Datasets:
Parallel-Reasoning
/
sosp_sft_data

Dataset card Data Studio Files Community
nums
listlengths
4
4
target
int64
10
100
solution
listlengths
3
3
optimal_path
stringlengths
282
529
start_size
int64
4
4
search_path
stringlengths
505
16.8k
rating
float64
0
0.99
search_type
stringclasses
5 values
heuristic
stringclasses
2 values
[ 13, 77, 11, 37 ]
43
[ "13+37=50", "77/11=7", "50-7=43" ]
Current State: 43:[13, 77, 11, 37], Operations: [] Exploring Operation: 13+37=50, Resulting Numbers: [77, 11, 50] Generated Node #2: [77, 11, 50] from Operation: 13+37=50 Current State: 43:[77, 11, 50], Operations: ['13+37=50'] Exploring Operation: 77/11=7, Resulting Numbers: [50, 7] Generated Node #3: [50, 7] from Operation: 77/11=7 Current State: 43:[50, 7], Operations: ['13+37=50', '77/11=7'] Exploring Operation: 50-7=43, Resulting Numbers: [43] 43,43 equal: Goal Reached
4
Current State: 43:[13, 77, 11, 37], Operations: [] Exploring Operation: 77-37=40, Resulting Numbers: [13, 11, 40] Generated Node #0,0: 43:[13, 11, 40] Operation: 77-37=40 Exploring Operation: 11+37=48, Resulting Numbers: [13, 77, 48] Generated Node #0,1: 43:[13, 77, 48] Operation: 11+37=48 Exploring Operation: 77-11=66, Resulting Numbers: [13, 37, 66] Generated Node #0,2: 43:[13, 37, 66] Operation: 77-11=66 Exploring Operation: 77-13=64, Resulting Numbers: [11, 37, 64] Generated Node #0,3: 43:[11, 37, 64] Operation: 77-13=64 Exploring Operation: 13+11=24, Resulting Numbers: [77, 37, 24] Generated Node #0,4: 43:[77, 37, 24] Operation: 13+11=24 Moving to Node #0,2 Current State: 43:[13, 37, 66], Operations: ['77-11=66'] Exploring Operation: 66-37=29, Resulting Numbers: [13, 29] Generated Node #0,2,0: 43:[13, 29] Operation: 66-37=29 Exploring Operation: 66-13=53, Resulting Numbers: [37, 53] Generated Node #0,2,1: 43:[37, 53] Operation: 66-13=53 Exploring Operation: 37-13=24, Resulting Numbers: [66, 24] Generated Node #0,2,2: 43:[66, 24] Operation: 37-13=24 Exploring Operation: 13+37=50, Resulting Numbers: [66, 50] Generated Node #0,2,3: 43:[66, 50] Operation: 13+37=50 Exploring Operation: 13+66=79, Resulting Numbers: [37, 79] Generated Node #0,2,4: 43:[37, 79] Operation: 13+66=79 Moving to Node #0,4 Current State: 43:[77, 37, 24], Operations: ['13+11=24'] Exploring Operation: 77-24=53, Resulting Numbers: [37, 53] Generated Node #0,4,0: 43:[37, 53] Operation: 77-24=53 Exploring Operation: 37+24=61, Resulting Numbers: [77, 61] Generated Node #0,4,1: 43:[77, 61] Operation: 37+24=61 Exploring Operation: 77+24=101, Resulting Numbers: [37, 101] Generated Node #0,4,2: 43:[37, 101] Operation: 77+24=101 Exploring Operation: 77-37=40, Resulting Numbers: [24, 40] Generated Node #0,4,3: 43:[24, 40] Operation: 77-37=40 Exploring Operation: 37-24=13, Resulting Numbers: [77, 13] Generated Node #0,4,4: 43:[77, 13] Operation: 37-24=13 Start Sub Search at level 1: Moving to Node #0,4,0 Current State: 43:[37, 53], Operations: ['13+11=24', '77-24=53'] Exploring Operation: 53-37=16, Resulting Numbers: [16] 16,43 unequal: No Solution Exploring Operation: 37+53=90, Resulting Numbers: [90] 90,43 unequal: No Solution Exploring Operation: 37*53=1961, Resulting Numbers: [1961] 1961,43 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,3 Current State: 43:[24, 40], Operations: ['13+11=24', '77-37=40'] Exploring Operation: 24*40=960, Resulting Numbers: [960] 960,43 unequal: No Solution Exploring Operation: 40-24=16, Resulting Numbers: [16] 16,43 unequal: No Solution Exploring Operation: 24+40=64, Resulting Numbers: [64] 64,43 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,1 Current State: 43:[77, 61], Operations: ['13+11=24', '37+24=61'] Exploring Operation: 77*61=4697, Resulting Numbers: [4697] 4697,43 unequal: No Solution Exploring Operation: 77-61=16, Resulting Numbers: [16] 16,43 unequal: No Solution Exploring Operation: 77+61=138, Resulting Numbers: [138] 138,43 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,2 Current State: 43:[37, 101], Operations: ['13+11=24', '77+24=101'] Exploring Operation: 101-37=64, Resulting Numbers: [64] 64,43 unequal: No Solution Exploring Operation: 37+101=138, Resulting Numbers: [138] 138,43 unequal: No Solution Exploring Operation: 37*101=3737, Resulting Numbers: [3737] 3737,43 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,4 Current State: 43:[77, 13], Operations: ['13+11=24', '37-24=13'] Exploring Operation: 77+13=90, Resulting Numbers: [90] 90,43 unequal: No Solution Exploring Operation: 77-13=64, Resulting Numbers: [64] 64,43 unequal: No Solution Exploring Operation: 77*13=1001, Resulting Numbers: [1001] 1001,43 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,3 Current State: 43:[11, 37, 64], Operations: ['77-13=64'] Exploring Operation: 37-11=26, Resulting Numbers: [64, 26] Generated Node #0,3,0: 43:[64, 26] Operation: 37-11=26 Exploring Operation: 64-11=53, Resulting Numbers: [37, 53] Generated Node #0,3,1: 43:[37, 53] Operation: 64-11=53 Exploring Operation: 11+64=75, Resulting Numbers: [37, 75] Generated Node #0,3,2: 43:[37, 75] Operation: 11+64=75 Exploring Operation: 64-37=27, Resulting Numbers: [11, 27] Generated Node #0,3,3: 43:[11, 27] Operation: 64-37=27 Exploring Operation: 11+37=48, Resulting Numbers: [64, 48] Generated Node #0,3,4: 43:[64, 48] Operation: 11+37=48 Moving to Node #0,0 Current State: 43:[13, 11, 40], Operations: ['77-37=40'] Exploring Operation: 13+40=53, Resulting Numbers: [11, 53] Generated Node #0,0,0: 43:[11, 53] Operation: 13+40=53 Exploring Operation: 13+11=24, Resulting Numbers: [40, 24] Generated Node #0,0,1: 43:[40, 24] Operation: 13+11=24 Exploring Operation: 13-11=2, Resulting Numbers: [40, 2] Generated Node #0,0,2: 43:[40, 2] Operation: 13-11=2 Exploring Operation: 40-11=29, Resulting Numbers: [13, 29] Generated Node #0,0,3: 43:[13, 29] Operation: 40-11=29 Exploring Operation: 11+40=51, Resulting Numbers: [13, 51] Generated Node #0,0,4: 43:[13, 51] Operation: 11+40=51 Moving to Node #0,1 Current State: 43:[13, 77, 48], Operations: ['11+37=48'] Exploring Operation: 77-13=64, Resulting Numbers: [48, 64] Generated Node #0,1,0: 43:[48, 64] Operation: 77-13=64 Exploring Operation: 13+48=61, Resulting Numbers: [77, 61] Generated Node #0,1,1: 43:[77, 61] Operation: 13+48=61 Exploring Operation: 77-48=29, Resulting Numbers: [13, 29] Generated Node #0,1,2: 43:[13, 29] Operation: 77-48=29 Exploring Operation: 13+77=90, Resulting Numbers: [48, 90] Generated Node #0,1,3: 43:[48, 90] Operation: 13+77=90 Exploring Operation: 48-13=35, Resulting Numbers: [77, 35] Generated Node #0,1,4: 43:[77, 35] Operation: 48-13=35 Moving to Node #0,2,1 Current State: 43:[37, 53], Operations: ['77-11=66', '66-13=53'] Exploring Operation: 53-37=16, Resulting Numbers: [16] 16,43 unequal: No Solution Exploring Operation: 37+53=90, Resulting Numbers: [90] 90,43 unequal: No Solution Exploring Operation: 37*53=1961, Resulting Numbers: [1961] 1961,43 unequal: No Solution Moving to Node #0,3,1 Current State: 43:[37, 53], Operations: ['77-13=64', '64-11=53'] Exploring Operation: 37+53=90, Resulting Numbers: [90] 90,43 unequal: No Solution Exploring Operation: 53-37=16, Resulting Numbers: [16] 16,43 unequal: No Solution Exploring Operation: 37*53=1961, Resulting Numbers: [1961] 1961,43 unequal: No Solution Moving to Node #0,0,1 Current State: 43:[40, 24], Operations: ['77-37=40', '13+11=24'] Exploring Operation: 40+24=64, Resulting Numbers: [64] 64,43 unequal: No Solution Exploring Operation: 40-24=16, Resulting Numbers: [16] 16,43 unequal: No Solution Exploring Operation: 40*24=960, Resulting Numbers: [960] 960,43 unequal: No Solution Moving to Node #0,3,4 Current State: 43:[64, 48], Operations: ['77-13=64', '11+37=48'] Exploring Operation: 64*48=3072, Resulting Numbers: [3072] 3072,43 unequal: No Solution Exploring Operation: 64+48=112, Resulting Numbers: [112] 112,43 unequal: No Solution Exploring Operation: 64-48=16, Resulting Numbers: [16] 16,43 unequal: No Solution Moving to Node #0,1,0 Current State: 43:[48, 64], Operations: ['11+37=48', '77-13=64'] Exploring Operation: 48+64=112, Resulting Numbers: [112] 112,43 unequal: No Solution Exploring Operation: 64-48=16, Resulting Numbers: [16] 16,43 unequal: No Solution Exploring Operation: 48*64=3072, Resulting Numbers: [3072] 3072,43 unequal: No Solution Moving to Node #0,2,3 Current State: 43:[66, 50], Operations: ['77-11=66', '13+37=50'] Exploring Operation: 66-50=16, Resulting Numbers: [16] 16,43 unequal: No Solution Exploring Operation: 66+50=116, Resulting Numbers: [116] 116,43 unequal: No Solution Exploring Operation: 66*50=3300, Resulting Numbers: [3300] 3300,43 unequal: No Solution Moving to Node #0,0,4 Current State: 43:[13, 51], Operations: ['77-37=40', '11+40=51'] Exploring Operation: 13+51=64, Resulting Numbers: [64] 64,43 unequal: No Solution Exploring Operation: 51-13=38, Resulting Numbers: [38] 38,43 unequal: No Solution Exploring Operation: 13*51=663, Resulting Numbers: [663] 663,43 unequal: No Solution Moving to Node #0,3,2 Current State: 43:[37, 75], Operations: ['77-13=64', '11+64=75'] Exploring Operation: 37*75=2775, Resulting Numbers: [2775] 2775,43 unequal: No Solution Exploring Operation: 37+75=112, Resulting Numbers: [112] 112,43 unequal: No Solution Exploring Operation: 75-37=38, Resulting Numbers: [38] 38,43 unequal: No Solution Moving to Node #0,3,0 Current State: 43:[64, 26], Operations: ['77-13=64', '37-11=26'] Exploring Operation: 64-26=38, Resulting Numbers: [38] 38,43 unequal: No Solution Exploring Operation: 64+26=90, Resulting Numbers: [90] 90,43 unequal: No Solution Exploring Operation: 64*26=1664, Resulting Numbers: [1664] 1664,43 unequal: No Solution Moving to Node #0,0,0 Current State: 43:[11, 53], Operations: ['77-37=40', '13+40=53'] Exploring Operation: 53-11=42, Resulting Numbers: [42] 42,43 unequal: No Solution Exploring Operation: 11+53=64, Resulting Numbers: [64] 64,43 unequal: No Solution Exploring Operation: 11*53=583, Resulting Numbers: [583] 583,43 unequal: No Solution Moving to Node #0,2,2 Current State: 43:[66, 24], Operations: ['77-11=66', '37-13=24'] Exploring Operation: 66-24=42, Resulting Numbers: [42] 42,43 unequal: No Solution Exploring Operation: 66*24=1584, Resulting Numbers: [1584] 1584,43 unequal: No Solution Exploring Operation: 66+24=90, Resulting Numbers: [90] 90,43 unequal: No Solution Moving to Node #0,1,4 Current State: 43:[77, 35], Operations: ['11+37=48', '48-13=35'] Exploring Operation: 77*35=2695, Resulting Numbers: [2695] 2695,43 unequal: No Solution Exploring Operation: 77-35=42, Resulting Numbers: [42] 42,43 unequal: No Solution Exploring Operation: 77+35=112, Resulting Numbers: [112] 112,43 unequal: No Solution Moving to Node #0,2,4 Current State: 43:[37, 79], Operations: ['77-11=66', '13+66=79'] Exploring Operation: 37*79=2923, Resulting Numbers: [2923] 2923,43 unequal: No Solution Exploring Operation: 79-37=42, Resulting Numbers: [42] 42,43 unequal: No Solution Exploring Operation: 37+79=116, Resulting Numbers: [116] 116,43 unequal: No Solution Moving to Node #0,0,3 Current State: 43:[13, 29], Operations: ['77-37=40', '40-11=29'] Exploring Operation: 13+29=42, Resulting Numbers: [42] 42,43 unequal: No Solution Exploring Operation: 29-13=16, Resulting Numbers: [16] 16,43 unequal: No Solution Exploring Operation: 13*29=377, Resulting Numbers: [377] 377,43 unequal: No Solution Moving to Node #0,0,2 Current State: 43:[40, 2], Operations: ['77-37=40', '13-11=2'] Exploring Operation: 40*2=80, Resulting Numbers: [80] 80,43 unequal: No Solution Exploring Operation: 40-2=38, Resulting Numbers: [38] 38,43 unequal: No Solution Exploring Operation: 40/2=20, Resulting Numbers: [20] 20,43 unequal: No Solution Exploring Operation: 40+2=42, Resulting Numbers: [42] 42,43 unequal: No Solution Moving to Node #0,2,0 Current State: 43:[13, 29], Operations: ['77-11=66', '66-37=29'] Exploring Operation: 13+29=42, Resulting Numbers: [42] 42,43 unequal: No Solution Exploring Operation: 13*29=377, Resulting Numbers: [377] 377,43 unequal: No Solution Exploring Operation: 29-13=16, Resulting Numbers: [16] 16,43 unequal: No Solution Moving to Node #0,1,2 Current State: 43:[13, 29], Operations: ['11+37=48', '77-48=29'] Exploring Operation: 13+29=42, Resulting Numbers: [42] 42,43 unequal: No Solution Exploring Operation: 13*29=377, Resulting Numbers: [377] 377,43 unequal: No Solution Exploring Operation: 29-13=16, Resulting Numbers: [16] 16,43 unequal: No Solution Moving to Node #0,3,3 Current State: 43:[11, 27], Operations: ['77-13=64', '64-37=27'] Exploring Operation: 27-11=16, Resulting Numbers: [16] 16,43 unequal: No Solution Exploring Operation: 11+27=38, Resulting Numbers: [38] 38,43 unequal: No Solution Exploring Operation: 11*27=297, Resulting Numbers: [297] 297,43 unequal: No Solution Moving to Node #0,1,1 Current State: 43:[77, 61], Operations: ['11+37=48', '13+48=61'] Exploring Operation: 77-61=16, Resulting Numbers: [16] 16,43 unequal: No Solution Exploring Operation: 77*61=4697, Resulting Numbers: [4697] 4697,43 unequal: No Solution Exploring Operation: 77+61=138, Resulting Numbers: [138] 138,43 unequal: No Solution Moving to Node #0,1,3 Current State: 43:[48, 90], Operations: ['11+37=48', '13+77=90'] Exploring Operation: 48*90=4320, Resulting Numbers: [4320] 4320,43 unequal: No Solution Exploring Operation: 48+90=138, Resulting Numbers: [138] 138,43 unequal: No Solution Exploring Operation: 90-48=42, Resulting Numbers: [42] 42,43 unequal: No Solution No solution found.
0
hs_5
mult_heuristic
[ 16, 75, 94, 49 ]
14
[ "75-16=59", "94-49=45", "59-45=14" ]
Current State: 14:[16, 75, 94, 49], Operations: [] Exploring Operation: 75-16=59, Resulting Numbers: [94, 49, 59] Generated Node #2: [94, 49, 59] from Operation: 75-16=59 Current State: 14:[94, 49, 59], Operations: ['75-16=59'] Exploring Operation: 94-49=45, Resulting Numbers: [59, 45] Generated Node #3: [59, 45] from Operation: 94-49=45 Current State: 14:[59, 45], Operations: ['75-16=59', '94-49=45'] Exploring Operation: 59-45=14, Resulting Numbers: [14] 14,14 equal: Goal Reached
4
Current State: 14:[16, 75, 94, 49], Operations: [] Exploring Operation: 94-16=78, Resulting Numbers: [75, 49, 78] Generated Node #0,0: 14:[75, 49, 78] Operation: 94-16=78 Exploring Operation: 75-16=59, Resulting Numbers: [94, 49, 59] Generated Node #0,1: 14:[94, 49, 59] Operation: 75-16=59 Exploring Operation: 94-75=19, Resulting Numbers: [16, 49, 19] Generated Node #0,2: 14:[16, 49, 19] Operation: 94-75=19 Exploring Operation: 75-49=26, Resulting Numbers: [16, 94, 26] Generated Node #0,3: 14:[16, 94, 26] Operation: 75-49=26 Exploring Operation: 94-49=45, Resulting Numbers: [16, 75, 45] Generated Node #0,4: 14:[16, 75, 45] Operation: 94-49=45 Moving to Node #0,2 Current State: 14:[16, 49, 19], Operations: ['94-75=19'] Exploring Operation: 16+49=65, Resulting Numbers: [19, 65] Generated Node #0,2,0: 14:[19, 65] Operation: 16+49=65 Exploring Operation: 19-16=3, Resulting Numbers: [49, 3] Generated Node #0,2,1: 14:[49, 3] Operation: 19-16=3 Exploring Operation: 49-16=33, Resulting Numbers: [19, 33] Generated Node #0,2,2: 14:[19, 33] Operation: 49-16=33 Exploring Operation: 49-19=30, Resulting Numbers: [16, 30] Generated Node #0,2,3: 14:[16, 30] Operation: 49-19=30 Exploring Operation: 16+19=35, Resulting Numbers: [49, 35] Generated Node #0,2,4: 14:[49, 35] Operation: 16+19=35 Moving to Node #0,4 Current State: 14:[16, 75, 45], Operations: ['94-49=45'] Exploring Operation: 16+75=91, Resulting Numbers: [45, 91] Generated Node #0,4,0: 14:[45, 91] Operation: 16+75=91 Exploring Operation: 75-16=59, Resulting Numbers: [45, 59] Generated Node #0,4,1: 14:[45, 59] Operation: 75-16=59 Exploring Operation: 45-16=29, Resulting Numbers: [75, 29] Generated Node #0,4,2: 14:[75, 29] Operation: 45-16=29 Exploring Operation: 16+45=61, Resulting Numbers: [75, 61] Generated Node #0,4,3: 14:[75, 61] Operation: 16+45=61 Exploring Operation: 75-45=30, Resulting Numbers: [16, 30] Generated Node #0,4,4: 14:[16, 30] Operation: 75-45=30 Moving to Node #0,3 Current State: 14:[16, 94, 26], Operations: ['75-49=26'] Exploring Operation: 94-26=68, Resulting Numbers: [16, 68] Generated Node #0,3,0: 14:[16, 68] Operation: 94-26=68 Exploring Operation: 26-16=10, Resulting Numbers: [94, 10] Generated Node #0,3,1: 14:[94, 10] Operation: 26-16=10 Exploring Operation: 16+26=42, Resulting Numbers: [94, 42] Generated Node #0,3,2: 14:[94, 42] Operation: 16+26=42 Exploring Operation: 94-16=78, Resulting Numbers: [26, 78] Generated Node #0,3,3: 14:[26, 78] Operation: 94-16=78 Exploring Operation: 16+94=110, Resulting Numbers: [26, 110] Generated Node #0,3,4: 14:[26, 110] Operation: 16+94=110 Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 14:[16, 68], Operations: ['75-49=26', '94-26=68'] Exploring Operation: 16+68=84, Resulting Numbers: [84] 84,14 unequal: No Solution Exploring Operation: 68-16=52, Resulting Numbers: [52] 52,14 unequal: No Solution Exploring Operation: 16*68=1088, Resulting Numbers: [1088] 1088,14 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 14:[26, 78], Operations: ['75-49=26', '94-16=78'] Exploring Operation: 78/26=3, Resulting Numbers: [3] 3,14 unequal: No Solution Exploring Operation: 26+78=104, Resulting Numbers: [104] 104,14 unequal: No Solution Exploring Operation: 26*78=2028, Resulting Numbers: [2028] 2028,14 unequal: No Solution Exploring Operation: 78-26=52, Resulting Numbers: [52] 52,14 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 14:[94, 10], Operations: ['75-49=26', '26-16=10'] Exploring Operation: 94-10=84, Resulting Numbers: [84] 84,14 unequal: No Solution Exploring Operation: 94+10=104, Resulting Numbers: [104] 104,14 unequal: No Solution Exploring Operation: 94*10=940, Resulting Numbers: [940] 940,14 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 14:[94, 42], Operations: ['75-49=26', '16+26=42'] Exploring Operation: 94-42=52, Resulting Numbers: [52] 52,14 unequal: No Solution Exploring Operation: 94+42=136, Resulting Numbers: [136] 136,14 unequal: No Solution Exploring Operation: 94*42=3948, Resulting Numbers: [3948] 3948,14 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,4 Current State: 14:[26, 110], Operations: ['75-49=26', '16+94=110'] Exploring Operation: 26*110=2860, Resulting Numbers: [2860] 2860,14 unequal: No Solution Exploring Operation: 26+110=136, Resulting Numbers: [136] 136,14 unequal: No Solution Exploring Operation: 110-26=84, Resulting Numbers: [84] 84,14 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,0 Current State: 14:[75, 49, 78], Operations: ['94-16=78'] Exploring Operation: 75+78=153, Resulting Numbers: [49, 153] Generated Node #0,0,0: 14:[49, 153] Operation: 75+78=153 Exploring Operation: 78-49=29, Resulting Numbers: [75, 29] Generated Node #0,0,1: 14:[75, 29] Operation: 78-49=29 Exploring Operation: 75+49=124, Resulting Numbers: [78, 124] Generated Node #0,0,2: 14:[78, 124] Operation: 75+49=124 Exploring Operation: 78-75=3, Resulting Numbers: [49, 3] Generated Node #0,0,3: 14:[49, 3] Operation: 78-75=3 Exploring Operation: 75-49=26, Resulting Numbers: [78, 26] Generated Node #0,0,4: 14:[78, 26] Operation: 75-49=26 Moving to Node #0,1 Current State: 14:[94, 49, 59], Operations: ['75-16=59'] Exploring Operation: 94-49=45, Resulting Numbers: [59, 45] Generated Node #0,1,0: 14:[59, 45] Operation: 94-49=45 Exploring Operation: 94+49=143, Resulting Numbers: [59, 143] Generated Node #0,1,1: 14:[59, 143] Operation: 94+49=143 Exploring Operation: 94+59=153, Resulting Numbers: [49, 153] Generated Node #0,1,2: 14:[49, 153] Operation: 94+59=153 Exploring Operation: 59-49=10, Resulting Numbers: [94, 10] Generated Node #0,1,3: 14:[94, 10] Operation: 59-49=10 Exploring Operation: 94-59=35, Resulting Numbers: [49, 35] Generated Node #0,1,4: 14:[49, 35] Operation: 94-59=35 Start Sub Search at level 1: Moving to Node #0,1,4 Current State: 14:[49, 35], Operations: ['75-16=59', '94-59=35'] Exploring Operation: 49-35=14, Resulting Numbers: [14] 14,14 equal: Goal Reached Moving to Node #0 Current State: 14:[16, 75, 94, 49], Operations: [] Exploring Operation: 75-16=59, Resulting Numbers: [94, 49, 59] Generated Node #0,1: 14:[94, 49, 59] Operation: 75-16=59 Moving to Node #0,1 Current State: 14:[94, 49, 59], Operations: ['75-16=59'] Exploring Operation: 94-59=35, Resulting Numbers: [49, 35] Generated Node #0,1,4: 14:[49, 35] Operation: 94-59=35 Moving to Node #0,1,4 Current State: 14:[49, 35], Operations: ['75-16=59', '94-59=35'] Exploring Operation: 49-35=14, Resulting Numbers: [14] 14,14 equal: Goal Reached Exit Sub Search at level 1
0.955729
hs_5
sum_heuristic
[ 90, 29, 68, 92 ]
18
[ "29+68=97", "97-92=5", "90/5=18" ]
Current State: 18:[90, 29, 68, 92], Operations: [] Exploring Operation: 29+68=97, Resulting Numbers: [90, 92, 97] Generated Node #2: [90, 92, 97] from Operation: 29+68=97 Current State: 18:[90, 92, 97], Operations: ['29+68=97'] Exploring Operation: 97-92=5, Resulting Numbers: [90, 5] Generated Node #3: [90, 5] from Operation: 97-92=5 Current State: 18:[90, 5], Operations: ['29+68=97', '97-92=5'] Exploring Operation: 90/5=18, Resulting Numbers: [18] 18,18 equal: Goal Reached
4
Current State: 18:[90, 29, 68, 92], Operations: [] Exploring Operation: 90-68=22, Resulting Numbers: [29, 92, 22] Generated Node #0,0: 18:[29, 92, 22] Operation: 90-68=22 Exploring Operation: 92-90=2, Resulting Numbers: [29, 68, 2] Generated Node #0,1: 18:[29, 68, 2] Operation: 92-90=2 Moving to Node #0,1 Current State: 18:[29, 68, 2], Operations: ['92-90=2'] Exploring Operation: 68-29=39, Resulting Numbers: [2, 39] Generated Node #0,1,0: 18:[2, 39] Operation: 68-29=39 Exploring Operation: 68/2=34, Resulting Numbers: [29, 34] Generated Node #0,1,1: 18:[29, 34] Operation: 68/2=34 Moving to Node #0,0 Current State: 18:[29, 92, 22], Operations: ['90-68=22'] Exploring Operation: 92-22=70, Resulting Numbers: [29, 70] Generated Node #0,0,0: 18:[29, 70] Operation: 92-22=70 Exploring Operation: 92-29=63, Resulting Numbers: [22, 63] Generated Node #0,0,1: 18:[22, 63] Operation: 92-29=63 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 18:[22, 63], Operations: ['90-68=22', '92-29=63'] Exploring Operation: 22+63=85, Resulting Numbers: [85] 85,18 unequal: No Solution Exploring Operation: 63-22=41, Resulting Numbers: [41] 41,18 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 18:[29, 70], Operations: ['90-68=22', '92-22=70'] Exploring Operation: 29+70=99, Resulting Numbers: [99] 99,18 unequal: No Solution Exploring Operation: 70-29=41, Resulting Numbers: [41] 41,18 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1,0 Current State: 18:[2, 39], Operations: ['92-90=2', '68-29=39'] Exploring Operation: 2+39=41, Resulting Numbers: [41] 41,18 unequal: No Solution Exploring Operation: 39-2=37, Resulting Numbers: [37] 37,18 unequal: No Solution Moving to Node #0,1,1 Current State: 18:[29, 34], Operations: ['92-90=2', '68/2=34'] Exploring Operation: 29+34=63, Resulting Numbers: [63] 63,18 unequal: No Solution Exploring Operation: 34-29=5, Resulting Numbers: [5] 5,18 unequal: No Solution No solution found.
0
hs_2
mult_heuristic
[ 46, 27, 16, 45 ]
23
[ "27+16=43", "45-43=2", "46/2=23" ]
Current State: 23:[46, 27, 16, 45], Operations: [] Exploring Operation: 27+16=43, Resulting Numbers: [46, 45, 43] Generated Node #2: [46, 45, 43] from Operation: 27+16=43 Current State: 23:[46, 45, 43], Operations: ['27+16=43'] Exploring Operation: 45-43=2, Resulting Numbers: [46, 2] Generated Node #3: [46, 2] from Operation: 45-43=2 Current State: 23:[46, 2], Operations: ['27+16=43', '45-43=2'] Exploring Operation: 46/2=23, Resulting Numbers: [23] 23,23 equal: Goal Reached
4
Current State: 23:[46, 27, 16, 45], Operations: [] Exploring Operation: 46-45=1, Resulting Numbers: [27, 16, 1] Generated Node #0,0: 23:[27, 16, 1] Operation: 46-45=1 Exploring Operation: 46-27=19, Resulting Numbers: [16, 45, 19] Generated Node #0,1: 23:[16, 45, 19] Operation: 46-27=19 Exploring Operation: 46-16=30, Resulting Numbers: [27, 45, 30] Generated Node #0,2: 23:[27, 45, 30] Operation: 46-16=30 Exploring Operation: 45-16=29, Resulting Numbers: [46, 27, 29] Generated Node #0,3: 23:[46, 27, 29] Operation: 45-16=29 Moving to Node #0,0 Current State: 23:[27, 16, 1], Operations: ['46-45=1'] Exploring Operation: 16+1=17, Resulting Numbers: [27, 17] Generated Node #0,0,0: 23:[27, 17] Operation: 16+1=17 Exploring Operation: 27*1=27, Resulting Numbers: [16, 27] Generated Node #0,0,1: 23:[16, 27] Operation: 27*1=27 Exploring Operation: 27/1=27, Resulting Numbers: [16, 27] Generated Node #0,0,2: 23:[16, 27] Operation: 27/1=27 Exploring Operation: 27-1=26, Resulting Numbers: [16, 26] Generated Node #0,0,3: 23:[16, 26] Operation: 27-1=26 Moving to Node #0,2 Current State: 23:[27, 45, 30], Operations: ['46-16=30'] Exploring Operation: 45-27=18, Resulting Numbers: [30, 18] Generated Node #0,2,0: 23:[30, 18] Operation: 45-27=18 Exploring Operation: 27+45=72, Resulting Numbers: [30, 72] Generated Node #0,2,1: 23:[30, 72] Operation: 27+45=72 Exploring Operation: 30-27=3, Resulting Numbers: [45, 3] Generated Node #0,2,2: 23:[45, 3] Operation: 30-27=3 Exploring Operation: 45-30=15, Resulting Numbers: [27, 15] Generated Node #0,2,3: 23:[27, 15] Operation: 45-30=15 Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 23:[30, 18], Operations: ['46-16=30', '45-27=18'] Exploring Operation: 30*18=540, Resulting Numbers: [540] 540,23 unequal: No Solution Exploring Operation: 30-18=12, Resulting Numbers: [12] 12,23 unequal: No Solution Exploring Operation: 30+18=48, Resulting Numbers: [48] 48,23 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 23:[27, 15], Operations: ['46-16=30', '45-30=15'] Exploring Operation: 27+15=42, Resulting Numbers: [42] 42,23 unequal: No Solution Exploring Operation: 27*15=405, Resulting Numbers: [405] 405,23 unequal: No Solution Exploring Operation: 27-15=12, Resulting Numbers: [12] 12,23 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 23:[45, 3], Operations: ['46-16=30', '30-27=3'] Exploring Operation: 45-3=42, Resulting Numbers: [42] 42,23 unequal: No Solution Exploring Operation: 45+3=48, Resulting Numbers: [48] 48,23 unequal: No Solution Exploring Operation: 45*3=135, Resulting Numbers: [135] 135,23 unequal: No Solution Exploring Operation: 45/3=15, Resulting Numbers: [15] 15,23 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 23:[30, 72], Operations: ['46-16=30', '27+45=72'] Exploring Operation: 30*72=2160, Resulting Numbers: [2160] 2160,23 unequal: No Solution Exploring Operation: 72-30=42, Resulting Numbers: [42] 42,23 unequal: No Solution Exploring Operation: 30+72=102, Resulting Numbers: [102] 102,23 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1 Current State: 23:[16, 45, 19], Operations: ['46-27=19'] Exploring Operation: 16+45=61, Resulting Numbers: [19, 61] Generated Node #0,1,0: 23:[19, 61] Operation: 16+45=61 Exploring Operation: 16+19=35, Resulting Numbers: [45, 35] Generated Node #0,1,1: 23:[45, 35] Operation: 16+19=35 Exploring Operation: 45-19=26, Resulting Numbers: [16, 26] Generated Node #0,1,2: 23:[16, 26] Operation: 45-19=26 Exploring Operation: 45-16=29, Resulting Numbers: [19, 29] Generated Node #0,1,3: 23:[19, 29] Operation: 45-16=29 Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 23:[16, 26], Operations: ['46-27=19', '45-19=26'] Exploring Operation: 16*26=416, Resulting Numbers: [416] 416,23 unequal: No Solution Exploring Operation: 16+26=42, Resulting Numbers: [42] 42,23 unequal: No Solution Exploring Operation: 26-16=10, Resulting Numbers: [10] 10,23 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 23:[19, 29], Operations: ['46-27=19', '45-16=29'] Exploring Operation: 29-19=10, Resulting Numbers: [10] 10,23 unequal: No Solution Exploring Operation: 19*29=551, Resulting Numbers: [551] 551,23 unequal: No Solution Exploring Operation: 19+29=48, Resulting Numbers: [48] 48,23 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 23:[45, 35], Operations: ['46-27=19', '16+19=35'] Exploring Operation: 45+35=80, Resulting Numbers: [80] 80,23 unequal: No Solution Exploring Operation: 45*35=1575, Resulting Numbers: [1575] 1575,23 unequal: No Solution Exploring Operation: 45-35=10, Resulting Numbers: [10] 10,23 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 23:[19, 61], Operations: ['46-27=19', '16+45=61'] Exploring Operation: 61-19=42, Resulting Numbers: [42] 42,23 unequal: No Solution Exploring Operation: 19*61=1159, Resulting Numbers: [1159] 1159,23 unequal: No Solution Exploring Operation: 19+61=80, Resulting Numbers: [80] 80,23 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,3 Current State: 23:[46, 27, 29], Operations: ['45-16=29'] Exploring Operation: 29-27=2, Resulting Numbers: [46, 2] Generated Node #0,3,0: 23:[46, 2] Operation: 29-27=2 Exploring Operation: 46-27=19, Resulting Numbers: [29, 19] Generated Node #0,3,1: 23:[29, 19] Operation: 46-27=19 Exploring Operation: 46+27=73, Resulting Numbers: [29, 73] Generated Node #0,3,2: 23:[29, 73] Operation: 46+27=73 Exploring Operation: 46-29=17, Resulting Numbers: [27, 17] Generated Node #0,3,3: 23:[27, 17] Operation: 46-29=17 Moving to Node #0,0,0 Current State: 23:[27, 17], Operations: ['46-45=1', '16+1=17'] Exploring Operation: 27+17=44, Resulting Numbers: [44] 44,23 unequal: No Solution Exploring Operation: 27*17=459, Resulting Numbers: [459] 459,23 unequal: No Solution Exploring Operation: 27-17=10, Resulting Numbers: [10] 10,23 unequal: No Solution Moving to Node #0,3,3 Current State: 23:[27, 17], Operations: ['45-16=29', '46-29=17'] Exploring Operation: 27*17=459, Resulting Numbers: [459] 459,23 unequal: No Solution Exploring Operation: 27-17=10, Resulting Numbers: [10] 10,23 unequal: No Solution Exploring Operation: 27+17=44, Resulting Numbers: [44] 44,23 unequal: No Solution Moving to Node #0,0,3 Current State: 23:[16, 26], Operations: ['46-45=1', '27-1=26'] Exploring Operation: 16*26=416, Resulting Numbers: [416] 416,23 unequal: No Solution Exploring Operation: 26-16=10, Resulting Numbers: [10] 10,23 unequal: No Solution Exploring Operation: 16+26=42, Resulting Numbers: [42] 42,23 unequal: No Solution Moving to Node #0,3,1 Current State: 23:[29, 19], Operations: ['45-16=29', '46-27=19'] Exploring Operation: 29*19=551, Resulting Numbers: [551] 551,23 unequal: No Solution Exploring Operation: 29+19=48, Resulting Numbers: [48] 48,23 unequal: No Solution Exploring Operation: 29-19=10, Resulting Numbers: [10] 10,23 unequal: No Solution Moving to Node #0,0,1 Current State: 23:[16, 27], Operations: ['46-45=1', '27*1=27'] Exploring Operation: 16+27=43, Resulting Numbers: [43] 43,23 unequal: No Solution Exploring Operation: 27-16=11, Resulting Numbers: [11] 11,23 unequal: No Solution Exploring Operation: 16*27=432, Resulting Numbers: [432] 432,23 unequal: No Solution Moving to Node #0,0,2 Current State: 23:[16, 27], Operations: ['46-45=1', '27/1=27'] Exploring Operation: 16+27=43, Resulting Numbers: [43] 43,23 unequal: No Solution Exploring Operation: 27-16=11, Resulting Numbers: [11] 11,23 unequal: No Solution Exploring Operation: 16*27=432, Resulting Numbers: [432] 432,23 unequal: No Solution Moving to Node #0,3,0 Current State: 23:[46, 2], Operations: ['45-16=29', '29-27=2'] Exploring Operation: 46-2=44, Resulting Numbers: [44] 44,23 unequal: No Solution Exploring Operation: 46+2=48, Resulting Numbers: [48] 48,23 unequal: No Solution Exploring Operation: 46*2=92, Resulting Numbers: [92] 92,23 unequal: No Solution Exploring Operation: 46/2=23, Resulting Numbers: [23] 23,23 equal: Goal Reached Moving to Node #0 Current State: 23:[46, 27, 16, 45], Operations: [] Exploring Operation: 45-16=29, Resulting Numbers: [46, 27, 29] Generated Node #0,3: 23:[46, 27, 29] Operation: 45-16=29 Moving to Node #0,3 Current State: 23:[46, 27, 29], Operations: ['45-16=29'] Exploring Operation: 29-27=2, Resulting Numbers: [46, 2] Generated Node #0,3,0: 23:[46, 2] Operation: 29-27=2 Moving to Node #0,3,0 Current State: 23:[46, 2], Operations: ['45-16=29', '29-27=2'] Exploring Operation: 46/2=23, Resulting Numbers: [23] 23,23 equal: Goal Reached
0.938368
hs_4
mult_heuristic
[ 25, 36, 3, 53 ]
40
[ "53-25=28", "36/3=12", "28+12=40" ]
Current State: 40:[25, 36, 3, 53], Operations: [] Exploring Operation: 53-25=28, Resulting Numbers: [36, 3, 28] Generated Node #2: [36, 3, 28] from Operation: 53-25=28 Current State: 40:[36, 3, 28], Operations: ['53-25=28'] Exploring Operation: 36/3=12, Resulting Numbers: [28, 12] Generated Node #3: [28, 12] from Operation: 36/3=12 Current State: 40:[28, 12], Operations: ['53-25=28', '36/3=12'] Exploring Operation: 28+12=40, Resulting Numbers: [40] 40,40 equal: Goal Reached
4
Current State: 40:[25, 36, 3, 53], Operations: [] Exploring Operation: 53-36=17, Resulting Numbers: [25, 3, 17] Generated Node #0,0: 40:[25, 3, 17] Operation: 53-36=17 Moving to Node #0,0 Current State: 40:[25, 3, 17], Operations: ['53-36=17'] Exploring Operation: 25-17=8, Resulting Numbers: [3, 8] Generated Node #0,0,0: 40:[3, 8] Operation: 25-17=8 Moving to Node #0,0,0 Current State: 40:[3, 8], Operations: ['53-36=17', '25-17=8'] Exploring Operation: 8-3=5, Resulting Numbers: [5] 5,40 unequal: No Solution No solution found.
