: 31+89=120, Resulting Numbers: [6, 37, 120]\nGenerated Node #2: [6, 37, 120] from Operation: 31+89=120\nCurrent State: 17:[6, 37, 120], Operations: ['31+89=120']\nExploring Operation: 120/6=20, Resulting Numbers: [37, 20]\nGenerated Node #3: [37, 20] from Operation: 120/6=20\nCurrent State: 17:[37, 20], Operations: ['31+89=120', '120/6=20']\nExploring Operation: 37-20=17, Resulting Numbers: [17]\n17,17 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 36, + 13, + 15, + 2 + ], + "target": 78, + "solution": [ + "15*2=30", + "36-30=6", + "13*6=78" + ], + "optimal_path": "Current State: 78:[36, 13, 15, 2], Operations: []\nExploring Operation: 15*2=30, Resulting Numbers: [36, 13, 30]\nGenerated Node #2: [36, 13, 30] from Operation: 15*2=30\nCurrent State: 78:[36, 13, 30], Operations: ['15*2=30']\nExploring Operation: 36-30=6, Resulting Numbers: [13, 6]\nGenerated Node #3: [13, 6] from Operation: 36-30=6\nCurrent State: 78:[13, 6], Operations: ['15*2=30', '36-30=6']\nExploring Operation: 13*6=78, Resulting Numbers: [78]\n78,78 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 95, + 22, + 21, + 96 + ], + "target": 44, + "solution": [ + "95-22=73", + "21+96=117", + "117-73=44" + ], + "optimal_path": "Current State: 44:[95, 22, 21, 96], Operations: []\nExploring Operation: 95-22=73, Resulting Numbers: [21, 96, 73]\nGenerated Node #2: [21, 96, 73] from Operation: 95-22=73\nCurrent State: 44:[21, 96, 73], Operations: ['95-22=73']\nExploring Operation: 21+96=117, Resulting Numbers: [73, 117]\nGenerated Node #3: [73, 117] from Operation: 21+96=117\nCurrent State: 44:[73, 117], Operations: ['95-22=73', '21+96=117']\nExploring Operation: 117-73=44, Resulting Numbers: [44]\n44,44 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 70, + 82, + 20, + 42 + ], + "target": 72, + "solution": [ + "82-42=40", + "40/20=2", + "70+2=72" + ], + "optimal_path": "Current State: 72:[70, 82, 20, 42], Operations: []\nExploring Operation: 82-42=40, Resulting Numbers: [70, 20, 40]\nGenerated Node #2: [70, 20, 40] from Operation: 82-42=40\nCurrent State: 72:[70, 20, 40], Operations: ['82-42=40']\nExploring Operation: 40/20=2, Resulting Numbers: [70, 2]\nGenerated Node #3: [70, 2] from Operation: 40/20=2\nCurrent State: 72:[70, 2], Operations: ['82-42=40', '40/20=2']\nExploring Operation: 70+2=72, Resulting Numbers: [72]\n72,72 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 2, + 72, + 64, + 61 + ], + "target": 48, + "solution": [ + "2*72=144", + "64-61=3", + "144/3=48" + ], + "optimal_path": "Current State: 48:[2, 72, 64, 61], Operations: []\nExploring Operation: 2*72=144, Resulting Numbers: [64, 61, 144]\nGenerated Node #2: [64, 61, 144] from Operation: 2*72=144\nCurrent State: 48:[64, 61, 144], Operations: ['2*72=144']\nExploring Operation: 64-61=3, Resulting Numbers: [144, 3]\nGenerated Node #3: [144, 3] from Operation: 64-61=3\nCurrent State: 48:[144, 3], Operations: ['2*72=144', '64-61=3']\nExploring Operation: 144/3=48, Resulting Numbers: [48]\n48,48 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 1, + 97, + 99, + 28 + ], + "target": 58, + "solution": [ + "1+28=29", + "99-97=2", + "29*2=58" + ], + "optimal_path": "Current State: 58:[1, 