0
hs_1
sum_heuristic
[ 18, 12, 58, 14 ]
94
[ "14-12=2", "18*2=36", "58+36=94" ]
Current State: 94:[18, 12, 58, 14], Operations: [] Exploring Operation: 14-12=2, Resulting Numbers: [18, 58, 2] Generated Node #2: [18, 58, 2] from Operation: 14-12=2 Current State: 94:[18, 58, 2], Operations: ['14-12=2'] Exploring Operation: 18*2=36, Resulting Numbers: [58, 36] Generated Node #3: [58, 36] from Operation: 18*2=36 Current State: 94:[58, 36], Operations: ['14-12=2', '18*2=36'] Exploring Operation: 58+36=94, Resulting Numbers: [94] 94,94 equal: Goal Reached
4
Current State: 94:[18, 12, 58, 14], Operations: [] Exploring Operation: 18-14=4, Resulting Numbers: [12, 58, 4] Generated Node #0,0: 94:[12, 58, 4] Operation: 18-14=4 Exploring Operation: 14-12=2, Resulting Numbers: [18, 58, 2] Generated Node #0,1: 94:[18, 58, 2] Operation: 14-12=2 Exploring Operation: 18-12=6, Resulting Numbers: [58, 14, 6] Generated Node #0,2: 94:[58, 14, 6] Operation: 18-12=6 Exploring Operation: 58-18=40, Resulting Numbers: [12, 14, 40] Generated Node #0,3: 94:[12, 14, 40] Operation: 58-18=40 Start Sub Search at level 1: Moving to Node #0,0 Current State: 94:[12, 58, 4], Operations: ['18-14=4'] Exploring Operation: 12*4=48, Resulting Numbers: [58, 48] Generated Node #0,0,0: 94:[58, 48] Operation: 12*4=48 Exploring Operation: 12-4=8, Resulting Numbers: [58, 8] Generated Node #0,0,1: 94:[58, 8] Operation: 12-4=8 Exploring Operation: 12/4=3, Resulting Numbers: [58, 3] Generated Node #0,0,2: 94:[58, 3] Operation: 12/4=3 Exploring Operation: 58-12=46, Resulting Numbers: [4, 46] Generated Node #0,0,3: 94:[4, 46] Operation: 58-12=46 Moving to Node #0,0,3 Current State: 94:[4, 46], Operations: ['18-14=4', '58-12=46'] Exploring Operation: 4+46=50, Resulting Numbers: [50] 50,94 unequal: No Solution Exploring Operation: 46-4=42, Resulting Numbers: [42] 42,94 unequal: No Solution Exploring Operation: 4*46=184, Resulting Numbers: [184] 184,94 unequal: No Solution Moving to Node #0,0,2 Current State: 94:[58, 3], Operations: ['18-14=4', '12/4=3'] Exploring Operation: 58+3=61, Resulting Numbers: [61] 61,94 unequal: No Solution Exploring Operation: 58-3=55, Resulting Numbers: [55] 55,94 unequal: No Solution Exploring Operation: 58*3=174, Resulting Numbers: [174] 174,94 unequal: No Solution Moving to Node #0,0,0 Current State: 94:[58, 48], Operations: ['18-14=4', '12*4=48'] Exploring Operation: 58+48=106, Resulting Numbers: [106] 106,94 unequal: No Solution Exploring Operation: 58*48=2784, Resulting Numbers: [2784] 2784,94 unequal: No Solution Exploring Operation: 58-48=10, Resulting Numbers: [10] 10,94 unequal: No Solution Moving to Node #0,0,1 Current State: 94:[58, 8], Operations: ['18-14=4', '12-4=8'] Exploring Operation: 58*8=464, Resulting Numbers: [464] 464,94 unequal: No Solution Exploring Operation: 58-8=50, Resulting Numbers: [50] 50,94 unequal: No Solution Exploring Operation: 58+8=66, Resulting Numbers: [66] 66,94 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 94:[18, 58, 2], Operations: ['14-12=2'] Exploring Operation: 58-18=40, Resulting Numbers: [2, 40] Generated Node #0,1,0: 94:[2, 40] Operation: 58-18=40 Exploring Operation: 18+58=76, Resulting Numbers: [2, 76] Generated Node #0,1,1: 94:[2, 76] Operation: 18+58=76 Exploring Operation: 18/2=9, Resulting Numbers: [58, 9] Generated Node #0,1,2: 94:[58, 9] Operation: 18/2=9 Exploring Operation: 18*2=36, Resulting Numbers: [58, 36] Generated Node #0,1,3: 94:[58, 36] Operation: 18*2=36 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 94:[2, 40], Operations: ['14-12=2', '58-18=40'] Exploring Operation: 40/2=20, Resulting Numbers: [20] 20,94 unequal: No Solution Exploring Operation: 2+40=42, Resulting Numbers: [42] 42,94 unequal: No Solution Exploring Operation: 40-2=38, Resulting Numbers: [38] 38,94 unequal: No Solution Exploring Operation: 2*40=80, Resulting Numbers: [80] 80,94 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 94:[2, 76], Operations: ['14-12=2', '18+58=76'] Exploring Operation: 2+76=78, Resulting Numbers: [78] 78,94 unequal: No Solution Exploring Operation: 76/2=38, Resulting Numbers: [38] 38,94 unequal: No Solution Exploring Operation: 76-2=74, Resulting Numbers: [74] 74,94 unequal: No Solution Exploring Operation: 2*76=152, Resulting Numbers: [152] 152,94 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 94:[58, 9], Operations: ['14-12=2', '18/2=9'] Exploring Operation: 58-9=49, Resulting Numbers: [49] 49,94 unequal: No Solution Exploring Operation: 58+9=67, Resulting Numbers: [67] 67,94 unequal: No Solution Exploring Operation: 58*9=522, Resulting Numbers: [522] 522,94 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,3 Current State: 94:[58, 36], Operations: ['14-12=2', '18*2=36'] Exploring Operation: 58*36=2088, Resulting Numbers: [2088] 2088,94 unequal: No Solution Exploring Operation: 58+36=94, Resulting Numbers: [94] 94,94 equal: Goal Reached Moving to Node #0 Current State: 94:[18, 12, 58, 14], Operations: [] Exploring Operation: 14-12=2, Resulting Numbers: [18, 58, 2] Generated Node #0,1: 94:[18, 58, 2] Operation: 14-12=2 Moving to Node #0,1 Current State: 94:[18, 58, 2], Operations: ['14-12=2'] Exploring Operation: 18*2=36, Resulting Numbers: [58, 36] Generated Node #0,1,3: 94:[58, 36] Operation: 18*2=36 Moving to Node #0,1,3 Current State: 94:[58, 36], Operations: ['14-12=2', '18*2=36'] Exploring Operation: 58+36=94, Resulting Numbers: [94] 94,94 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.96441
hs_4
mult_heuristic
[ 84, 11, 48, 63 ]
88
[ "84-11=73", "63-48=15", "73+15=88" ]
Current State: 88:[84, 11, 48, 63], Operations: [] Exploring Operation: 84-11=73, Resulting Numbers: [48, 63, 73] Generated Node #2: [48, 63, 73] from Operation: 84-11=73 Current State: 88:[48, 63, 73], Operations: ['84-11=73'] Exploring Operation: 63-48=15, Resulting Numbers: [73, 15] Generated Node #3: [73, 15] from Operation: 63-48=15 Current State: 88:[73, 15], Operations: ['84-11=73', '63-48=15'] Exploring Operation: 73+15=88, Resulting Numbers: [88] 88,88 equal: Goal Reached
4
Current State: 88:[84, 11, 48, 63], Operations: [] Exploring Operation: 63-48=15, Resulting Numbers: [84, 11, 15] Generated Node #0,0: 88:[84, 11, 15] Operation: 63-48=15 Exploring Operation: 63-11=52, Resulting Numbers: [84, 48, 52] Generated Node #0,1: 88:[84, 48, 52] Operation: 63-11=52 Exploring Operation: 84-63=21, Resulting Numbers: [11, 48, 21] Generated Node #0,2: 88:[11, 48, 21] Operation: 84-63=21 Start Sub Search at level 1: Moving to Node #0,2 Current State: 88:[11, 48, 21], Operations: ['84-63=21'] Exploring Operation: 48-11=37, Resulting Numbers: [21, 37] Generated Node #0,2,0: 88:[21, 37] Operation: 48-11=37 Exploring Operation: 21-11=10, Resulting Numbers: [48, 10] Generated Node #0,2,1: 88:[48, 10] Operation: 21-11=10 Exploring Operation: 48-21=27, Resulting Numbers: [11, 27] Generated Node #0,2,2: 88:[11, 27] Operation: 48-21=27 Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 88:[48, 10], Operations: ['84-63=21', '21-11=10'] Exploring Operation: 48*10=480, Resulting Numbers: [480] 480,88 unequal: No Solution Exploring Operation: 48+10=58, Resulting Numbers: [58] 58,88 unequal: No Solution Exploring Operation: 48-10=38, Resulting Numbers: [38] 38,88 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 88:[11, 27], Operations: ['84-63=21', '48-21=27'] Exploring Operation: 11+27=38, Resulting Numbers: [38] 38,88 unequal: No Solution Exploring Operation: 27-11=16, Resulting Numbers: [16] 16,88 unequal: No Solution Exploring Operation: 11*27=297, Resulting Numbers: [297] 297,88 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 88:[21, 37], Operations: ['84-63=21', '48-11=37'] Exploring Operation: 21+37=58, Resulting Numbers: [58] 58,88 unequal: No Solution Exploring Operation: 21*37=777, Resulting Numbers: [777] 777,88 unequal: No Solution Exploring Operation: 37-21=16, Resulting Numbers: [16] 16,88 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 88:[84, 11, 15], Operations: ['63-48=15'] Exploring Operation: 11+15=26, Resulting Numbers: [84, 26] Generated Node #0,0,0: 88:[84, 26] Operation: 11+15=26 Exploring Operation: 84+11=95, Resulting Numbers: [15, 95] Generated Node #0,0,1: 88:[15, 95] Operation: 84+11=95 Exploring Operation: 15-11=4, Resulting Numbers: [84, 4] Generated Node #0,0,2: 88:[84, 4] Operation: 15-11=4 Moving to Node #0,0,2 Current State: 88:[84, 4], Operations: ['63-48=15', '15-11=4'] Exploring Operation: 84/4=21, Resulting Numbers: [21] 21,88 unequal: No Solution Exploring Operation: 84-4=80, Resulting Numbers: [80] 80,88 unequal: No Solution Exploring Operation: 84+4=88, Resulting Numbers: [88] 88,88 equal: Goal Reached Moving to Node #0 Current State: 88:[84, 11, 48, 63], Operations: [] Exploring Operation: 63-48=15, Resulting Numbers: [84, 11, 15] Generated Node #0,0: 88:[84, 11, 15] Operation: 63-48=15 Moving to Node #0,0 Current State: 88:[84, 11, 15], Operations: ['63-48=15'] Exploring Operation: 15-11=4, Resulting Numbers: [84, 4] Generated Node #0,0,2: 88:[84, 4] Operation: 15-11=4 Moving to Node #0,0,2 Current State: 88:[84, 4], Operations: ['63-48=15', '15-11=4'] Exploring Operation: 84+4=88, Resulting Numbers: [88] 88,88 equal: Goal Reached Exit Sub Search at level 1
0.978299
hs_3
mult_heuristic
[ 1, 93, 37, 2 ]
58
[ "1*93=93", "37-2=35", "93-35=58" ]
Current State: 58:[1, 93, 37, 2], Operations: [] Exploring Operation: 1*93=93, Resulting Numbers: [37, 2, 93] Generated Node #2: [37, 2, 93] from Operation: 1*93=93 Current State: 58:[37, 2, 93], Operations: ['1*93=93'] Exploring Operation: 37-2=35, Resulting Numbers: [93, 35] Generated Node #3: [93, 35] from Operation: 37-2=35 Current State: 58:[93, 35], Operations: ['1*93=93', '37-2=35'] Exploring Operation: 93-35=58, Resulting Numbers: [58] 58,58 equal: Goal Reached
4
Current State: 58:[1, 93, 37, 2], Operations: [] Exploring Operation: 93-37=56, Resulting Numbers: [1, 2, 56] Generated Node #0,0: 58:[1, 2, 56] Operation: 93-37=56 Moving to Node #0,0 Current State: 58:[1, 2, 56], Operations: ['93-37=56'] Exploring Operation: 1+56=57, Resulting Numbers: [2, 57] Generated Node #0,0,0: 58:[2, 57] Operation: 1+56=57 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 58:[2, 57], Operations: ['93-37=56', '1+56=57'] Exploring Operation: 2+57=59, Resulting Numbers: [59] 59,58 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
sum_heuristic
[ 61, 10, 32, 39 ]
42
[ "61+39=100", "100/10=10", "32+10=42" ]
Current State: 42:[61, 10, 32, 39], Operations: [] Exploring Operation: 61+39=100, Resulting Numbers: [10, 32, 100] Generated Node #2: [10, 32, 100] from Operation: 61+39=100 Current State: 42:[10, 32, 100], Operations: ['61+39=100'] Exploring Operation: 100/10=10, Resulting Numbers: [32, 10] Generated Node #3: [32, 10] from Operation: 100/10=10 Current State: 42:[32, 10], Operations: ['61+39=100', '100/10=10'] Exploring Operation: 32+10=42, Resulting Numbers: [42] 42,42 equal: Goal Reached
4
Current State: 42:[61, 10, 32, 39], Operations: [] Exploring Operation: 61-39=22, Resulting Numbers: [10, 32, 22] Generated Node #0,0: 42:[10, 32, 22] Operation: 61-39=22 Exploring Operation: 61-32=29, Resulting Numbers: [10, 39, 29] Generated Node #0,1: 42:[10, 39, 29] Operation: 61-32=29 Moving to Node #0,0 Current State: 42:[10, 32, 22], Operations: ['61-39=22'] Exploring Operation: 10+32=42, Resulting Numbers: [22, 42] Generated Node #0,0,0: 42:[22, 42] Operation: 10+32=42 Exploring Operation: 32-10=22, Resulting Numbers: [22, 22] Generated Node #0,0,1: 42:[22, 22] Operation: 32-10=22 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 42:[22, 42], Operations: ['61-39=22', '10+32=42'] Exploring Operation: 42-22=20, Resulting Numbers: [20] 20,42 unequal: No Solution Exploring Operation: 22+42=64, Resulting Numbers: [64] 64,42 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 42:[22, 22], Operations: ['61-39=22', '32-10=22'] Exploring Operation: 22+22=44, Resulting Numbers: [44] 44,42 unequal: No Solution Exploring Operation: 22/22=1, Resulting Numbers: [1] 1,42 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1 Current State: 42:[10, 39, 29], Operations: ['61-32=29'] Exploring Operation: 10+29=39, Resulting Numbers: [39, 39] Generated Node #0,1,0: 42:[39, 39] Operation: 10+29=39 Exploring Operation: 29-10=19, Resulting Numbers: [39, 19] Generated Node #0,1,1: 42:[39, 19] Operation: 29-10=19 Moving to Node #0,1,1 Current State: 42:[39, 19], Operations: ['61-32=29', '29-10=19'] Exploring Operation: 39-19=20, Resulting Numbers: [20] 20,42 unequal: No Solution Exploring Operation: 39+19=58, Resulting Numbers: [58] 58,42 unequal: No Solution Moving to Node #0,1,0 Current State: 42:[39, 39], Operations: ['61-32=29', '10+29=39'] Exploring Operation: 39/39=1, Resulting Numbers: [1] 1,42 unequal: No Solution Exploring Operation: 39-39=0, Resulting Numbers: [0] 0,42 unequal: No Solution No solution found.
0
hs_2
sum_heuristic
[ 47, 1, 7, 13 ]
54
[ "47+1=48", "13-7=6", "48+6=54" ]
Current State: 54:[47, 1, 7, 13], Operations: [] Exploring Operation: 47+1=48, Resulting Numbers: [7, 13, 48] Generated Node #2: [7, 13, 48] from Operation: 47+1=48 Current State: 54:[7, 13, 48], Operations: ['47+1=48'] Exploring Operation: 13-7=6, Resulting Numbers: [48, 6] Generated Node #3: [48, 6] from Operation: 13-7=6 Current State: 54:[48, 6], Operations: ['47+1=48', '13-7=6'] Exploring Operation: 48+6=54, Resulting Numbers: [54] 54,54 equal: Goal Reached
4
Current State: 54:[47, 1, 7, 13], Operations: [] Exploring Operation: 47+13=60, Resulting Numbers: [1, 7, 60] Generated Node #0,0: 54:[1, 7, 60] Operation: 47+13=60 Exploring Operation: 13-7=6, Resulting Numbers: [47, 1, 6] Generated Node #0,1: 54:[47, 1, 6] Operation: 13-7=6 Exploring Operation: 47+7=54, Resulting Numbers: [1, 13, 54] Generated Node #0,2: 54:[1, 13, 54] Operation: 47+7=54 Start Sub Search at level 1: Moving to Node #0,2 Current State: 54:[1, 13, 54], Operations: ['47+7=54'] Exploring Operation: 1+13=14, Resulting Numbers: [54, 14] Generated Node #0,2,0: 54:[54, 14] Operation: 1+13=14 Exploring Operation: 1*13=13, Resulting Numbers: [54, 13] Generated Node #0,2,1: 54:[54, 13] Operation: 1*13=13 Exploring Operation: 13-1=12, Resulting Numbers: [54, 12] Generated Node #0,2,2: 54:[54, 12] Operation: 13-1=12 Moving to Node #0,2,2 Current State: 54:[54, 12], Operations: ['47+7=54', '13-1=12'] Exploring Operation: 54*12=648, Resulting Numbers: [648] 648,54 unequal: No Solution Exploring Operation: 54-12=42, Resulting Numbers: [42] 42,54 unequal: No Solution Exploring Operation: 54+12=66, Resulting Numbers: [66] 66,54 unequal: No Solution Moving to Node #0,2,0 Current State: 54:[54, 14], Operations: ['47+7=54', '1+13=14'] Exploring Operation: 54*14=756, Resulting Numbers: [756] 756,54 unequal: No Solution Exploring Operation: 54+14=68, Resulting Numbers: [68] 68,54 unequal: No Solution Exploring Operation: 54-14=40, Resulting Numbers: [40] 40,54 unequal: No Solution Moving to Node #0,2,1 Current State: 54:[54, 13], Operations: ['47+7=54', '1*13=13'] Exploring Operation: 54+13=67, Resulting Numbers: [67] 67,54 unequal: No Solution Exploring Operation: 54-13=41, Resulting Numbers: [41] 41,54 unequal: No Solution Exploring Operation: 54*13=702, Resulting Numbers: [702] 702,54 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 54:[1, 7, 60], Operations: ['47+13=60'] Exploring Operation: 7-1=6, Resulting Numbers: [60, 6] Generated Node #0,0,0: 54:[60, 6] Operation: 7-1=6 Exploring Operation: 60-1=59, Resulting Numbers: [7, 59] Generated Node #0,0,1: 54:[7, 59] Operation: 60-1=59 Exploring Operation: 60-7=53, Resulting Numbers: [1, 53] Generated Node #0,0,2: 54:[1, 53] Operation: 60-7=53 Moving to Node #0,0,2 Current State: 54:[1, 53], Operations: ['47+13=60', '60-7=53'] Exploring Operation: 53/1=53, Resulting Numbers: [53] 53,54 unequal: No Solution Exploring Operation: 1+53=54, Resulting Numbers: [54] 54,54 equal: Goal Reached Moving to Node #0 Current State: 54:[47, 1, 7, 13], Operations: [] Exploring Operation: 47+13=60, Resulting Numbers: [1, 7, 60] Generated Node #0,0: 54:[1, 7, 60] Operation: 47+13=60 Moving to Node #0,0 Current State: 54:[1, 7, 60], Operations: ['47+13=60'] Exploring Operation: 60-7=53, Resulting Numbers: [1, 53] Generated Node #0,0,2: 54:[1, 53] Operation: 60-7=53 Moving to Node #0,0,2 Current State: 54:[1, 53], Operations: ['47+13=60', '60-7=53'] Exploring Operation: 1+53=54, Resulting Numbers: [54] 54,54 equal: Goal Reached Exit Sub Search at level 1
0.979167
hs_3
sum_heuristic
[ 94, 23, 66, 41 ]
10
[ "94+23=117", "66+41=107", "117-107=10" ]
Current State: 10:[94, 23, 66, 41], Operations: [] Exploring Operation: 94+23=117, Resulting Numbers: [66, 41, 117] Generated Node #2: [66, 41, 117] from Operation: 94+23=117 Current State: 10:[66, 41, 117], Operations: ['94+23=117'] Exploring Operation: 66+41=107, Resulting Numbers: [117, 107] Generated Node #3: [117, 107] from Operation: 66+41=107 Current State: 10:[117, 107], Operations: ['94+23=117', '66+41=107'] Exploring Operation: 117-107=10, Resulting Numbers: [10] 10,10 equal: Goal Reached
4
Current State: 10:[94, 23, 66, 41], Operations: [] Exploring Operation: 94-41=53, Resulting Numbers: [23, 66, 53] Generated Node #0,0: 10:[23, 66, 53] Operation: 94-41=53 Exploring Operation: 94-66=28, Resulting Numbers: [23, 41, 28] Generated Node #0,1: 10:[23, 41, 28] Operation: 94-66=28 Exploring Operation: 66-41=25, Resulting Numbers: [94, 23, 25] Generated Node #0,2: 10:[94, 23, 25] Operation: 66-41=25 Start Sub Search at level 1: Moving to Node #0,1 Current State: 10:[23, 41, 28], Operations: ['94-66=28'] Exploring Operation: 41-23=18, Resulting Numbers: [28, 18] Generated Node #0,1,0: 10:[28, 18] Operation: 41-23=18 Exploring Operation: 28-23=5, Resulting Numbers: [41, 5] Generated Node #0,1,1: 10:[41, 5] Operation: 28-23=5 Exploring Operation: 41-28=13, Resulting Numbers: [23, 13] Generated Node #0,1,2: 10:[23, 13] Operation: 41-28=13 Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 10:[23, 13], Operations: ['94-66=28', '41-28=13'] Exploring Operation: 23*13=299, Resulting Numbers: [299] 299,10 unequal: No Solution Exploring Operation: 23-13=10, Resulting Numbers: [10] 10,10 equal: Goal Reached Moving to Node #0 Current State: 10:[94, 23, 66, 41], Operations: [] Exploring Operation: 94-66=28, Resulting Numbers: [23, 41, 28] Generated Node #0,1: 10:[23, 41, 28] Operation: 94-66=28 Moving to Node #0,1 Current State: 10:[23, 41, 28], Operations: ['94-66=28'] Exploring Operation: 41-28=13, Resulting Numbers: [23, 13] Generated Node #0,1,2: 10:[23, 13] Operation: 41-28=13 Moving to Node #0,1,2 Current State: 10:[23, 13], Operations: ['94-66=28', '41-28=13'] Exploring Operation: 23-13=10, Resulting Numbers: [10] 10,10 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.989583
hs_3
mult_heuristic
[ 14, 31, 18, 32 ]
92
[ "18-14=4", "31*4=124", "124-32=92" ]
Current State: 92:[14, 31, 18, 32], Operations: [] Exploring Operation: 18-14=4, Resulting Numbers: [31, 32, 4] Generated Node #2: [31, 32, 4] from Operation: 18-14=4 Current State: 92:[31, 32, 4], Operations: ['18-14=4'] Exploring Operation: 31*4=124, Resulting Numbers: [32, 124] Generated Node #3: [32, 124] from Operation: 31*4=124 Current State: 92:[32, 124], Operations: ['18-14=4', '31*4=124'] Exploring Operation: 124-32=92, Resulting Numbers: [92] 92,92 equal: Goal Reached
4
Current State: 92:[14, 31, 18, 32], Operations: [] Exploring Operation: 14+32=46, Resulting Numbers: [31, 18, 46] Generated Node #0,0: 92:[31, 18, 46] Operation: 14+32=46 Moving to Node #0,0 Current State: 92:[31, 18, 46], Operations: ['14+32=46'] Exploring Operation: 31+18=49, Resulting Numbers: [46, 49] Generated Node #0,0,0: 92:[46, 49] Operation: 31+18=49 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 92:[46, 49], Operations: ['14+32=46', '31+18=49'] Exploring Operation: 49-46=3, Resulting Numbers: [3] 3,92 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
sum_heuristic
[ 81, 3, 97, 79 ]
92
[ "81+3=84", "97+79=176", "176-84=92" ]
Current State: 92:[81, 3, 97, 79], Operations: [] Exploring Operation: 81+3=84, Resulting Numbers: [97, 79, 84] Generated Node #2: [97, 79, 84] from Operation: 81+3=84 Current State: 92:[97, 79, 84], Operations: ['81+3=84'] Exploring Operation: 97+79=176, Resulting Numbers: [84, 176] Generated Node #3: [84, 176] from Operation: 97+79=176 Current State: 92:[84, 176], Operations: ['81+3=84', '97+79=176'] Exploring Operation: 176-84=92, Resulting Numbers: [92] 92,92 equal: Goal Reached
4
Current State: 92:[81, 3, 97, 79], Operations: [] Exploring Operation: 81-79=2, Resulting Numbers: [3, 97, 2] Generated Node #0,0: 92:[3, 97, 2] Operation: 81-79=2 Exploring Operation: 97-79=18, Resulting Numbers: [81, 3, 18] Generated Node #0,1: 92:[81, 3, 18] Operation: 97-79=18 Exploring Operation: 81/3=27, Resulting Numbers: [97, 79, 27] Generated Node #0,2: 92:[97, 79, 27] Operation: 81/3=27 Exploring Operation: 97-81=16, Resulting Numbers: [3, 79, 16] Generated Node #0,3: 92:[3, 79, 16] Operation: 97-81=16 Exploring Operation: 81+3=84, Resulting Numbers: [97, 79, 84] Generated Node #0,4: 92:[97, 79, 84] Operation: 81+3=84 Moving to Node #0,0 Current State: 92:[3, 97, 2], Operations: ['81-79=2'] Exploring Operation: 97-3=94, Resulting Numbers: [2, 94] Generated Node #0,0,0: 92:[2, 94] Operation: 97-3=94 Exploring Operation: 3+2=5, Resulting Numbers: [97, 5] Generated Node #0,0,1: 92:[97, 5] Operation: 3+2=5 Exploring Operation: 3*2=6, Resulting Numbers: [97, 6] Generated Node #0,0,2: 92:[97, 6] Operation: 3*2=6 Exploring Operation: 97-2=95, Resulting Numbers: [3, 95] Generated Node #0,0,3: 92:[3, 95] Operation: 97-2=95 Exploring Operation: 3-2=1, Resulting Numbers: [97, 1] Generated Node #0,0,4: 92:[97, 1] Operation: 3-2=1 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 92:[2, 94], Operations: ['81-79=2', '97-3=94'] Exploring Operation: 2*94=188, Resulting Numbers: [188] 188,92 unequal: No Solution Exploring Operation: 94/2=47, Resulting Numbers: [47] 47,92 unequal: No Solution Exploring Operation: 94-2=92, Resulting Numbers: [92] 92,92 equal: Goal Reached Moving to Node #0 Current State: 92:[81, 3, 97, 79], Operations: [] Exploring Operation: 81-79=2, Resulting Numbers: [3, 97, 2] Generated Node #0,0: 92:[3, 97, 2] Operation: 81-79=2 Moving to Node #0,0 Current State: 92:[3, 97, 2], Operations: ['81-79=2'] Exploring Operation: 97-3=94, Resulting Numbers: [2, 94] Generated Node #0,0,0: 92:[2, 94] Operation: 97-3=94 Moving to Node #0,0,0 Current State: 92:[2, 94], Operations: ['81-79=2', '97-3=94'] Exploring Operation: 94-2=92, Resulting Numbers: [92] 92,92 equal: Goal Reached Exit Sub Search at level 1
0.985243
hs_5
mult_heuristic
[ 27, 87, 29, 38 ]
62
[ "27+38=65", "87/29=3", "65-3=62" ]
Current State: 62:[27, 87, 29, 38], Operations: [] Exploring Operation: 27+38=65, Resulting Numbers: [87, 29, 65] Generated Node #2: [87, 29, 65] from Operation: 27+38=65 Current State: 62:[87, 29, 65], Operations: ['27+38=65'] Exploring Operation: 87/29=3, Resulting Numbers: [65, 3] Generated Node #3: [65, 3] from Operation: 87/29=3 Current State: 62:[65, 3], Operations: ['27+38=65', '87/29=3'] Exploring Operation: 65-3=62, Resulting Numbers: [62] 62,62 equal: Goal Reached
4
Current State: 62:[27, 87, 29, 38], Operations: [] Exploring Operation: 87/29=3, Resulting Numbers: [27, 38, 3] Generated Node #0,0: 62:[27, 38, 3] Operation: 87/29=3 Exploring Operation: 87-29=58, Resulting Numbers: [27, 38, 58] Generated Node #0,1: 62:[27, 38, 58] Operation: 87-29=58 Exploring Operation: 87-27=60, Resulting Numbers: [29, 38, 60] Generated Node #0,2: 62:[29, 38, 60] Operation: 87-27=60 Start Sub Search at level 1: Moving to Node #0,2 Current State: 62:[29, 38, 60], Operations: ['87-27=60'] Exploring Operation: 60-29=31, Resulting Numbers: [38, 31] Generated Node #0,2,0: 62:[38, 31] Operation: 60-29=31 Exploring Operation: 29+38=67, Resulting Numbers: [60, 67] Generated Node #0,2,1: 62:[60, 67] Operation: 29+38=67 Exploring Operation: 38-29=9, Resulting Numbers: [60, 9] Generated Node #0,2,2: 62:[60, 9] Operation: 38-29=9 Moving to Node #0,2,0 Current State: 62:[38, 31], Operations: ['87-27=60', '60-29=31'] Exploring Operation: 38+31=69, Resulting Numbers: [69] 69,62 unequal: No Solution Exploring Operation: 38*31=1178, Resulting Numbers: [1178] 1178,62 unequal: No Solution Exploring Operation: 38-31=7, Resulting Numbers: [7] 7,62 unequal: No Solution Moving to Node #0,2,1 Current State: 62:[60, 67], Operations: ['87-27=60', '29+38=67'] Exploring Operation: 60*67=4020, Resulting Numbers: [4020] 4020,62 unequal: No Solution Exploring Operation: 67-60=7, Resulting Numbers: [7] 7,62 unequal: No Solution Exploring Operation: 60+67=127, Resulting Numbers: [127] 127,62 unequal: No Solution Moving to Node #0,2,2 Current State: 62:[60, 9], Operations: ['87-27=60', '38-29=9'] Exploring Operation: 60-9=51, Resulting Numbers: [51] 51,62 unequal: No Solution Exploring Operation: 60*9=540, Resulting Numbers: [540] 540,62 unequal: No Solution Exploring Operation: 60+9=69, Resulting Numbers: [69] 69,62 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 62:[27, 38, 3], Operations: ['87/29=3'] Exploring Operation: 27+3=30, Resulting Numbers: [38, 30] Generated Node #0,0,0: 62:[38, 30] Operation: 27+3=30 Exploring Operation: 38-3=35, Resulting Numbers: [27, 35] Generated Node #0,0,1: 62:[27, 35] Operation: 38-3=35 Exploring Operation: 27+38=65, Resulting Numbers: [3, 65] Generated Node #0,0,2: 62:[3, 65] Operation: 27+38=65 Moving to Node #0,0,2 Current State: 62:[3, 65], Operations: ['87/29=3', '27+38=65'] Exploring Operation: 65-3=62, Resulting Numbers: [62] 62,62 equal: Goal Reached Moving to Node #0 Current State: 62:[27, 87, 29, 38], Operations: [] Exploring Operation: 87/29=3, Resulting Numbers: [27, 38, 3] Generated Node #0,0: 62:[27, 38, 3] Operation: 87/29=3 Moving to Node #0,0 Current State: 62:[27, 38, 3], Operations: ['87/29=3'] Exploring Operation: 27+38=65, Resulting Numbers: [3, 65] Generated Node #0,0,2: 62:[3, 65] Operation: 27+38=65 Moving to Node #0,0,2 Current State: 62:[3, 65], Operations: ['87/29=3', '27+38=65'] Exploring Operation: 65-3=62, Resulting Numbers: [62] 62,62 equal: Goal Reached Exit Sub Search at level 1
0.980035
hs_3
mult_heuristic
[ 32, 2, 5, 96 ]
22
[ "32+5=37", "2*37=74", "96-74=22" ]
Current State: 22:[32, 2, 5, 96], Operations: [] Exploring Operation: 32+5=37, Resulting Numbers: [2, 96, 37] Generated Node #2: [2, 96, 37] from Operation: 32+5=37 Current State: 22:[2, 96, 37], Operations: ['32+5=37'] Exploring Operation: 2*37=74, Resulting Numbers: [96, 74] Generated Node #3: [96, 74] from Operation: 2*37=74 Current State: 22:[96, 74], Operations: ['32+5=37', '2*37=74'] Exploring Operation: 96-74=22, Resulting Numbers: [22] 22,22 equal: Goal Reached
4
Current State: 22:[32, 2, 5, 96], Operations: [] Exploring Operation: 96/2=48, Resulting Numbers: [32, 5, 48] Generated Node #0,0: 22:[32, 5, 48] Operation: 96/2=48 Exploring Operation: 96-32=64, Resulting Numbers: [2, 5, 64] Generated Node #0,1: 22:[2, 5, 64] Operation: 96-32=64 Exploring Operation: 96/32=3, Resulting Numbers: [2, 5, 3] Generated Node #0,2: 22:[2, 5, 3] Operation: 96/32=3 Moving to Node #0,2 Current State: 22:[2, 5, 3], Operations: ['96/32=3'] Exploring Operation: 2*5=10, Resulting Numbers: [3, 10] Generated Node #0,2,0: 22:[3, 10] Operation: 2*5=10 Exploring Operation: 5-2=3, Resulting Numbers: [3, 3] Generated Node #0,2,1: 22:[3, 3] Operation: 5-2=3 Exploring Operation: 5-3=2, Resulting Numbers: [2, 2] Generated Node #0,2,2: 22:[2, 2] Operation: 5-3=2 Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 22:[2, 2], Operations: ['96/32=3', '5-3=2'] Exploring Operation: 2+2=4, Resulting Numbers: [4] 4,22 unequal: No Solution Exploring Operation: 2*2=4, Resulting Numbers: [4] 4,22 unequal: No Solution Exploring Operation: 2/2=1, Resulting Numbers: [1] 1,22 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 22:[3, 10], Operations: ['96/32=3', '2*5=10'] Exploring Operation: 3+10=13, Resulting Numbers: [13] 13,22 unequal: No Solution Exploring Operation: 10-3=7, Resulting Numbers: [7] 7,22 unequal: No Solution Exploring Operation: 3*10=30, Resulting Numbers: [30] 30,22 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 22:[3, 3], Operations: ['96/32=3', '5-2=3'] Exploring Operation: 3*3=9, Resulting Numbers: [9] 9,22 unequal: No Solution Exploring Operation: 3-3=0, Resulting Numbers: [0] 0,22 unequal: No Solution Exploring Operation: 3/3=1, Resulting Numbers: [1] 1,22 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,0 Current State: 22:[32, 5, 48], Operations: ['96/2=48'] Exploring Operation: 32-5=27, Resulting Numbers: [48, 27] Generated Node #0,0,0: 22:[48, 27] Operation: 32-5=27 Exploring Operation: 48-32=16, Resulting Numbers: [5, 16] Generated Node #0,0,1: 22:[5, 16] Operation: 48-32=16 Exploring Operation: 48-5=43, Resulting Numbers: [32, 43] Generated Node #0,0,2: 22:[32, 43] Operation: 48-5=43 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 22:[5, 16], Operations: ['96/2=48', '48-32=16'] Exploring Operation: 5+16=21, Resulting Numbers: [21] 21,22 unequal: No Solution Exploring Operation: 5*16=80, Resulting Numbers: [80] 80,22 unequal: No Solution Exploring Operation: 16-5=11, Resulting Numbers: [11] 11,22 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 22:[48, 27], Operations: ['96/2=48', '32-5=27'] Exploring Operation: 48-27=21, Resulting Numbers: [21] 21,22 unequal: No Solution Exploring Operation: 48+27=75, Resulting Numbers: [75] 75,22 unequal: No Solution Exploring Operation: 48*27=1296, Resulting Numbers: [1296] 1296,22 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 22:[32, 43], Operations: ['96/2=48', '48-5=43'] Exploring Operation: 32+43=75, Resulting Numbers: [75] 75,22 unequal: No Solution Exploring Operation: 32*43=1376, Resulting Numbers: [1376] 1376,22 unequal: No Solution Exploring Operation: 43-32=11, Resulting Numbers: [11] 11,22 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1 Current State: 22:[2, 5, 64], Operations: ['96-32=64'] Exploring Operation: 64-5=59, Resulting Numbers: [2, 59] Generated Node #0,1,0: 22:[2, 59] Operation: 64-5=59 Exploring Operation: 2*5=10, Resulting Numbers: [64, 10] Generated Node #0,1,1: 22:[64, 10] Operation: 2*5=10 Exploring Operation: 64/2=32, Resulting Numbers: [5, 32] Generated Node #0,1,2: 22:[5, 32] Operation: 64/2=32 Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 22:[5, 32], Operations: ['96-32=64', '64/2=32'] Exploring Operation: 5+32=37, Resulting Numbers: [37] 37,22 unequal: No Solution Exploring Operation: 5*32=160, Resulting Numbers: [160] 160,22 unequal: No Solution Exploring Operation: 32-5=27, Resulting Numbers: [27] 27,22 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 22:[2, 59], Operations: ['96-32=64', '64-5=59'] Exploring Operation: 59-2=57, Resulting Numbers: [57] 57,22 unequal: No Solution Exploring Operation: 2*59=118, Resulting Numbers: [118] 118,22 unequal: No Solution Exploring Operation: 2+59=61, Resulting Numbers: [61] 61,22 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 22:[64, 10], Operations: ['96-32=64', '2*5=10'] Exploring Operation: 64*10=640, Resulting Numbers: [640] 640,22 unequal: No Solution Exploring Operation: 64-10=54, Resulting Numbers: [54] 54,22 unequal: No Solution Exploring Operation: 64+10=74, Resulting Numbers: [74] 74,22 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_3
sum_heuristic
[ 98, 3, 66, 19 ]
27
[ "98+19=117", "117/3=39", "66-39=27" ]
Current State: 27:[98, 3, 66, 19], Operations: [] Exploring Operation: 98+19=117, Resulting Numbers: [3, 66, 117] Generated Node #2: [3, 66, 117] from Operation: 98+19=117 Current State: 27:[3, 66, 117], Operations: ['98+19=117'] Exploring Operation: 117/3=39, Resulting Numbers: [66, 39] Generated Node #3: [66, 39] from Operation: 117/3=39 Current State: 27:[66, 39], Operations: ['98+19=117', '117/3=39'] Exploring Operation: 66-39=27, Resulting Numbers: [27] 27,27 equal: Goal Reached
4
Current State: 27:[98, 3, 66, 19], Operations: [] Exploring Operation: 98-19=79, Resulting Numbers: [3, 66, 79] Generated Node #0,0: 27:[3, 66, 79] Operation: 98-19=79 Exploring Operation: 66/3=22, Resulting Numbers: [98, 19, 22] Generated Node #0,1: 27:[98, 19, 22] Operation: 66/3=22 Exploring Operation: 66-19=47, Resulting Numbers: [98, 3, 47] Generated Node #0,2: 27:[98, 3, 47] Operation: 66-19=47 Exploring Operation: 98-66=32, Resulting Numbers: [3, 19, 32] Generated Node #0,3: 27:[3, 19, 32] Operation: 98-66=32 Moving to Node #0,3 Current State: 27:[3, 19, 32], Operations: ['98-66=32'] Exploring Operation: 32-19=13, Resulting Numbers: [3, 13] Generated Node #0,3,0: 27:[3, 13] Operation: 32-19=13 Exploring Operation: 3+19=22, Resulting Numbers: [32, 22] Generated Node #0,3,1: 27:[32, 22] Operation: 3+19=22 Exploring Operation: 32-3=29, Resulting Numbers: [19, 29] Generated Node #0,3,2: 27:[19, 29] Operation: 32-3=29 Exploring Operation: 19-3=16, Resulting Numbers: [32, 16] Generated Node #0,3,3: 27:[32, 16] Operation: 19-3=16 Moving to Node #0,1 Current State: 27:[98, 19, 22], Operations: ['66/3=22'] Exploring Operation: 98-22=76, Resulting Numbers: [19, 76] Generated Node #0,1,0: 27:[19, 76] Operation: 98-22=76 Exploring Operation: 22-19=3, Resulting Numbers: [98, 3] Generated Node #0,1,1: 27:[98, 3] Operation: 22-19=3 Exploring Operation: 19+22=41, Resulting Numbers: [98, 41] Generated Node #0,1,2: 27:[98, 41] Operation: 19+22=41 Exploring Operation: 98-19=79, Resulting Numbers: [22, 79] Generated Node #0,1,3: 27:[22, 79] Operation: 98-19=79 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 27:[19, 76], Operations: ['66/3=22', '98-22=76'] Exploring Operation: 76-19=57, Resulting Numbers: [57] 57,27 unequal: No Solution Exploring Operation: 76/19=4, Resulting Numbers: [4] 4,27 unequal: No Solution Exploring Operation: 19*76=1444, Resulting Numbers: [1444] 1444,27 unequal: No Solution Exploring Operation: 19+76=95, Resulting Numbers: [95] 95,27 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 27:[22, 79], Operations: ['66/3=22', '98-19=79'] Exploring Operation: 79-22=57, Resulting Numbers: [57] 57,27 unequal: No Solution Exploring Operation: 22+79=101, Resulting Numbers: [101] 101,27 unequal: No Solution Exploring Operation: 22*79=1738, Resulting Numbers: [1738] 1738,27 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 27:[98, 3], Operations: ['66/3=22', '22-19=3'] Exploring Operation: 98*3=294, Resulting Numbers: [294] 294,27 unequal: No Solution Exploring Operation: 98+3=101, Resulting Numbers: [101] 101,27 unequal: No Solution Exploring Operation: 98-3=95, Resulting Numbers: [95] 95,27 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 27:[98, 41], Operations: ['66/3=22', '19+22=41'] Exploring Operation: 98+41=139, Resulting Numbers: [139] 139,27 unequal: No Solution Exploring Operation: 98-41=57, Resulting Numbers: [57] 57,27 unequal: No Solution Exploring Operation: 98*41=4018, Resulting Numbers: [4018] 4018,27 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,2 Current State: 27:[98, 3, 47], Operations: ['66-19=47'] Exploring Operation: 47-3=44, Resulting Numbers: [98, 44] Generated Node #0,2,0: 27:[98, 44] Operation: 47-3=44 Exploring Operation: 98-3=95, Resulting Numbers: [47, 95] Generated Node #0,2,1: 27:[47, 95] Operation: 98-3=95 Exploring Operation: 98+3=101, Resulting Numbers: [47, 101] Generated Node #0,2,2: 27:[47, 101] Operation: 98+3=101 Exploring Operation: 98-47=51, Resulting Numbers: [3, 51] Generated Node #0,2,3: 27:[3, 51] Operation: 98-47=51 Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 27:[3, 51], Operations: ['66-19=47', '98-47=51'] Exploring Operation: 51/3=17, Resulting Numbers: [17] 17,27 unequal: No Solution Exploring Operation: 3+51=54, Resulting Numbers: [54] 54,27 unequal: No Solution Exploring Operation: 51-3=48, Resulting Numbers: [48] 48,27 unequal: No Solution Exploring Operation: 3*51=153, Resulting Numbers: [153] 153,27 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 27:[98, 44], Operations: ['66-19=47', '47-3=44'] Exploring Operation: 98*44=4312, Resulting Numbers: [4312] 4312,27 unequal: No Solution Exploring Operation: 98-44=54, Resulting Numbers: [54] 54,27 unequal: No Solution Exploring Operation: 98+44=142, Resulting Numbers: [142] 142,27 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 27:[47, 95], Operations: ['66-19=47', '98-3=95'] Exploring Operation: 95-47=48, Resulting Numbers: [48] 48,27 unequal: No Solution Exploring Operation: 47*95=4465, Resulting Numbers: [4465] 4465,27 unequal: No Solution Exploring Operation: 47+95=142, Resulting Numbers: [142] 142,27 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 27:[47, 101], Operations: ['66-19=47', '98+3=101'] Exploring Operation: 47*101=4747, Resulting Numbers: [4747] 4747,27 unequal: No Solution Exploring Operation: 101-47=54, Resulting Numbers: [54] 54,27 unequal: No Solution Exploring Operation: 47+101=148, Resulting Numbers: [148] 148,27 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,0 Current State: 27:[3, 66, 79], Operations: ['98-19=79'] Exploring Operation: 79-66=13, Resulting Numbers: [3, 13] Generated Node #0,0,0: 27:[3, 13] Operation: 79-66=13 Exploring Operation: 66/3=22, Resulting Numbers: [79, 22] Generated Node #0,0,1: 27:[79, 22] Operation: 66/3=22 Exploring Operation: 66-3=63, Resulting Numbers: [79, 63] Generated Node #0,0,2: 27:[79, 63] Operation: 66-3=63 Exploring Operation: 79-3=76, Resulting Numbers: [66, 76] Generated Node #0,0,3: 27:[66, 76] Operation: 79-3=76 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 27:[3, 13], Operations: ['98-19=79', '79-66=13'] Exploring Operation: 3+13=16, Resulting Numbers: [16] 16,27 unequal: No Solution Exploring Operation: 13-3=10, Resulting Numbers: [10] 10,27 unequal: No Solution Exploring Operation: 3*13=39, Resulting Numbers: [39] 39,27 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 27:[79, 22], Operations: ['98-19=79', '66/3=22'] Exploring Operation: 79-22=57, Resulting Numbers: [57] 57,27 unequal: No Solution Exploring Operation: 79+22=101, Resulting Numbers: [101] 101,27 unequal: No Solution Exploring Operation: 79*22=1738, Resulting Numbers: [1738] 1738,27 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 27:[79, 63], Operations: ['98-19=79', '66-3=63'] Exploring Operation: 79-63=16, Resulting Numbers: [16] 16,27 unequal: No Solution Exploring Operation: 79*63=4977, Resulting Numbers: [4977] 4977,27 unequal: No Solution Exploring Operation: 79+63=142, Resulting Numbers: [142] 142,27 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 27:[66, 76], Operations: ['98-19=79', '79-3=76'] Exploring Operation: 66+76=142, Resulting Numbers: [142] 142,27 unequal: No Solution Exploring Operation: 66*76=5016, Resulting Numbers: [5016] 5016,27 unequal: No Solution Exploring Operation: 76-66=10, Resulting Numbers: [10] 10,27 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,3,0 Current State: 27:[3, 13], Operations: ['98-66=32', '32-19=13'] Exploring Operation: 13-3=10, Resulting Numbers: [10] 10,27 unequal: No Solution Exploring Operation: 3+13=16, Resulting Numbers: [16] 16,27 unequal: No Solution Exploring Operation: 3*13=39, Resulting Numbers: [39] 39,27 unequal: No Solution Moving to Node #0,3,2 Current State: 27:[19, 29], Operations: ['98-66=32', '32-3=29'] Exploring Operation: 29-19=10, Resulting Numbers: [10] 10,27 unequal: No Solution Exploring Operation: 19+29=48, Resulting Numbers: [48] 48,27 unequal: No Solution Exploring Operation: 19*29=551, Resulting Numbers: [551] 551,27 unequal: No Solution Moving to Node #0,3,1 Current State: 27:[32, 22], Operations: ['98-66=32', '3+19=22'] Exploring Operation: 32+22=54, Resulting Numbers: [54] 54,27 unequal: No Solution Exploring Operation: 32-22=10, Resulting Numbers: [10] 10,27 unequal: No Solution Exploring Operation: 32*22=704, Resulting Numbers: [704] 704,27 unequal: No Solution Moving to Node #0,3,3 Current State: 27:[32, 16], Operations: ['98-66=32', '19-3=16'] Exploring Operation: 32-16=16, Resulting Numbers: [16] 16,27 unequal: No Solution Exploring Operation: 32*16=512, Resulting Numbers: [512] 512,27 unequal: No Solution Exploring Operation: 32/16=2, Resulting Numbers: [2] 2,27 unequal: No Solution Exploring Operation: 32+16=48, Resulting Numbers: [48] 48,27 unequal: No Solution No solution found.
0
hs_4
mult_heuristic
[ 68, 72, 39, 56 ]
91
[ "72-68=4", "39+56=95", "95-4=91" ]
Current State: 91:[68, 72, 39, 56], Operations: [] Exploring Operation: 72-68=4, Resulting Numbers: [39, 56, 4] Generated Node #2: [39, 56, 4] from Operation: 72-68=4 Current State: 91:[39, 56, 4], Operations: ['72-68=4'] Exploring Operation: 39+56=95, Resulting Numbers: [4, 95] Generated Node #3: [4, 95] from Operation: 39+56=95 Current State: 91:[4, 95], Operations: ['72-68=4', '39+56=95'] Exploring Operation: 95-4=91, Resulting Numbers: [91] 91,91 equal: Goal Reached
4
Current State: 91:[68, 72, 39, 56], Operations: [] Exploring Operation: 72-68=4, Resulting Numbers: [39, 56, 4] Generated Node #0,0: 91:[39, 56, 4] Operation: 72-68=4 Exploring Operation: 39+56=95, Resulting Numbers: [68, 72, 95] Generated Node #0,1: 91:[68, 72, 95] Operation: 39+56=95 Exploring Operation: 56-39=17, Resulting Numbers: [68, 72, 17] Generated Node #0,2: 91:[68, 72, 17] Operation: 56-39=17 Exploring Operation: 68-56=12, Resulting Numbers: [72, 39, 12] Generated Node #0,3: 91:[72, 39, 12] Operation: 68-56=12 Exploring Operation: 72-56=16, Resulting Numbers: [68, 39, 16] Generated Node #0,4: 91:[68, 39, 16] Operation: 72-56=16 Moving to Node #0,1 Current State: 91:[68, 72, 95], Operations: ['39+56=95'] Exploring Operation: 95-68=27, Resulting Numbers: [72, 27] Generated Node #0,1,0: 91:[72, 27] Operation: 95-68=27 Exploring Operation: 72-68=4, Resulting Numbers: [95, 4] Generated Node #0,1,1: 91:[95, 4] Operation: 72-68=4 Exploring Operation: 68+95=163, Resulting Numbers: [72, 163] Generated Node #0,1,2: 91:[72, 163] Operation: 68+95=163 Exploring Operation: 95-72=23, Resulting Numbers: [68, 23] Generated Node #0,1,3: 91:[68, 23] Operation: 95-72=23 Exploring Operation: 68+72=140, Resulting Numbers: [95, 140] Generated Node #0,1,4: 91:[95, 140] Operation: 68+72=140 Moving to Node #0,3 Current State: 91:[72, 39, 12], Operations: ['68-56=12'] Exploring Operation: 39-12=27, Resulting Numbers: [72, 27] Generated Node #0,3,0: 91:[72, 27] Operation: 39-12=27 Exploring Operation: 72+39=111, Resulting Numbers: [12, 111] Generated Node #0,3,1: 91:[12, 111] Operation: 72+39=111 Exploring Operation: 72-39=33, Resulting Numbers: [12, 33] Generated Node #0,3,2: 91:[12, 33] Operation: 72-39=33 Exploring Operation: 72/12=6, Resulting Numbers: [39, 6] Generated Node #0,3,3: 91:[39, 6] Operation: 72/12=6 Exploring Operation: 72+12=84, Resulting Numbers: [39, 84] Generated Node #0,3,4: 91:[39, 84] Operation: 72+12=84 Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 91:[12, 111], Operations: ['68-56=12', '72+39=111'] Exploring Operation: 12*111=1332, Resulting Numbers: [1332] 1332,91 unequal: No Solution Exploring Operation: 12+111=123, Resulting Numbers: [123] 123,91 unequal: No Solution Exploring Operation: 111-12=99, Resulting Numbers: [99] 99,91 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 91:[12, 33], Operations: ['68-56=12', '72-39=33'] Exploring Operation: 12*33=396, Resulting Numbers: [396] 396,91 unequal: No Solution Exploring Operation: 12+33=45, Resulting Numbers: [45] 45,91 unequal: No Solution Exploring Operation: 33-12=21, Resulting Numbers: [21] 21,91 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 91:[39, 6], Operations: ['68-56=12', '72/12=6'] Exploring Operation: 39-6=33, Resulting Numbers: [33] 33,91 unequal: No Solution Exploring Operation: 39*6=234, Resulting Numbers: [234] 234,91 unequal: No Solution Exploring Operation: 39+6=45, Resulting Numbers: [45] 45,91 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 91:[72, 27], Operations: ['68-56=12', '39-12=27'] Exploring Operation: 72*27=1944, Resulting Numbers: [1944] 1944,91 unequal: No Solution Exploring Operation: 72-27=45, Resulting Numbers: [45] 45,91 unequal: No Solution Exploring Operation: 72+27=99, Resulting Numbers: [99] 99,91 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,4 Current State: 91:[39, 84], Operations: ['68-56=12', '72+12=84'] Exploring Operation: 39*84=3276, Resulting Numbers: [3276] 3276,91 unequal: No Solution Exploring Operation: 39+84=123, Resulting Numbers: [123] 123,91 unequal: No Solution Exploring Operation: 84-39=45, Resulting Numbers: [45] 45,91 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,2 Current State: 91:[68, 72, 17], Operations: ['56-39=17'] Exploring Operation: 72-68=4, Resulting Numbers: [17, 4] Generated Node #0,2,0: 91:[17, 4] Operation: 72-68=4 Exploring Operation: 68+72=140, Resulting Numbers: [17, 140] Generated Node #0,2,1: 91:[17, 140] Operation: 68+72=140 Exploring Operation: 72+17=89, Resulting Numbers: [68, 89] Generated Node #0,2,2: 91:[68, 89] Operation: 72+17=89 Exploring Operation: 68+17=85, Resulting Numbers: [72, 85] Generated Node #0,2,3: 91:[72, 85] Operation: 68+17=85 Exploring Operation: 68/17=4, Resulting Numbers: [72, 4] Generated Node #0,2,4: 91:[72, 4] Operation: 68/17=4 Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 91:[17, 4], Operations: ['56-39=17', '72-68=4'] Exploring Operation: 17*4=68, Resulting Numbers: [68] 68,91 unequal: No Solution Exploring Operation: 17-4=13, Resulting Numbers: [13] 13,91 unequal: No Solution Exploring Operation: 17+4=21, Resulting Numbers: [21] 21,91 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,4 Current State: 91:[72, 4], Operations: ['56-39=17', '68/17=4'] Exploring Operation: 72/4=18, Resulting Numbers: [18] 18,91 unequal: No Solution Exploring Operation: 72*4=288, Resulting Numbers: [288] 288,91 unequal: No Solution Exploring Operation: 72-4=68, Resulting Numbers: [68] 68,91 unequal: No Solution Exploring Operation: 72+4=76, Resulting Numbers: [76] 76,91 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 91:[68, 89], Operations: ['56-39=17', '72+17=89'] Exploring Operation: 68+89=157, Resulting Numbers: [157] 157,91 unequal: No Solution Exploring Operation: 89-68=21, Resulting Numbers: [21] 21,91 unequal: No Solution Exploring Operation: 68*89=6052, Resulting Numbers: [6052] 6052,91 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 91:[72, 85], Operations: ['56-39=17', '68+17=85'] Exploring Operation: 85-72=13, Resulting Numbers: [13] 13,91 unequal: No Solution Exploring Operation: 72*85=6120, Resulting Numbers: [6120] 6120,91 unequal: No Solution Exploring Operation: 72+85=157, Resulting Numbers: [157] 157,91 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 91:[17, 140], Operations: ['56-39=17', '68+72=140'] Exploring Operation: 17+140=157, Resulting Numbers: [157] 157,91 unequal: No Solution Exploring Operation: 17*140=2380, Resulting Numbers: [2380] 2380,91 unequal: No Solution Exploring Operation: 140-17=123, Resulting Numbers: [123] 123,91 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,4 Current State: 91:[68, 39, 16], Operations: ['72-56=16'] Exploring Operation: 39+16=55, Resulting Numbers: [68, 55] Generated Node #0,4,0: 91:[68, 55] Operation: 39+16=55 Exploring Operation: 68+16=84, Resulting Numbers: [39, 84] Generated Node #0,4,1: 91:[39, 84] Operation: 68+16=84 Exploring Operation: 68-39=29, Resulting Numbers: [16, 29] Generated Node #0,4,2: 91:[16, 29] Operation: 68-39=29 Exploring Operation: 39-16=23, Resulting Numbers: [68, 23] Generated Node #0,4,3: 91:[68, 23] Operation: 39-16=23 Exploring Operation: 68+39=107, Resulting Numbers: [16, 107] Generated Node #0,4,4: 91:[16, 107] Operation: 68+39=107 Start Sub Search at level 1: Moving to Node #0,4,2 Current State: 91:[16, 29], Operations: ['72-56=16', '68-39=29'] Exploring Operation: 16*29=464, Resulting Numbers: [464] 464,91 unequal: No Solution Exploring Operation: 29-16=13, Resulting Numbers: [13] 13,91 unequal: No Solution Exploring Operation: 16+29=45, Resulting Numbers: [45] 45,91 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,4 Current State: 91:[16, 107], Operations: ['72-56=16', '68+39=107'] Exploring Operation: 16*107=1712, Resulting Numbers: [1712] 1712,91 unequal: No Solution Exploring Operation: 107-16=91, Resulting Numbers: [91] 91,91 equal: Goal Reached Moving to Node #0 Current State: 91:[68, 72, 39, 56], Operations: [] Exploring Operation: 72-56=16, Resulting Numbers: [68, 39, 16] Generated Node #0,4: 91:[68, 39, 16] Operation: 72-56=16 Moving to Node #0,4 Current State: 91:[68, 39, 16], Operations: ['72-56=16'] Exploring Operation: 68+39=107, Resulting Numbers: [16, 107] Generated Node #0,4,4: 91:[16, 107] Operation: 68+39=107 Moving to Node #0,4,4 Current State: 91:[16, 107], Operations: ['72-56=16', '68+39=107'] Exploring Operation: 107-16=91, Resulting Numbers: [91] 91,91 equal: Goal Reached Exit Sub Search at level 1
0.943576
hs_5
mult_heuristic
[ 3, 4, 31, 37 ]
60
[ "3*31=93", "37-4=33", "93-33=60" ]
Current State: 60:[3, 4, 31, 37], Operations: [] Exploring Operation: 3*31=93, Resulting Numbers: [4, 37, 93] Generated Node #2: [4, 37, 93] from Operation: 3*31=93 Current State: 60:[4, 37, 93], Operations: ['3*31=93'] Exploring Operation: 37-4=33, Resulting Numbers: [93, 33] Generated Node #3: [93, 33] from Operation: 37-4=33 Current State: 60:[93, 33], Operations: ['3*31=93', '37-4=33'] Exploring Operation: 93-33=60, Resulting Numbers: [60] 60,60 equal: Goal Reached
4
Current State: 60:[3, 4, 31, 37], Operations: [] Exploring Operation: 37-4=33, Resulting Numbers: [3, 31, 33] Generated Node #0,0: 60:[3, 31, 33] Operation: 37-4=33 Exploring Operation: 37-31=6, Resulting Numbers: [3, 4, 6] Generated Node #0,1: 60:[3, 4, 6] Operation: 37-31=6 Moving to Node #0,1 Current State: 60:[3, 4, 6], Operations: ['37-31=6'] Exploring Operation: 6-3=3, Resulting Numbers: [4, 3] Generated Node #0,1,0: 60:[4, 3] Operation: 6-3=3 Exploring Operation: 3*4=12, Resulting Numbers: [6, 12] Generated Node #0,1,1: 60:[6, 12] Operation: 3*4=12 Moving to Node #0,0 Current State: 60:[3, 31, 33], Operations: ['37-4=33'] Exploring Operation: 33-31=2, Resulting Numbers: [3, 2] Generated Node #0,0,0: 60:[3, 2] Operation: 33-31=2 Exploring Operation: 33-3=30, Resulting Numbers: [31, 30] Generated Node #0,0,1: 60:[31, 30] Operation: 33-3=30 Moving to Node #0,1,0 Current State: 60:[4, 3], Operations: ['37-31=6', '6-3=3'] Exploring Operation: 4*3=12, Resulting Numbers: [12] 12,60 unequal: No Solution Exploring Operation: 4+3=7, Resulting Numbers: [7] 7,60 unequal: No Solution Moving to Node #0,0,0 Current State: 60:[3, 2], Operations: ['37-4=33', '33-31=2'] Exploring Operation: 3+2=5, Resulting Numbers: [5] 5,60 unequal: No Solution Exploring Operation: 3*2=6, Resulting Numbers: [6] 6,60 unequal: No Solution Moving to Node #0,1,1 Current State: 60:[6, 12], Operations: ['37-31=6', '3*4=12'] Exploring Operation: 12/6=2, Resulting Numbers: [2] 2,60 unequal: No Solution Exploring Operation: 12-6=6, Resulting Numbers: [6] 6,60 unequal: No Solution Moving to Node #0,0,1 Current State: 60:[31, 30], Operations: ['37-4=33', '33-3=30'] Exploring Operation: 31-30=1, Resulting Numbers: [1] 1,60 unequal: No Solution Exploring Operation: 31+30=61, Resulting Numbers: [61] 61,60 unequal: No Solution No solution found.
0
hs_2
mult_heuristic
[ 89, 64, 64, 65 ]
65
[ "64-64=0", "89*0=0", "65+0=65" ]
Current State: 65:[89, 64, 64, 65], Operations: [] Exploring Operation: 64-64=0, Resulting Numbers: [89, 65, 0] Generated Node #2: [89, 65, 0] from Operation: 64-64=0 Current State: 65:[89, 65, 0], Operations: ['64-64=0'] Exploring Operation: 89*0=0, Resulting Numbers: [65, 0] Generated Node #3: [65, 0] from Operation: 89*0=0 Current State: 65:[65, 0], Operations: ['64-64=0', '89*0=0'] Exploring Operation: 65+0=65, Resulting Numbers: [65] 65,65 equal: Goal Reached
4
Current State: 65:[89, 64, 64, 65], Operations: [] Exploring Operation: 89-65=24, Resulting Numbers: [64, 64, 24] Generated Node #0,0: 65:[64, 64, 24] Operation: 89-65=24 Exploring Operation: 89-64=25, Resulting Numbers: [64, 65, 25] Generated Node #0,1: 65:[64, 65, 25] Operation: 89-64=25 Exploring Operation: 64-64=0, Resulting Numbers: [89, 65, 0] Generated Node #0,2: 65:[89, 65, 0] Operation: 64-64=0 Exploring Operation: 89-64=25, Resulting Numbers: [64, 65, 25] Generated Node #0,3: 65:[64, 65, 25] Operation: 89-64=25 Exploring Operation: 64/64=1, Resulting Numbers: [89, 65, 1] Generated Node #0,4: 65:[89, 65, 1] Operation: 64/64=1 Moving to Node #0,0 Current State: 65:[64, 64, 24], Operations: ['89-65=24'] Exploring Operation: 64/64=1, Resulting Numbers: [24, 1] Generated Node #0,0,0: 65:[24, 1] Operation: 64/64=1 Exploring Operation: 64-24=40, Resulting Numbers: [64, 40] Generated Node #0,0,1: 65:[64, 40] Operation: 64-24=40 Exploring Operation: 64-64=0, Resulting Numbers: [24, 0] Generated Node #0,0,2: 65:[24, 0] Operation: 64-64=0 Exploring Operation: 64+24=88, Resulting Numbers: [64, 88] Generated Node #0,0,3: 65:[64, 88] Operation: 64+24=88 Exploring Operation: 64+24=88, Resulting Numbers: [64, 88] Generated Node #0,0,4: 65:[64, 88] Operation: 64+24=88 Moving to Node #0,3 Current State: 65:[64, 65, 25], Operations: ['89-64=25'] Exploring Operation: 64-25=39, Resulting Numbers: [65, 39] Generated Node #0,3,0: 65:[65, 39] Operation: 64-25=39 Exploring Operation: 64+25=89, Resulting Numbers: [65, 89] Generated Node #0,3,1: 65:[65, 89] Operation: 64+25=89 Exploring Operation: 65-25=40, Resulting Numbers: [64, 40] Generated Node #0,3,2: 65:[64, 40] Operation: 65-25=40 Exploring Operation: 65-64=1, Resulting Numbers: [25, 1] Generated Node #0,3,3: 65:[25, 1] Operation: 65-64=1 Exploring Operation: 65+25=90, Resulting Numbers: [64, 90] Generated Node #0,3,4: 65:[64, 90] Operation: 65+25=90 Moving to Node #0,1 Current State: 65:[64, 65, 25], Operations: ['89-64=25'] Exploring Operation: 64-25=39, Resulting Numbers: [65, 39] Generated Node #0,1,0: 65:[65, 39] Operation: 64-25=39 Exploring Operation: 65+25=90, Resulting Numbers: [64, 90] Generated Node #0,1,1: 65:[64, 90] Operation: 65+25=90 Exploring Operation: 64+25=89, Resulting Numbers: [65, 89] Generated Node #0,1,2: 65:[65, 89] Operation: 64+25=89 Exploring Operation: 65-25=40, Resulting Numbers: [64, 40] Generated Node #0,1,3: 65:[64, 40] Operation: 65-25=40 Exploring Operation: 65-64=1, Resulting Numbers: [25, 1] Generated Node #0,1,4: 65:[25, 1] Operation: 65-64=1 Start Sub Search at level 1: Moving to Node #0,1,4 Current State: 65:[25, 1], Operations: ['89-64=25', '65-64=1'] Exploring Operation: 25*1=25, Resulting Numbers: [25] 25,65 unequal: No Solution Exploring Operation: 25-1=24, Resulting Numbers: [24] 24,65 unequal: No Solution Exploring Operation: 25/1=25, Resulting Numbers: [25] 25,65 unequal: No Solution Exploring Operation: 25+1=26, Resulting Numbers: [26] 26,65 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 65:[65, 89], Operations: ['89-64=25', '64+25=89'] Exploring Operation: 65+89=154, Resulting Numbers: [154] 154,65 unequal: No Solution Exploring Operation: 65*89=5785, Resulting Numbers: [5785] 5785,65 unequal: No Solution Exploring Operation: 89-65=24, Resulting Numbers: [24] 24,65 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 65:[65, 39], Operations: ['89-64=25', '64-25=39'] Exploring Operation: 65-39=26, Resulting Numbers: [26] 26,65 unequal: No Solution Exploring Operation: 65*39=2535, Resulting Numbers: [2535] 2535,65 unequal: No Solution Exploring Operation: 65+39=104, Resulting Numbers: [104] 104,65 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 65:[64, 90], Operations: ['89-64=25', '65+25=90'] Exploring Operation: 90-64=26, Resulting Numbers: [26] 26,65 unequal: No Solution Exploring Operation: 64+90=154, Resulting Numbers: [154] 154,65 unequal: No Solution Exploring Operation: 64*90=5760, Resulting Numbers: [5760] 5760,65 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 65:[64, 40], Operations: ['89-64=25', '65-25=40'] Exploring Operation: 64*40=2560, Resulting Numbers: [2560] 2560,65 unequal: No Solution Exploring Operation: 64+40=104, Resulting Numbers: [104] 104,65 unequal: No Solution Exploring Operation: 64-40=24, Resulting Numbers: [24] 24,65 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,4 Current State: 65:[89, 65, 1], Operations: ['64/64=1'] Exploring Operation: 89*1=89, Resulting Numbers: [65, 89] Generated Node #0,4,0: 65:[65, 89] Operation: 89*1=89 Exploring Operation: 89/1=89, Resulting Numbers: [65, 89] Generated Node #0,4,1: 65:[65, 89] Operation: 89/1=89 Exploring Operation: 65*1=65, Resulting Numbers: [89, 65] Generated Node #0,4,2: 65:[89, 65] Operation: 65*1=65 Exploring Operation: 89-1=88, Resulting Numbers: [65, 88] Generated Node #0,4,3: 65:[65, 88] Operation: 89-1=88 Exploring Operation: 89-65=24, Resulting Numbers: [1, 24] Generated Node #0,4,4: 65:[1, 24] Operation: 89-65=24 Start Sub Search at level 1: Moving to Node #0,4,4 Current State: 65:[1, 24], Operations: ['64/64=1', '89-65=24'] Exploring Operation: 1+24=25, Resulting Numbers: [25] 25,65 unequal: No Solution Exploring Operation: 1*24=24, Resulting Numbers: [24] 24,65 unequal: No Solution Exploring Operation: 24/1=24, Resulting Numbers: [24] 24,65 unequal: No Solution Exploring Operation: 24-1=23, Resulting Numbers: [23] 23,65 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,3 Current State: 65:[65, 88], Operations: ['64/64=1', '89-1=88'] Exploring Operation: 88-65=23, Resulting Numbers: [23] 23,65 unequal: No Solution Exploring Operation: 65*88=5720, Resulting Numbers: [5720] 5720,65 unequal: No Solution Exploring Operation: 65+88=153, Resulting Numbers: [153] 153,65 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,0 Current State: 65:[65, 89], Operations: ['64/64=1', '89*1=89'] Exploring Operation: 65+89=154, Resulting Numbers: [154] 154,65 unequal: No Solution Exploring Operation: 65*89=5785, Resulting Numbers: [5785] 5785,65 unequal: No Solution Exploring Operation: 89-65=24, Resulting Numbers: [24] 24,65 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,1 Current State: 65:[65, 89], Operations: ['64/64=1', '89/1=89'] Exploring Operation: 89-65=24, Resulting Numbers: [24] 24,65 unequal: No Solution Exploring Operation: 65*89=5785, Resulting Numbers: [5785] 5785,65 unequal: No Solution Exploring Operation: 65+89=154, Resulting Numbers: [154] 154,65 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,2 Current State: 65:[89, 65], Operations: ['64/64=1', '65*1=65'] Exploring Operation: 89-65=24, Resulting Numbers: [24] 24,65 unequal: No Solution Exploring Operation: 89+65=154, Resulting Numbers: [154] 154,65 unequal: No Solution Exploring Operation: 89*65=5785, Resulting Numbers: [5785] 5785,65 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,2 Current State: 65:[89, 65, 0], Operations: ['64-64=0'] Exploring Operation: 89-65=24, Resulting Numbers: [0, 24] Generated Node #0,2,0: 65:[0, 24] Operation: 89-65=24 Exploring Operation: 89*0=0, Resulting Numbers: [65, 0] Generated Node #0,2,1: 65:[65, 0] Operation: 89*0=0 Exploring Operation: 65+0=65, Resulting Numbers: [89, 65] Generated Node #0,2,2: 65:[89, 65] Operation: 65+0=65 Exploring Operation: 89+0=89, Resulting Numbers: [65, 89] Generated Node #0,2,3: 65:[65, 89] Operation: 89+0=89 Exploring Operation: 89-0=89, Resulting Numbers: [65, 89] Generated Node #0,2,4: 65:[65, 89] Operation: 89-0=89 Moving to Node #0,2,1 Current State: 65:[65, 0], Operations: ['64-64=0', '89*0=0'] Exploring Operation: 65*0=0, Resulting Numbers: [0] 0,65 unequal: No Solution Exploring Operation: 65-0=65, Resulting Numbers: [65] 65,65 equal: Goal Reached Moving to Node #0 Current State: 65:[89, 64, 64, 65], Operations: [] Exploring Operation: 64-64=0, Resulting Numbers: [89, 65, 0] Generated Node #0,2: 65:[89, 65, 0] Operation: 64-64=0 Moving to Node #0,2 Current State: 65:[89, 65, 0], Operations: ['64-64=0'] Exploring Operation: 89*0=0, Resulting Numbers: [65, 0] Generated Node #0,2,1: 65:[65, 0] Operation: 89*0=0 Moving to Node #0,2,1 Current State: 65:[65, 0], Operations: ['64-64=0', '89*0=0'] Exploring Operation: 65-0=65, Resulting Numbers: [65] 65,65 equal: Goal Reached
0.940972
hs_5
mult_heuristic
[ 64, 27, 39, 90 ]
45
[ "64-27=37", "39-37=2", "90/2=45" ]
Current State: 45:[64, 27, 39, 90], Operations: [] Exploring Operation: 64-27=37, Resulting Numbers: [39, 90, 37] Generated Node #2: [39, 90, 37] from Operation: 64-27=37 Current State: 45:[39, 90, 37], Operations: ['64-27=37'] Exploring Operation: 39-37=2, Resulting Numbers: [90, 2] Generated Node #3: [90, 2] from Operation: 39-37=2 Current State: 45:[90, 2], Operations: ['64-27=37', '39-37=2'] Exploring Operation: 90/2=45, Resulting Numbers: [45] 45,45 equal: Goal Reached
4
Current State: 45:[64, 27, 39, 90], Operations: [] Exploring Operation: 64-27=37, Resulting Numbers: [39, 90, 37] Generated Node #0,0: 45:[39, 90, 37] Operation: 64-27=37 Exploring Operation: 90-64=26, Resulting Numbers: [27, 39, 26] Generated Node #0,1: 45:[27, 39, 26] Operation: 90-64=26 Exploring Operation: 90-39=51, Resulting Numbers: [64, 27, 51] Generated Node #0,2: 45:[64, 27, 51] Operation: 90-39=51 Exploring Operation: 90-27=63, Resulting Numbers: [64, 39, 63] Generated Node #0,3: 45:[64, 39, 63] Operation: 90-27=63 Moving to Node #0,1 Current State: 45:[27, 39, 26], Operations: ['90-64=26'] Exploring Operation: 27-26=1, Resulting Numbers: [39, 1] Generated Node #0,1,0: 45:[39, 1] Operation: 27-26=1 Exploring Operation: 39-26=13, Resulting Numbers: [27, 13] Generated Node #0,1,1: 45:[27, 13] Operation: 39-26=13 Exploring Operation: 39-27=12, Resulting Numbers: [26, 12] Generated Node #0,1,2: 45:[26, 12] Operation: 39-27=12 Exploring Operation: 27+26=53, Resulting Numbers: [39, 53] Generated Node #0,1,3: 45:[39, 53] Operation: 27+26=53 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 45:[39, 1], Operations: ['90-64=26', '27-26=1'] Exploring Operation: 39+1=40, Resulting Numbers: [40] 40,45 unequal: No Solution Exploring Operation: 39*1=39, Resulting Numbers: [39] 39,45 unequal: No Solution Exploring Operation: 39-1=38, Resulting Numbers: [38] 38,45 unequal: No Solution Exploring Operation: 39/1=39, Resulting Numbers: [39] 39,45 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 45:[27, 13], Operations: ['90-64=26', '39-26=13'] Exploring Operation: 27+13=40, Resulting Numbers: [40] 40,45 unequal: No Solution Exploring Operation: 27-13=14, Resulting Numbers: [14] 14,45 unequal: No Solution Exploring Operation: 27*13=351, Resulting Numbers: [351] 351,45 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 45:[26, 12], Operations: ['90-64=26', '39-27=12'] Exploring Operation: 26-12=14, Resulting Numbers: [14] 14,45 unequal: No Solution Exploring Operation: 26+12=38, Resulting Numbers: [38] 38,45 unequal: No Solution Exploring Operation: 26*12=312, Resulting Numbers: [312] 312,45 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 45:[39, 53], Operations: ['90-64=26', '27+26=53'] Exploring Operation: 39+53=92, Resulting Numbers: [92] 92,45 unequal: No Solution Exploring Operation: 53-39=14, Resulting Numbers: [14] 14,45 unequal: No Solution Exploring Operation: 39*53=2067, Resulting Numbers: [2067] 2067,45 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,2 Current State: 45:[64, 27, 51], Operations: ['90-39=51'] Exploring Operation: 51-27=24, Resulting Numbers: [64, 24] Generated Node #0,2,0: 45:[64, 24] Operation: 51-27=24 Exploring Operation: 64-27=37, Resulting Numbers: [51, 37] Generated Node #0,2,1: 45:[51, 37] Operation: 64-27=37 Exploring Operation: 64-51=13, Resulting Numbers: [27, 13] Generated Node #0,2,2: 45:[27, 13] Operation: 64-51=13 Exploring Operation: 64+27=91, Resulting Numbers: [51, 91] Generated Node #0,2,3: 45:[51, 91] Operation: 64+27=91 Moving to Node #0,3 Current State: 45:[64, 39, 63], Operations: ['90-27=63'] Exploring Operation: 63-39=24, Resulting Numbers: [64, 24] Generated Node #0,3,0: 45:[64, 24] Operation: 63-39=24 Exploring Operation: 64-63=1, Resulting Numbers: [39, 1] Generated Node #0,3,1: 45:[39, 1] Operation: 64-63=1 Exploring Operation: 64+39=103, Resulting Numbers: [63, 103] Generated Node #0,3,2: 45:[63, 103] Operation: 64+39=103 Exploring Operation: 64-39=25, Resulting Numbers: [63, 25] Generated Node #0,3,3: 45:[63, 25] Operation: 64-39=25 Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 45:[39, 1], Operations: ['90-27=63', '64-63=1'] Exploring Operation: 39*1=39, Resulting Numbers: [39] 39,45 unequal: No Solution Exploring Operation: 39+1=40, Resulting Numbers: [40] 40,45 unequal: No Solution Exploring Operation: 39-1=38, Resulting Numbers: [38] 38,45 unequal: No Solution Exploring Operation: 39/1=39, Resulting Numbers: [39] 39,45 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 45:[64, 24], Operations: ['90-27=63', '63-39=24'] Exploring Operation: 64-24=40, Resulting Numbers: [40] 40,45 unequal: No Solution Exploring Operation: 64*24=1536, Resulting Numbers: [1536] 1536,45 unequal: No Solution Exploring Operation: 64+24=88, Resulting Numbers: [88] 88,45 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 45:[63, 25], Operations: ['90-27=63', '64-39=25'] Exploring Operation: 63-25=38, Resulting Numbers: [38] 38,45 unequal: No Solution Exploring Operation: 63*25=1575, Resulting Numbers: [1575] 1575,45 unequal: No Solution Exploring Operation: 63+25=88, Resulting Numbers: [88] 88,45 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 45:[63, 103], Operations: ['90-27=63', '64+39=103'] Exploring Operation: 63+103=166, Resulting Numbers: [166] 166,45 unequal: No Solution Exploring Operation: 63*103=6489, Resulting Numbers: [6489] 6489,45 unequal: No Solution Exploring Operation: 103-63=40, Resulting Numbers: [40] 40,45 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,0 Current State: 45:[39, 90, 37], Operations: ['64-27=37'] Exploring Operation: 39-37=2, Resulting Numbers: [90, 2] Generated Node #0,0,0: 45:[90, 2] Operation: 39-37=2 Exploring Operation: 90-37=53, Resulting Numbers: [39, 53] Generated Node #0,0,1: 45:[39, 53] Operation: 90-37=53 Exploring Operation: 90-39=51, Resulting Numbers: [37, 51] Generated Node #0,0,2: 45:[37, 51] Operation: 90-39=51 Exploring Operation: 39+37=76, Resulting Numbers: [90, 76] Generated Node #0,0,3: 45:[90, 76] Operation: 39+37=76 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 45:[39, 53], Operations: ['64-27=37', '90-37=53'] Exploring Operation: 39+53=92, Resulting Numbers: [92] 92,45 unequal: No Solution Exploring Operation: 53-39=14, Resulting Numbers: [14] 14,45 unequal: No Solution Exploring Operation: 39*53=2067, Resulting Numbers: [2067] 2067,45 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 45:[37, 51], Operations: ['64-27=37', '90-39=51'] Exploring Operation: 37*51=1887, Resulting Numbers: [1887] 1887,45 unequal: No Solution Exploring Operation: 51-37=14, Resulting Numbers: [14] 14,45 unequal: No Solution Exploring Operation: 37+51=88, Resulting Numbers: [88] 88,45 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 45:[90, 2], Operations: ['64-27=37', '39-37=2'] Exploring Operation: 90*2=180, Resulting Numbers: [180] 180,45 unequal: No Solution Exploring Operation: 90/2=45, Resulting Numbers: [45] 45,45 equal: Goal Reached Moving to Node #0 Current State: 45:[64, 27, 39, 90], Operations: [] Exploring Operation: 64-27=37, Resulting Numbers: [39, 90, 37] Generated Node #0,0: 45:[39, 90, 37] Operation: 64-27=37 Moving to Node #0,0 Current State: 45:[39, 90, 37], Operations: ['64-27=37'] Exploring Operation: 39-37=2, Resulting Numbers: [90, 2] Generated Node #0,0,0: 45:[90, 2] Operation: 39-37=2 Moving to Node #0,0,0 Current State: 45:[90, 2], Operations: ['64-27=37', '39-37=2'] Exploring Operation: 90/2=45, Resulting Numbers: [45] 45,45 equal: Goal Reached Exit Sub Search at level 1
0.949653
hs_4
sum_heuristic
[ 2, 50, 43, 48 ]
31
[ "48/2=24", "50-43=7", "24+7=31" ]
Current State: 31:[2, 50, 43, 48], Operations: [] Exploring Operation: 48/2=24, Resulting Numbers: [50, 43, 24] Generated Node #2: [50, 43, 24] from Operation: 48/2=24 Current State: 31:[50, 43, 24], Operations: ['48/2=24'] Exploring Operation: 50-43=7, Resulting Numbers: [24, 7] Generated Node #3: [24, 7] from Operation: 50-43=7 Current State: 31:[24, 7], Operations: ['48/2=24', '50-43=7'] Exploring Operation: 24+7=31, Resulting Numbers: [31] 31,31 equal: Goal Reached
4
Current State: 31:[2, 50, 43, 48], Operations: [] Exploring Operation: 48/2=24, Resulting Numbers: [50, 43, 24] Generated Node #0,0: 31:[50, 43, 24] Operation: 48/2=24 Exploring Operation: 50-2=48, Resulting Numbers: [43, 48, 48] Generated Node #0,1: 31:[43, 48, 48] Operation: 50-2=48 Exploring Operation: 43-2=41, Resulting Numbers: [50, 48, 41] Generated Node #0,2: 31:[50, 48, 41] Operation: 43-2=41 Exploring Operation: 50/2=25, Resulting Numbers: [43, 48, 25] Generated Node #0,3: 31:[43, 48, 25] Operation: 50/2=25 Start Sub Search at level 1: Moving to Node #0,3 Current State: 31:[43, 48, 25], Operations: ['50/2=25'] Exploring Operation: 43+25=68, Resulting Numbers: [48, 68] Generated Node #0,3,0: 31:[48, 68] Operation: 43+25=68 Exploring Operation: 48-25=23, Resulting Numbers: [43, 23] Generated Node #0,3,1: 31:[43, 23] Operation: 48-25=23 Exploring Operation: 43-25=18, Resulting Numbers: [48, 18] Generated Node #0,3,2: 31:[48, 18] Operation: 43-25=18 Exploring Operation: 48-43=5, Resulting Numbers: [25, 5] Generated Node #0,3,3: 31:[25, 5] Operation: 48-43=5 Start Sub Search at level 2: Moving to Node #0,3,1 Current State: 31:[43, 23], Operations: ['50/2=25', '48-25=23'] Exploring Operation: 43+23=66, Resulting Numbers: [66] 66,31 unequal: No Solution Exploring Operation: 43-23=20, Resulting Numbers: [20] 20,31 unequal: No Solution Exploring Operation: 43*23=989, Resulting Numbers: [989] 989,31 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,2 Current State: 31:[48, 18], Operations: ['50/2=25', '43-25=18'] Exploring Operation: 48-18=30, Resulting Numbers: [30] 30,31 unequal: No Solution Exploring Operation: 48*18=864, Resulting Numbers: [864] 864,31 unequal: No Solution Exploring Operation: 48+18=66, Resulting Numbers: [66] 66,31 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,3 Current State: 31:[25, 5], Operations: ['50/2=25', '48-43=5'] Exploring Operation: 25*5=125, Resulting Numbers: [125] 125,31 unequal: No Solution Exploring Operation: 25-5=20, Resulting Numbers: [20] 20,31 unequal: No Solution Exploring Operation: 25+5=30, Resulting Numbers: [30] 30,31 unequal: No Solution Exploring Operation: 25/5=5, Resulting Numbers: [5] 5,31 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,0 Current State: 31:[48, 68], Operations: ['50/2=25', '43+25=68'] Exploring Operation: 48+68=116, Resulting Numbers: [116] 116,31 unequal: No Solution Exploring Operation: 68-48=20, Resulting Numbers: [20] 20,31 unequal: No Solution Exploring Operation: 48*68=3264, Resulting Numbers: [3264] 3264,31 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 31:[50, 43, 24], Operations: ['48/2=24'] Exploring Operation: 43-24=19, Resulting Numbers: [50, 19] Generated Node #0,0,0: 31:[50, 19] Operation: 43-24=19 Exploring Operation: 50+24=74, Resulting Numbers: [43, 74] Generated Node #0,0,1: 31:[43, 74] Operation: 50+24=74 Exploring Operation: 50-43=7, Resulting Numbers: [24, 7] Generated Node #0,0,2: 31:[24, 7] Operation: 50-43=7 Exploring Operation: 50-24=26, Resulting Numbers: [43, 26] Generated Node #0,0,3: 31:[43, 26] Operation: 50-24=26 Moving to Node #0,0,3 Current State: 31:[43, 26], Operations: ['48/2=24', '50-24=26'] Exploring Operation: 43-26=17, Resulting Numbers: [17] 17,31 unequal: No Solution Exploring Operation: 43*26=1118, Resulting Numbers: [1118] 1118,31 unequal: No Solution Exploring Operation: 43+26=69, Resulting Numbers: [69] 69,31 unequal: No Solution Moving to Node #0,0,2 Current State: 31:[24, 7], Operations: ['48/2=24', '50-43=7'] Exploring Operation: 24+7=31, Resulting Numbers: [31] 31,31 equal: Goal Reached Moving to Node #0 Current State: 31:[2, 50, 43, 48], Operations: [] Exploring Operation: 48/2=24, Resulting Numbers: [50, 43, 24] Generated Node #0,0: 31:[50, 43, 24] Operation: 48/2=24 Moving to Node #0,0 Current State: 31:[50, 43, 24], Operations: ['48/2=24'] Exploring Operation: 50-43=7, Resulting Numbers: [24, 7] Generated Node #0,0,2: 31:[24, 7] Operation: 50-43=7 Moving to Node #0,0,2 Current State: 31:[24, 7], Operations: ['48/2=24', '50-43=7'] Exploring Operation: 24+7=31, Resulting Numbers: [31] 31,31 equal: Goal Reached Exit Sub Search at level 1
0.971354
hs_4
sum_heuristic
[ 94, 40, 20, 3 ]
50
[ "94*20=1880", "1880/40=47", "3+47=50" ]
Current State: 50:[94, 40, 20, 3], Operations: [] Exploring Operation: 94*20=1880, Resulting Numbers: [40, 3, 1880] Generated Node #2: [40, 3, 1880] from Operation: 94*20=1880 Current State: 50:[40, 3, 1880], Operations: ['94*20=1880'] Exploring Operation: 1880/40=47, Resulting Numbers: [3, 47] Generated Node #3: [3, 47] from Operation: 1880/40=47 Current State: 50:[3, 47], Operations: ['94*20=1880', '1880/40=47'] Exploring Operation: 3+47=50, Resulting Numbers: [50] 50,50 equal: Goal Reached
4
Current State: 50:[94, 40, 20, 3], Operations: [] Exploring Operation: 94-40=54, Resulting Numbers: [20, 3, 54] Generated Node #0,0: 50:[20, 3, 54] Operation: 94-40=54 Exploring Operation: 94-20=74, Resulting Numbers: [40, 3, 74] Generated Node #0,1: 50:[40, 3, 74] Operation: 94-20=74 Moving to Node #0,0 Current State: 50:[20, 3, 54], Operations: ['94-40=54'] Exploring Operation: 20+3=23, Resulting Numbers: [54, 23] Generated Node #0,0,0: 50:[54, 23] Operation: 20+3=23 Exploring Operation: 54-3=51, Resulting Numbers: [20, 51] Generated Node #0,0,1: 50:[20, 51] Operation: 54-3=51 Moving to Node #0,1 Current State: 50:[40, 3, 74], Operations: ['94-20=74'] Exploring Operation: 40+3=43, Resulting Numbers: [74, 43] Generated Node #0,1,0: 50:[74, 43] Operation: 40+3=43 Exploring Operation: 74-40=34, Resulting Numbers: [3, 34] Generated Node #0,1,1: 50:[3, 34] Operation: 74-40=34 Moving to Node #0,0,0 Current State: 50:[54, 23], Operations: ['94-40=54', '20+3=23'] Exploring Operation: 54-23=31, Resulting Numbers: [31] 31,50 unequal: No Solution Exploring Operation: 54+23=77, Resulting Numbers: [77] 77,50 unequal: No Solution Moving to Node #0,0,1 Current State: 50:[20, 51], Operations: ['94-40=54', '54-3=51'] Exploring Operation: 51-20=31, Resulting Numbers: [31] 31,50 unequal: No Solution Exploring Operation: 20+51=71, Resulting Numbers: [71] 71,50 unequal: No Solution Moving to Node #0,1,1 Current State: 50:[3, 34], Operations: ['94-20=74', '74-40=34'] Exploring Operation: 34-3=31, Resulting Numbers: [31] 31,50 unequal: No Solution Exploring Operation: 3+34=37, Resulting Numbers: [37] 37,50 unequal: No Solution Moving to Node #0,1,0 Current State: 50:[74, 43], Operations: ['94-20=74', '40+3=43'] Exploring Operation: 74-43=31, Resulting Numbers: [31] 31,50 unequal: No Solution Exploring Operation: 74+43=117, Resulting Numbers: [117] 117,50 unequal: No Solution No solution found.