97, 99, 28], Operations: []\nExploring Operation: 1+28=29, Resulting Numbers: [97, 99, 29]\nGenerated Node #2: [97, 99, 29] from Operation: 1+28=29\nCurrent State: 58:[97, 99, 29], Operations: ['1+28=29']\nExploring Operation: 99-97=2, Resulting Numbers: [29, 2]\nGenerated Node #3: [29, 2] from Operation: 99-97=2\nCurrent State: 58:[29, 2], Operations: ['1+28=29', '99-97=2']\nExploring Operation: 29*2=58, Resulting Numbers: [58]\n58,58 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 73, + 41, + 13, + 4 + ], + "target": 21, + "solution": [ + "73-41=32", + "32/4=8", + "13+8=21" + ], + "optimal_path": "Current State: 21:[73, 41, 13, 4], Operations: []\nExploring Operation: 73-41=32, Resulting Numbers: [13, 4, 32]\nGenerated Node #2: [13, 4, 32] from Operation: 73-41=32\nCurrent State: 21:[13, 4, 32], Operations: ['73-41=32']\nExploring Operation: 32/4=8, Resulting Numbers: [13, 8]\nGenerated Node #3: [13, 8] from Operation: 32/4=8\nCurrent State: 21:[13, 8], Operations: ['73-41=32', '32/4=8']\nExploring Operation: 13+8=21, Resulting Numbers: [21]\n21,21 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 36, + 89, + 38, + 37 + ], + "target": 52, + "solution": [ + "89-36=53", + "38-37=1", + "53-1=52" + ], + "optimal_path": "Current State: 52:[36, 89, 38, 37], Operations: []\nExploring Operation: 89-36=53, Resulting Numbers: [38, 37, 53]\nGenerated Node #2: [38, 37, 53] from Operation: 89-36=53\nCurrent State: 52:[38, 37, 53], Operations: ['89-36=53']\nExploring Operation: 38-37=1, Resulting Numbers: [53, 1]\nGenerated Node #3: [53, 1] from Operation: 38-37=1\nCurrent State: 52:[53, 1], Operations: ['89-36=53', '38-37=1']\nExploring Operation: 53-1=52, Resulting Numbers: [52]\n52,52 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 8, + 5, + 9, + 2 + ], + "target": 34, + "solution": [ + "9-5=4", + "8*4=32", + "2+32=34" + ], + "optimal_path": "Current State: 34:[8, 5, 9, 2], Operations: []\nExploring Operation: 9-5=4, Resulting Numbers: [8, 2, 4]\nGenerated Node #2: [8, 2, 4] from Operation: 9-5=4\nCurrent State: 34:[8, 2, 4], Operations: ['9-5=4']\nExploring Operation: 8*4=32, Resulting Numbers: [2, 32]\nGenerated Node #3: [2, 32] from Operation: 8*4=32\nCurrent State: 34:[2, 32], Operations: ['9-5=4', '8*4=32']\nExploring Operation: 2+32=34, Resulting Numbers: [34]\n34,34 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 9, + 78, + 1, + 33 + ], + "target": 55, + "solution": [ + "9+78=87", + "33-1=32", + "87-32=55" + ], + "optimal_path": "Current State: 55:[9, 78, 1, 33], Operations: []\nExploring Operation: 9+78=87, Resulting Numbers: [1, 33, 87]\nGenerated Node #2: [1, 33, 87] from Operation: 9+78=87\nCurrent State: 55:[1, 33, 87], Operations: ['9+78=87']\nExploring Operation: 33-1=32, Resulting Numbers: [87, 32]\nGenerated Node #3: [87, 32] from Operation: 33-1=32\nCurrent State: 55:[87, 32], Operations: ['9+78=87', '33-1=32']\nExploring Operation: 87-32=55, Resulting Numbers: [55]\n55,55 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 51, + 97, + 93, + 41 + ], + "target": 97, + "solution": [ + "93-51=42", + "42-41=1", + "97*1=97" + ], + "optimal_path": "Current State: 97:[51, 97, 93, 41], Operations: []\nExploring Operation: 93-51=42, Resulting Numbers: [97, 41, 42]\nGenerated Node #2: [97, 41, 42] from Operation: 93-51=42\nCurrent State: 97:[97, 41, 42], Operations: ['93-51=42']\nExploring Operation: 42-41=1, Resulting Numbers: [97, 1]\nGenerated Node #3: [97, 1] from Operation: 42-41=1\nCurrent State: 97:[97, 1], Operations: ['93-51=42', '42-41=1']\nExploring Operation: 97*1=97, Resulting Numbers: [97]\n97,97 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 91, + 79, + 83, + 11 + ], + "target": 84, + "solution": [ + "91-79=12", + "83-11=72", + "12+72=84" + ], + "optimal_path": "Current State: 84:[91, 79, 83, 11], Operations: []\nExploring Operation: 91-79=12, Resulting Numbers: [83, 11, 12]\nGenerated Node #2: [83, 11, 12] from Operation: 91-79=12\nCurrent State: 84:[83, 11, 12], Operations: ['91-79=12']\nExploring Operation: 83-11=72, Resulting Numbers: [12, 72]\nGenerated Node #3: [12, 72] from Operation: 83-11=72\nCurrent State: 84:[12, 72], Operations: ['91-79=12', '83-11=72']\nExploring Operation: 12+72=84, Resulting Numbers: [84]\n84,84 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 63, + 18, + 9, + 23 + ], + "target": 14, + "solution": [ + "63+18=81", + "81/9=9", + "23-9=14" + ], + "optimal_path": "Current State: 14:[63, 18, 9, 23], Operations: []\nExploring Operation: 63+18=81, Resulting Numbers: [9, 23, 81]\nGenerated Node #2: [9, 23, 81] from Operation: 63+18=81\nCurrent State: 14:[9, 23, 81], Operations: ['63+18=81']\nExploring Operation: 81/9=9, Resulting Numbers: [23, 9]\nGenerated Node #3: [23, 9] from Operation: 81/9=9\nCurrent State: 14:[23, 9], Operations: ['63+18=81', '81/9=9']\nExploring Operation: 23-9=14, Resulting Numbers: [14]\n14,14 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 22, + 69, + 28, + 56 + ], + "target": 94, + "solution": [ + "69-22=47", + "56/28=2", + "47*2=94" + ], + "optimal_path": "Current State: 94:[22, 69, 28, 56], Operations: []\nExploring Operation: 69-22=47, Resulting Numbers: [28, 56, 47]\nGenerated Node #2: [28, 56, 47] from Operation: 69-22=47\nCurrent State: 94:[28, 56, 47], Operations: ['69-22=47']\nExploring Operation: 56/28=2, Resulting Numbers: [47, 2]\nGenerated Node #3: [47, 2] from Operation: 56/28=2\nCurrent State: 94:[47, 2], Operations: ['69-22=47', '56/28=2']\nExploring Operation: 47*2=94, Resulting Numbers: [94]\n94,94 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 48, + 35, + 46, + 78 + ], + "target": 19, + "solution": [ + "48-35=13", + "78-46=32", + "32-13=19" + ], + "optimal_path": "Current State: 19:[48, 35, 46, 78], Operations: []\nExploring Operation: 48-35=13, Resulting Numbers: [46, 78, 13]\nGenerated Node #2: [46, 78, 13] from Operation: 48-35=13\nCurrent State: 19:[46, 78, 13], Operations: ['48-35=13']\nExploring Operation: 78-46=32, Resulting Numbers: [13, 32]\nGenerated Node #3: [13, 32] from Operation: 78-46=32\nCurrent State: 19:[13, 32], Operations: ['48-35=13', '78-46=32']\nExploring Operation: 32-13=19, Resulting Numbers: [19]\n19,19 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 69, + 29, + 27, + 71 + ], + "target": 28, + "solution": [ + "71-69=2", + "29+27=56", + "56/2=28" + ], + "optimal_path": "Current State: 28:[69, 