0
hs_2
sum_heuristic
[ 74, 23, 30, 6 ]
92
[ "74+23=97", "30/6=5", "97-5=92" ]
Current State: 92:[74, 23, 30, 6], Operations: [] Exploring Operation: 74+23=97, Resulting Numbers: [30, 6, 97] Generated Node #2: [30, 6, 97] from Operation: 74+23=97 Current State: 92:[30, 6, 97], Operations: ['74+23=97'] Exploring Operation: 30/6=5, Resulting Numbers: [97, 5] Generated Node #3: [97, 5] from Operation: 30/6=5 Current State: 92:[97, 5], Operations: ['74+23=97', '30/6=5'] Exploring Operation: 97-5=92, Resulting Numbers: [92] 92,92 equal: Goal Reached
4
Current State: 92:[74, 23, 30, 6], Operations: [] Exploring Operation: 74-30=44, Resulting Numbers: [23, 6, 44] Generated Node #0,0: 92:[23, 6, 44] Operation: 74-30=44 Exploring Operation: 74+23=97, Resulting Numbers: [30, 6, 97] Generated Node #0,1: 92:[30, 6, 97] Operation: 74+23=97 Start Sub Search at level 1: Moving to Node #0,0 Current State: 92:[23, 6, 44], Operations: ['74-30=44'] Exploring Operation: 6+44=50, Resulting Numbers: [23, 50] Generated Node #0,0,0: 92:[23, 50] Operation: 6+44=50 Exploring Operation: 44-23=21, Resulting Numbers: [6, 21] Generated Node #0,0,1: 92:[6, 21] Operation: 44-23=21 Moving to Node #0,0,0 Current State: 92:[23, 50], Operations: ['74-30=44', '6+44=50'] Exploring Operation: 50-23=27, Resulting Numbers: [27] 27,92 unequal: No Solution Exploring Operation: 23+50=73, Resulting Numbers: [73] 73,92 unequal: No Solution Moving to Node #0,0,1 Current State: 92:[6, 21], Operations: ['74-30=44', '44-23=21'] Exploring Operation: 21-6=15, Resulting Numbers: [15] 15,92 unequal: No Solution Exploring Operation: 6+21=27, Resulting Numbers: [27] 27,92 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 92:[30, 6, 97], Operations: ['74+23=97'] Exploring Operation: 30-6=24, Resulting Numbers: [97, 24] Generated Node #0,1,0: 92:[97, 24] Operation: 30-6=24 Exploring Operation: 30/6=5, Resulting Numbers: [97, 5] Generated Node #0,1,1: 92:[97, 5] Operation: 30/6=5 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 92:[97, 24], Operations: ['74+23=97', '30-6=24'] Exploring Operation: 97+24=121, Resulting Numbers: [121] 121,92 unequal: No Solution Exploring Operation: 97-24=73, Resulting Numbers: [73] 73,92 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 92:[97, 5], Operations: ['74+23=97', '30/6=5'] Exploring Operation: 97-5=92, Resulting Numbers: [92] 92,92 equal: Goal Reached Moving to Node #0 Current State: 92:[74, 23, 30, 6], Operations: [] Exploring Operation: 74+23=97, Resulting Numbers: [30, 6, 97] Generated Node #0,1: 92:[30, 6, 97] Operation: 74+23=97 Moving to Node #0,1 Current State: 92:[30, 6, 97], Operations: ['74+23=97'] Exploring Operation: 30/6=5, Resulting Numbers: [97, 5] Generated Node #0,1,1: 92:[97, 5] Operation: 30/6=5 Moving to Node #0,1,1 Current State: 92:[97, 5], Operations: ['74+23=97', '30/6=5'] Exploring Operation: 97-5=92, Resulting Numbers: [92] 92,92 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.985243
hs_2
sum_heuristic
[ 91, 7, 82, 9 ]
88
[ "91-82=9", "9*9=81", "7+81=88" ]
Current State: 88:[91, 7, 82, 9], Operations: [] Exploring Operation: 91-82=9, Resulting Numbers: [7, 9, 9] Generated Node #2: [7, 9, 9] from Operation: 91-82=9 Current State: 88:[7, 9, 9], Operations: ['91-82=9'] Exploring Operation: 9*9=81, Resulting Numbers: [7, 81] Generated Node #3: [7, 81] from Operation: 9*9=81 Current State: 88:[7, 81], Operations: ['91-82=9', '9*9=81'] Exploring Operation: 7+81=88, Resulting Numbers: [88] 88,88 equal: Goal Reached
4
Current State: 88:[91, 7, 82, 9], Operations: [] Exploring Operation: 91-82=9, Resulting Numbers: [7, 9, 9] Generated Node #0,0: 88:[7, 9, 9] Operation: 91-82=9 Exploring Operation: 7+82=89, Resulting Numbers: [91, 9, 89] Generated Node #0,1: 88:[91, 9, 89] Operation: 7+82=89 Exploring Operation: 82+9=91, Resulting Numbers: [91, 7, 91] Generated Node #0,2: 88:[91, 7, 91] Operation: 82+9=91 Moving to Node #0,0 Current State: 88:[7, 9, 9], Operations: ['91-82=9'] Exploring Operation: 9/9=1, Resulting Numbers: [7, 1] Generated Node #0,0,0: 88:[7, 1] Operation: 9/9=1 Exploring Operation: 9-7=2, Resulting Numbers: [9, 2] Generated Node #0,0,1: 88:[9, 2] Operation: 9-7=2 Exploring Operation: 9-7=2, Resulting Numbers: [9, 2] Generated Node #0,0,2: 88:[9, 2] Operation: 9-7=2 Moving to Node #0,1 Current State: 88:[91, 9, 89], Operations: ['7+82=89'] Exploring Operation: 91-9=82, Resulting Numbers: [89, 82] Generated Node #0,1,0: 88:[89, 82] Operation: 91-9=82 Exploring Operation: 91-89=2, Resulting Numbers: [9, 2] Generated Node #0,1,1: 88:[9, 2] Operation: 91-89=2 Exploring Operation: 89-9=80, Resulting Numbers: [91, 80] Generated Node #0,1,2: 88:[91, 80] Operation: 89-9=80 Moving to Node #0,2 Current State: 88:[91, 7, 91], Operations: ['82+9=91'] Exploring Operation: 91-91=0, Resulting Numbers: [7, 0] Generated Node #0,2,0: 88:[7, 0] Operation: 91-91=0 Exploring Operation: 91/91=1, Resulting Numbers: [7, 1] Generated Node #0,2,1: 88:[7, 1] Operation: 91/91=1 Exploring Operation: 91/7=13, Resulting Numbers: [91, 13] Generated Node #0,2,2: 88:[91, 13] Operation: 91/7=13 Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 88:[7, 1], Operations: ['82+9=91', '91/91=1'] Exploring Operation: 7/1=7, Resulting Numbers: [7] 7,88 unequal: No Solution Exploring Operation: 7+1=8, Resulting Numbers: [8] 8,88 unequal: No Solution Exploring Operation: 7*1=7, Resulting Numbers: [7] 7,88 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 88:[7, 0], Operations: ['82+9=91', '91-91=0'] Exploring Operation: 7*0=0, Resulting Numbers: [0] 0,88 unequal: No Solution Exploring Operation: 7+0=7, Resulting Numbers: [7] 7,88 unequal: No Solution Exploring Operation: 7-0=7, Resulting Numbers: [7] 7,88 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 88:[91, 13], Operations: ['82+9=91', '91/7=13'] Exploring Operation: 91/13=7, Resulting Numbers: [7] 7,88 unequal: No Solution Exploring Operation: 91+13=104, Resulting Numbers: [104] 104,88 unequal: No Solution Exploring Operation: 91-13=78, Resulting Numbers: [78] 78,88 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,0,1 Current State: 88:[9, 2], Operations: ['91-82=9', '9-7=2'] Exploring Operation: 9*2=18, Resulting Numbers: [18] 18,88 unequal: No Solution Exploring Operation: 9+2=11, Resulting Numbers: [11] 11,88 unequal: No Solution Exploring Operation: 9-2=7, Resulting Numbers: [7] 7,88 unequal: No Solution Moving to Node #0,0,2 Current State: 88:[9, 2], Operations: ['91-82=9', '9-7=2'] Exploring Operation: 9-2=7, Resulting Numbers: [7] 7,88 unequal: No Solution Exploring Operation: 9*2=18, Resulting Numbers: [18] 18,88 unequal: No Solution Exploring Operation: 9+2=11, Resulting Numbers: [11] 11,88 unequal: No Solution Moving to Node #0,1,1 Current State: 88:[9, 2], Operations: ['7+82=89', '91-89=2'] Exploring Operation: 9*2=18, Resulting Numbers: [18] 18,88 unequal: No Solution Exploring Operation: 9+2=11, Resulting Numbers: [11] 11,88 unequal: No Solution Exploring Operation: 9-2=7, Resulting Numbers: [7] 7,88 unequal: No Solution Moving to Node #0,0,0 Current State: 88:[7, 1], Operations: ['91-82=9', '9/9=1'] Exploring Operation: 7+1=8, Resulting Numbers: [8] 8,88 unequal: No Solution Exploring Operation: 7/1=7, Resulting Numbers: [7] 7,88 unequal: No Solution Exploring Operation: 7*1=7, Resulting Numbers: [7] 7,88 unequal: No Solution Moving to Node #0,1,0 Current State: 88:[89, 82], Operations: ['7+82=89', '91-9=82'] Exploring Operation: 89-82=7, Resulting Numbers: [7] 7,88 unequal: No Solution Exploring Operation: 89+82=171, Resulting Numbers: [171] 171,88 unequal: No Solution Exploring Operation: 89*82=7298, Resulting Numbers: [7298] 7298,88 unequal: No Solution Moving to Node #0,1,2 Current State: 88:[91, 80], Operations: ['7+82=89', '89-9=80'] Exploring Operation: 91-80=11, Resulting Numbers: [11] 11,88 unequal: No Solution Exploring Operation: 91+80=171, Resulting Numbers: [171] 171,88 unequal: No Solution Exploring Operation: 91*80=7280, Resulting Numbers: [7280] 7280,88 unequal: No Solution No solution found.
0
hs_3
mult_heuristic
[ 5, 56, 74, 21 ]
44
[ "56-5=51", "74+21=95", "95-51=44" ]
Current State: 44:[5, 56, 74, 21], Operations: [] Exploring Operation: 56-5=51, Resulting Numbers: [74, 21, 51] Generated Node #2: [74, 21, 51] from Operation: 56-5=51 Current State: 44:[74, 21, 51], Operations: ['56-5=51'] Exploring Operation: 74+21=95, Resulting Numbers: [51, 95] Generated Node #3: [51, 95] from Operation: 74+21=95 Current State: 44:[51, 95], Operations: ['56-5=51', '74+21=95'] Exploring Operation: 95-51=44, Resulting Numbers: [44] 44,44 equal: Goal Reached
4
Current State: 44:[5, 56, 74, 21], Operations: [] Exploring Operation: 74-56=18, Resulting Numbers: [5, 21, 18] Generated Node #0,0: 44:[5, 21, 18] Operation: 74-56=18 Exploring Operation: 74-21=53, Resulting Numbers: [5, 56, 53] Generated Node #0,1: 44:[5, 56, 53] Operation: 74-21=53 Start Sub Search at level 1: Moving to Node #0,0 Current State: 44:[5, 21, 18], Operations: ['74-56=18'] Exploring Operation: 21-18=3, Resulting Numbers: [5, 3] Generated Node #0,0,0: 44:[5, 3] Operation: 21-18=3 Exploring Operation: 5+18=23, Resulting Numbers: [21, 23] Generated Node #0,0,1: 44:[21, 23] Operation: 5+18=23 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 44:[5, 3], Operations: ['74-56=18', '21-18=3'] Exploring Operation: 5+3=8, Resulting Numbers: [8] 8,44 unequal: No Solution Exploring Operation: 5-3=2, Resulting Numbers: [2] 2,44 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 44:[21, 23], Operations: ['74-56=18', '5+18=23'] Exploring Operation: 21+23=44, Resulting Numbers: [44] 44,44 equal: Goal Reached Moving to Node #0 Current State: 44:[5, 56, 74, 21], Operations: [] Exploring Operation: 74-56=18, Resulting Numbers: [5, 21, 18] Generated Node #0,0: 44:[5, 21, 18] Operation: 74-56=18 Moving to Node #0,0 Current State: 44:[5, 21, 18], Operations: ['74-56=18'] Exploring Operation: 5+18=23, Resulting Numbers: [21, 23] Generated Node #0,0,1: 44:[21, 23] Operation: 5+18=23 Moving to Node #0,0,1 Current State: 44:[21, 23], Operations: ['74-56=18', '5+18=23'] Exploring Operation: 21+23=44, Resulting Numbers: [44] 44,44 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.990451
hs_2
sum_heuristic
[ 64, 79, 78, 41 ]
24
[ "64+79=143", "78+41=119", "143-119=24" ]
Current State: 24:[64, 79, 78, 41], Operations: [] Exploring Operation: 64+79=143, Resulting Numbers: [78, 41, 143] Generated Node #2: [78, 41, 143] from Operation: 64+79=143 Current State: 24:[78, 41, 143], Operations: ['64+79=143'] Exploring Operation: 78+41=119, Resulting Numbers: [143, 119] Generated Node #3: [143, 119] from Operation: 78+41=119 Current State: 24:[143, 119], Operations: ['64+79=143', '78+41=119'] Exploring Operation: 143-119=24, Resulting Numbers: [24] 24,24 equal: Goal Reached
4
Current State: 24:[64, 79, 78, 41], Operations: [] Exploring Operation: 79-78=1, Resulting Numbers: [64, 41, 1] Generated Node #0,0: 24:[64, 41, 1] Operation: 79-78=1 Exploring Operation: 79-64=15, Resulting Numbers: [78, 41, 15] Generated Node #0,1: 24:[78, 41, 15] Operation: 79-64=15 Start Sub Search at level 1: Moving to Node #0,0 Current State: 24:[64, 41, 1], Operations: ['79-78=1'] Exploring Operation: 64-1=63, Resulting Numbers: [41, 63] Generated Node #0,0,0: 24:[41, 63] Operation: 64-1=63 Exploring Operation: 64-41=23, Resulting Numbers: [1, 23] Generated Node #0,0,1: 24:[1, 23] Operation: 64-41=23 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 24:[1, 23], Operations: ['79-78=1', '64-41=23'] Exploring Operation: 1+23=24, Resulting Numbers: [24] 24,24 equal: Goal Reached Moving to Node #0 Current State: 24:[64, 79, 78, 41], Operations: [] Exploring Operation: 79-78=1, Resulting Numbers: [64, 41, 1] Generated Node #0,0: 24:[64, 41, 1] Operation: 79-78=1 Moving to Node #0,0 Current State: 24:[64, 41, 1], Operations: ['79-78=1'] Exploring Operation: 64-41=23, Resulting Numbers: [1, 23] Generated Node #0,0,1: 24:[1, 23] Operation: 64-41=23 Moving to Node #0,0,1 Current State: 24:[1, 23], Operations: ['79-78=1', '64-41=23'] Exploring Operation: 1+23=24, Resulting Numbers: [24] 24,24 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.992188
hs_2
sum_heuristic
[ 17, 73, 83, 85 ]
58
[ "73-17=56", "85-83=2", "56+2=58" ]
Current State: 58:[17, 73, 83, 85], Operations: [] Exploring Operation: 73-17=56, Resulting Numbers: [83, 85, 56] Generated Node #2: [83, 85, 56] from Operation: 73-17=56 Current State: 58:[83, 85, 56], Operations: ['73-17=56'] Exploring Operation: 85-83=2, Resulting Numbers: [56, 2] Generated Node #3: [56, 2] from Operation: 85-83=2 Current State: 58:[56, 2], Operations: ['73-17=56', '85-83=2'] Exploring Operation: 56+2=58, Resulting Numbers: [58] 58,58 equal: Goal Reached
4
Current State: 58:[17, 73, 83, 85], Operations: [] Exploring Operation: 85-73=12, Resulting Numbers: [17, 83, 12] Generated Node #0,0: 58:[17, 83, 12] Operation: 85-73=12 Exploring Operation: 85/17=5, Resulting Numbers: [73, 83, 5] Generated Node #0,1: 58:[73, 83, 5] Operation: 85/17=5 Exploring Operation: 83-73=10, Resulting Numbers: [17, 85, 10] Generated Node #0,2: 58:[17, 85, 10] Operation: 83-73=10 Exploring Operation: 85-83=2, Resulting Numbers: [17, 73, 2] Generated Node #0,3: 58:[17, 73, 2] Operation: 85-83=2 Exploring Operation: 83-17=66, Resulting Numbers: [73, 85, 66] Generated Node #0,4: 58:[73, 85, 66] Operation: 83-17=66 Start Sub Search at level 1: Moving to Node #0,3 Current State: 58:[17, 73, 2], Operations: ['85-83=2'] Exploring Operation: 73-17=56, Resulting Numbers: [2, 56] Generated Node #0,3,0: 58:[2, 56] Operation: 73-17=56 Exploring Operation: 17-2=15, Resulting Numbers: [73, 15] Generated Node #0,3,1: 58:[73, 15] Operation: 17-2=15 Exploring Operation: 17*2=34, Resulting Numbers: [73, 34] Generated Node #0,3,2: 58:[73, 34] Operation: 17*2=34 Exploring Operation: 17+2=19, Resulting Numbers: [73, 19] Generated Node #0,3,3: 58:[73, 19] Operation: 17+2=19 Exploring Operation: 73-2=71, Resulting Numbers: [17, 71] Generated Node #0,3,4: 58:[17, 71] Operation: 73-2=71 Start Sub Search at level 2: Moving to Node #0,3,0 Current State: 58:[2, 56], Operations: ['85-83=2', '73-17=56'] Exploring Operation: 2+56=58, Resulting Numbers: [58] 58,58 equal: Goal Reached Moving to Node #0 Current State: 58:[17, 73, 83, 85], Operations: [] Exploring Operation: 85-83=2, Resulting Numbers: [17, 73, 2] Generated Node #0,3: 58:[17, 73, 2] Operation: 85-83=2 Moving to Node #0,3 Current State: 58:[17, 73, 2], Operations: ['85-83=2'] Exploring Operation: 73-17=56, Resulting Numbers: [2, 56] Generated Node #0,3,0: 58:[2, 56] Operation: 73-17=56 Moving to Node #0,3,0 Current State: 58:[2, 56], Operations: ['85-83=2', '73-17=56'] Exploring Operation: 2+56=58, Resulting Numbers: [58] 58,58 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.986979
hs_5
mult_heuristic
[ 60, 67, 61, 44 ]
24
[ "67-60=7", "61-44=17", "7+17=24" ]
Current State: 24:[60, 67, 61, 44], Operations: [] Exploring Operation: 67-60=7, Resulting Numbers: [61, 44, 7] Generated Node #2: [61, 44, 7] from Operation: 67-60=7 Current State: 24:[61, 44, 7], Operations: ['67-60=7'] Exploring Operation: 61-44=17, Resulting Numbers: [7, 17] Generated Node #3: [7, 17] from Operation: 61-44=17 Current State: 24:[7, 17], Operations: ['67-60=7', '61-44=17'] Exploring Operation: 7+17=24, Resulting Numbers: [24] 24,24 equal: Goal Reached
4
Current State: 24:[60, 67, 61, 44], Operations: [] Exploring Operation: 67-61=6, Resulting Numbers: [60, 44, 6] Generated Node #0,0: 24:[60, 44, 6] Operation: 67-61=6 Start Sub Search at level 1: Moving to Node #0,0 Current State: 24:[60, 44, 6], Operations: ['67-61=6'] Exploring Operation: 60-44=16, Resulting Numbers: [6, 16] Generated Node #0,0,0: 24:[6, 16] Operation: 60-44=16 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 24:[6, 16], Operations: ['67-61=6', '60-44=16'] Exploring Operation: 6+16=22, Resulting Numbers: [22] 22,24 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
mult_heuristic
[ 40, 50, 32, 56 ]
34
[ "50-40=10", "56-32=24", "10+24=34" ]
Current State: 34:[40, 50, 32, 56], Operations: [] Exploring Operation: 50-40=10, Resulting Numbers: [32, 56, 10] Generated Node #2: [32, 56, 10] from Operation: 50-40=10 Current State: 34:[32, 56, 10], Operations: ['50-40=10'] Exploring Operation: 56-32=24, Resulting Numbers: [10, 24] Generated Node #3: [10, 24] from Operation: 56-32=24 Current State: 34:[10, 24], Operations: ['50-40=10', '56-32=24'] Exploring Operation: 10+24=34, Resulting Numbers: [34] 34,34 equal: Goal Reached
4
Current State: 34:[40, 50, 32, 56], Operations: [] Exploring Operation: 56-50=6, Resulting Numbers: [40, 32, 6] Generated Node #0,0: 34:[40, 32, 6] Operation: 56-50=6 Exploring Operation: 56-40=16, Resulting Numbers: [50, 32, 16] Generated Node #0,1: 34:[50, 32, 16] Operation: 56-40=16 Exploring Operation: 50-32=18, Resulting Numbers: [40, 56, 18] Generated Node #0,2: 34:[40, 56, 18] Operation: 50-32=18 Exploring Operation: 56-32=24, Resulting Numbers: [40, 50, 24] Generated Node #0,3: 34:[40, 50, 24] Operation: 56-32=24 Start Sub Search at level 1: Moving to Node #0,0 Current State: 34:[40, 32, 6], Operations: ['56-50=6'] Exploring Operation: 40+6=46, Resulting Numbers: [32, 46] Generated Node #0,0,0: 34:[32, 46] Operation: 40+6=46 Exploring Operation: 40-6=34, Resulting Numbers: [32, 34] Generated Node #0,0,1: 34:[32, 34] Operation: 40-6=34 Exploring Operation: 40-32=8, Resulting Numbers: [6, 8] Generated Node #0,0,2: 34:[6, 8] Operation: 40-32=8 Exploring Operation: 32+6=38, Resulting Numbers: [40, 38] Generated Node #0,0,3: 34:[40, 38] Operation: 32+6=38 Moving to Node #0,0,1 Current State: 34:[32, 34], Operations: ['56-50=6', '40-6=34'] Exploring Operation: 34-32=2, Resulting Numbers: [2] 2,34 unequal: No Solution Exploring Operation: 32*34=1088, Resulting Numbers: [1088] 1088,34 unequal: No Solution Exploring Operation: 32+34=66, Resulting Numbers: [66] 66,34 unequal: No Solution Moving to Node #0,0,3 Current State: 34:[40, 38], Operations: ['56-50=6', '32+6=38'] Exploring Operation: 40+38=78, Resulting Numbers: [78] 78,34 unequal: No Solution Exploring Operation: 40-38=2, Resulting Numbers: [2] 2,34 unequal: No Solution Exploring Operation: 40*38=1520, Resulting Numbers: [1520] 1520,34 unequal: No Solution Moving to Node #0,0,2 Current State: 34:[6, 8], Operations: ['56-50=6', '40-32=8'] Exploring Operation: 6*8=48, Resulting Numbers: [48] 48,34 unequal: No Solution Exploring Operation: 6+8=14, Resulting Numbers: [14] 14,34 unequal: No Solution Exploring Operation: 8-6=2, Resulting Numbers: [2] 2,34 unequal: No Solution Moving to Node #0,0,0 Current State: 34:[32, 46], Operations: ['56-50=6', '40+6=46'] Exploring Operation: 32*46=1472, Resulting Numbers: [1472] 1472,34 unequal: No Solution Exploring Operation: 32+46=78, Resulting Numbers: [78] 78,34 unequal: No Solution Exploring Operation: 46-32=14, Resulting Numbers: [14] 14,34 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 34:[50, 32, 16], Operations: ['56-40=16'] Exploring Operation: 50-32=18, Resulting Numbers: [16, 18] Generated Node #0,1,0: 34:[16, 18] Operation: 50-32=18 Exploring Operation: 50-16=34, Resulting Numbers: [32, 34] Generated Node #0,1,1: 34:[32, 34] Operation: 50-16=34 Exploring Operation: 32-16=16, Resulting Numbers: [50, 16] Generated Node #0,1,2: 34:[50, 16] Operation: 32-16=16 Exploring Operation: 32/16=2, Resulting Numbers: [50, 2] Generated Node #0,1,3: 34:[50, 2] Operation: 32/16=2 Moving to Node #0,1,0 Current State: 34:[16, 18], Operations: ['56-40=16', '50-32=18'] Exploring Operation: 16*18=288, Resulting Numbers: [288] 288,34 unequal: No Solution Exploring Operation: 18-16=2, Resulting Numbers: [2] 2,34 unequal: No Solution Exploring Operation: 16+18=34, Resulting Numbers: [34] 34,34 equal: Goal Reached Moving to Node #0 Current State: 34:[40, 50, 32, 56], Operations: [] Exploring Operation: 56-40=16, Resulting Numbers: [50, 32, 16] Generated Node #0,1: 34:[50, 32, 16] Operation: 56-40=16 Moving to Node #0,1 Current State: 34:[50, 32, 16], Operations: ['56-40=16'] Exploring Operation: 50-32=18, Resulting Numbers: [16, 18] Generated Node #0,1,0: 34:[16, 18] Operation: 50-32=18 Moving to Node #0,1,0 Current State: 34:[16, 18], Operations: ['56-40=16', '50-32=18'] Exploring Operation: 16+18=34, Resulting Numbers: [34] 34,34 equal: Goal Reached Exit Sub Search at level 1
0.97309
hs_4
sum_heuristic
[ 54, 13, 84, 95 ]
30
[ "54-13=41", "95-84=11", "41-11=30" ]
Current State: 30:[54, 13, 84, 95], Operations: [] Exploring Operation: 54-13=41, Resulting Numbers: [84, 95, 41] Generated Node #2: [84, 95, 41] from Operation: 54-13=41 Current State: 30:[84, 95, 41], Operations: ['54-13=41'] Exploring Operation: 95-84=11, Resulting Numbers: [41, 11] Generated Node #3: [41, 11] from Operation: 95-84=11 Current State: 30:[41, 11], Operations: ['54-13=41', '95-84=11'] Exploring Operation: 41-11=30, Resulting Numbers: [30] 30,30 equal: Goal Reached
4
Current State: 30:[54, 13, 84, 95], Operations: [] Exploring Operation: 84-54=30, Resulting Numbers: [13, 95, 30] Generated Node #0,0: 30:[13, 95, 30] Operation: 84-54=30 Exploring Operation: 95-84=11, Resulting Numbers: [54, 13, 11] Generated Node #0,1: 30:[54, 13, 11] Operation: 95-84=11 Moving to Node #0,1 Current State: 30:[54, 13, 11], Operations: ['95-84=11'] Exploring Operation: 54-11=43, Resulting Numbers: [13, 43] Generated Node #0,1,0: 30:[13, 43] Operation: 54-11=43 Exploring Operation: 54-13=41, Resulting Numbers: [11, 41] Generated Node #0,1,1: 30:[11, 41] Operation: 54-13=41 Moving to Node #0,0 Current State: 30:[13, 95, 30], Operations: ['84-54=30'] Exploring Operation: 95-13=82, Resulting Numbers: [30, 82] Generated Node #0,0,0: 30:[30, 82] Operation: 95-13=82 Exploring Operation: 95-30=65, Resulting Numbers: [13, 65] Generated Node #0,0,1: 30:[13, 65] Operation: 95-30=65 Moving to Node #0,1,1 Current State: 30:[11, 41], Operations: ['95-84=11', '54-13=41'] Exploring Operation: 41-11=30, Resulting Numbers: [30] 30,30 equal: Goal Reached Moving to Node #0 Current State: 30:[54, 13, 84, 95], Operations: [] Exploring Operation: 95-84=11, Resulting Numbers: [54, 13, 11] Generated Node #0,1: 30:[54, 13, 11] Operation: 95-84=11 Moving to Node #0,1 Current State: 30:[54, 13, 11], Operations: ['95-84=11'] Exploring Operation: 54-13=41, Resulting Numbers: [11, 41] Generated Node #0,1,1: 30:[11, 41] Operation: 54-13=41 Moving to Node #0,1,1 Current State: 30:[11, 41], Operations: ['95-84=11', '54-13=41'] Exploring Operation: 41-11=30, Resulting Numbers: [30] 30,30 equal: Goal Reached
0.990451
hs_2
sum_heuristic
[ 30, 5, 25, 12 ]
12
[ "30-5=25", "25+12=37", "37-25=12" ]
Current State: 12:[30, 5, 25, 12], Operations: [] Exploring Operation: 30-5=25, Resulting Numbers: [25, 12, 25] Generated Node #2: [25, 12, 25] from Operation: 30-5=25 Current State: 12:[25, 12, 25], Operations: ['30-5=25'] Exploring Operation: 25+12=37, Resulting Numbers: [37] 37,12 equal: Goal Reached Exploring Operation: 37-25=12, Resulting Numbers: [12] 12,12 equal: Goal Reached
4
Current State: 12:[30, 5, 25, 12], Operations: [] Exploring Operation: 30-12=18, Resulting Numbers: [5, 25, 18] Generated Node #0,0: 12:[5, 25, 18] Operation: 30-12=18 Exploring Operation: 25/5=5, Resulting Numbers: [30, 12, 5] Generated Node #0,1: 12:[30, 12, 5] Operation: 25/5=5 Exploring Operation: 30/5=6, Resulting Numbers: [25, 12, 6] Generated Node #0,2: 12:[25, 12, 6] Operation: 30/5=6 Exploring Operation: 30-25=5, Resulting Numbers: [5, 12, 5] Generated Node #0,3: 12:[5, 12, 5] Operation: 30-25=5 Start Sub Search at level 1: Moving to Node #0,3 Current State: 12:[5, 12, 5], Operations: ['30-25=5'] Exploring Operation: 5-5=0, Resulting Numbers: [12, 0] Generated Node #0,3,0: 12:[12, 0] Operation: 5-5=0 Exploring Operation: 5+5=10, Resulting Numbers: [12, 10] Generated Node #0,3,1: 12:[12, 10] Operation: 5+5=10 Exploring Operation: 12-5=7, Resulting Numbers: [5, 7] Generated Node #0,3,2: 12:[5, 7] Operation: 12-5=7 Exploring Operation: 5/5=1, Resulting Numbers: [12, 1] Generated Node #0,3,3: 12:[12, 1] Operation: 5/5=1 Start Sub Search at level 2: Moving to Node #0,3,3 Current State: 12:[12, 1], Operations: ['30-25=5', '5/5=1'] Exploring Operation: 12*1=12, Resulting Numbers: [12] 12,12 equal: Goal Reached Moving to Node #0 Current State: 12:[30, 5, 25, 12], Operations: [] Exploring Operation: 30-25=5, Resulting Numbers: [5, 12, 5] Generated Node #0,3: 12:[5, 12, 5] Operation: 30-25=5 Moving to Node #0,3 Current State: 12:[5, 12, 5], Operations: ['30-25=5'] Exploring Operation: 5/5=1, Resulting Numbers: [12, 1] Generated Node #0,3,3: 12:[12, 1] Operation: 5/5=1 Moving to Node #0,3,3 Current State: 12:[12, 1], Operations: ['30-25=5', '5/5=1'] Exploring Operation: 12*1=12, Resulting Numbers: [12] 12,12 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.988715
hs_4
mult_heuristic
[ 6, 33, 92, 7 ]
18
[ "92+7=99", "6*99=594", "594/33=18" ]
Current State: 18:[6, 33, 92, 7], Operations: [] Exploring Operation: 92+7=99, Resulting Numbers: [6, 33, 99] Generated Node #2: [6, 33, 99] from Operation: 92+7=99 Current State: 18:[6, 33, 99], Operations: ['92+7=99'] Exploring Operation: 6*99=594, Resulting Numbers: [33, 594] Generated Node #3: [33, 594] from Operation: 6*99=594 Current State: 18:[33, 594], Operations: ['92+7=99', '6*99=594'] Exploring Operation: 594/33=18, Resulting Numbers: [18] 18,18 equal: Goal Reached
4
Current State: 18:[6, 33, 92, 7], Operations: [] Exploring Operation: 92-33=59, Resulting Numbers: [6, 7, 59] Generated Node #0,0: 18:[6, 7, 59] Operation: 92-33=59 Exploring Operation: 33-7=26, Resulting Numbers: [6, 92, 26] Generated Node #0,1: 18:[6, 92, 26] Operation: 33-7=26 Start Sub Search at level 1: Moving to Node #0,0 Current State: 18:[6, 7, 59], Operations: ['92-33=59'] Exploring Operation: 59-6=53, Resulting Numbers: [7, 53] Generated Node #0,0,0: 18:[7, 53] Operation: 59-6=53 Exploring Operation: 59-7=52, Resulting Numbers: [6, 52] Generated Node #0,0,1: 18:[6, 52] Operation: 59-7=52 Moving to Node #0,0,1 Current State: 18:[6, 52], Operations: ['92-33=59', '59-7=52'] Exploring Operation: 6+52=58, Resulting Numbers: [58] 58,18 unequal: No Solution Exploring Operation: 52-6=46, Resulting Numbers: [46] 46,18 unequal: No Solution Moving to Node #0,0,0 Current State: 18:[7, 53], Operations: ['92-33=59', '59-6=53'] Exploring Operation: 53-7=46, Resulting Numbers: [46] 46,18 unequal: No Solution Exploring Operation: 7+53=60, Resulting Numbers: [60] 60,18 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 18:[6, 92, 26], Operations: ['33-7=26'] Exploring Operation: 92-26=66, Resulting Numbers: [6, 66] Generated Node #0,1,0: 18:[6, 66] Operation: 92-26=66 Exploring Operation: 92-6=86, Resulting Numbers: [26, 86] Generated Node #0,1,1: 18:[26, 86] Operation: 92-6=86 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 18:[6, 66], Operations: ['33-7=26', '92-26=66'] Exploring Operation: 66-6=60, Resulting Numbers: [60] 60,18 unequal: No Solution Exploring Operation: 66/6=11, Resulting Numbers: [11] 11,18 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 18:[26, 86], Operations: ['33-7=26', '92-6=86'] Exploring Operation: 86-26=60, Resulting Numbers: [60] 60,18 unequal: No Solution Exploring Operation: 26+86=112, Resulting Numbers: [112] 112,18 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_2
mult_heuristic
[ 19, 66, 47, 43 ]
43
[ "66-19=47", "47+43=90", "90-47=43" ]
Current State: 43:[19, 66, 47, 43], Operations: [] Exploring Operation: 66-19=47, Resulting Numbers: [47, 43, 47] Generated Node #2: [47, 43, 47] from Operation: 66-19=47 Current State: 43:[47, 43, 47], Operations: ['66-19=47'] Exploring Operation: 47+43=90, Resulting Numbers: [90] 90,43 equal: Goal Reached Exploring Operation: 90-47=43, Resulting Numbers: [43] 43,43 equal: Goal Reached
4
Current State: 43:[19, 66, 47, 43], Operations: [] Exploring Operation: 66-19=47, Resulting Numbers: [47, 43, 47] Generated Node #0,0: 43:[47, 43, 47] Operation: 66-19=47 Moving to Node #0,0 Current State: 43:[47, 43, 47], Operations: ['66-19=47'] Exploring Operation: 47/47=1, Resulting Numbers: [43, 1] Generated Node #0,0,0: 43:[43, 1] Operation: 47/47=1 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 43:[43, 1], Operations: ['66-19=47', '47/47=1'] Exploring Operation: 43*1=43, Resulting Numbers: [43] 43,43 equal: Goal Reached Moving to Node #0 Current State: 43:[19, 66, 47, 43], Operations: [] Exploring Operation: 66-19=47, Resulting Numbers: [47, 43, 47] Generated Node #0,0: 43:[47, 43, 47] Operation: 66-19=47 Moving to Node #0,0 Current State: 43:[47, 43, 47], Operations: ['66-19=47'] Exploring Operation: 47/47=1, Resulting Numbers: [43, 1] Generated Node #0,0,0: 43:[43, 1] Operation: 47/47=1 Moving to Node #0,0,0 Current State: 43:[43, 1], Operations: ['66-19=47', '47/47=1'] Exploring Operation: 43*1=43, Resulting Numbers: [43] 43,43 equal: Goal Reached Exit Sub Search at level 1
0.993924
hs_1
sum_heuristic
[ 94, 25, 46, 27 ]
18
[ "94-25=69", "46*27=1242", "1242/69=18" ]
Current State: 18:[94, 25, 46, 27], Operations: [] Exploring Operation: 94-25=69, Resulting Numbers: [46, 27, 69] Generated Node #2: [46, 27, 69] from Operation: 94-25=69 Current State: 18:[46, 27, 69], Operations: ['94-25=69'] Exploring Operation: 46*27=1242, Resulting Numbers: [69, 1242] Generated Node #3: [69, 1242] from Operation: 46*27=1242 Current State: 18:[69, 1242], Operations: ['94-25=69', '46*27=1242'] Exploring Operation: 1242/69=18, Resulting Numbers: [18] 18,18 equal: Goal Reached
4
Current State: 18:[94, 25, 46, 27], Operations: [] Exploring Operation: 46-27=19, Resulting Numbers: [94, 25, 19] Generated Node #0,0: 18:[94, 25, 19] Operation: 46-27=19 Exploring Operation: 46-25=21, Resulting Numbers: [94, 27, 21] Generated Node #0,1: 18:[94, 27, 21] Operation: 46-25=21 Exploring Operation: 94-46=48, Resulting Numbers: [25, 27, 48] Generated Node #0,2: 18:[25, 27, 48] Operation: 94-46=48 Exploring Operation: 94-27=67, Resulting Numbers: [25, 46, 67] Generated Node #0,3: 18:[25, 46, 67] Operation: 94-27=67 Exploring Operation: 94-25=69, Resulting Numbers: [46, 27, 69] Generated Node #0,4: 18:[46, 27, 69] Operation: 94-25=69 Moving to Node #0,2 Current State: 18:[25, 27, 48], Operations: ['94-46=48'] Exploring Operation: 25+27=52, Resulting Numbers: [48, 52] Generated Node #0,2,0: 18:[48, 52] Operation: 25+27=52 Exploring Operation: 48-25=23, Resulting Numbers: [27, 23] Generated Node #0,2,1: 18:[27, 23] Operation: 48-25=23 Exploring Operation: 27-25=2, Resulting Numbers: [48, 2] Generated Node #0,2,2: 18:[48, 2] Operation: 27-25=2 Exploring Operation: 48-27=21, Resulting Numbers: [25, 21] Generated Node #0,2,3: 18:[25, 21] Operation: 48-27=21 Exploring Operation: 25+48=73, Resulting Numbers: [27, 73] Generated Node #0,2,4: 18:[27, 73] Operation: 25+48=73 Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 18:[25, 21], Operations: ['94-46=48', '48-27=21'] Exploring Operation: 25+21=46, Resulting Numbers: [46] 46,18 unequal: No Solution Exploring Operation: 25*21=525, Resulting Numbers: [525] 525,18 unequal: No Solution Exploring Operation: 25-21=4, Resulting Numbers: [4] 4,18 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 18:[27, 23], Operations: ['94-46=48', '48-25=23'] Exploring Operation: 27-23=4, Resulting Numbers: [4] 4,18 unequal: No Solution Exploring Operation: 27+23=50, Resulting Numbers: [50] 50,18 unequal: No Solution Exploring Operation: 27*23=621, Resulting Numbers: [621] 621,18 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 18:[48, 2], Operations: ['94-46=48', '27-25=2'] Exploring Operation: 48-2=46, Resulting Numbers: [46] 46,18 unequal: No Solution Exploring Operation: 48*2=96, Resulting Numbers: [96] 96,18 unequal: No Solution Exploring Operation: 48/2=24, Resulting Numbers: [24] 24,18 unequal: No Solution Exploring Operation: 48+2=50, Resulting Numbers: [50] 50,18 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 18:[48, 52], Operations: ['94-46=48', '25+27=52'] Exploring Operation: 48*52=2496, Resulting Numbers: [2496] 2496,18 unequal: No Solution Exploring Operation: 48+52=100, Resulting Numbers: [100] 100,18 unequal: No Solution Exploring Operation: 52-48=4, Resulting Numbers: [4] 4,18 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,4 Current State: 18:[27, 73], Operations: ['94-46=48', '25+48=73'] Exploring Operation: 27+73=100, Resulting Numbers: [100] 100,18 unequal: No Solution Exploring Operation: 27*73=1971, Resulting Numbers: [1971] 1971,18 unequal: No Solution Exploring Operation: 73-27=46, Resulting Numbers: [46] 46,18 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,3 Current State: 18:[25, 46, 67], Operations: ['94-27=67'] Exploring Operation: 46-25=21, Resulting Numbers: [67, 21] Generated Node #0,3,0: 18:[67, 21] Operation: 46-25=21 Exploring Operation: 67-25=42, Resulting Numbers: [46, 42] Generated Node #0,3,1: 18:[46, 42] Operation: 67-25=42 Exploring Operation: 25+67=92, Resulting Numbers: [46, 92] Generated Node #0,3,2: 18:[46, 92] Operation: 25+67=92 Exploring Operation: 25+46=71, Resulting Numbers: [67, 71] Generated Node #0,3,3: 18:[67, 71] Operation: 25+46=71 Exploring Operation: 67-46=21, Resulting Numbers: [25, 21] Generated Node #0,3,4: 18:[25, 21] Operation: 67-46=21 Start Sub Search at level 1: Moving to Node #0,3,4 Current State: 18:[25, 21], Operations: ['94-27=67', '67-46=21'] Exploring Operation: 25+21=46, Resulting Numbers: [46] 46,18 unequal: No Solution Exploring Operation: 25-21=4, Resulting Numbers: [4] 4,18 unequal: No Solution Exploring Operation: 25*21=525, Resulting Numbers: [525] 525,18 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 18:[67, 21], Operations: ['94-27=67', '46-25=21'] Exploring Operation: 67+21=88, Resulting Numbers: [88] 88,18 unequal: No Solution Exploring Operation: 67*21=1407, Resulting Numbers: [1407] 1407,18 unequal: No Solution Exploring Operation: 67-21=46, Resulting Numbers: [46] 46,18 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 18:[46, 42], Operations: ['94-27=67', '67-25=42'] Exploring Operation: 46+42=88, Resulting Numbers: [88] 88,18 unequal: No Solution Exploring Operation: 46*42=1932, Resulting Numbers: [1932] 1932,18 unequal: No Solution Exploring Operation: 46-42=4, Resulting Numbers: [4] 4,18 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 18:[46, 92], Operations: ['94-27=67', '25+67=92'] Exploring Operation: 46*92=4232, Resulting Numbers: [4232] 4232,18 unequal: No Solution Exploring Operation: 46+92=138, Resulting Numbers: [138] 138,18 unequal: No Solution Exploring Operation: 92/46=2, Resulting Numbers: [2] 2,18 unequal: No Solution Exploring Operation: 92-46=46, Resulting Numbers: [46] 46,18 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 18:[67, 71], Operations: ['94-27=67', '25+46=71'] Exploring Operation: 67+71=138, Resulting Numbers: [138] 138,18 unequal: No Solution Exploring Operation: 67*71=4757, Resulting Numbers: [4757] 4757,18 unequal: No Solution Exploring Operation: 71-67=4, Resulting Numbers: [4] 4,18 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,0 Current State: 18:[94, 25, 19], Operations: ['46-27=19'] Exploring Operation: 25-19=6, Resulting Numbers: [94, 6] Generated Node #0,0,0: 18:[94, 6] Operation: 25-19=6 Exploring Operation: 94-25=69, Resulting Numbers: [19, 69] Generated Node #0,0,1: 18:[19, 69] Operation: 94-25=69 Exploring Operation: 94+25=119, Resulting Numbers: [19, 119] Generated Node #0,0,2: 18:[19, 119] Operation: 94+25=119 Exploring Operation: 94-19=75, Resulting Numbers: [25, 75] Generated Node #0,0,3: 18:[25, 75] Operation: 94-19=75 Exploring Operation: 94+19=113, Resulting Numbers: [25, 113] Generated Node #0,0,4: 18:[25, 113] Operation: 94+19=113 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 18:[19, 69], Operations: ['46-27=19', '94-25=69'] Exploring Operation: 69-19=50, Resulting Numbers: [50] 50,18 unequal: No Solution Exploring Operation: 19+69=88, Resulting Numbers: [88] 88,18 unequal: No Solution Exploring Operation: 19*69=1311, Resulting Numbers: [1311] 1311,18 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 18:[25, 75], Operations: ['46-27=19', '94-19=75'] Exploring Operation: 25*75=1875, Resulting Numbers: [1875] 1875,18 unequal: No Solution Exploring Operation: 75/25=3, Resulting Numbers: [3] 3,18 unequal: No Solution Exploring Operation: 25+75=100, Resulting Numbers: [100] 100,18 unequal: No Solution Exploring Operation: 75-25=50, Resulting Numbers: [50] 50,18 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 18:[94, 6], Operations: ['46-27=19', '25-19=6'] Exploring Operation: 94-6=88, Resulting Numbers: [88] 88,18 unequal: No Solution Exploring Operation: 94+6=100, Resulting Numbers: [100] 100,18 unequal: No Solution Exploring Operation: 94*6=564, Resulting Numbers: [564] 564,18 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 18:[19, 119], Operations: ['46-27=19', '94+25=119'] Exploring Operation: 19+119=138, Resulting Numbers: [138] 138,18 unequal: No Solution Exploring Operation: 19*119=2261, Resulting Numbers: [2261] 2261,18 unequal: No Solution Exploring Operation: 119-19=100, Resulting Numbers: [100] 100,18 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,4 Current State: 18:[25, 113], Operations: ['46-27=19', '94+19=113'] Exploring Operation: 113-25=88, Resulting Numbers: [88] 88,18 unequal: No Solution Exploring Operation: 25+113=138, Resulting Numbers: [138] 138,18 unequal: No Solution Exploring Operation: 25*113=2825, Resulting Numbers: [2825] 2825,18 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1 Current State: 18:[94, 27, 21], Operations: ['46-25=21'] Exploring Operation: 94-27=67, Resulting Numbers: [21, 67] Generated Node #0,1,0: 18:[21, 67] Operation: 94-27=67 Exploring Operation: 27-21=6, Resulting Numbers: [94, 6] Generated Node #0,1,1: 18:[94, 6] Operation: 27-21=6 Exploring Operation: 94+21=115, Resulting Numbers: [27, 115] Generated Node #0,1,2: 18:[27, 115] Operation: 94+21=115 Exploring Operation: 94+27=121, Resulting Numbers: [21, 121] Generated Node #0,1,3: 18:[21, 121] Operation: 94+27=121 Exploring Operation: 94-21=73, Resulting Numbers: [27, 73] Generated Node #0,1,4: 18:[27, 73] Operation: 94-21=73 Moving to Node #0,4 Current State: 18:[46, 27, 69], Operations: ['94-25=69'] Exploring Operation: 69-27=42, Resulting Numbers: [46, 42] Generated Node #0,4,0: 18:[46, 42] Operation: 69-27=42 Exploring Operation: 69-46=23, Resulting Numbers: [27, 23] Generated Node #0,4,1: 18:[27, 23] Operation: 69-46=23 Exploring Operation: 46+69=115, Resulting Numbers: [27, 115] Generated Node #0,4,2: 18:[27, 115] Operation: 46+69=115 Exploring Operation: 46-27=19, Resulting Numbers: [69, 19] Generated Node #0,4,3: 18:[69, 19] Operation: 46-27=19 Exploring Operation: 46+27=73, Resulting Numbers: [69, 73] Generated Node #0,4,4: 18:[69, 73] Operation: 46+27=73 Moving to Node #0,4,1 Current State: 18:[27, 23], Operations: ['94-25=69', '69-46=23'] Exploring Operation: 27-23=4, Resulting Numbers: [4] 4,18 unequal: No Solution Exploring Operation: 27+23=50, Resulting Numbers: [50] 50,18 unequal: No Solution Exploring Operation: 27*23=621, Resulting Numbers: [621] 621,18 unequal: No Solution Moving to Node #0,1,0 Current State: 18:[21, 67], Operations: ['46-25=21', '94-27=67'] Exploring Operation: 67-21=46, Resulting Numbers: [46] 46,18 unequal: No Solution Exploring Operation: 21*67=1407, Resulting Numbers: [1407] 1407,18 unequal: No Solution Exploring Operation: 21+67=88, Resulting Numbers: [88] 88,18 unequal: No Solution Moving to Node #0,4,0 Current State: 18:[46, 42], Operations: ['94-25=69', '69-27=42'] Exploring Operation: 46-42=4, Resulting Numbers: [4] 4,18 unequal: No Solution Exploring Operation: 46+42=88, Resulting Numbers: [88] 88,18 unequal: No Solution Exploring Operation: 46*42=1932, Resulting Numbers: [1932] 1932,18 unequal: No Solution Moving to Node #0,4,3 Current State: 18:[69, 19], Operations: ['94-25=69', '46-27=19'] Exploring Operation: 69+19=88, Resulting Numbers: [88] 88,18 unequal: No Solution Exploring Operation: 69*19=1311, Resulting Numbers: [1311] 1311,18 unequal: No Solution Exploring Operation: 69-19=50, Resulting Numbers: [50] 50,18 unequal: No Solution Moving to Node #0,1,4 Current State: 18:[27, 73], Operations: ['46-25=21', '94-21=73'] Exploring Operation: 27*73=1971, Resulting Numbers: [1971] 1971,18 unequal: No Solution Exploring Operation: 73-27=46, Resulting Numbers: [46] 46,18 unequal: No Solution Exploring Operation: 27+73=100, Resulting Numbers: [100] 100,18 unequal: No Solution Moving to Node #0,1,1 Current State: 18:[94, 6], Operations: ['46-25=21', '27-21=6'] Exploring Operation: 94*6=564, Resulting Numbers: [564] 564,18 unequal: No Solution Exploring Operation: 94+6=100, Resulting Numbers: [100] 100,18 unequal: No Solution Exploring Operation: 94-6=88, Resulting Numbers: [88] 88,18 unequal: No Solution Moving to Node #0,4,2 Current State: 18:[27, 115], Operations: ['94-25=69', '46+69=115'] Exploring Operation: 27+115=142, Resulting Numbers: [142] 142,18 unequal: No Solution Exploring Operation: 115-27=88, Resulting Numbers: [88] 88,18 unequal: No Solution Exploring Operation: 27*115=3105, Resulting Numbers: [3105] 3105,18 unequal: No Solution Moving to Node #0,4,4 Current State: 18:[69, 73], Operations: ['94-25=69', '46+27=73'] Exploring Operation: 69+73=142, Resulting Numbers: [142] 142,18 unequal: No Solution Exploring Operation: 69*73=5037, Resulting Numbers: [5037] 5037,18 unequal: No Solution Exploring Operation: 73-69=4, Resulting Numbers: [4] 4,18 unequal: No Solution Moving to Node #0,1,3 Current State: 18:[21, 121], Operations: ['46-25=21', '94+27=121'] Exploring Operation: 21+121=142, Resulting Numbers: [142] 142,18 unequal: No Solution Exploring Operation: 21*121=2541, Resulting Numbers: [2541] 2541,18 unequal: No Solution Exploring Operation: 121-21=100, Resulting Numbers: [100] 100,18 unequal: No Solution Moving to Node #0,1,2 Current State: 18:[27, 115], Operations: ['46-25=21', '94+21=115'] Exploring Operation: 115-27=88, Resulting Numbers: [88] 88,18 unequal: No Solution Exploring Operation: 27*115=3105, Resulting Numbers: [3105] 3105,18 unequal: No Solution Exploring Operation: 27+115=142, Resulting Numbers: [142] 142,18 unequal: No Solution No solution found.
0
hs_5
mult_heuristic
[ 19, 34, 58, 76 ]
88
[ "76/19=4", "34+58=92", "92-4=88" ]
Current State: 88:[19, 34, 58, 76], Operations: [] Exploring Operation: 76/19=4, Resulting Numbers: [34, 58, 4] Generated Node #2: [34, 58, 4] from Operation: 76/19=4 Current State: 88:[34, 58, 4], Operations: ['76/19=4'] Exploring Operation: 34+58=92, Resulting Numbers: [4, 92] Generated Node #3: [4, 92] from Operation: 34+58=92 Current State: 88:[4, 92], Operations: ['76/19=4', '34+58=92'] Exploring Operation: 92-4=88, Resulting Numbers: [88] 88,88 equal: Goal Reached
4
Current State: 88:[19, 34, 58, 76], Operations: [] Exploring Operation: 34+58=92, Resulting Numbers: [19, 76, 92] Generated Node #0,0: 88:[19, 76, 92] Operation: 34+58=92 Exploring Operation: 58-34=24, Resulting Numbers: [19, 76, 24] Generated Node #0,1: 88:[19, 76, 24] Operation: 58-34=24 Exploring Operation: 76-58=18, Resulting Numbers: [19, 34, 18] Generated Node #0,2: 88:[19, 34, 18] Operation: 76-58=18 Start Sub Search at level 1: Moving to Node #0,1 Current State: 88:[19, 76, 24], Operations: ['58-34=24'] Exploring Operation: 76/19=4, Resulting Numbers: [24, 4] Generated Node #0,1,0: 88:[24, 4] Operation: 76/19=4 Exploring Operation: 76-24=52, Resulting Numbers: [19, 52] Generated Node #0,1,1: 88:[19, 52] Operation: 76-24=52 Exploring Operation: 19+76=95, Resulting Numbers: [24, 95] Generated Node #0,1,2: 88:[24, 95] Operation: 19+76=95 Moving to Node #0,1,0 Current State: 88:[24, 4], Operations: ['58-34=24', '76/19=4'] Exploring Operation: 24+4=28, Resulting Numbers: [28] 28,88 unequal: No Solution Exploring Operation: 24-4=20, Resulting Numbers: [20] 20,88 unequal: No Solution Exploring Operation: 24/4=6, Resulting Numbers: [6] 6,88 unequal: No Solution Moving to Node #0,1,2 Current State: 88:[24, 95], Operations: ['58-34=24', '19+76=95'] Exploring Operation: 95-24=71, Resulting Numbers: [71] 71,88 unequal: No Solution Exploring Operation: 24+95=119, Resulting Numbers: [119] 119,88 unequal: No Solution Exploring Operation: 24*95=2280, Resulting Numbers: [2280] 2280,88 unequal: No Solution Moving to Node #0,1,1 Current State: 88:[19, 52], Operations: ['58-34=24', '76-24=52'] Exploring Operation: 52-19=33, Resulting Numbers: [33] 33,88 unequal: No Solution Exploring Operation: 19*52=988, Resulting Numbers: [988] 988,88 unequal: No Solution Exploring Operation: 19+52=71, Resulting Numbers: [71] 71,88 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 88:[19, 34, 18], Operations: ['76-58=18'] Exploring Operation: 19-18=1, Resulting Numbers: [34, 1] Generated Node #0,2,0: 88:[34, 1] Operation: 19-18=1 Exploring Operation: 34-18=16, Resulting Numbers: [19, 16] Generated Node #0,2,1: 88:[19, 16] Operation: 34-18=16 Exploring Operation: 34-19=15, Resulting Numbers: [18, 15] Generated Node #0,2,2: 88:[18, 15] Operation: 34-19=15 Moving to Node #0,2,1 Current State: 88:[19, 16], Operations: ['76-58=18', '34-18=16'] Exploring Operation: 19+16=35, Resulting Numbers: [35] 35,88 unequal: No Solution Exploring Operation: 19-16=3, Resulting Numbers: [3] 3,88 unequal: No Solution Exploring Operation: 19*16=304, Resulting Numbers: [304] 304,88 unequal: No Solution Moving to Node #0,2,2 Current State: 88:[18, 15], Operations: ['76-58=18', '34-19=15'] Exploring Operation: 18-15=3, Resulting Numbers: [3] 3,88 unequal: No Solution Exploring Operation: 18+15=33, Resulting Numbers: [33] 33,88 unequal: No Solution Exploring Operation: 18*15=270, Resulting Numbers: [270] 270,88 unequal: No Solution Moving to Node #0,2,0 Current State: 88:[34, 1], Operations: ['76-58=18', '19-18=1'] Exploring Operation: 34*1=34, Resulting Numbers: [34] 34,88 unequal: No Solution Exploring Operation: 34+1=35, Resulting Numbers: [35] 35,88 unequal: No Solution Exploring Operation: 34/1=34, Resulting Numbers: [34] 34,88 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 88:[19, 76, 92], Operations: ['34+58=92'] Exploring Operation: 76/19=4, Resulting Numbers: [92, 4] Generated Node #0,0,0: 88:[92, 4] Operation: 76/19=4 Exploring Operation: 19+76=95, Resulting Numbers: [92, 95] Generated Node #0,0,1: 88:[92, 95] Operation: 19+76=95 Exploring Operation: 92-76=16, Resulting Numbers: [19, 16] Generated Node #0,0,2: 88:[19, 16] Operation: 92-76=16 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 88:[92, 4], Operations: ['34+58=92', '76/19=4'] Exploring Operation: 92/4=23, Resulting Numbers: [23] 23,88 unequal: No Solution Exploring Operation: 92-4=88, Resulting Numbers: [88] 88,88 equal: Goal Reached Moving to Node #0 Current State: 88:[19, 34, 58, 76], Operations: [] Exploring Operation: 34+58=92, Resulting Numbers: [19, 76, 92] Generated Node #0,0: 88:[19, 76, 92] Operation: 34+58=92 Moving to Node #0,0 Current State: 88:[19, 76, 92], Operations: ['34+58=92'] Exploring Operation: 76/19=4, Resulting Numbers: [92, 4] Generated Node #0,0,0: 88:[92, 4] Operation: 76/19=4 Moving to Node #0,0,0 Current State: 88:[92, 4], Operations: ['34+58=92', '76/19=4'] Exploring Operation: 92-4=88, Resulting Numbers: [88] 88,88 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.96875
hs_3
sum_heuristic
[ 57, 53, 45, 3 ]
79
[ "57/3=19", "53+45=98", "98-19=79" ]
Current State: 79:[57, 53, 45, 3], Operations: [] Exploring Operation: 57/3=19, Resulting Numbers: [53, 45, 19] Generated Node #2: [53, 45, 19] from Operation: 57/3=19 Current State: 79:[53, 45, 19], Operations: ['57/3=19'] Exploring Operation: 53+45=98, Resulting Numbers: [19, 98] Generated Node #3: [19, 98] from Operation: 53+45=98 Current State: 79:[19, 98], Operations: ['57/3=19', '53+45=98'] Exploring Operation: 98-19=79, Resulting Numbers: [79] 79,79 equal: Goal Reached
4
Current State: 79:[57, 53, 45, 3], Operations: [] Exploring Operation: 57+3=60, Resulting Numbers: [53, 45, 60] Generated Node #0,0: 79:[53, 45, 60] Operation: 57+3=60 Start Sub Search at level 1: Moving to Node #0,0 Current State: 79:[53, 45, 60], Operations: ['57+3=60'] Exploring Operation: 53+45=98, Resulting Numbers: [60, 98] Generated Node #0,0,0: 79:[60, 98] Operation: 53+45=98 Moving to Node #0,0,0 Current State: 79:[60, 98], Operations: ['57+3=60', '53+45=98'] Exploring Operation: 98-60=38, Resulting Numbers: [38] 38,79 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
mult_heuristic
[ 8, 55, 61, 76 ]
24
[ "55+61=116", "76+116=192", "192/8=24" ]
Current State: 24:[8, 55, 61, 76], Operations: [] Exploring Operation: 55+61=116, Resulting Numbers: [8, 76, 116] Generated Node #2: [8, 76, 116] from Operation: 55+61=116 Current State: 24:[8, 76, 116], Operations: ['55+61=116'] Exploring Operation: 76+116=192, Resulting Numbers: [8, 192] Generated Node #3: [8, 192] from Operation: 76+116=192 Current State: 24:[8, 192], Operations: ['55+61=116', '76+116=192'] Exploring Operation: 192/8=24, Resulting Numbers: [24] 24,24 equal: Goal Reached
4
Current State: 24:[8, 55, 61, 76], Operations: [] Exploring Operation: 76-61=15, Resulting Numbers: [8, 55, 15] Generated Node #0,0: 24:[8, 55, 15] Operation: 76-61=15 Start Sub Search at level 1: Moving to Node #0,0 Current State: 24:[8, 55, 15], Operations: ['76-61=15'] Exploring Operation: 55-15=40, Resulting Numbers: [8, 40] Generated Node #0,0,0: 24:[8, 40] Operation: 55-15=40 Moving to Node #0,0,0 Current State: 24:[8, 40], Operations: ['76-61=15', '55-15=40'] Exploring Operation: 40/8=5, Resulting Numbers: [5] 5,24 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
sum_heuristic
[ 10, 10, 59, 80 ]
59
[ "10-10=0", "80*0=0", "59+0=59" ]
Current State: 59:[10, 10, 59, 80], Operations: [] Exploring Operation: 10-10=0, Resulting Numbers: [59, 80, 0] Generated Node #2: [59, 80, 0] from Operation: 10-10=0 Current State: 59:[59, 80, 0], Operations: ['10-10=0'] Exploring Operation: 80*0=0, Resulting Numbers: [59, 0] Generated Node #3: [59, 0] from Operation: 80*0=0 Current State: 59:[59, 0], Operations: ['10-10=0', '80*0=0'] Exploring Operation: 59+0=59, Resulting Numbers: [59] 59,59 equal: Goal Reached
4
Current State: 59:[10, 10, 59, 80], Operations: [] Exploring Operation: 10+10=20, Resulting Numbers: [59, 80, 20] Generated Node #0,0: 59:[59, 80, 20] Operation: 10+10=20 Moving to Node #0,0 Current State: 59:[59, 80, 20], Operations: ['10+10=20'] Exploring Operation: 80-20=60, Resulting Numbers: [59, 60] Generated Node #0,0,0: 59:[59, 60] Operation: 80-20=60 Moving to Node #0,0,0 Current State: 59:[59, 60], Operations: ['10+10=20', '80-20=60'] Exploring Operation: 60-59=1, Resulting Numbers: [1] 1,59 unequal: No Solution No solution found.