29, 27, 71], Operations: []\nExploring Operation: 71-69=2, Resulting Numbers: [29, 27, 2]\nGenerated Node #2: [29, 27, 2] from Operation: 71-69=2\nCurrent State: 28:[29, 27, 2], Operations: ['71-69=2']\nExploring Operation: 29+27=56, Resulting Numbers: [2, 56]\nGenerated Node #3: [2, 56] from Operation: 29+27=56\nCurrent State: 28:[2, 56], Operations: ['71-69=2', '29+27=56']\nExploring Operation: 56/2=28, Resulting Numbers: [28]\n28,28 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 77, + 16, + 49, + 81 + ], + "target": 53, + "solution": [ + "81-77=4", + "16/4=4", + "49+4=53" + ], + "optimal_path": "Current State: 53:[77, 16, 49, 81], Operations: []\nExploring Operation: 81-77=4, Resulting Numbers: [16, 49, 4]\nGenerated Node #2: [16, 49, 4] from Operation: 81-77=4\nCurrent State: 53:[16, 49, 4], Operations: ['81-77=4']\nExploring Operation: 16/4=4, Resulting Numbers: [49, 4]\nGenerated Node #3: [49, 4] from Operation: 16/4=4\nCurrent State: 53:[49, 4], Operations: ['81-77=4', '16/4=4']\nExploring Operation: 49+4=53, Resulting Numbers: [53]\n53,53 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 31, + 92, + 48, + 48 + ], + "target": 27, + "solution": [ + "31+92=123", + "48+48=96", + "123-96=27" + ], + "optimal_path": "Current State: 27:[31, 92, 48, 48], Operations: []\nExploring Operation: 31+92=123, Resulting Numbers: [48, 48, 123]\nGenerated Node #2: [48, 48, 123] from Operation: 31+92=123\nCurrent State: 27:[48, 48, 123], Operations: ['31+92=123']\nExploring Operation: 48+48=96, Resulting Numbers: [123, 96]\nGenerated Node #3: [123, 96] from Operation: 48+48=96\nCurrent State: 27:[123, 96], Operations: ['31+92=123', '48+48=96']\nExploring Operation: 123-96=27, Resulting Numbers: [27]\n27,27 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 2, + 98, + 14, + 80 + ], + "target": 64, + "solution": [ + "98+14=112", + "112-80=32", + "2*32=64" + ], + "optimal_path": "Current State: 64:[2, 98, 14, 80], Operations: []\nExploring Operation: 98+14=112, Resulting Numbers: [2, 80, 112]\nGenerated Node #2: [2, 80, 112] from Operation: 98+14=112\nCurrent State: 64:[2, 80, 112], Operations: ['98+14=112']\nExploring Operation: 112-80=32, Resulting Numbers: [2, 32]\nGenerated Node #3: [2, 32] from Operation: 112-80=32\nCurrent State: 64:[2, 32], Operations: ['98+14=112', '112-80=32']\nExploring Operation: 2*32=64, Resulting Numbers: [64]\n64,64 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 29, + 71, + 2, + 25 + ], + "target": 98, + "solution": [ + "29+25=54", + "54/2=27", + "71+27=98" + ], + "optimal_path": "Current State: 98:[29, 71, 2, 25], Operations: []\nExploring Operation: 29+25=54, Resulting Numbers: [71, 2, 54]\nGenerated Node #2: [71, 2, 54] from Operation: 29+25=54\nCurrent State: 98:[71, 2, 54], Operations: ['29+25=54']\nExploring Operation: 54/2=27, Resulting Numbers: [71, 27]\nGenerated Node #3: [71, 27] from Operation: 54/2=27\nCurrent State: 98:[71, 27], Operations: ['29+25=54', '54/2=27']\nExploring Operation: 71+27=98, Resulting Numbers: [98]\n98,98 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 49, + 94, + 36, + 4 + ], + "target": 85, + "solution": [ + "94-49=45", + "36+4=40", + "45+40=85" + ], + "optimal_path": "Current