0
hs_1
sum_heuristic
[ 82, 47, 3, 28 ]
94
[ "3*28=84", "84-82=2", "47*2=94" ]
Current State: 94:[82, 47, 3, 28], Operations: [] Exploring Operation: 3*28=84, Resulting Numbers: [82, 47, 84] Generated Node #2: [82, 47, 84] from Operation: 3*28=84 Current State: 94:[82, 47, 84], Operations: ['3*28=84'] Exploring Operation: 84-82=2, Resulting Numbers: [47, 2] Generated Node #3: [47, 2] from Operation: 84-82=2 Current State: 94:[47, 2], Operations: ['3*28=84', '84-82=2'] Exploring Operation: 47*2=94, Resulting Numbers: [94] 94,94 equal: Goal Reached
4
Current State: 94:[82, 47, 3, 28], Operations: [] Exploring Operation: 82+3=85, Resulting Numbers: [47, 28, 85] Generated Node #0,0: 94:[47, 28, 85] Operation: 82+3=85 Exploring Operation: 82-28=54, Resulting Numbers: [47, 3, 54] Generated Node #0,1: 94:[47, 3, 54] Operation: 82-28=54 Exploring Operation: 3*28=84, Resulting Numbers: [82, 47, 84] Generated Node #0,2: 94:[82, 47, 84] Operation: 3*28=84 Exploring Operation: 3+28=31, Resulting Numbers: [82, 47, 31] Generated Node #0,3: 94:[82, 47, 31] Operation: 3+28=31 Exploring Operation: 82+28=110, Resulting Numbers: [47, 3, 110] Generated Node #0,4: 94:[47, 3, 110] Operation: 82+28=110 Start Sub Search at level 1: Moving to Node #0,1 Current State: 94:[47, 3, 54], Operations: ['82-28=54'] Exploring Operation: 54-3=51, Resulting Numbers: [47, 51] Generated Node #0,1,0: 94:[47, 51] Operation: 54-3=51 Exploring Operation: 54-47=7, Resulting Numbers: [3, 7] Generated Node #0,1,1: 94:[3, 7] Operation: 54-47=7 Exploring Operation: 47+3=50, Resulting Numbers: [54, 50] Generated Node #0,1,2: 94:[54, 50] Operation: 47+3=50 Exploring Operation: 47-3=44, Resulting Numbers: [54, 44] Generated Node #0,1,3: 94:[54, 44] Operation: 47-3=44 Exploring Operation: 47+54=101, Resulting Numbers: [3, 101] Generated Node #0,1,4: 94:[3, 101] Operation: 47+54=101 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 94:[47, 51], Operations: ['82-28=54', '54-3=51'] Exploring Operation: 47*51=2397, Resulting Numbers: [2397] 2397,94 unequal: No Solution Exploring Operation: 47+51=98, Resulting Numbers: [98] 98,94 unequal: No Solution Exploring Operation: 51-47=4, Resulting Numbers: [4] 4,94 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 94:[3, 7], Operations: ['82-28=54', '54-47=7'] Exploring Operation: 3*7=21, Resulting Numbers: [21] 21,94 unequal: No Solution Exploring Operation: 3+7=10, Resulting Numbers: [10] 10,94 unequal: No Solution Exploring Operation: 7-3=4, Resulting Numbers: [4] 4,94 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,4 Current State: 94:[3, 101], Operations: ['82-28=54', '47+54=101'] Exploring Operation: 3+101=104, Resulting Numbers: [104] 104,94 unequal: No Solution Exploring Operation: 101-3=98, Resulting Numbers: [98] 98,94 unequal: No Solution Exploring Operation: 3*101=303, Resulting Numbers: [303] 303,94 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 94:[54, 50], Operations: ['82-28=54', '47+3=50'] Exploring Operation: 54-50=4, Resulting Numbers: [4] 4,94 unequal: No Solution Exploring Operation: 54+50=104, Resulting Numbers: [104] 104,94 unequal: No Solution Exploring Operation: 54*50=2700, Resulting Numbers: [2700] 2700,94 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,3 Current State: 94:[54, 44], Operations: ['82-28=54', '47-3=44'] Exploring Operation: 54+44=98, Resulting Numbers: [98] 98,94 unequal: No Solution Exploring Operation: 54*44=2376, Resulting Numbers: [2376] 2376,94 unequal: No Solution Exploring Operation: 54-44=10, Resulting Numbers: [10] 10,94 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4 Current State: 94:[47, 3, 110], Operations: ['82+28=110'] Exploring Operation: 110-47=63, Resulting Numbers: [3, 63] Generated Node #0,4,0: 94:[3, 63] Operation: 110-47=63 Exploring Operation: 110-3=107, Resulting Numbers: [47, 107] Generated Node #0,4,1: 94:[47, 107] Operation: 110-3=107 Exploring Operation: 47+3=50, Resulting Numbers: [110, 50] Generated Node #0,4,2: 94:[110, 50] Operation: 47+3=50 Exploring Operation: 3+110=113, Resulting Numbers: [47, 113] Generated Node #0,4,3: 94:[47, 113] Operation: 3+110=113 Exploring Operation: 47-3=44, Resulting Numbers: [110, 44] Generated Node #0,4,4: 94:[110, 44] Operation: 47-3=44 Start Sub Search at level 2: Moving to Node #0,4,1 Current State: 94:[47, 107], Operations: ['82+28=110', '110-3=107'] Exploring Operation: 47*107=5029, Resulting Numbers: [5029] 5029,94 unequal: No Solution Exploring Operation: 47+107=154, Resulting Numbers: [154] 154,94 unequal: No Solution Exploring Operation: 107-47=60, Resulting Numbers: [60] 60,94 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,0 Current State: 94:[3, 63], Operations: ['82+28=110', '110-47=63'] Exploring Operation: 63-3=60, Resulting Numbers: [60] 60,94 unequal: No Solution Exploring Operation: 3+63=66, Resulting Numbers: [66] 66,94 unequal: No Solution Exploring Operation: 63/3=21, Resulting Numbers: [21] 21,94 unequal: No Solution Exploring Operation: 3*63=189, Resulting Numbers: [189] 189,94 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,2 Current State: 94:[110, 50], Operations: ['82+28=110', '47+3=50'] Exploring Operation: 110-50=60, Resulting Numbers: [60] 60,94 unequal: No Solution Exploring Operation: 110+50=160, Resulting Numbers: [160] 160,94 unequal: No Solution Exploring Operation: 110*50=5500, Resulting Numbers: [5500] 5500,94 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,3 Current State: 94:[47, 113], Operations: ['82+28=110', '3+110=113'] Exploring Operation: 47+113=160, Resulting Numbers: [160] 160,94 unequal: No Solution Exploring Operation: 113-47=66, Resulting Numbers: [66] 66,94 unequal: No Solution Exploring Operation: 47*113=5311, Resulting Numbers: [5311] 5311,94 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,4 Current State: 94:[110, 44], Operations: ['82+28=110', '47-3=44'] Exploring Operation: 110-44=66, Resulting Numbers: [66] 66,94 unequal: No Solution Exploring Operation: 110*44=4840, Resulting Numbers: [4840] 4840,94 unequal: No Solution Exploring Operation: 110+44=154, Resulting Numbers: [154] 154,94 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 94:[82, 47, 84], Operations: ['3*28=84'] Exploring Operation: 84-47=37, Resulting Numbers: [82, 37] Generated Node #0,2,0: 94:[82, 37] Operation: 84-47=37 Exploring Operation: 84-82=2, Resulting Numbers: [47, 2] Generated Node #0,2,1: 94:[47, 2] Operation: 84-82=2 Exploring Operation: 82+47=129, Resulting Numbers: [84, 129] Generated Node #0,2,2: 94:[84, 129] Operation: 82+47=129 Exploring Operation: 82-47=35, Resulting Numbers: [84, 35] Generated Node #0,2,3: 94:[84, 35] Operation: 82-47=35 Exploring Operation: 47+84=131, Resulting Numbers: [82, 131] Generated Node #0,2,4: 94:[82, 131] Operation: 47+84=131 Moving to Node #0,2,1 Current State: 94:[47, 2], Operations: ['3*28=84', '84-82=2'] Exploring Operation: 47*2=94, Resulting Numbers: [94] 94,94 equal: Goal Reached Moving to Node #0 Current State: 94:[82, 47, 3, 28], Operations: [] Exploring Operation: 3*28=84, Resulting Numbers: [82, 47, 84] Generated Node #0,2: 94:[82, 47, 84] Operation: 3*28=84 Moving to Node #0,2 Current State: 94:[82, 47, 84], Operations: ['3*28=84'] Exploring Operation: 84-82=2, Resulting Numbers: [47, 2] Generated Node #0,2,1: 94:[47, 2] Operation: 84-82=2 Moving to Node #0,2,1 Current State: 94:[47, 2], Operations: ['3*28=84', '84-82=2'] Exploring Operation: 47*2=94, Resulting Numbers: [94] 94,94 equal: Goal Reached Exit Sub Search at level 1
0.951389
hs_5
mult_heuristic
[ 75, 35, 1, 23 ]
16
[ "75-35=40", "1+23=24", "40-24=16" ]
Current State: 16:[75, 35, 1, 23], Operations: [] Exploring Operation: 75-35=40, Resulting Numbers: [1, 23, 40] Generated Node #2: [1, 23, 40] from Operation: 75-35=40 Current State: 16:[1, 23, 40], Operations: ['75-35=40'] Exploring Operation: 1+23=24, Resulting Numbers: [40, 24] Generated Node #3: [40, 24] from Operation: 1+23=24 Current State: 16:[40, 24], Operations: ['75-35=40', '1+23=24'] Exploring Operation: 40-24=16, Resulting Numbers: [16] 16,16 equal: Goal Reached
4
Current State: 16:[75, 35, 1, 23], Operations: [] Exploring Operation: 75-23=52, Resulting Numbers: [35, 1, 52] Generated Node #0,0: 16:[35, 1, 52] Operation: 75-23=52 Exploring Operation: 35-23=12, Resulting Numbers: [75, 1, 12] Generated Node #0,1: 16:[75, 1, 12] Operation: 35-23=12 Exploring Operation: 75-35=40, Resulting Numbers: [1, 23, 40] Generated Node #0,2: 16:[1, 23, 40] Operation: 75-35=40 Start Sub Search at level 1: Moving to Node #0,2 Current State: 16:[1, 23, 40], Operations: ['75-35=40'] Exploring Operation: 40-23=17, Resulting Numbers: [1, 17] Generated Node #0,2,0: 16:[1, 17] Operation: 40-23=17 Exploring Operation: 23-1=22, Resulting Numbers: [40, 22] Generated Node #0,2,1: 16:[40, 22] Operation: 23-1=22 Exploring Operation: 40-1=39, Resulting Numbers: [23, 39] Generated Node #0,2,2: 16:[23, 39] Operation: 40-1=39 Moving to Node #0,2,0 Current State: 16:[1, 17], Operations: ['75-35=40', '40-23=17'] Exploring Operation: 17/1=17, Resulting Numbers: [17] 17,16 unequal: No Solution Exploring Operation: 1*17=17, Resulting Numbers: [17] 17,16 unequal: No Solution Exploring Operation: 17-1=16, Resulting Numbers: [16] 16,16 equal: Goal Reached Moving to Node #0 Current State: 16:[75, 35, 1, 23], Operations: [] Exploring Operation: 75-35=40, Resulting Numbers: [1, 23, 40] Generated Node #0,2: 16:[1, 23, 40] Operation: 75-35=40 Moving to Node #0,2 Current State: 16:[1, 23, 40], Operations: ['75-35=40'] Exploring Operation: 40-23=17, Resulting Numbers: [1, 17] Generated Node #0,2,0: 16:[1, 17] Operation: 40-23=17 Moving to Node #0,2,0 Current State: 16:[1, 17], Operations: ['75-35=40', '40-23=17'] Exploring Operation: 17-1=16, Resulting Numbers: [16] 16,16 equal: Goal Reached Exit Sub Search at level 1
0.988715
hs_3
sum_heuristic
[ 19, 84, 3, 86 ]
25
[ "86-84=2", "3*2=6", "19+6=25" ]
Current State: 25:[19, 84, 3, 86], Operations: [] Exploring Operation: 86-84=2, Resulting Numbers: [19, 3, 2] Generated Node #2: [19, 3, 2] from Operation: 86-84=2 Current State: 25:[19, 3, 2], Operations: ['86-84=2'] Exploring Operation: 3*2=6, Resulting Numbers: [19, 6] Generated Node #3: [19, 6] from Operation: 3*2=6 Current State: 25:[19, 6], Operations: ['86-84=2', '3*2=6'] Exploring Operation: 19+6=25, Resulting Numbers: [25] 25,25 equal: Goal Reached
4
Current State: 25:[19, 84, 3, 86], Operations: [] Exploring Operation: 84/3=28, Resulting Numbers: [19, 86, 28] Generated Node #0,0: 25:[19, 86, 28] Operation: 84/3=28 Exploring Operation: 86-84=2, Resulting Numbers: [19, 3, 2] Generated Node #0,1: 25:[19, 3, 2] Operation: 86-84=2 Exploring Operation: 86-19=67, Resulting Numbers: [84, 3, 67] Generated Node #0,2: 25:[84, 3, 67] Operation: 86-19=67 Exploring Operation: 19+3=22, Resulting Numbers: [84, 86, 22] Generated Node #0,3: 25:[84, 86, 22] Operation: 19+3=22 Exploring Operation: 84-19=65, Resulting Numbers: [3, 86, 65] Generated Node #0,4: 25:[3, 86, 65] Operation: 84-19=65 Moving to Node #0,1 Current State: 25:[19, 3, 2], Operations: ['86-84=2'] Exploring Operation: 3*2=6, Resulting Numbers: [19, 6] Generated Node #0,1,0: 25:[19, 6] Operation: 3*2=6 Exploring Operation: 3+2=5, Resulting Numbers: [19, 5] Generated Node #0,1,1: 25:[19, 5] Operation: 3+2=5 Exploring Operation: 19-2=17, Resulting Numbers: [3, 17] Generated Node #0,1,2: 25:[3, 17] Operation: 19-2=17 Exploring Operation: 19+3=22, Resulting Numbers: [2, 22] Generated Node #0,1,3: 25:[2, 22] Operation: 19+3=22 Exploring Operation: 19+2=21, Resulting Numbers: [3, 21] Generated Node #0,1,4: 25:[3, 21] Operation: 19+2=21 Moving to Node #0,0 Current State: 25:[19, 86, 28], Operations: ['84/3=28'] Exploring Operation: 86-19=67, Resulting Numbers: [28, 67] Generated Node #0,0,0: 25:[28, 67] Operation: 86-19=67 Exploring Operation: 28-19=9, Resulting Numbers: [86, 9] Generated Node #0,0,1: 25:[86, 9] Operation: 28-19=9 Exploring Operation: 86-28=58, Resulting Numbers: [19, 58] Generated Node #0,0,2: 25:[19, 58] Operation: 86-28=58 Exploring Operation: 19+28=47, Resulting Numbers: [86, 47] Generated Node #0,0,3: 25:[86, 47] Operation: 19+28=47 Exploring Operation: 19+86=105, Resulting Numbers: [28, 105] Generated Node #0,0,4: 25:[28, 105] Operation: 19+86=105 Moving to Node #0,2 Current State: 25:[84, 3, 67], Operations: ['86-19=67'] Exploring Operation: 84+3=87, Resulting Numbers: [67, 87] Generated Node #0,2,0: 25:[67, 87] Operation: 84+3=87 Exploring Operation: 84/3=28, Resulting Numbers: [67, 28] Generated Node #0,2,1: 25:[67, 28] Operation: 84/3=28 Exploring Operation: 67-3=64, Resulting Numbers: [84, 64] Generated Node #0,2,2: 25:[84, 64] Operation: 67-3=64 Exploring Operation: 84-67=17, Resulting Numbers: [3, 17] Generated Node #0,2,3: 25:[3, 17] Operation: 84-67=17 Exploring Operation: 84-3=81, Resulting Numbers: [67, 81] Generated Node #0,2,4: 25:[67, 81] Operation: 84-3=81 Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 25:[3, 17], Operations: ['86-19=67', '84-67=17'] Exploring Operation: 3*17=51, Resulting Numbers: [51] 51,25 unequal: No Solution Exploring Operation: 3+17=20, Resulting Numbers: [20] 20,25 unequal: No Solution Exploring Operation: 17-3=14, Resulting Numbers: [14] 14,25 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 25:[67, 28], Operations: ['86-19=67', '84/3=28'] Exploring Operation: 67*28=1876, Resulting Numbers: [1876] 1876,25 unequal: No Solution Exploring Operation: 67-28=39, Resulting Numbers: [39] 39,25 unequal: No Solution Exploring Operation: 67+28=95, Resulting Numbers: [95] 95,25 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 25:[84, 64], Operations: ['86-19=67', '67-3=64'] Exploring Operation: 84*64=5376, Resulting Numbers: [5376] 5376,25 unequal: No Solution Exploring Operation: 84+64=148, Resulting Numbers: [148] 148,25 unequal: No Solution Exploring Operation: 84-64=20, Resulting Numbers: [20] 20,25 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,4 Current State: 25:[67, 81], Operations: ['86-19=67', '84-3=81'] Exploring Operation: 81-67=14, Resulting Numbers: [14] 14,25 unequal: No Solution Exploring Operation: 67*81=5427, Resulting Numbers: [5427] 5427,25 unequal: No Solution Exploring Operation: 67+81=148, Resulting Numbers: [148] 148,25 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 25:[67, 87], Operations: ['86-19=67', '84+3=87'] Exploring Operation: 67*87=5829, Resulting Numbers: [5829] 5829,25 unequal: No Solution Exploring Operation: 67+87=154, Resulting Numbers: [154] 154,25 unequal: No Solution Exploring Operation: 87-67=20, Resulting Numbers: [20] 20,25 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,4 Current State: 25:[3, 86, 65], Operations: ['84-19=65'] Exploring Operation: 86-3=83, Resulting Numbers: [65, 83] Generated Node #0,4,0: 25:[65, 83] Operation: 86-3=83 Exploring Operation: 3+65=68, Resulting Numbers: [86, 68] Generated Node #0,4,1: 25:[86, 68] Operation: 3+65=68 Exploring Operation: 3+86=89, Resulting Numbers: [65, 89] Generated Node #0,4,2: 25:[65, 89] Operation: 3+86=89 Exploring Operation: 65-3=62, Resulting Numbers: [86, 62] Generated Node #0,4,3: 25:[86, 62] Operation: 65-3=62 Exploring Operation: 86-65=21, Resulting Numbers: [3, 21] Generated Node #0,4,4: 25:[3, 21] Operation: 86-65=21 Start Sub Search at level 1: Moving to Node #0,4,4 Current State: 25:[3, 21], Operations: ['84-19=65', '86-65=21'] Exploring Operation: 21-3=18, Resulting Numbers: [18] 18,25 unequal: No Solution Exploring Operation: 21/3=7, Resulting Numbers: [7] 7,25 unequal: No Solution Exploring Operation: 3*21=63, Resulting Numbers: [63] 63,25 unequal: No Solution Exploring Operation: 3+21=24, Resulting Numbers: [24] 24,25 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,0 Current State: 25:[65, 83], Operations: ['84-19=65', '86-3=83'] Exploring Operation: 65+83=148, Resulting Numbers: [148] 148,25 unequal: No Solution Exploring Operation: 65*83=5395, Resulting Numbers: [5395] 5395,25 unequal: No Solution Exploring Operation: 83-65=18, Resulting Numbers: [18] 18,25 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,3 Current State: 25:[86, 62], Operations: ['84-19=65', '65-3=62'] Exploring Operation: 86-62=24, Resulting Numbers: [24] 24,25 unequal: No Solution Exploring Operation: 86*62=5332, Resulting Numbers: [5332] 5332,25 unequal: No Solution Exploring Operation: 86+62=148, Resulting Numbers: [148] 148,25 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,1 Current State: 25:[86, 68], Operations: ['84-19=65', '3+65=68'] Exploring Operation: 86+68=154, Resulting Numbers: [154] 154,25 unequal: No Solution Exploring Operation: 86*68=5848, Resulting Numbers: [5848] 5848,25 unequal: No Solution Exploring Operation: 86-68=18, Resulting Numbers: [18] 18,25 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,2 Current State: 25:[65, 89], Operations: ['84-19=65', '3+86=89'] Exploring Operation: 65+89=154, Resulting Numbers: [154] 154,25 unequal: No Solution Exploring Operation: 65*89=5785, Resulting Numbers: [5785] 5785,25 unequal: No Solution Exploring Operation: 89-65=24, Resulting Numbers: [24] 24,25 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,3 Current State: 25:[84, 86, 22], Operations: ['19+3=22'] Exploring Operation: 84+22=106, Resulting Numbers: [86, 106] Generated Node #0,3,0: 25:[86, 106] Operation: 84+22=106 Exploring Operation: 86-22=64, Resulting Numbers: [84, 64] Generated Node #0,3,1: 25:[84, 64] Operation: 86-22=64 Exploring Operation: 84-22=62, Resulting Numbers: [86, 62] Generated Node #0,3,2: 25:[86, 62] Operation: 84-22=62 Exploring Operation: 86-84=2, Resulting Numbers: [22, 2] Generated Node #0,3,3: 25:[22, 2] Operation: 86-84=2 Exploring Operation: 86+22=108, Resulting Numbers: [84, 108] Generated Node #0,3,4: 25:[84, 108] Operation: 86+22=108 Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 25:[22, 2], Operations: ['19+3=22', '86-84=2'] Exploring Operation: 22+2=24, Resulting Numbers: [24] 24,25 unequal: No Solution Exploring Operation: 22-2=20, Resulting Numbers: [20] 20,25 unequal: No Solution Exploring Operation: 22*2=44, Resulting Numbers: [44] 44,25 unequal: No Solution Exploring Operation: 22/2=11, Resulting Numbers: [11] 11,25 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 25:[84, 64], Operations: ['19+3=22', '86-22=64'] Exploring Operation: 84*64=5376, Resulting Numbers: [5376] 5376,25 unequal: No Solution Exploring Operation: 84+64=148, Resulting Numbers: [148] 148,25 unequal: No Solution Exploring Operation: 84-64=20, Resulting Numbers: [20] 20,25 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 25:[86, 62], Operations: ['19+3=22', '84-22=62'] Exploring Operation: 86+62=148, Resulting Numbers: [148] 148,25 unequal: No Solution Exploring Operation: 86*62=5332, Resulting Numbers: [5332] 5332,25 unequal: No Solution Exploring Operation: 86-62=24, Resulting Numbers: [24] 24,25 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 25:[86, 106], Operations: ['19+3=22', '84+22=106'] Exploring Operation: 106-86=20, Resulting Numbers: [20] 20,25 unequal: No Solution Exploring Operation: 86*106=9116, Resulting Numbers: [9116] 9116,25 unequal: No Solution Exploring Operation: 86+106=192, Resulting Numbers: [192] 192,25 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,4 Current State: 25:[84, 108], Operations: ['19+3=22', '86+22=108'] Exploring Operation: 108-84=24, Resulting Numbers: [24] 24,25 unequal: No Solution Exploring Operation: 84+108=192, Resulting Numbers: [192] 192,25 unequal: No Solution Exploring Operation: 84*108=9072, Resulting Numbers: [9072] 9072,25 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1,1 Current State: 25:[19, 5], Operations: ['86-84=2', '3+2=5'] Exploring Operation: 19*5=95, Resulting Numbers: [95] 95,25 unequal: No Solution Exploring Operation: 19-5=14, Resulting Numbers: [14] 14,25 unequal: No Solution Exploring Operation: 19+5=24, Resulting Numbers: [24] 24,25 unequal: No Solution Moving to Node #0,1,4 Current State: 25:[3, 21], Operations: ['86-84=2', '19+2=21'] Exploring Operation: 3+21=24, Resulting Numbers: [24] 24,25 unequal: No Solution Exploring Operation: 21-3=18, Resulting Numbers: [18] 18,25 unequal: No Solution Exploring Operation: 21/3=7, Resulting Numbers: [7] 7,25 unequal: No Solution Exploring Operation: 3*21=63, Resulting Numbers: [63] 63,25 unequal: No Solution Moving to Node #0,1,3 Current State: 25:[2, 22], Operations: ['86-84=2', '19+3=22'] Exploring Operation: 22/2=11, Resulting Numbers: [11] 11,25 unequal: No Solution Exploring Operation: 2*22=44, Resulting Numbers: [44] 44,25 unequal: No Solution Exploring Operation: 22-2=20, Resulting Numbers: [20] 20,25 unequal: No Solution Exploring Operation: 2+22=24, Resulting Numbers: [24] 24,25 unequal: No Solution Moving to Node #0,1,0 Current State: 25:[19, 6], Operations: ['86-84=2', '3*2=6'] Exploring Operation: 19+6=25, Resulting Numbers: [25] 25,25 equal: Goal Reached Moving to Node #0 Current State: 25:[19, 84, 3, 86], Operations: [] Exploring Operation: 86-84=2, Resulting Numbers: [19, 3, 2] Generated Node #0,1: 25:[19, 3, 2] Operation: 86-84=2 Moving to Node #0,1 Current State: 25:[19, 3, 2], Operations: ['86-84=2'] Exploring Operation: 3*2=6, Resulting Numbers: [19, 6] Generated Node #0,1,0: 25:[19, 6] Operation: 3*2=6 Moving to Node #0,1,0 Current State: 25:[19, 6], Operations: ['86-84=2', '3*2=6'] Exploring Operation: 19+6=25, Resulting Numbers: [25] 25,25 equal: Goal Reached
0.919271
hs_5
mult_heuristic
[ 27, 5, 32, 5 ]
50
[ "27-5=22", "32-22=10", "5*10=50" ]
Current State: 50:[27, 5, 32, 5], Operations: [] Exploring Operation: 27-5=22, Resulting Numbers: [32, 22] Generated Node #2: [32, 22] from Operation: 27-5=22 Current State: 50:[32, 22], Operations: ['27-5=22'] Exploring Operation: 32-22=10, Resulting Numbers: [10] 10,50 equal: Goal Reached Exploring Operation: 5*10=50, Resulting Numbers: [50] 50,50 equal: Goal Reached
4
Current State: 50:[27, 5, 32, 5], Operations: [] Exploring Operation: 32-5=27, Resulting Numbers: [27, 5, 27] Generated Node #0,0: 50:[27, 5, 27] Operation: 32-5=27 Exploring Operation: 32-27=5, Resulting Numbers: [5, 5, 5] Generated Node #0,1: 50:[5, 5, 5] Operation: 32-27=5 Exploring Operation: 32-5=27, Resulting Numbers: [27, 5, 27] Generated Node #0,2: 50:[27, 5, 27] Operation: 32-5=27 Start Sub Search at level 1: Moving to Node #0,1 Current State: 50:[5, 5, 5], Operations: ['32-27=5'] Exploring Operation: 5+5=10, Resulting Numbers: [5, 10] Generated Node #0,1,0: 50:[5, 10] Operation: 5+5=10 Exploring Operation: 5+5=10, Resulting Numbers: [5, 10] Generated Node #0,1,1: 50:[5, 10] Operation: 5+5=10 Exploring Operation: 5*5=25, Resulting Numbers: [5, 25] Generated Node #0,1,2: 50:[5, 25] Operation: 5*5=25 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 50:[5, 10], Operations: ['32-27=5', '5+5=10'] Exploring Operation: 10-5=5, Resulting Numbers: [5] 5,50 unequal: No Solution Exploring Operation: 5*10=50, Resulting Numbers: [50] 50,50 equal: Goal Reached Moving to Node #0 Current State: 50:[27, 5, 32, 5], Operations: [] Exploring Operation: 32-27=5, Resulting Numbers: [5, 5, 5] Generated Node #0,1: 50:[5, 5, 5] Operation: 32-27=5 Moving to Node #0,1 Current State: 50:[5, 5, 5], Operations: ['32-27=5'] Exploring Operation: 5+5=10, Resulting Numbers: [5, 10] Generated Node #0,1,0: 50:[5, 10] Operation: 5+5=10 Moving to Node #0,1,0 Current State: 50:[5, 10], Operations: ['32-27=5', '5+5=10'] Exploring Operation: 5*10=50, Resulting Numbers: [50] 50,50 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.989583
hs_3
mult_heuristic
[ 28, 90, 86, 2 ]
56
[ "28/2=14", "90-86=4", "14*4=56" ]
Current State: 56:[28, 90, 86, 2], Operations: [] Exploring Operation: 28/2=14, Resulting Numbers: [90, 86, 14] Generated Node #2: [90, 86, 14] from Operation: 28/2=14 Current State: 56:[90, 86, 14], Operations: ['28/2=14'] Exploring Operation: 90-86=4, Resulting Numbers: [14, 4] Generated Node #3: [14, 4] from Operation: 90-86=4 Current State: 56:[14, 4], Operations: ['28/2=14', '90-86=4'] Exploring Operation: 14*4=56, Resulting Numbers: [56] 56,56 equal: Goal Reached
4
Current State: 56:[28, 90, 86, 2], Operations: [] Exploring Operation: 90-86=4, Resulting Numbers: [28, 2, 4] Generated Node #0,0: 56:[28, 2, 4] Operation: 90-86=4 Start Sub Search at level 1: Moving to Node #0,0 Current State: 56:[28, 2, 4], Operations: ['90-86=4'] Exploring Operation: 28*2=56, Resulting Numbers: [4, 56] Generated Node #0,0,0: 56:[4, 56] Operation: 28*2=56 Moving to Node #0,0,0 Current State: 56:[4, 56], Operations: ['90-86=4', '28*2=56'] Exploring Operation: 56/4=14, Resulting Numbers: [14] 14,56 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
mult_heuristic
[ 52, 4, 38, 76 ]
20
[ "52-38=14", "4*14=56", "76-56=20" ]
Current State: 20:[52, 4, 38, 76], Operations: [] Exploring Operation: 52-38=14, Resulting Numbers: [4, 76, 14] Generated Node #2: [4, 76, 14] from Operation: 52-38=14 Current State: 20:[4, 76, 14], Operations: ['52-38=14'] Exploring Operation: 4*14=56, Resulting Numbers: [76, 56] Generated Node #3: [76, 56] from Operation: 4*14=56 Current State: 20:[76, 56], Operations: ['52-38=14', '4*14=56'] Exploring Operation: 76-56=20, Resulting Numbers: [20] 20,20 equal: Goal Reached
4
Current State: 20:[52, 4, 38, 76], Operations: [] Exploring Operation: 76-52=24, Resulting Numbers: [4, 38, 24] Generated Node #0,0: 20:[4, 38, 24] Operation: 76-52=24 Exploring Operation: 76/38=2, Resulting Numbers: [52, 4, 2] Generated Node #0,1: 20:[52, 4, 2] Operation: 76/38=2 Start Sub Search at level 1: Moving to Node #0,0 Current State: 20:[4, 38, 24], Operations: ['76-52=24'] Exploring Operation: 38-24=14, Resulting Numbers: [4, 14] Generated Node #0,0,0: 20:[4, 14] Operation: 38-24=14 Exploring Operation: 38-4=34, Resulting Numbers: [24, 34] Generated Node #0,0,1: 20:[24, 34] Operation: 38-4=34 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 20:[4, 14], Operations: ['76-52=24', '38-24=14'] Exploring Operation: 14-4=10, Resulting Numbers: [10] 10,20 unequal: No Solution Exploring Operation: 4+14=18, Resulting Numbers: [18] 18,20 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 20:[24, 34], Operations: ['76-52=24', '38-4=34'] Exploring Operation: 24+34=58, Resulting Numbers: [58] 58,20 unequal: No Solution Exploring Operation: 34-24=10, Resulting Numbers: [10] 10,20 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 20:[52, 4, 2], Operations: ['76/38=2'] Exploring Operation: 52/4=13, Resulting Numbers: [2, 13] Generated Node #0,1,0: 20:[2, 13] Operation: 52/4=13 Exploring Operation: 52/2=26, Resulting Numbers: [4, 26] Generated Node #0,1,1: 20:[4, 26] Operation: 52/2=26 Moving to Node #0,1,0 Current State: 20:[2, 13], Operations: ['76/38=2', '52/4=13'] Exploring Operation: 2+13=15, Resulting Numbers: [15] 15,20 unequal: No Solution Exploring Operation: 13-2=11, Resulting Numbers: [11] 11,20 unequal: No Solution Moving to Node #0,1,1 Current State: 20:[4, 26], Operations: ['76/38=2', '52/2=26'] Exploring Operation: 26-4=22, Resulting Numbers: [22] 22,20 unequal: No Solution Exploring Operation: 4+26=30, Resulting Numbers: [30] 30,20 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_2
sum_heuristic
[ 50, 88, 78, 39 ]
19
[ "88-50=38", "78/39=2", "38/2=19" ]
Current State: 19:[50, 88, 78, 39], Operations: [] Exploring Operation: 88-50=38, Resulting Numbers: [78, 39, 38] Generated Node #2: [78, 39, 38] from Operation: 88-50=38 Current State: 19:[78, 39, 38], Operations: ['88-50=38'] Exploring Operation: 78/39=2, Resulting Numbers: [38, 2] Generated Node #3: [38, 2] from Operation: 78/39=2 Current State: 19:[38, 2], Operations: ['88-50=38', '78/39=2'] Exploring Operation: 38/2=19, Resulting Numbers: [19] 19,19 equal: Goal Reached
4
Current State: 19:[50, 88, 78, 39], Operations: [] Exploring Operation: 88-50=38, Resulting Numbers: [78, 39, 38] Generated Node #0,0: 19:[78, 39, 38] Operation: 88-50=38 Exploring Operation: 88-78=10, Resulting Numbers: [50, 39, 10] Generated Node #0,1: 19:[50, 39, 10] Operation: 88-78=10 Exploring Operation: 78/39=2, Resulting Numbers: [50, 88, 2] Generated Node #0,2: 19:[50, 88, 2] Operation: 78/39=2 Exploring Operation: 78-50=28, Resulting Numbers: [88, 39, 28] Generated Node #0,3: 19:[88, 39, 28] Operation: 78-50=28 Start Sub Search at level 1: Moving to Node #0,1 Current State: 19:[50, 39, 10], Operations: ['88-78=10'] Exploring Operation: 50/10=5, Resulting Numbers: [39, 5] Generated Node #0,1,0: 19:[39, 5] Operation: 50/10=5 Exploring Operation: 50-39=11, Resulting Numbers: [10, 11] Generated Node #0,1,1: 19:[10, 11] Operation: 50-39=11 Exploring Operation: 39-10=29, Resulting Numbers: [50, 29] Generated Node #0,1,2: 19:[50, 29] Operation: 39-10=29 Exploring Operation: 50-10=40, Resulting Numbers: [39, 40] Generated Node #0,1,3: 19:[39, 40] Operation: 50-10=40 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 19:[10, 11], Operations: ['88-78=10', '50-39=11'] Exploring Operation: 10*11=110, Resulting Numbers: [110] 110,19 unequal: No Solution Exploring Operation: 11-10=1, Resulting Numbers: [1] 1,19 unequal: No Solution Exploring Operation: 10+11=21, Resulting Numbers: [21] 21,19 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 19:[39, 5], Operations: ['88-78=10', '50/10=5'] Exploring Operation: 39+5=44, Resulting Numbers: [44] 44,19 unequal: No Solution Exploring Operation: 39*5=195, Resulting Numbers: [195] 195,19 unequal: No Solution Exploring Operation: 39-5=34, Resulting Numbers: [34] 34,19 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 19:[50, 29], Operations: ['88-78=10', '39-10=29'] Exploring Operation: 50*29=1450, Resulting Numbers: [1450] 1450,19 unequal: No Solution Exploring Operation: 50+29=79, Resulting Numbers: [79] 79,19 unequal: No Solution Exploring Operation: 50-29=21, Resulting Numbers: [21] 21,19 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,3 Current State: 19:[39, 40], Operations: ['88-78=10', '50-10=40'] Exploring Operation: 40-39=1, Resulting Numbers: [1] 1,19 unequal: No Solution Exploring Operation: 39*40=1560, Resulting Numbers: [1560] 1560,19 unequal: No Solution Exploring Operation: 39+40=79, Resulting Numbers: [79] 79,19 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 19:[78, 39, 38], Operations: ['88-50=38'] Exploring Operation: 78/39=2, Resulting Numbers: [38, 2] Generated Node #0,0,0: 19:[38, 2] Operation: 78/39=2 Exploring Operation: 39-38=1, Resulting Numbers: [78, 1] Generated Node #0,0,1: 19:[78, 1] Operation: 39-38=1 Exploring Operation: 78-38=40, Resulting Numbers: [39, 40] Generated Node #0,0,2: 19:[39, 40] Operation: 78-38=40 Exploring Operation: 78-39=39, Resulting Numbers: [38, 39] Generated Node #0,0,3: 19:[38, 39] Operation: 78-39=39 Moving to Node #0,0,0 Current State: 19:[38, 2], Operations: ['88-50=38', '78/39=2'] Exploring Operation: 38*2=76, Resulting Numbers: [76] 76,19 unequal: No Solution Exploring Operation: 38-2=36, Resulting Numbers: [36] 36,19 unequal: No Solution Exploring Operation: 38+2=40, Resulting Numbers: [40] 40,19 unequal: No Solution Exploring Operation: 38/2=19, Resulting Numbers: [19] 19,19 equal: Goal Reached Moving to Node #0 Current State: 19:[50, 88, 78, 39], Operations: [] Exploring Operation: 88-50=38, Resulting Numbers: [78, 39, 38] Generated Node #0,0: 19:[78, 39, 38] Operation: 88-50=38 Moving to Node #0,0 Current State: 19:[78, 39, 38], Operations: ['88-50=38'] Exploring Operation: 78/39=2, Resulting Numbers: [38, 2] Generated Node #0,0,0: 19:[38, 2] Operation: 78/39=2 Moving to Node #0,0,0 Current State: 19:[38, 2], Operations: ['88-50=38', '78/39=2'] Exploring Operation: 38/2=19, Resulting Numbers: [19] 19,19 equal: Goal Reached Exit Sub Search at level 1
0.972222
hs_4
mult_heuristic
[ 52, 29, 32, 41 ]
50
[ "52-29=23", "32+41=73", "73-23=50" ]
Current State: 50:[52, 29, 32, 41], Operations: [] Exploring Operation: 52-29=23, Resulting Numbers: [32, 41, 23] Generated Node #2: [32, 41, 23] from Operation: 52-29=23 Current State: 50:[32, 41, 23], Operations: ['52-29=23'] Exploring Operation: 32+41=73, Resulting Numbers: [23, 73] Generated Node #3: [23, 73] from Operation: 32+41=73 Current State: 50:[23, 73], Operations: ['52-29=23', '32+41=73'] Exploring Operation: 73-23=50, Resulting Numbers: [50] 50,50 equal: Goal Reached
4
Current State: 50:[52, 29, 32, 41], Operations: [] Exploring Operation: 41-32=9, Resulting Numbers: [52, 29, 9] Generated Node #0,0: 50:[52, 29, 9] Operation: 41-32=9 Start Sub Search at level 1: Moving to Node #0,0 Current State: 50:[52, 29, 9], Operations: ['41-32=9'] Exploring Operation: 52-29=23, Resulting Numbers: [9, 23] Generated Node #0,0,0: 50:[9, 23] Operation: 52-29=23 Moving to Node #0,0,0 Current State: 50:[9, 23], Operations: ['41-32=9', '52-29=23'] Exploring Operation: 23-9=14, Resulting Numbers: [14] 14,50 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
mult_heuristic
[ 38, 70, 69, 33 ]
72
[ "38+70=108", "69-33=36", "108-36=72" ]
Current State: 72:[38, 70, 69, 33], Operations: [] Exploring Operation: 38+70=108, Resulting Numbers: [69, 33, 108] Generated Node #2: [69, 33, 108] from Operation: 38+70=108 Current State: 72:[69, 33, 108], Operations: ['38+70=108'] Exploring Operation: 69-33=36, Resulting Numbers: [108, 36] Generated Node #3: [108, 36] from Operation: 69-33=36 Current State: 72:[108, 36], Operations: ['38+70=108', '69-33=36'] Exploring Operation: 108-36=72, Resulting Numbers: [72] 72,72 equal: Goal Reached
4
Current State: 72:[38, 70, 69, 33], Operations: [] Exploring Operation: 69-33=36, Resulting Numbers: [38, 70, 36] Generated Node #0,0: 72:[38, 70, 36] Operation: 69-33=36 Exploring Operation: 38+33=71, Resulting Numbers: [70, 69, 71] Generated Node #0,1: 72:[70, 69, 71] Operation: 38+33=71 Start Sub Search at level 1: Moving to Node #0,0 Current State: 72:[38, 70, 36], Operations: ['69-33=36'] Exploring Operation: 70-38=32, Resulting Numbers: [36, 32] Generated Node #0,0,0: 72:[36, 32] Operation: 70-38=32 Exploring Operation: 38-36=2, Resulting Numbers: [70, 2] Generated Node #0,0,1: 72:[70, 2] Operation: 38-36=2 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 72:[70, 2], Operations: ['69-33=36', '38-36=2'] Exploring Operation: 70/2=35, Resulting Numbers: [35] 35,72 unequal: No Solution Exploring Operation: 70+2=72, Resulting Numbers: [72] 72,72 equal: Goal Reached Moving to Node #0 Current State: 72:[38, 70, 69, 33], Operations: [] Exploring Operation: 69-33=36, Resulting Numbers: [38, 70, 36] Generated Node #0,0: 72:[38, 70, 36] Operation: 69-33=36 Moving to Node #0,0 Current State: 72:[38, 70, 36], Operations: ['69-33=36'] Exploring Operation: 38-36=2, Resulting Numbers: [70, 2] Generated Node #0,0,1: 72:[70, 2] Operation: 38-36=2 Moving to Node #0,0,1 Current State: 72:[70, 2], Operations: ['69-33=36', '38-36=2'] Exploring Operation: 70+2=72, Resulting Numbers: [72] 72,72 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.991319
hs_2
mult_heuristic
[ 72, 34, 14, 35 ]
13
[ "34*35=1190", "1190/14=85", "85-72=13" ]
Current State: 13:[72, 34, 14, 35], Operations: [] Exploring Operation: 34*35=1190, Resulting Numbers: [72, 14, 1190] Generated Node #2: [72, 14, 1190] from Operation: 34*35=1190 Current State: 13:[72, 14, 1190], Operations: ['34*35=1190'] Exploring Operation: 1190/14=85, Resulting Numbers: [72, 85] Generated Node #3: [72, 85] from Operation: 1190/14=85 Current State: 13:[72, 85], Operations: ['34*35=1190', '1190/14=85'] Exploring Operation: 85-72=13, Resulting Numbers: [13] 13,13 equal: Goal Reached
4
Current State: 13:[72, 34, 14, 35], Operations: [] Exploring Operation: 72-34=38, Resulting Numbers: [14, 35, 38] Generated Node #0,0: 13:[14, 35, 38] Operation: 72-34=38 Exploring Operation: 72-35=37, Resulting Numbers: [34, 14, 37] Generated Node #0,1: 13:[34, 14, 37] Operation: 72-35=37 Moving to Node #0,1 Current State: 13:[34, 14, 37], Operations: ['72-35=37'] Exploring Operation: 37-34=3, Resulting Numbers: [14, 3] Generated Node #0,1,0: 13:[14, 3] Operation: 37-34=3 Exploring Operation: 34-14=20, Resulting Numbers: [37, 20] Generated Node #0,1,1: 13:[37, 20] Operation: 34-14=20 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 13:[14, 3], Operations: ['72-35=37', '37-34=3'] Exploring Operation: 14-3=11, Resulting Numbers: [11] 11,13 unequal: No Solution Exploring Operation: 14+3=17, Resulting Numbers: [17] 17,13 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 13:[37, 20], Operations: ['72-35=37', '34-14=20'] Exploring Operation: 37-20=17, Resulting Numbers: [17] 17,13 unequal: No Solution Exploring Operation: 37+20=57, Resulting Numbers: [57] 57,13 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,0 Current State: 13:[14, 35, 38], Operations: ['72-34=38'] Exploring Operation: 38-35=3, Resulting Numbers: [14, 3] Generated Node #0,0,0: 13:[14, 3] Operation: 38-35=3 Exploring Operation: 35-14=21, Resulting Numbers: [38, 21] Generated Node #0,0,1: 13:[38, 21] Operation: 35-14=21 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 13:[14, 3], Operations: ['72-34=38', '38-35=3'] Exploring Operation: 14+3=17, Resulting Numbers: [17] 17,13 unequal: No Solution Exploring Operation: 14-3=11, Resulting Numbers: [11] 11,13 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 13:[38, 21], Operations: ['72-34=38', '35-14=21'] Exploring Operation: 38-21=17, Resulting Numbers: [17] 17,13 unequal: No Solution Exploring Operation: 38+21=59, Resulting Numbers: [59] 59,13 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_2
sum_heuristic
[ 96, 6, 18, 8 ]
54
[ "96*6=576", "576/8=72", "72-18=54" ]
Current State: 54:[96, 6, 18, 8], Operations: [] Exploring Operation: 96*6=576, Resulting Numbers: [18, 8, 576] Generated Node #2: [18, 8, 576] from Operation: 96*6=576 Current State: 54:[18, 8, 576], Operations: ['96*6=576'] Exploring Operation: 576/8=72, Resulting Numbers: [18, 72] Generated Node #3: [18, 72] from Operation: 576/8=72 Current State: 54:[18, 72], Operations: ['96*6=576', '576/8=72'] Exploring Operation: 72-18=54, Resulting Numbers: [54] 54,54 equal: Goal Reached
4
Current State: 54:[96, 6, 18, 8], Operations: [] Exploring Operation: 96/8=12, Resulting Numbers: [6, 18, 12] Generated Node #0,0: 54:[6, 18, 12] Operation: 96/8=12 Exploring Operation: 96-8=88, Resulting Numbers: [6, 18, 88] Generated Node #0,1: 54:[6, 18, 88] Operation: 96-8=88 Exploring Operation: 96/6=16, Resulting Numbers: [18, 8, 16] Generated Node #0,2: 54:[18, 8, 16] Operation: 96/6=16 Exploring Operation: 96-6=90, Resulting Numbers: [18, 8, 90] Generated Node #0,3: 54:[18, 8, 90] Operation: 96-6=90 Exploring Operation: 96-18=78, Resulting Numbers: [6, 8, 78] Generated Node #0,4: 54:[6, 8, 78] Operation: 96-18=78 Moving to Node #0,0 Current State: 54:[6, 18, 12], Operations: ['96/8=12'] Exploring Operation: 18-12=6, Resulting Numbers: [6, 6] Generated Node #0,0,0: 54:[6, 6] Operation: 18-12=6 Exploring Operation: 6+12=18, Resulting Numbers: [18, 18] Generated Node #0,0,1: 54:[18, 18] Operation: 6+12=18 Exploring Operation: 12-6=6, Resulting Numbers: [18, 6] Generated Node #0,0,2: 54:[18, 6] Operation: 12-6=6 Exploring Operation: 18/6=3, Resulting Numbers: [12, 3] Generated Node #0,0,3: 54:[12, 3] Operation: 18/6=3 Exploring Operation: 12/6=2, Resulting Numbers: [18, 2] Generated Node #0,0,4: 54:[18, 2] Operation: 12/6=2 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 54:[6, 6], Operations: ['96/8=12', '18-12=6'] Exploring Operation: 6/6=1, Resulting Numbers: [1] 1,54 unequal: No Solution Exploring Operation: 6-6=0, Resulting Numbers: [0] 0,54 unequal: No Solution Exploring Operation: 6+6=12, Resulting Numbers: [12] 12,54 unequal: No Solution Exploring Operation: 6*6=36, Resulting Numbers: [36] 36,54 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 54:[18, 18], Operations: ['96/8=12', '6+12=18'] Exploring Operation: 18+18=36, Resulting Numbers: [36] 36,54 unequal: No Solution Exploring Operation: 18*18=324, Resulting Numbers: [324] 324,54 unequal: No Solution Exploring Operation: 18-18=0, Resulting Numbers: [0] 0,54 unequal: No Solution Exploring Operation: 18/18=1, Resulting Numbers: [1] 1,54 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 54:[18, 6], Operations: ['96/8=12', '12-6=6'] Exploring Operation: 18/6=3, Resulting Numbers: [3] 3,54 unequal: No Solution Exploring Operation: 18-6=12, Resulting Numbers: [12] 12,54 unequal: No Solution Exploring Operation: 18*6=108, Resulting Numbers: [108] 108,54 unequal: No Solution Exploring Operation: 18+6=24, Resulting Numbers: [24] 24,54 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,4 Current State: 54:[18, 2], Operations: ['96/8=12', '12/6=2'] Exploring Operation: 18*2=36, Resulting Numbers: [36] 36,54 unequal: No Solution Exploring Operation: 18-2=16, Resulting Numbers: [16] 16,54 unequal: No Solution Exploring Operation: 18+2=20, Resulting Numbers: [20] 20,54 unequal: No Solution Exploring Operation: 18/2=9, Resulting Numbers: [9] 9,54 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 54:[12, 3], Operations: ['96/8=12', '18/6=3'] Exploring Operation: 12+3=15, Resulting Numbers: [15] 15,54 unequal: No Solution Exploring Operation: 12/3=4, Resulting Numbers: [4] 4,54 unequal: No Solution Exploring Operation: 12-3=9, Resulting Numbers: [9] 9,54 unequal: No Solution Exploring Operation: 12*3=36, Resulting Numbers: [36] 36,54 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,2 Current State: 54:[18, 8, 16], Operations: ['96/6=16'] Exploring Operation: 18+8=26, Resulting Numbers: [16, 26] Generated Node #0,2,0: 54:[16, 26] Operation: 18+8=26 Exploring Operation: 16/8=2, Resulting Numbers: [18, 2] Generated Node #0,2,1: 54:[18, 2] Operation: 16/8=2 Exploring Operation: 16-8=8, Resulting Numbers: [18, 8] Generated Node #0,2,2: 54:[18, 8] Operation: 16-8=8 Exploring Operation: 18-16=2, Resulting Numbers: [8, 2] Generated Node #0,2,3: 54:[8, 2] Operation: 18-16=2 Exploring Operation: 18-8=10, Resulting Numbers: [16, 10] Generated Node #0,2,4: 54:[16, 10] Operation: 18-8=10 Moving to Node #0,4 Current State: 54:[6, 8, 78], Operations: ['96-18=78'] Exploring Operation: 78-8=70, Resulting Numbers: [6, 70] Generated Node #0,4,0: 54:[6, 70] Operation: 78-8=70 Exploring Operation: 8-6=2, Resulting Numbers: [78, 2] Generated Node #0,4,1: 54:[78, 2] Operation: 8-6=2 Exploring Operation: 78/6=13, Resulting Numbers: [8, 13] Generated Node #0,4,2: 54:[8, 13] Operation: 78/6=13 Exploring Operation: 6+8=14, Resulting Numbers: [78, 14] Generated Node #0,4,3: 54:[78, 14] Operation: 6+8=14 Exploring Operation: 78-6=72, Resulting Numbers: [8, 72] Generated Node #0,4,4: 54:[8, 72] Operation: 78-6=72 Moving to Node #0,1 Current State: 54:[6, 18, 88], Operations: ['96-8=88'] Exploring Operation: 88-18=70, Resulting Numbers: [6, 70] Generated Node #0,1,0: 54:[6, 70] Operation: 88-18=70 Exploring Operation: 18-6=12, Resulting Numbers: [88, 12] Generated Node #0,1,1: 54:[88, 12] Operation: 18-6=12 Exploring Operation: 18/6=3, Resulting Numbers: [88, 3] Generated Node #0,1,2: 54:[88, 3] Operation: 18/6=3 Exploring Operation: 6+18=24, Resulting Numbers: [88, 24] Generated Node #0,1,3: 54:[88, 24] Operation: 6+18=24 Exploring Operation: 88-6=82, Resulting Numbers: [18, 82] Generated Node #0,1,4: 54:[18, 82] Operation: 88-6=82 Moving to Node #0,3 Current State: 54:[18, 8, 90], Operations: ['96-6=90'] Exploring Operation: 18+8=26, Resulting Numbers: [90, 26] Generated Node #0,3,0: 54:[90, 26] Operation: 18+8=26 Exploring Operation: 18-8=10, Resulting Numbers: [90, 10] Generated Node #0,3,1: 54:[90, 10] Operation: 18-8=10 Exploring Operation: 90-18=72, Resulting Numbers: [8, 72] Generated Node #0,3,2: 54:[8, 72] Operation: 90-18=72 Exploring Operation: 90-8=82, Resulting Numbers: [18, 82] Generated Node #0,3,3: 54:[18, 82] Operation: 90-8=82 Exploring Operation: 90/18=5, Resulting Numbers: [8, 5] Generated Node #0,3,4: 54:[8, 5] Operation: 90/18=5 Moving to Node #0,2,1 Current State: 54:[18, 2], Operations: ['96/6=16', '16/8=2'] Exploring Operation: 18/2=9, Resulting Numbers: [9] 9,54 unequal: No Solution Exploring Operation: 18*2=36, Resulting Numbers: [36] 36,54 unequal: No Solution Exploring Operation: 18-2=16, Resulting Numbers: [16] 16,54 unequal: No Solution Exploring Operation: 18+2=20, Resulting Numbers: [20] 20,54 unequal: No Solution Moving to Node #0,2,3 Current State: 54:[8, 2], Operations: ['96/6=16', '18-16=2'] Exploring Operation: 8+2=10, Resulting Numbers: [10] 10,54 unequal: No Solution Exploring Operation: 8*2=16, Resulting Numbers: [16] 16,54 unequal: No Solution Exploring Operation: 8/2=4, Resulting Numbers: [4] 4,54 unequal: No Solution Exploring Operation: 8-2=6, Resulting Numbers: [6] 6,54 unequal: No Solution Moving to Node #0,2,2 Current State: 54:[18, 8], Operations: ['96/6=16', '16-8=8'] Exploring Operation: 18-8=10, Resulting Numbers: [10] 10,54 unequal: No Solution Exploring Operation: 18*8=144, Resulting Numbers: [144] 144,54 unequal: No Solution Exploring Operation: 18+8=26, Resulting Numbers: [26] 26,54 unequal: No Solution Moving to Node #0,3,4 Current State: 54:[8, 5], Operations: ['96-6=90', '90/18=5'] Exploring Operation: 8-5=3, Resulting Numbers: [3] 3,54 unequal: No Solution Exploring Operation: 8+5=13, Resulting Numbers: [13] 13,54 unequal: No Solution Exploring Operation: 8*5=40, Resulting Numbers: [40] 40,54 unequal: No Solution Moving to Node #0,2,4 Current State: 54:[16, 10], Operations: ['96/6=16', '18-8=10'] Exploring Operation: 16-10=6, Resulting Numbers: [6] 6,54 unequal: No Solution Exploring Operation: 16*10=160, Resulting Numbers: [160] 160,54 unequal: No Solution Exploring Operation: 16+10=26, Resulting Numbers: [26] 26,54 unequal: No Solution Moving to Node #0,2,0 Current State: 54:[16, 26], Operations: ['96/6=16', '18+8=26'] Exploring Operation: 16+26=42, Resulting Numbers: [42] 42,54 unequal: No Solution Exploring Operation: 26-16=10, Resulting Numbers: [10] 10,54 unequal: No Solution Exploring Operation: 16*26=416, Resulting Numbers: [416] 416,54 unequal: No Solution Moving to Node #0,4,2 Current State: 54:[8, 13], Operations: ['96-18=78', '78/6=13'] Exploring Operation: 13-8=5, Resulting Numbers: [5] 5,54 unequal: No Solution Exploring Operation: 8+13=21, Resulting Numbers: [21] 21,54 unequal: No Solution Exploring Operation: 8*13=104, Resulting Numbers: [104] 104,54 unequal: No Solution Moving to Node #0,4,0 Current State: 54:[6, 70], Operations: ['96-18=78', '78-8=70'] Exploring Operation: 70-6=64, Resulting Numbers: [64] 64,54 unequal: No Solution Exploring Operation: 6+70=76, Resulting Numbers: [76] 76,54 unequal: No Solution Exploring Operation: 6*70=420, Resulting Numbers: [420] 420,54 unequal: No Solution Moving to Node #0,1,0 Current State: 54:[6, 70], Operations: ['96-8=88', '88-18=70'] Exploring Operation: 6+70=76, Resulting Numbers: [76] 76,54 unequal: No Solution Exploring Operation: 70-6=64, Resulting Numbers: [64] 64,54 unequal: No Solution Exploring Operation: 6*70=420, Resulting Numbers: [420] 420,54 unequal: No Solution Moving to Node #0,3,2 Current State: 54:[8, 72], Operations: ['96-6=90', '90-18=72'] Exploring Operation: 72-8=64, Resulting Numbers: [64] 64,54 unequal: No Solution Exploring Operation: 72/8=9, Resulting Numbers: [9] 9,54 unequal: No Solution Exploring Operation: 8*72=576, Resulting Numbers: [576] 576,54 unequal: No Solution Exploring Operation: 8+72=80, Resulting Numbers: [80] 80,54 unequal: No Solution Moving to Node #0,4,4 Current State: 54:[8, 72], Operations: ['96-18=78', '78-6=72'] Exploring Operation: 8*72=576, Resulting Numbers: [576] 576,54 unequal: No Solution Exploring Operation: 72-8=64, Resulting Numbers: [64] 64,54 unequal: No Solution Exploring Operation: 8+72=80, Resulting Numbers: [80] 80,54 unequal: No Solution Exploring Operation: 72/8=9, Resulting Numbers: [9] 9,54 unequal: No Solution Moving to Node #0,4,1 Current State: 54:[78, 2], Operations: ['96-18=78', '8-6=2'] Exploring Operation: 78+2=80, Resulting Numbers: [80] 80,54 unequal: No Solution Exploring Operation: 78*2=156, Resulting Numbers: [156] 156,54 unequal: No Solution Exploring Operation: 78-2=76, Resulting Numbers: [76] 76,54 unequal: No Solution Exploring Operation: 78/2=39, Resulting Numbers: [39] 39,54 unequal: No Solution Moving to Node #0,1,4 Current State: 54:[18, 82], Operations: ['96-8=88', '88-6=82'] Exploring Operation: 82-18=64, Resulting Numbers: [64] 64,54 unequal: No Solution Exploring Operation: 18*82=1476, Resulting Numbers: [1476] 1476,54 unequal: No Solution Exploring Operation: 18+82=100, Resulting Numbers: [100] 100,54 unequal: No Solution Moving to Node #0,3,3 Current State: 54:[18, 82], Operations: ['96-6=90', '90-8=82'] Exploring Operation: 18*82=1476, Resulting Numbers: [1476] 1476,54 unequal: No Solution Exploring Operation: 82-18=64, Resulting Numbers: [64] 64,54 unequal: No Solution Exploring Operation: 18+82=100, Resulting Numbers: [100] 100,54 unequal: No Solution Moving to Node #0,4,3 Current State: 54:[78, 14], Operations: ['96-18=78', '6+8=14'] Exploring Operation: 78+14=92, Resulting Numbers: [92] 92,54 unequal: No Solution Exploring Operation: 78*14=1092, Resulting Numbers: [1092] 1092,54 unequal: No Solution Exploring Operation: 78-14=64, Resulting Numbers: [64] 64,54 unequal: No Solution Moving to Node #0,1,2 Current State: 54:[88, 3], Operations: ['96-8=88', '18/6=3'] Exploring Operation: 88+3=91, Resulting Numbers: [91] 91,54 unequal: No Solution Exploring Operation: 88*3=264, Resulting Numbers: [264] 264,54 unequal: No Solution Exploring Operation: 88-3=85, Resulting Numbers: [85] 85,54 unequal: No Solution Moving to Node #0,3,0 Current State: 54:[90, 26], Operations: ['96-6=90', '18+8=26'] Exploring Operation: 90+26=116, Resulting Numbers: [116] 116,54 unequal: No Solution Exploring Operation: 90*26=2340, Resulting Numbers: [2340] 2340,54 unequal: No Solution Exploring Operation: 90-26=64, Resulting Numbers: [64] 64,54 unequal: No Solution Moving to Node #0,1,1 Current State: 54:[88, 12], Operations: ['96-8=88', '18-6=12'] Exploring Operation: 88-12=76, Resulting Numbers: [76] 76,54 unequal: No Solution Exploring Operation: 88*12=1056, Resulting Numbers: [1056] 1056,54 unequal: No Solution Exploring Operation: 88+12=100, Resulting Numbers: [100] 100,54 unequal: No Solution Moving to Node #0,1,3 Current State: 54:[88, 24], Operations: ['96-8=88', '6+18=24'] Exploring Operation: 88+24=112, Resulting Numbers: [112] 112,54 unequal: No Solution Exploring Operation: 88-24=64, Resulting Numbers: [64] 64,54 unequal: No Solution Exploring Operation: 88*24=2112, Resulting Numbers: [2112] 2112,54 unequal: No Solution Moving to Node #0,3,1 Current State: 54:[90, 10], Operations: ['96-6=90', '18-8=10'] Exploring Operation: 90-10=80, Resulting Numbers: [80] 80,54 unequal: No Solution Exploring Operation: 90+10=100, Resulting Numbers: [100] 100,54 unequal: No Solution Exploring Operation: 90*10=900, Resulting Numbers: [900] 900,54 unequal: No Solution Exploring Operation: 90/10=9, Resulting Numbers: [9] 9,54 unequal: No Solution No solution found.
0
hs_5
sum_heuristic
[ 65, 93, 59, 5 ]
92
[ "93-65=28", "59+5=64", "28+64=92" ]
Current State: 92:[65, 93, 59, 5], Operations: [] Exploring Operation: 93-65=28, Resulting Numbers: [59, 5, 28] Generated Node #2: [59, 5, 28] from Operation: 93-65=28 Current State: 92:[59, 5, 28], Operations: ['93-65=28'] Exploring Operation: 59+5=64, Resulting Numbers: [28, 64] Generated Node #3: [28, 64] from Operation: 59+5=64 Current State: 92:[28, 64], Operations: ['93-65=28', '59+5=64'] Exploring Operation: 28+64=92, Resulting Numbers: [92] 92,92 equal: Goal Reached
4
Current State: 92:[65, 93, 59, 5], Operations: [] Exploring Operation: 65-59=6, Resulting Numbers: [93, 5, 6] Generated Node #0,0: 92:[93, 5, 6] Operation: 65-59=6 Exploring Operation: 93-65=28, Resulting Numbers: [59, 5, 28] Generated Node #0,1: 92:[59, 5, 28] Operation: 93-65=28 Moving to Node #0,0 Current State: 92:[93, 5, 6], Operations: ['65-59=6'] Exploring Operation: 93-5=88, Resulting Numbers: [6, 88] Generated Node #0,0,0: 92:[6, 88] Operation: 93-5=88 Exploring Operation: 6-5=1, Resulting Numbers: [93, 1] Generated Node #0,0,1: 92:[93, 1] Operation: 6-5=1 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 92:[93, 1], Operations: ['65-59=6', '6-5=1'] Exploring Operation: 93-1=92, Resulting Numbers: [92] 92,92 equal: Goal Reached Moving to Node #0 Current State: 92:[65, 93, 59, 5], Operations: [] Exploring Operation: 65-59=6, Resulting Numbers: [93, 5, 6] Generated Node #0,0: 92:[93, 5, 6] Operation: 65-59=6 Moving to Node #0,0 Current State: 92:[93, 5, 6], Operations: ['65-59=6'] Exploring Operation: 6-5=1, Resulting Numbers: [93, 1] Generated Node #0,0,1: 92:[93, 1] Operation: 6-5=1 Moving to Node #0,0,1 Current State: 92:[93, 1], Operations: ['65-59=6', '6-5=1'] Exploring Operation: 93-1=92, Resulting Numbers: [92] 92,92 equal: Goal Reached Exit Sub Search at level 1
0.992188
hs_2
sum_heuristic
[ 30, 36, 14, 63 ]
55
[ "36-30=6", "63-14=49", "6+49=55" ]
Current State: 55:[30, 36, 14, 63], Operations: [] Exploring Operation: 36-30=6, Resulting Numbers: [14, 63, 6] Generated Node #2: [14, 63, 6] from Operation: 36-30=6 Current State: 55:[14, 63, 6], Operations: ['36-30=6'] Exploring Operation: 63-14=49, Resulting Numbers: [6, 49] Generated Node #3: [6, 49] from Operation: 63-14=49 Current State: 55:[6, 49], Operations: ['36-30=6', '63-14=49'] Exploring Operation: 6+49=55, Resulting Numbers: [55] 55,55 equal: Goal Reached
4
Current State: 55:[30, 36, 14, 63], Operations: [] Exploring Operation: 36-30=6, Resulting Numbers: [14, 63, 6] Generated Node #0,0: 55:[14, 63, 6] Operation: 36-30=6 Moving to Node #0,0 Current State: 55:[14, 63, 6], Operations: ['36-30=6'] Exploring Operation: 63-6=57, Resulting Numbers: [14, 57] Generated Node #0,0,0: 55:[14, 57] Operation: 63-6=57 Moving to Node #0,0,0 Current State: 55:[14, 57], Operations: ['36-30=6', '63-6=57'] Exploring Operation: 57-14=43, Resulting Numbers: [43] 43,55 unequal: No Solution No solution found.
0
hs_1
sum_heuristic
[ 6, 34, 8, 3 ]
62
[ "8-6=2", "34-3=31", "2*31=62" ]
Current State: 62:[6, 34, 8, 3], Operations: [] Exploring Operation: 8-6=2, Resulting Numbers: [34, 3, 2] Generated Node #2: [34, 3, 2] from Operation: 8-6=2 Current State: 62:[34, 3, 2], Operations: ['8-6=2'] Exploring Operation: 34-3=31, Resulting Numbers: [2, 31] Generated Node #3: [2, 31] from Operation: 34-3=31 Current State: 62:[2, 31], Operations: ['8-6=2', '34-3=31'] Exploring Operation: 2*31=62, Resulting Numbers: [62] 62,62 equal: Goal Reached
4
Current State: 62:[6, 34, 8, 3], Operations: [] Exploring Operation: 6-3=3, Resulting Numbers: [34, 8, 3] Generated Node #0,0: 62:[34, 8, 3] Operation: 6-3=3 Exploring Operation: 8-6=2, Resulting Numbers: [34, 3, 2] Generated Node #0,1: 62:[34, 3, 2] Operation: 8-6=2 Exploring Operation: 34-6=28, Resulting Numbers: [8, 3, 28] Generated Node #0,2: 62:[8, 3, 28] Operation: 34-6=28 Exploring Operation: 34-8=26, Resulting Numbers: [6, 3, 26] Generated Node #0,3: 62:[6, 3, 26] Operation: 34-8=26 Exploring Operation: 6/3=2, Resulting Numbers: [34, 8, 2] Generated Node #0,4: 62:[34, 8, 2] Operation: 6/3=2 Start Sub Search at level 1: Moving to Node #0,1 Current State: 62:[34, 3, 2], Operations: ['8-6=2'] Exploring Operation: 34-3=31, Resulting Numbers: [2, 31] Generated Node #0,1,0: 62:[2, 31] Operation: 34-3=31 Exploring Operation: 34+2=36, Resulting Numbers: [3, 36] Generated Node #0,1,1: 62:[3, 36] Operation: 34+2=36 Exploring Operation: 3-2=1, Resulting Numbers: [34, 1] Generated Node #0,1,2: 62:[34, 1] Operation: 3-2=1 Exploring Operation: 34-2=32, Resulting Numbers: [3, 32] Generated Node #0,1,3: 62:[3, 32] Operation: 34-2=32 Exploring Operation: 34+3=37, Resulting Numbers: [2, 37] Generated Node #0,1,4: 62:[2, 37] Operation: 34+3=37 Moving to Node #0,1,0 Current State: 62:[2, 31], Operations: ['8-6=2', '34-3=31'] Exploring Operation: 2+31=33, Resulting Numbers: [33] 33,62 unequal: No Solution Exploring Operation: 2*31=62, Resulting Numbers: [62] 62,62 equal: Goal Reached Moving to Node #0 Current State: 62:[6, 34, 8, 3], Operations: [] Exploring Operation: 8-6=2, Resulting Numbers: [34, 3, 2] Generated Node #0,1: 62:[34, 3, 2] Operation: 8-6=2 Moving to Node #0,1 Current State: 62:[34, 3, 2], Operations: ['8-6=2'] Exploring Operation: 34-3=31, Resulting Numbers: [2, 31] Generated Node #0,1,0: 62:[2, 31] Operation: 34-3=31 Moving to Node #0,1,0 Current State: 62:[2, 31], Operations: ['8-6=2', '34-3=31'] Exploring Operation: 2*31=62, Resulting Numbers: [62] 62,62 equal: Goal Reached Exit Sub Search at level 1
0.986111
hs_5
mult_heuristic
[ 29, 21, 91, 28 ]
69
[ "29+21=50", "91+28=119", "119-50=69" ]
Current State: 69:[29, 21, 91, 28], Operations: [] Exploring Operation: 29+21=50, Resulting Numbers: [91, 28, 50] Generated Node #2: [91, 28, 50] from Operation: 29+21=50 Current State: 69:[91, 28, 50], Operations: ['29+21=50'] Exploring Operation: 91+28=119, Resulting Numbers: [50, 119] Generated Node #3: [50, 119] from Operation: 91+28=119 Current State: 69:[50, 119], Operations: ['29+21=50', '91+28=119'] Exploring Operation: 119-50=69, Resulting Numbers: [69] 69,69 equal: Goal Reached
4
Current State: 69:[29, 21, 91, 28], Operations: [] Exploring Operation: 29-21=8, Resulting Numbers: [91, 28, 8] Generated Node #0,0: 69:[91, 28, 8] Operation: 29-21=8 Exploring Operation: 91-28=63, Resulting Numbers: [29, 21, 63] Generated Node #0,1: 69:[29, 21, 63] Operation: 91-28=63 Exploring Operation: 29-28=1, Resulting Numbers: [21, 91, 1] Generated Node #0,2: 69:[21, 91, 1] Operation: 29-28=1 Exploring Operation: 91-29=62, Resulting Numbers: [21, 28, 62] Generated Node #0,3: 69:[21, 28, 62] Operation: 91-29=62 Exploring Operation: 91-21=70, Resulting Numbers: [29, 28, 70] Generated Node #0,4: 69:[29, 28, 70] Operation: 91-21=70 Moving to Node #0,4 Current State: 69:[29, 28, 70], Operations: ['91-21=70'] Exploring Operation: 29-28=1, Resulting Numbers: [70, 1] Generated Node #0,4,0: 69:[70, 1] Operation: 29-28=1 Exploring Operation: 70-28=42, Resulting Numbers: [29, 42] Generated Node #0,4,1: 69:[29, 42] Operation: 70-28=42 Exploring Operation: 29+28=57, Resulting Numbers: [70, 57] Generated Node #0,4,2: 69:[70, 57] Operation: 29+28=57 Exploring Operation: 29+70=99, Resulting Numbers: [28, 99] Generated Node #0,4,3: 69:[28, 99] Operation: 29+70=99 Exploring Operation: 70-29=41, Resulting Numbers: [28, 41] Generated Node #0,4,4: 69:[28, 41] Operation: 70-29=41 Start Sub Search at level 1: Moving to Node #0,4,0 Current State: 69:[70, 1], Operations: ['91-21=70', '29-28=1'] Exploring Operation: 70+1=71, Resulting Numbers: [71] 71,69 unequal: No Solution Exploring Operation: 70/1=70, Resulting Numbers: [70] 70,69 unequal: No Solution Exploring Operation: 70-1=69, Resulting Numbers: [69] 69,69 equal: Goal Reached Moving to Node #0 Current State: 69:[29, 21, 91, 28], Operations: [] Exploring Operation: 91-21=70, Resulting Numbers: [29, 28, 70] Generated Node #0,4: 69:[29, 28, 70] Operation: 91-21=70 Moving to Node #0,4 Current State: 69:[29, 28, 70], Operations: ['91-21=70'] Exploring Operation: 29-28=1, Resulting Numbers: [70, 1] Generated Node #0,4,0: 69:[70, 1] Operation: 29-28=1 Moving to Node #0,4,0 Current State: 69:[70, 1], Operations: ['91-21=70', '29-28=1'] Exploring Operation: 70-1=69, Resulting Numbers: [69] 69,69 equal: Goal Reached Exit Sub Search at level 1
0.985243
hs_5
mult_heuristic
[ 47, 9, 4, 18 ]
79
[ "18-4=14", "9*14=126", "126-47=79" ]
Current State: 79:[47, 9, 4, 18], Operations: [] Exploring Operation: 18-4=14, Resulting Numbers: [47, 9, 14] Generated Node #2: [47, 9, 14] from Operation: 18-4=14 Current State: 79:[47, 9, 14], Operations: ['18-4=14'] Exploring Operation: 9*14=126, Resulting Numbers: [47, 126] Generated Node #3: [47, 126] from Operation: 9*14=126 Current State: 79:[47, 126], Operations: ['18-4=14', '9*14=126'] Exploring Operation: 126-47=79, Resulting Numbers: [79] 79,79 equal: Goal Reached
4
Current State: 79:[47, 9, 4, 18], Operations: [] Exploring Operation: 9*4=36, Resulting Numbers: [47, 18, 36] Generated Node #0,0: 79:[47, 18, 36] Operation: 9*4=36 Exploring Operation: 47+4=51, Resulting Numbers: [9, 18, 51] Generated Node #0,1: 79:[9, 18, 51] Operation: 47+4=51 Exploring Operation: 4*18=72, Resulting Numbers: [47, 9, 72] Generated Node #0,2: 79:[47, 9, 72] Operation: 4*18=72 Exploring Operation: 47+9=56, Resulting Numbers: [4, 18, 56] Generated Node #0,3: 79:[4, 18, 56] Operation: 47+9=56 Start Sub Search at level 1: Moving to Node #0,2 Current State: 79:[47, 9, 72], Operations: ['4*18=72'] Exploring Operation: 47+9=56, Resulting Numbers: [72, 56] Generated Node #0,2,0: 79:[72, 56] Operation: 47+9=56 Exploring Operation: 72-9=63, Resulting Numbers: [47, 63] Generated Node #0,2,1: 79:[47, 63] Operation: 72-9=63 Exploring Operation: 47-9=38, Resulting Numbers: [72, 38] Generated Node #0,2,2: 79:[72, 38] Operation: 47-9=38 Exploring Operation: 9+72=81, Resulting Numbers: [47, 81] Generated Node #0,2,3: 79:[47, 81] Operation: 9+72=81 Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 79:[72, 56], Operations: ['4*18=72', '47+9=56'] Exploring Operation: 72+56=128, Resulting Numbers: [128] 128,79 unequal: No Solution Exploring Operation: 72*56=4032, Resulting Numbers: [4032] 4032,79 unequal: No Solution Exploring Operation: 72-56=16, Resulting Numbers: [16] 16,79 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,3 Current State: 79:[47, 81], Operations: ['4*18=72', '9+72=81'] Exploring Operation: 47+81=128, Resulting Numbers: [128] 128,79 unequal: No Solution Exploring Operation: 81-47=34, Resulting Numbers: [34] 34,79 unequal: No Solution Exploring Operation: 47*81=3807, Resulting Numbers: [3807] 3807,79 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 79:[47, 63], Operations: ['4*18=72', '72-9=63'] Exploring Operation: 63-47=16, Resulting Numbers: [16] 16,79 unequal: No Solution Exploring Operation: 47*63=2961, Resulting Numbers: [2961] 2961,79 unequal: No Solution Exploring Operation: 47+63=110, Resulting Numbers: [110] 110,79 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 79:[72, 38], Operations: ['4*18=72', '47-9=38'] Exploring Operation: 72-38=34, Resulting Numbers: [34] 34,79 unequal: No Solution Exploring Operation: 72*38=2736, Resulting Numbers: [2736] 2736,79 unequal: No Solution Exploring Operation: 72+38=110, Resulting Numbers: [110] 110,79 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 79:[47, 18, 36], Operations: ['9*4=36'] Exploring Operation: 47-18=29, Resulting Numbers: [36, 29] Generated Node #0,0,0: 79:[36, 29] Operation: 47-18=29 Exploring Operation: 47+18=65, Resulting Numbers: [36, 65] Generated Node #0,0,1: 79:[36, 65] Operation: 47+18=65 Exploring Operation: 18+36=54, Resulting Numbers: [47, 54] Generated Node #0,0,2: 79:[47, 54] Operation: 18+36=54 Exploring Operation: 47+36=83, Resulting Numbers: [18, 83] Generated Node #0,0,3: 79:[18, 83] Operation: 47+36=83 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 79:[36, 65], Operations: ['9*4=36', '47+18=65'] Exploring Operation: 36*65=2340, Resulting Numbers: [2340] 2340,79 unequal: No Solution Exploring Operation: 65-36=29, Resulting Numbers: [29] 29,79 unequal: No Solution Exploring Operation: 36+65=101, Resulting Numbers: [101] 101,79 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 79:[47, 54], Operations: ['9*4=36', '18+36=54'] Exploring Operation: 47*54=2538, Resulting Numbers: [2538] 2538,79 unequal: No Solution Exploring Operation: 47+54=101, Resulting Numbers: [101] 101,79 unequal: No Solution Exploring Operation: 54-47=7, Resulting Numbers: [7] 7,79 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,3 Current State: 79:[18, 83], Operations: ['9*4=36', '47+36=83'] Exploring Operation: 18+83=101, Resulting Numbers: [101] 101,79 unequal: No Solution Exploring Operation: 18*83=1494, Resulting Numbers: [1494] 1494,79 unequal: No Solution Exploring Operation: 83-18=65, Resulting Numbers: [65] 65,79 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 79:[36, 29], Operations: ['9*4=36', '47-18=29'] Exploring Operation: 36-29=7, Resulting Numbers: [7] 7,79 unequal: No Solution Exploring Operation: 36*29=1044, Resulting Numbers: [1044] 1044,79 unequal: No Solution Exploring Operation: 36+29=65, Resulting Numbers: [65] 65,79 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 79:[9, 18, 51], Operations: ['47+4=51'] Exploring Operation: 18+51=69, Resulting Numbers: [9, 69] Generated Node #0,1,0: 79:[9, 69] Operation: 18+51=69 Exploring Operation: 18-9=9, Resulting Numbers: [51, 9] Generated Node #0,1,1: 79:[51, 9] Operation: 18-9=9 Exploring Operation: 9+18=27, Resulting Numbers: [51, 27] Generated Node #0,1,2: 79:[51, 27] Operation: 9+18=27 Exploring Operation: 9+51=60, Resulting Numbers: [18, 60] Generated Node #0,1,3: 79:[18, 60] Operation: 9+51=60 Moving to Node #0,1,0 Current State: 79:[9, 69], Operations: ['47+4=51', '18+51=69'] Exploring Operation: 69-9=60, Resulting Numbers: [60] 60,79 unequal: No Solution Exploring Operation: 9*69=621, Resulting Numbers: [621] 621,79 unequal: No Solution Exploring Operation: 9+69=78, Resulting Numbers: [78] 78,79 unequal: No Solution Moving to Node #0,1,3 Current State: 79:[18, 60], Operations: ['47+4=51', '9+51=60'] Exploring Operation: 60-18=42, Resulting Numbers: [42] 42,79 unequal: No Solution Exploring Operation: 18+60=78, Resulting Numbers: [78] 78,79 unequal: No Solution Exploring Operation: 18*60=1080, Resulting Numbers: [1080] 1080,79 unequal: No Solution Moving to Node #0,1,2 Current State: 79:[51, 27], Operations: ['47+4=51', '9+18=27'] Exploring Operation: 51*27=1377, Resulting Numbers: [1377] 1377,79 unequal: No Solution Exploring Operation: 51-27=24, Resulting Numbers: [24] 24,79 unequal: No Solution Exploring Operation: 51+27=78, Resulting Numbers: [78] 78,79 unequal: No Solution Moving to Node #0,1,1 Current State: 79:[51, 9], Operations: ['47+4=51', '18-9=9'] Exploring Operation: 51+9=60, Resulting Numbers: [60] 60,79 unequal: No Solution Exploring Operation: 51*9=459, Resulting Numbers: [459] 459,79 unequal: No Solution Exploring Operation: 51-9=42, Resulting Numbers: [42] 42,79 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 79:[4, 18, 56], Operations: ['47+9=56'] Exploring Operation: 4+18=22, Resulting Numbers: [56, 22] Generated Node #0,3,0: 79:[56, 22] Operation: 4+18=22 Exploring Operation: 4*18=72, Resulting Numbers: [56, 72] Generated Node #0,3,1: 79:[56, 72] Operation: 4*18=72 Exploring Operation: 18+56=74, Resulting Numbers: [4, 74] Generated Node #0,3,2: 79:[4, 74] Operation: 18+56=74 Exploring Operation: 4+56=60, Resulting Numbers: [18, 60] Generated Node #0,3,3: 79:[18, 60] Operation: 4+56=60 Start Sub Search at level 2: Moving to Node #0,3,1 Current State: 79:[56, 72], Operations: ['47+9=56', '4*18=72'] Exploring Operation: 72-56=16, Resulting Numbers: [16] 16,79 unequal: No Solution Exploring Operation: 56*72=4032, Resulting Numbers: [4032] 4032,79 unequal: No Solution Exploring Operation: 56+72=128, Resulting Numbers: [128] 128,79 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,0 Current State: 79:[56, 22], Operations: ['47+9=56', '4+18=22'] Exploring Operation: 56-22=34, Resulting Numbers: [34] 34,79 unequal: No Solution Exploring Operation: 56*22=1232, Resulting Numbers: [1232] 1232,79 unequal: No Solution Exploring Operation: 56+22=78, Resulting Numbers: [78] 78,79 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,2 Current State: 79:[4, 74], Operations: ['47+9=56', '18+56=74'] Exploring Operation: 4+74=78, Resulting Numbers: [78] 78,79 unequal: No Solution Exploring Operation: 74-4=70, Resulting Numbers: [70] 70,79 unequal: No Solution Exploring Operation: 4*74=296, Resulting Numbers: [296] 296,79 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,3 Current State: 79:[18, 60], Operations: ['47+9=56', '4+56=60'] Exploring Operation: 60-18=42, Resulting Numbers: [42] 42,79 unequal: No Solution Exploring Operation: 18+60=78, Resulting Numbers: [78] 78,79 unequal: No Solution Exploring Operation: 18*60=1080, Resulting Numbers: [1080] 1080,79 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_4
mult_heuristic
[ 33, 39, 25, 32 ]
66
[ "39+25=64", "33*64=2112", "2112/32=66" ]
Current State: 66:[33, 39, 25, 32], Operations: [] Exploring Operation: 39+25=64, Resulting Numbers: [33, 32, 64] Generated Node #2: [33, 32, 64] from Operation: 39+25=64 Current State: 66:[33, 32, 64], Operations: ['39+25=64'] Exploring Operation: 33*64=2112, Resulting Numbers: [32, 2112] Generated Node #3: [32, 2112] from Operation: 33*64=2112 Current State: 66:[32, 2112], Operations: ['39+25=64', '33*64=2112'] Exploring Operation: 2112/32=66, Resulting Numbers: [66] 66,66 equal: Goal Reached
4
Current State: 66:[33, 39, 25, 32], Operations: [] Exploring Operation: 39+25=64, Resulting Numbers: [33, 32, 64] Generated Node #0,0: 66:[33, 32, 64] Operation: 39+25=64 Start Sub Search at level 1: Moving to Node #0,0 Current State: 66:[33, 32, 64], Operations: ['39+25=64'] Exploring Operation: 64/32=2, Resulting Numbers: [33, 2] Generated Node #0,0,0: 66:[33, 2] Operation: 64/32=2 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 66:[33, 2], Operations: ['39+25=64', '64/32=2'] Exploring Operation: 33*2=66, Resulting Numbers: [66] 66,66 equal: Goal Reached Moving to Node #0 Current State: 66:[33, 39, 25, 32], Operations: [] Exploring Operation: 39+25=64, Resulting Numbers: [33, 32, 64] Generated Node #0,0: 66:[33, 32, 64] Operation: 39+25=64 Moving to Node #0,0 Current State: 66:[33, 32, 64], Operations: ['39+25=64'] Exploring Operation: 64/32=2, Resulting Numbers: [33, 2] Generated Node #0,0,0: 66:[33, 2] Operation: 64/32=2 Moving to Node #0,0,0 Current State: 66:[33, 2], Operations: ['39+25=64', '64/32=2'] Exploring Operation: 33*2=66, Resulting Numbers: [66] 66,66 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.993924
hs_1
mult_heuristic
[ 78, 84, 95, 86 ]
88
[ "86-78=8", "95-84=11", "8*11=88" ]
Current State: 88:[78, 84, 95, 86], Operations: [] Exploring Operation: 86-78=8, Resulting Numbers: [84, 95, 8] Generated Node #2: [84, 95, 8] from Operation: 86-78=8 Current State: 88:[84, 95, 8], Operations: ['86-78=8'] Exploring Operation: 95-84=11, Resulting Numbers: [8, 11] Generated Node #3: [8, 11] from Operation: 95-84=11 Current State: 88:[8, 11], Operations: ['86-78=8', '95-84=11'] Exploring Operation: 8*11=88, Resulting Numbers: [88] 88,88 equal: Goal Reached
4
Current State: 88:[78, 84, 95, 86], Operations: [] Exploring Operation: 95-78=17, Resulting Numbers: [84, 86, 17] Generated Node #0,0: 88:[84, 86, 17] Operation: 95-78=17 Exploring Operation: 84-78=6, Resulting Numbers: [95, 86, 6] Generated Node #0,1: 88:[95, 86, 6] Operation: 84-78=6 Moving to Node #0,0 Current State: 88:[84, 86, 17], Operations: ['95-78=17'] Exploring Operation: 84+17=101, Resulting Numbers: [86, 101] Generated Node #0,0,0: 88:[86, 101] Operation: 84+17=101 Exploring Operation: 86-84=2, Resulting Numbers: [17, 2] Generated Node #0,0,1: 88:[17, 2] Operation: 86-84=2 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 88:[17, 2], Operations: ['95-78=17', '86-84=2'] Exploring Operation: 17-2=15, Resulting Numbers: [15] 15,88 unequal: No Solution Exploring Operation: 17+2=19, Resulting Numbers: [19] 19,88 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 88:[86, 101], Operations: ['95-78=17', '84+17=101'] Exploring Operation: 101-86=15, Resulting Numbers: [15] 15,88 unequal: No Solution Exploring Operation: 86+101=187, Resulting Numbers: [187] 187,88 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1 Current State: 88:[95, 86, 6], Operations: ['84-78=6'] Exploring Operation: 95-86=9, Resulting Numbers: [6, 9] Generated Node #0,1,0: 88:[6, 9] Operation: 95-86=9 Exploring Operation: 95-6=89, Resulting Numbers: [86, 89] Generated Node #0,1,1: 88:[86, 89] Operation: 95-6=89 Moving to Node #0,1,0 Current State: 88:[6, 9], Operations: ['84-78=6', '95-86=9'] Exploring Operation: 9-6=3, Resulting Numbers: [3] 3,88 unequal: No Solution Exploring Operation: 6+9=15, Resulting Numbers: [15] 15,88 unequal: No Solution Moving to Node #0,1,1 Current State: 88:[86, 89], Operations: ['84-78=6', '95-6=89'] Exploring Operation: 89-86=3, Resulting Numbers: [3] 3,88 unequal: No Solution Exploring Operation: 86+89=175, Resulting Numbers: [175] 175,88 unequal: No Solution No solution found.