State: 85:[49, 94, 36, 4], Operations: []\nExploring Operation: 94-49=45, Resulting Numbers: [36, 4, 45]\nGenerated Node #2: [36, 4, 45] from Operation: 94-49=45\nCurrent State: 85:[36, 4, 45], Operations: ['94-49=45']\nExploring Operation: 36+4=40, Resulting Numbers: [45, 40]\nGenerated Node #3: [45, 40] from Operation: 36+4=40\nCurrent State: 85:[45, 40], Operations: ['94-49=45', '36+4=40']\nExploring Operation: 45+40=85, Resulting Numbers: [85]\n85,85 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 57, + 66, + 25, + 65 + ], + "target": 10, + "solution": [ + "66-57=9", + "25+65=90", + "90/9=10" + ], + "optimal_path": "Current State: 10:[57, 66, 25, 65], Operations: []\nExploring Operation: 66-57=9, Resulting Numbers: [25, 65, 9]\nGenerated Node #2: [25, 65, 9] from Operation: 66-57=9\nCurrent State: 10:[25, 65, 9], Operations: ['66-57=9']\nExploring Operation: 25+65=90, Resulting Numbers: [9, 90]\nGenerated Node #3: [9, 90] from Operation: 25+65=90\nCurrent State: 10:[9, 90], Operations: ['66-57=9', '25+65=90']\nExploring Operation: 90/9=10, Resulting Numbers: [10]\n10,10 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 5, + 3, + 68, + 33 + ], + "target": 46, + "solution": [ + "5+33=38", + "3*38=114", + "114-68=46" + ], + "optimal_path": "Current State: 46:[5, 3, 68, 33], Operations: []\nExploring Operation: 5+33=38, Resulting Numbers: [3, 68, 38]\nGenerated Node #2: [3, 68, 38] from Operation: 5+33=38\nCurrent State: 46:[3, 68, 38], Operations: ['5+33=38']\nExploring Operation: 3*38=114, Resulting Numbers: [68, 114]\nGenerated Node #3: [68, 114] from Operation: 3*38=114\nCurrent State: 46:[68, 114], Operations: ['5+33=38', '3*38=114']\nExploring Operation: 114-68=46, Resulting Numbers: [46]\n46,46 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 90, + 36, + 52, + 51 + ], + "target": 58, + "solution": [ + "51-36=15", + "90/15=6", + "52+6=58" + ], + "optimal_path": "Current State: 58:[90, 36, 52, 51], Operations: []\nExploring Operation: 51-36=15, Resulting Numbers: [90, 52, 15]\nGenerated Node #2: [90, 52, 15] from Operation: 51-36=15\nCurrent State: 58:[90, 52, 15], Operations: ['51-36=15']\nExploring Operation: 90/15=6, Resulting Numbers: [52, 6]\nGenerated Node #3: [52, 6] from Operation: 90/15=6\nCurrent State: 58:[52, 6], Operations: ['51-36=15', '90/15=6']\nExploring Operation: 52+6=58, Resulting Numbers: [58]\n58,58 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 72, + 90, + 99, + 46 + ], + "target": 71, + "solution": [ + "90-72=18", + "99-46=53", + "18+53=71" + ], + "optimal_path": "Current State: 71:[72, 90, 99, 46], Operations: []\nExploring Operation: 90-72=18, Resulting Numbers: [99, 46, 18]\nGenerated Node #2: [99, 46, 18] from Operation: 90-72=18\nCurrent State: 71:[99, 46, 18], Operations: ['90-72=18']\nExploring Operation: 99-46=53, Resulting Numbers: [18, 53]\nGenerated Node #3: [18, 53] from Operation: 99-46=53\nCurrent State: 71:[18, 53], Operations: ['90-72=18', '99-46=53']\nExploring Operation: 18+53=71, Resulting Numbers: [71]\n71,71 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 91, + 40, + 3, + 5 + ], + "target": 59, + "solution": [ + "91-40=51", + "3+5=8", + "51+8=59" + ], + "optimal_path": "Current State: 59:[91, 40, 3, 5], Operations: []\nExploring Operation: 91-40=51, Resulting Numbers: [3, 5, 51]\nGenerated Node #2: [3, 5, 51] from Operation: 91-40=51\nCurrent State: 59:[3, 5, 51], Operations: ['91-40=51']\nExploring Operation: 3+5=8, Resulting Numbers: [51, 8]\nGenerated Node #3: [51, 8] from Operation: 3+5=8\nCurrent State: 59:[51, 8], Operations: ['91-40=51', '3+5=8']\nExploring Operation: 51+8=59, Resulting Numbers: [59]\n59,59 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 90, + 23, + 55, + 1 + ], + "target": 58, + "solution": [ + "90+23=113", + "55*1=55", + "113-55=58" + ], + "optimal_path": "Current State: 58:[90, 23, 55, 1], Operations: []\nExploring Operation: 90+23=113, Resulting Numbers: [55, 1, 113]\nGenerated Node #2: [55, 1, 113] from Operation: 90+23=113\nCurrent State: 58:[55, 1, 113], Operations: ['90+23=113']\nExploring Operation: 55*1=55, Resulting Numbers: [113, 55]\nGenerated Node #3: [113, 55] from Operation: 55*1=55\nCurrent State: 58:[113, 55], Operations: ['90+23=113', '55*1=55']\nExploring Operation: 113-55=58, Resulting Numbers: [58]\n58,58 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 10, + 60, + 13, + 7 + ], + "target": 70, + "solution": [ + "60-10=50", + "13+7=20", + "50+20=70" + ], + "optimal_path": "Current State: 70:[10, 60, 13, 7], Operations: []\nExploring Operation: 60-10=50, Resulting Numbers: [13, 7, 50]\nGenerated Node #2: [13, 7, 50] from Operation: 60-10=50\nCurrent State: 70:[13, 7, 50], Operations: ['60-10=50']\nExploring Operation: 13+7=20, Resulting Numbers: [50, 20]\nGenerated Node #3: [50, 20] from Operation: 13+7=20\nCurrent State: 70:[50, 20], Operations: ['60-10=50', '13+7=20']\nExploring Operation: 50+20=70, Resulting Numbers: [70]\n70,70 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 60, + 83, + 77, + 25 + ], + "target": 90, + "solution": [ + "83-77=6", + "25*6=150", + "150-60=90" + ], + "optimal_path": "Current State: 90:[60, 83, 77, 25], Operations: []\nExploring Operation: 83-77=6, Resulting Numbers: [60, 25, 6]\nGenerated Node #2: [60, 25, 6] from Operation: 83-77=6\nCurrent State: 90:[60, 25, 6], Operations: ['83-77=6']\nExploring Operation: 25*6=150, Resulting Numbers: [60, 150]\nGenerated Node #3: [60, 150] from Operation: 25*6=150\nCurrent State: 90:[60, 150], Operations: ['83-77=6', '25*6=150']\nExploring Operation: 150-60=90, Resulting Numbers: [90]\n90,90 equal: Goal Reached\n", + "start_size": 4 + }, + { + "nums": [ + 47, + 25, + 11, + 35 + ], + "target": 68, + "solution": [ + "47-25=22", + "11+35=46", + "22+46=68" + ], + "optimal_path": "Current State: 68:[47, 25, 11, 35], Operations: []\nExploring Operation: 47-25=22, Resulting Numbers: [11, 35, 22]\nGenerated Node #2: [11, 35, 22] from Operation: 47-25=22\nCurrent State: 68:[11, 35, 22], Operations: ['47-25=22']\nExploring Operation: 11+35=46, Resulting Numbers: [22, 46]\nGenerated Node #3: [22, 46] from Operation: 11+35=46\nCurrent State: 68:[22, 46], Operations: ['47-25=22', '11+35=46']\nExploring Operation: 22+46=68, Resulting Numbers: [68]\n68,68 equal: Goal Reached\n", + "start_size": 4 + } +] \ No newline at end of file