0
hs_2
mult_heuristic
[ 16, 88, 34, 36 ]
86
[ "34-16=18", "36/18=2", "88-2=86" ]
Current State: 86:[16, 88, 34, 36], Operations: [] Exploring Operation: 34-16=18, Resulting Numbers: [88, 36, 18] Generated Node #2: [88, 36, 18] from Operation: 34-16=18 Current State: 86:[88, 36, 18], Operations: ['34-16=18'] Exploring Operation: 36/18=2, Resulting Numbers: [88, 2] Generated Node #3: [88, 2] from Operation: 36/18=2 Current State: 86:[88, 2], Operations: ['34-16=18', '36/18=2'] Exploring Operation: 88-2=86, Resulting Numbers: [86] 86,86 equal: Goal Reached
4
Current State: 86:[16, 88, 34, 36], Operations: [] Exploring Operation: 16+34=50, Resulting Numbers: [88, 36, 50] Generated Node #0,0: 86:[88, 36, 50] Operation: 16+34=50 Exploring Operation: 16+36=52, Resulting Numbers: [88, 34, 52] Generated Node #0,1: 86:[88, 34, 52] Operation: 16+36=52 Exploring Operation: 34-16=18, Resulting Numbers: [88, 36, 18] Generated Node #0,2: 86:[88, 36, 18] Operation: 34-16=18 Exploring Operation: 36-16=20, Resulting Numbers: [88, 34, 20] Generated Node #0,3: 86:[88, 34, 20] Operation: 36-16=20 Exploring Operation: 36-34=2, Resulting Numbers: [16, 88, 2] Generated Node #0,4: 86:[16, 88, 2] Operation: 36-34=2 Moving to Node #0,0 Current State: 86:[88, 36, 50], Operations: ['16+34=50'] Exploring Operation: 88-50=38, Resulting Numbers: [36, 38] Generated Node #0,0,0: 86:[36, 38] Operation: 88-50=38 Exploring Operation: 36+50=86, Resulting Numbers: [88, 86] Generated Node #0,0,1: 86:[88, 86] Operation: 36+50=86 Exploring Operation: 50-36=14, Resulting Numbers: [88, 14] Generated Node #0,0,2: 86:[88, 14] Operation: 50-36=14 Exploring Operation: 88-36=52, Resulting Numbers: [50, 52] Generated Node #0,0,3: 86:[50, 52] Operation: 88-36=52 Exploring Operation: 88+36=124, Resulting Numbers: [50, 124] Generated Node #0,0,4: 86:[50, 124] Operation: 88+36=124 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 86:[88, 86], Operations: ['16+34=50', '36+50=86'] Exploring Operation: 88*86=7568, Resulting Numbers: [7568] 7568,86 unequal: No Solution Exploring Operation: 88-86=2, Resulting Numbers: [2] 2,86 unequal: No Solution Exploring Operation: 88+86=174, Resulting Numbers: [174] 174,86 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 86:[36, 38], Operations: ['16+34=50', '88-50=38'] Exploring Operation: 36*38=1368, Resulting Numbers: [1368] 1368,86 unequal: No Solution Exploring Operation: 38-36=2, Resulting Numbers: [2] 2,86 unequal: No Solution Exploring Operation: 36+38=74, Resulting Numbers: [74] 74,86 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 86:[88, 14], Operations: ['16+34=50', '50-36=14'] Exploring Operation: 88+14=102, Resulting Numbers: [102] 102,86 unequal: No Solution Exploring Operation: 88-14=74, Resulting Numbers: [74] 74,86 unequal: No Solution Exploring Operation: 88*14=1232, Resulting Numbers: [1232] 1232,86 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 86:[50, 52], Operations: ['16+34=50', '88-36=52'] Exploring Operation: 50*52=2600, Resulting Numbers: [2600] 2600,86 unequal: No Solution Exploring Operation: 50+52=102, Resulting Numbers: [102] 102,86 unequal: No Solution Exploring Operation: 52-50=2, Resulting Numbers: [2] 2,86 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,4 Current State: 86:[50, 124], Operations: ['16+34=50', '88+36=124'] Exploring Operation: 124-50=74, Resulting Numbers: [74] 74,86 unequal: No Solution Exploring Operation: 50*124=6200, Resulting Numbers: [6200] 6200,86 unequal: No Solution Exploring Operation: 50+124=174, Resulting Numbers: [174] 174,86 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,4 Current State: 86:[16, 88, 2], Operations: ['36-34=2'] Exploring Operation: 16*2=32, Resulting Numbers: [88, 32] Generated Node #0,4,0: 86:[88, 32] Operation: 16*2=32 Exploring Operation: 16/2=8, Resulting Numbers: [88, 8] Generated Node #0,4,1: 86:[88, 8] Operation: 16/2=8 Exploring Operation: 88-16=72, Resulting Numbers: [2, 72] Generated Node #0,4,2: 86:[2, 72] Operation: 88-16=72 Exploring Operation: 16-2=14, Resulting Numbers: [88, 14] Generated Node #0,4,3: 86:[88, 14] Operation: 16-2=14 Exploring Operation: 88-2=86, Resulting Numbers: [16, 86] Generated Node #0,4,4: 86:[16, 86] Operation: 88-2=86 Start Sub Search at level 1: Moving to Node #0,4,1 Current State: 86:[88, 8], Operations: ['36-34=2', '16/2=8'] Exploring Operation: 88*8=704, Resulting Numbers: [704] 704,86 unequal: No Solution Exploring Operation: 88+8=96, Resulting Numbers: [96] 96,86 unequal: No Solution Exploring Operation: 88/8=11, Resulting Numbers: [11] 11,86 unequal: No Solution Exploring Operation: 88-8=80, Resulting Numbers: [80] 80,86 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,0 Current State: 86:[88, 32], Operations: ['36-34=2', '16*2=32'] Exploring Operation: 88*32=2816, Resulting Numbers: [2816] 2816,86 unequal: No Solution Exploring Operation: 88-32=56, Resulting Numbers: [56] 56,86 unequal: No Solution Exploring Operation: 88+32=120, Resulting Numbers: [120] 120,86 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,2 Current State: 86:[2, 72], Operations: ['36-34=2', '88-16=72'] Exploring Operation: 72-2=70, Resulting Numbers: [70] 70,86 unequal: No Solution Exploring Operation: 72/2=36, Resulting Numbers: [36] 36,86 unequal: No Solution Exploring Operation: 2+72=74, Resulting Numbers: [74] 74,86 unequal: No Solution Exploring Operation: 2*72=144, Resulting Numbers: [144] 144,86 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,3 Current State: 86:[88, 14], Operations: ['36-34=2', '16-2=14'] Exploring Operation: 88-14=74, Resulting Numbers: [74] 74,86 unequal: No Solution Exploring Operation: 88+14=102, Resulting Numbers: [102] 102,86 unequal: No Solution Exploring Operation: 88*14=1232, Resulting Numbers: [1232] 1232,86 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,4 Current State: 86:[16, 86], Operations: ['36-34=2', '88-2=86'] Exploring Operation: 16+86=102, Resulting Numbers: [102] 102,86 unequal: No Solution Exploring Operation: 86-16=70, Resulting Numbers: [70] 70,86 unequal: No Solution Exploring Operation: 16*86=1376, Resulting Numbers: [1376] 1376,86 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1 Current State: 86:[88, 34, 52], Operations: ['16+36=52'] Exploring Operation: 88-52=36, Resulting Numbers: [34, 36] Generated Node #0,1,0: 86:[34, 36] Operation: 88-52=36 Exploring Operation: 52-34=18, Resulting Numbers: [88, 18] Generated Node #0,1,1: 86:[88, 18] Operation: 52-34=18 Exploring Operation: 88-34=54, Resulting Numbers: [52, 54] Generated Node #0,1,2: 86:[52, 54] Operation: 88-34=54 Exploring Operation: 88+34=122, Resulting Numbers: [52, 122] Generated Node #0,1,3: 86:[52, 122] Operation: 88+34=122 Exploring Operation: 34+52=86, Resulting Numbers: [88, 86] Generated Node #0,1,4: 86:[88, 86] Operation: 34+52=86 Start Sub Search at level 1: Moving to Node #0,1,4 Current State: 86:[88, 86], Operations: ['16+36=52', '34+52=86'] Exploring Operation: 88-86=2, Resulting Numbers: [2] 2,86 unequal: No Solution Exploring Operation: 88*86=7568, Resulting Numbers: [7568] 7568,86 unequal: No Solution Exploring Operation: 88+86=174, Resulting Numbers: [174] 174,86 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 86:[34, 36], Operations: ['16+36=52', '88-52=36'] Exploring Operation: 34+36=70, Resulting Numbers: [70] 70,86 unequal: No Solution Exploring Operation: 34*36=1224, Resulting Numbers: [1224] 1224,86 unequal: No Solution Exploring Operation: 36-34=2, Resulting Numbers: [2] 2,86 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 86:[88, 18], Operations: ['16+36=52', '52-34=18'] Exploring Operation: 88*18=1584, Resulting Numbers: [1584] 1584,86 unequal: No Solution Exploring Operation: 88+18=106, Resulting Numbers: [106] 106,86 unequal: No Solution Exploring Operation: 88-18=70, Resulting Numbers: [70] 70,86 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 86:[52, 54], Operations: ['16+36=52', '88-34=54'] Exploring Operation: 54-52=2, Resulting Numbers: [2] 2,86 unequal: No Solution Exploring Operation: 52*54=2808, Resulting Numbers: [2808] 2808,86 unequal: No Solution Exploring Operation: 52+54=106, Resulting Numbers: [106] 106,86 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 86:[52, 122], Operations: ['16+36=52', '88+34=122'] Exploring Operation: 52*122=6344, Resulting Numbers: [6344] 6344,86 unequal: No Solution Exploring Operation: 122-52=70, Resulting Numbers: [70] 70,86 unequal: No Solution Exploring Operation: 52+122=174, Resulting Numbers: [174] 174,86 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,2 Current State: 86:[88, 36, 18], Operations: ['34-16=18'] Exploring Operation: 36-18=18, Resulting Numbers: [88, 18] Generated Node #0,2,0: 86:[88, 18] Operation: 36-18=18 Exploring Operation: 88-18=70, Resulting Numbers: [36, 70] Generated Node #0,2,1: 86:[36, 70] Operation: 88-18=70 Exploring Operation: 36+18=54, Resulting Numbers: [88, 54] Generated Node #0,2,2: 86:[88, 54] Operation: 36+18=54 Exploring Operation: 88-36=52, Resulting Numbers: [18, 52] Generated Node #0,2,3: 86:[18, 52] Operation: 88-36=52 Exploring Operation: 36/18=2, Resulting Numbers: [88, 2] Generated Node #0,2,4: 86:[88, 2] Operation: 36/18=2 Moving to Node #0,3 Current State: 86:[88, 34, 20], Operations: ['36-16=20'] Exploring Operation: 88-20=68, Resulting Numbers: [34, 68] Generated Node #0,3,0: 86:[34, 68] Operation: 88-20=68 Exploring Operation: 88+20=108, Resulting Numbers: [34, 108] Generated Node #0,3,1: 86:[34, 108] Operation: 88+20=108 Exploring Operation: 34-20=14, Resulting Numbers: [88, 14] Generated Node #0,3,2: 86:[88, 14] Operation: 34-20=14 Exploring Operation: 88-34=54, Resulting Numbers: [20, 54] Generated Node #0,3,3: 86:[20, 54] Operation: 88-34=54 Exploring Operation: 34+20=54, Resulting Numbers: [88, 54] Generated Node #0,3,4: 86:[88, 54] Operation: 34+20=54 Moving to Node #0,2,4 Current State: 86:[88, 2], Operations: ['34-16=18', '36/18=2'] Exploring Operation: 88+2=90, Resulting Numbers: [90] 90,86 unequal: No Solution Exploring Operation: 88-2=86, Resulting Numbers: [86] 86,86 equal: Goal Reached Moving to Node #0 Current State: 86:[16, 88, 34, 36], Operations: [] Exploring Operation: 34-16=18, Resulting Numbers: [88, 36, 18] Generated Node #0,2: 86:[88, 36, 18] Operation: 34-16=18 Moving to Node #0,2 Current State: 86:[88, 36, 18], Operations: ['34-16=18'] Exploring Operation: 36/18=2, Resulting Numbers: [88, 2] Generated Node #0,2,4: 86:[88, 2] Operation: 36/18=2 Moving to Node #0,2,4 Current State: 86:[88, 2], Operations: ['34-16=18', '36/18=2'] Exploring Operation: 88-2=86, Resulting Numbers: [86] 86,86 equal: Goal Reached
0.927951
hs_5
mult_heuristic
[ 20, 3, 22, 55 ]
19
[ "22-20=2", "55+2=57", "57/3=19" ]
Current State: 19:[20, 3, 22, 55], Operations: [] Exploring Operation: 22-20=2, Resulting Numbers: [3, 55, 2] Generated Node #2: [3, 55, 2] from Operation: 22-20=2 Current State: 19:[3, 55, 2], Operations: ['22-20=2'] Exploring Operation: 55+2=57, Resulting Numbers: [3, 57] Generated Node #3: [3, 57] from Operation: 55+2=57 Current State: 19:[3, 57], Operations: ['22-20=2', '55+2=57'] Exploring Operation: 57/3=19, Resulting Numbers: [19] 19,19 equal: Goal Reached
4
Current State: 19:[20, 3, 22, 55], Operations: [] Exploring Operation: 55-3=52, Resulting Numbers: [20, 22, 52] Generated Node #0,0: 19:[20, 22, 52] Operation: 55-3=52 Exploring Operation: 22-3=19, Resulting Numbers: [20, 55, 19] Generated Node #0,1: 19:[20, 55, 19] Operation: 22-3=19 Exploring Operation: 55-20=35, Resulting Numbers: [3, 22, 35] Generated Node #0,2: 19:[3, 22, 35] Operation: 55-20=35 Exploring Operation: 55-22=33, Resulting Numbers: [20, 3, 33] Generated Node #0,3: 19:[20, 3, 33] Operation: 55-22=33 Moving to Node #0,3 Current State: 19:[20, 3, 33], Operations: ['55-22=33'] Exploring Operation: 20-3=17, Resulting Numbers: [33, 17] Generated Node #0,3,0: 19:[33, 17] Operation: 20-3=17 Exploring Operation: 33-3=30, Resulting Numbers: [20, 30] Generated Node #0,3,1: 19:[20, 30] Operation: 33-3=30 Exploring Operation: 33/3=11, Resulting Numbers: [20, 11] Generated Node #0,3,2: 19:[20, 11] Operation: 33/3=11 Exploring Operation: 20+3=23, Resulting Numbers: [33, 23] Generated Node #0,3,3: 19:[33, 23] Operation: 20+3=23 Moving to Node #0,2 Current State: 19:[3, 22, 35], Operations: ['55-20=35'] Exploring Operation: 3+22=25, Resulting Numbers: [35, 25] Generated Node #0,2,0: 19:[35, 25] Operation: 3+22=25 Exploring Operation: 35-3=32, Resulting Numbers: [22, 32] Generated Node #0,2,1: 19:[22, 32] Operation: 35-3=32 Exploring Operation: 3+35=38, Resulting Numbers: [22, 38] Generated Node #0,2,2: 19:[22, 38] Operation: 3+35=38 Exploring Operation: 22-3=19, Resulting Numbers: [35, 19] Generated Node #0,2,3: 19:[35, 19] Operation: 22-3=19 Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 19:[22, 32], Operations: ['55-20=35', '35-3=32'] Exploring Operation: 22+32=54, Resulting Numbers: [54] 54,19 unequal: No Solution Exploring Operation: 22*32=704, Resulting Numbers: [704] 704,19 unequal: No Solution Exploring Operation: 32-22=10, Resulting Numbers: [10] 10,19 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 19:[35, 19], Operations: ['55-20=35', '22-3=19'] Exploring Operation: 35*19=665, Resulting Numbers: [665] 665,19 unequal: No Solution Exploring Operation: 35+19=54, Resulting Numbers: [54] 54,19 unequal: No Solution Exploring Operation: 35-19=16, Resulting Numbers: [16] 16,19 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 19:[35, 25], Operations: ['55-20=35', '3+22=25'] Exploring Operation: 35+25=60, Resulting Numbers: [60] 60,19 unequal: No Solution Exploring Operation: 35*25=875, Resulting Numbers: [875] 875,19 unequal: No Solution Exploring Operation: 35-25=10, Resulting Numbers: [10] 10,19 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 19:[22, 38], Operations: ['55-20=35', '3+35=38'] Exploring Operation: 22+38=60, Resulting Numbers: [60] 60,19 unequal: No Solution Exploring Operation: 22*38=836, Resulting Numbers: [836] 836,19 unequal: No Solution Exploring Operation: 38-22=16, Resulting Numbers: [16] 16,19 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1 Current State: 19:[20, 55, 19], Operations: ['22-3=19'] Exploring Operation: 55-19=36, Resulting Numbers: [20, 36] Generated Node #0,1,0: 19:[20, 36] Operation: 55-19=36 Exploring Operation: 20+55=75, Resulting Numbers: [19, 75] Generated Node #0,1,1: 19:[19, 75] Operation: 20+55=75 Exploring Operation: 20-19=1, Resulting Numbers: [55, 1] Generated Node #0,1,2: 19:[55, 1] Operation: 20-19=1 Exploring Operation: 55-20=35, Resulting Numbers: [19, 35] Generated Node #0,1,3: 19:[19, 35] Operation: 55-20=35 Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 19:[19, 35], Operations: ['22-3=19', '55-20=35'] Exploring Operation: 19*35=665, Resulting Numbers: [665] 665,19 unequal: No Solution Exploring Operation: 19+35=54, Resulting Numbers: [54] 54,19 unequal: No Solution Exploring Operation: 35-19=16, Resulting Numbers: [16] 16,19 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 19:[20, 36], Operations: ['22-3=19', '55-19=36'] Exploring Operation: 20+36=56, Resulting Numbers: [56] 56,19 unequal: No Solution Exploring Operation: 20*36=720, Resulting Numbers: [720] 720,19 unequal: No Solution Exploring Operation: 36-20=16, Resulting Numbers: [16] 16,19 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 19:[55, 1], Operations: ['22-3=19', '20-19=1'] Exploring Operation: 55+1=56, Resulting Numbers: [56] 56,19 unequal: No Solution Exploring Operation: 55-1=54, Resulting Numbers: [54] 54,19 unequal: No Solution Exploring Operation: 55/1=55, Resulting Numbers: [55] 55,19 unequal: No Solution Exploring Operation: 55*1=55, Resulting Numbers: [55] 55,19 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 19:[19, 75], Operations: ['22-3=19', '20+55=75'] Exploring Operation: 75-19=56, Resulting Numbers: [56] 56,19 unequal: No Solution Exploring Operation: 19*75=1425, Resulting Numbers: [1425] 1425,19 unequal: No Solution Exploring Operation: 19+75=94, Resulting Numbers: [94] 94,19 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,0 Current State: 19:[20, 22, 52], Operations: ['55-3=52'] Exploring Operation: 52-22=30, Resulting Numbers: [20, 30] Generated Node #0,0,0: 19:[20, 30] Operation: 52-22=30 Exploring Operation: 52-20=32, Resulting Numbers: [22, 32] Generated Node #0,0,1: 19:[22, 32] Operation: 52-20=32 Exploring Operation: 22-20=2, Resulting Numbers: [52, 2] Generated Node #0,0,2: 19:[52, 2] Operation: 22-20=2 Exploring Operation: 20+22=42, Resulting Numbers: [52, 42] Generated Node #0,0,3: 19:[52, 42] Operation: 20+22=42 Moving to Node #0,3,2 Current State: 19:[20, 11], Operations: ['55-22=33', '33/3=11'] Exploring Operation: 20+11=31, Resulting Numbers: [31] 31,19 unequal: No Solution Exploring Operation: 20*11=220, Resulting Numbers: [220] 220,19 unequal: No Solution Exploring Operation: 20-11=9, Resulting Numbers: [9] 9,19 unequal: No Solution Moving to Node #0,3,1 Current State: 19:[20, 30], Operations: ['55-22=33', '33-3=30'] Exploring Operation: 30-20=10, Resulting Numbers: [10] 10,19 unequal: No Solution Exploring Operation: 20+30=50, Resulting Numbers: [50] 50,19 unequal: No Solution Exploring Operation: 20*30=600, Resulting Numbers: [600] 600,19 unequal: No Solution Moving to Node #0,0,0 Current State: 19:[20, 30], Operations: ['55-3=52', '52-22=30'] Exploring Operation: 20+30=50, Resulting Numbers: [50] 50,19 unequal: No Solution Exploring Operation: 30-20=10, Resulting Numbers: [10] 10,19 unequal: No Solution Exploring Operation: 20*30=600, Resulting Numbers: [600] 600,19 unequal: No Solution Moving to Node #0,3,0 Current State: 19:[33, 17], Operations: ['55-22=33', '20-3=17'] Exploring Operation: 33-17=16, Resulting Numbers: [16] 16,19 unequal: No Solution Exploring Operation: 33+17=50, Resulting Numbers: [50] 50,19 unequal: No Solution Exploring Operation: 33*17=561, Resulting Numbers: [561] 561,19 unequal: No Solution Moving to Node #0,0,1 Current State: 19:[22, 32], Operations: ['55-3=52', '52-20=32'] Exploring Operation: 22+32=54, Resulting Numbers: [54] 54,19 unequal: No Solution Exploring Operation: 32-22=10, Resulting Numbers: [10] 10,19 unequal: No Solution Exploring Operation: 22*32=704, Resulting Numbers: [704] 704,19 unequal: No Solution Moving to Node #0,3,3 Current State: 19:[33, 23], Operations: ['55-22=33', '20+3=23'] Exploring Operation: 33*23=759, Resulting Numbers: [759] 759,19 unequal: No Solution Exploring Operation: 33-23=10, Resulting Numbers: [10] 10,19 unequal: No Solution Exploring Operation: 33+23=56, Resulting Numbers: [56] 56,19 unequal: No Solution Moving to Node #0,0,2 Current State: 19:[52, 2], Operations: ['55-3=52', '22-20=2'] Exploring Operation: 52/2=26, Resulting Numbers: [26] 26,19 unequal: No Solution Exploring Operation: 52*2=104, Resulting Numbers: [104] 104,19 unequal: No Solution Exploring Operation: 52+2=54, Resulting Numbers: [54] 54,19 unequal: No Solution Exploring Operation: 52-2=50, Resulting Numbers: [50] 50,19 unequal: No Solution Moving to Node #0,0,3 Current State: 19:[52, 42], Operations: ['55-3=52', '20+22=42'] Exploring Operation: 52+42=94, Resulting Numbers: [94] 94,19 unequal: No Solution Exploring Operation: 52*42=2184, Resulting Numbers: [2184] 2184,19 unequal: No Solution Exploring Operation: 52-42=10, Resulting Numbers: [10] 10,19 unequal: No Solution No solution found.
0
hs_4
mult_heuristic
[ 99, 47, 17, 24 ]
93
[ "99-47=52", "17+24=41", "52+41=93" ]
Current State: 93:[99, 47, 17, 24], Operations: [] Exploring Operation: 99-47=52, Resulting Numbers: [17, 24, 52] Generated Node #2: [17, 24, 52] from Operation: 99-47=52 Current State: 93:[17, 24, 52], Operations: ['99-47=52'] Exploring Operation: 17+24=41, Resulting Numbers: [52, 41] Generated Node #3: [52, 41] from Operation: 17+24=41 Current State: 93:[52, 41], Operations: ['99-47=52', '17+24=41'] Exploring Operation: 52+41=93, Resulting Numbers: [93] 93,93 equal: Goal Reached
4
Current State: 93:[99, 47, 17, 24], Operations: [] Exploring Operation: 24-17=7, Resulting Numbers: [99, 47, 7] Generated Node #0,0: 93:[99, 47, 7] Operation: 24-17=7 Exploring Operation: 47-17=30, Resulting Numbers: [99, 24, 30] Generated Node #0,1: 93:[99, 24, 30] Operation: 47-17=30 Moving to Node #0,1 Current State: 93:[99, 24, 30], Operations: ['47-17=30'] Exploring Operation: 30-24=6, Resulting Numbers: [99, 6] Generated Node #0,1,0: 93:[99, 6] Operation: 30-24=6 Exploring Operation: 99-24=75, Resulting Numbers: [30, 75] Generated Node #0,1,1: 93:[30, 75] Operation: 99-24=75 Moving to Node #0,0 Current State: 93:[99, 47, 7], Operations: ['24-17=7'] Exploring Operation: 99-7=92, Resulting Numbers: [47, 92] Generated Node #0,0,0: 93:[47, 92] Operation: 99-7=92 Exploring Operation: 47-7=40, Resulting Numbers: [99, 40] Generated Node #0,0,1: 93:[99, 40] Operation: 47-7=40 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 93:[99, 40], Operations: ['24-17=7', '47-7=40'] Exploring Operation: 99-40=59, Resulting Numbers: [59] 59,93 unequal: No Solution Exploring Operation: 99+40=139, Resulting Numbers: [139] 139,93 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 93:[47, 92], Operations: ['24-17=7', '99-7=92'] Exploring Operation: 47+92=139, Resulting Numbers: [139] 139,93 unequal: No Solution Exploring Operation: 92-47=45, Resulting Numbers: [45] 45,93 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1,0 Current State: 93:[99, 6], Operations: ['47-17=30', '30-24=6'] Exploring Operation: 99-6=93, Resulting Numbers: [93] 93,93 equal: Goal Reached Moving to Node #0 Current State: 93:[99, 47, 17, 24], Operations: [] Exploring Operation: 47-17=30, Resulting Numbers: [99, 24, 30] Generated Node #0,1: 93:[99, 24, 30] Operation: 47-17=30 Moving to Node #0,1 Current State: 93:[99, 24, 30], Operations: ['47-17=30'] Exploring Operation: 30-24=6, Resulting Numbers: [99, 6] Generated Node #0,1,0: 93:[99, 6] Operation: 30-24=6 Moving to Node #0,1,0 Current State: 93:[99, 6], Operations: ['47-17=30', '30-24=6'] Exploring Operation: 99-6=93, Resulting Numbers: [93] 93,93 equal: Goal Reached
0.986979
hs_2
sum_heuristic
[ 93, 84, 5, 13 ]
74
[ "93-84=9", "5*13=65", "9+65=74" ]
Current State: 74:[93, 84, 5, 13], Operations: [] Exploring Operation: 93-84=9, Resulting Numbers: [5, 13, 9] Generated Node #2: [5, 13, 9] from Operation: 93-84=9 Current State: 74:[5, 13, 9], Operations: ['93-84=9'] Exploring Operation: 5*13=65, Resulting Numbers: [9, 65] Generated Node #3: [9, 65] from Operation: 5*13=65 Current State: 74:[9, 65], Operations: ['93-84=9', '5*13=65'] Exploring Operation: 9+65=74, Resulting Numbers: [74] 74,74 equal: Goal Reached
4
Current State: 74:[93, 84, 5, 13], Operations: [] Exploring Operation: 93-13=80, Resulting Numbers: [84, 5, 80] Generated Node #0,0: 74:[84, 5, 80] Operation: 93-13=80 Exploring Operation: 93-84=9, Resulting Numbers: [5, 13, 9] Generated Node #0,1: 74:[5, 13, 9] Operation: 93-84=9 Exploring Operation: 84-13=71, Resulting Numbers: [93, 5, 71] Generated Node #0,2: 74:[93, 5, 71] Operation: 84-13=71 Start Sub Search at level 1: Moving to Node #0,0 Current State: 74:[84, 5, 80], Operations: ['93-13=80'] Exploring Operation: 84-80=4, Resulting Numbers: [5, 4] Generated Node #0,0,0: 74:[5, 4] Operation: 84-80=4 Exploring Operation: 84-5=79, Resulting Numbers: [80, 79] Generated Node #0,0,1: 74:[80, 79] Operation: 84-5=79 Exploring Operation: 80-5=75, Resulting Numbers: [84, 75] Generated Node #0,0,2: 74:[84, 75] Operation: 80-5=75 Moving to Node #0,0,0 Current State: 74:[5, 4], Operations: ['93-13=80', '84-80=4'] Exploring Operation: 5+4=9, Resulting Numbers: [9] 9,74 unequal: No Solution Exploring Operation: 5-4=1, Resulting Numbers: [1] 1,74 unequal: No Solution Exploring Operation: 5*4=20, Resulting Numbers: [20] 20,74 unequal: No Solution Moving to Node #0,0,1 Current State: 74:[80, 79], Operations: ['93-13=80', '84-5=79'] Exploring Operation: 80+79=159, Resulting Numbers: [159] 159,74 unequal: No Solution Exploring Operation: 80-79=1, Resulting Numbers: [1] 1,74 unequal: No Solution Exploring Operation: 80*79=6320, Resulting Numbers: [6320] 6320,74 unequal: No Solution Moving to Node #0,0,2 Current State: 74:[84, 75], Operations: ['93-13=80', '80-5=75'] Exploring Operation: 84*75=6300, Resulting Numbers: [6300] 6300,74 unequal: No Solution Exploring Operation: 84-75=9, Resulting Numbers: [9] 9,74 unequal: No Solution Exploring Operation: 84+75=159, Resulting Numbers: [159] 159,74 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 74:[5, 13, 9], Operations: ['93-84=9'] Exploring Operation: 9-5=4, Resulting Numbers: [13, 4] Generated Node #0,1,0: 74:[13, 4] Operation: 9-5=4 Exploring Operation: 13-9=4, Resulting Numbers: [5, 4] Generated Node #0,1,1: 74:[5, 4] Operation: 13-9=4 Exploring Operation: 13-5=8, Resulting Numbers: [9, 8] Generated Node #0,1,2: 74:[9, 8] Operation: 13-5=8 Moving to Node #0,1,1 Current State: 74:[5, 4], Operations: ['93-84=9', '13-9=4'] Exploring Operation: 5*4=20, Resulting Numbers: [20] 20,74 unequal: No Solution Exploring Operation: 5+4=9, Resulting Numbers: [9] 9,74 unequal: No Solution Exploring Operation: 5-4=1, Resulting Numbers: [1] 1,74 unequal: No Solution Moving to Node #0,1,0 Current State: 74:[13, 4], Operations: ['93-84=9', '9-5=4'] Exploring Operation: 13-4=9, Resulting Numbers: [9] 9,74 unequal: No Solution Exploring Operation: 13*4=52, Resulting Numbers: [52] 52,74 unequal: No Solution Exploring Operation: 13+4=17, Resulting Numbers: [17] 17,74 unequal: No Solution Moving to Node #0,1,2 Current State: 74:[9, 8], Operations: ['93-84=9', '13-5=8'] Exploring Operation: 9*8=72, Resulting Numbers: [72] 72,74 unequal: No Solution Exploring Operation: 9+8=17, Resulting Numbers: [17] 17,74 unequal: No Solution Exploring Operation: 9-8=1, Resulting Numbers: [1] 1,74 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 74:[93, 5, 71], Operations: ['84-13=71'] Exploring Operation: 93-71=22, Resulting Numbers: [5, 22] Generated Node #0,2,0: 74:[5, 22] Operation: 93-71=22 Exploring Operation: 93-5=88, Resulting Numbers: [71, 88] Generated Node #0,2,1: 74:[71, 88] Operation: 93-5=88 Exploring Operation: 5+71=76, Resulting Numbers: [93, 76] Generated Node #0,2,2: 74:[93, 76] Operation: 5+71=76 Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 74:[71, 88], Operations: ['84-13=71', '93-5=88'] Exploring Operation: 71+88=159, Resulting Numbers: [159] 159,74 unequal: No Solution Exploring Operation: 71*88=6248, Resulting Numbers: [6248] 6248,74 unequal: No Solution Exploring Operation: 88-71=17, Resulting Numbers: [17] 17,74 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 74:[5, 22], Operations: ['84-13=71', '93-71=22'] Exploring Operation: 5+22=27, Resulting Numbers: [27] 27,74 unequal: No Solution Exploring Operation: 22-5=17, Resulting Numbers: [17] 17,74 unequal: No Solution Exploring Operation: 5*22=110, Resulting Numbers: [110] 110,74 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 74:[93, 76], Operations: ['84-13=71', '5+71=76'] Exploring Operation: 93-76=17, Resulting Numbers: [17] 17,74 unequal: No Solution Exploring Operation: 93+76=169, Resulting Numbers: [169] 169,74 unequal: No Solution Exploring Operation: 93*76=7068, Resulting Numbers: [7068] 7068,74 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_3
sum_heuristic
[ 12, 66, 61, 28 ]
14
[ "61-28=33", "66/33=2", "12+2=14" ]
Current State: 14:[12, 66, 61, 28], Operations: [] Exploring Operation: 61-28=33, Resulting Numbers: [12, 66, 33] Generated Node #2: [12, 66, 33] from Operation: 61-28=33 Current State: 14:[12, 66, 33], Operations: ['61-28=33'] Exploring Operation: 66/33=2, Resulting Numbers: [12, 2] Generated Node #3: [12, 2] from Operation: 66/33=2 Current State: 14:[12, 2], Operations: ['61-28=33', '66/33=2'] Exploring Operation: 12+2=14, Resulting Numbers: [14] 14,14 equal: Goal Reached
4
Current State: 14:[12, 66, 61, 28], Operations: [] Exploring Operation: 66-12=54, Resulting Numbers: [61, 28, 54] Generated Node #0,0: 14:[61, 28, 54] Operation: 66-12=54 Exploring Operation: 66-61=5, Resulting Numbers: [12, 28, 5] Generated Node #0,1: 14:[12, 28, 5] Operation: 66-61=5 Exploring Operation: 66-28=38, Resulting Numbers: [12, 61, 38] Generated Node #0,2: 14:[12, 61, 38] Operation: 66-28=38 Exploring Operation: 61-28=33, Resulting Numbers: [12, 66, 33] Generated Node #0,3: 14:[12, 66, 33] Operation: 61-28=33 Start Sub Search at level 1: Moving to Node #0,1 Current State: 14:[12, 28, 5], Operations: ['66-61=5'] Exploring Operation: 12-5=7, Resulting Numbers: [28, 7] Generated Node #0,1,0: 14:[28, 7] Operation: 12-5=7 Exploring Operation: 28-12=16, Resulting Numbers: [5, 16] Generated Node #0,1,1: 14:[5, 16] Operation: 28-12=16 Exploring Operation: 28-5=23, Resulting Numbers: [12, 23] Generated Node #0,1,2: 14:[12, 23] Operation: 28-5=23 Exploring Operation: 12+5=17, Resulting Numbers: [28, 17] Generated Node #0,1,3: 14:[28, 17] Operation: 12+5=17 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 14:[5, 16], Operations: ['66-61=5', '28-12=16'] Exploring Operation: 16-5=11, Resulting Numbers: [11] 11,14 unequal: No Solution Exploring Operation: 5+16=21, Resulting Numbers: [21] 21,14 unequal: No Solution Exploring Operation: 5*16=80, Resulting Numbers: [80] 80,14 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 14:[12, 23], Operations: ['66-61=5', '28-5=23'] Exploring Operation: 12+23=35, Resulting Numbers: [35] 35,14 unequal: No Solution Exploring Operation: 23-12=11, Resulting Numbers: [11] 11,14 unequal: No Solution Exploring Operation: 12*23=276, Resulting Numbers: [276] 276,14 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 14:[28, 7], Operations: ['66-61=5', '12-5=7'] Exploring Operation: 28*7=196, Resulting Numbers: [196] 196,14 unequal: No Solution Exploring Operation: 28+7=35, Resulting Numbers: [35] 35,14 unequal: No Solution Exploring Operation: 28/7=4, Resulting Numbers: [4] 4,14 unequal: No Solution Exploring Operation: 28-7=21, Resulting Numbers: [21] 21,14 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,3 Current State: 14:[28, 17], Operations: ['66-61=5', '12+5=17'] Exploring Operation: 28+17=45, Resulting Numbers: [45] 45,14 unequal: No Solution Exploring Operation: 28-17=11, Resulting Numbers: [11] 11,14 unequal: No Solution Exploring Operation: 28*17=476, Resulting Numbers: [476] 476,14 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 14:[12, 61, 38], Operations: ['66-28=38'] Exploring Operation: 12+61=73, Resulting Numbers: [38, 73] Generated Node #0,2,0: 14:[38, 73] Operation: 12+61=73 Exploring Operation: 61-12=49, Resulting Numbers: [38, 49] Generated Node #0,2,1: 14:[38, 49] Operation: 61-12=49 Exploring Operation: 61-38=23, Resulting Numbers: [12, 23] Generated Node #0,2,2: 14:[12, 23] Operation: 61-38=23 Exploring Operation: 38-12=26, Resulting Numbers: [61, 26] Generated Node #0,2,3: 14:[61, 26] Operation: 38-12=26 Moving to Node #0,2,2 Current State: 14:[12, 23], Operations: ['66-28=38', '61-38=23'] Exploring Operation: 23-12=11, Resulting Numbers: [11] 11,14 unequal: No Solution Exploring Operation: 12*23=276, Resulting Numbers: [276] 276,14 unequal: No Solution Exploring Operation: 12+23=35, Resulting Numbers: [35] 35,14 unequal: No Solution Moving to Node #0,2,3 Current State: 14:[61, 26], Operations: ['66-28=38', '38-12=26'] Exploring Operation: 61*26=1586, Resulting Numbers: [1586] 1586,14 unequal: No Solution Exploring Operation: 61-26=35, Resulting Numbers: [35] 35,14 unequal: No Solution Exploring Operation: 61+26=87, Resulting Numbers: [87] 87,14 unequal: No Solution Moving to Node #0,2,1 Current State: 14:[38, 49], Operations: ['66-28=38', '61-12=49'] Exploring Operation: 38*49=1862, Resulting Numbers: [1862] 1862,14 unequal: No Solution Exploring Operation: 49-38=11, Resulting Numbers: [11] 11,14 unequal: No Solution Exploring Operation: 38+49=87, Resulting Numbers: [87] 87,14 unequal: No Solution Moving to Node #0,2,0 Current State: 14:[38, 73], Operations: ['66-28=38', '12+61=73'] Exploring Operation: 38*73=2774, Resulting Numbers: [2774] 2774,14 unequal: No Solution Exploring Operation: 73-38=35, Resulting Numbers: [35] 35,14 unequal: No Solution Exploring Operation: 38+73=111, Resulting Numbers: [111] 111,14 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 14:[12, 66, 33], Operations: ['61-28=33'] Exploring Operation: 66/33=2, Resulting Numbers: [12, 2] Generated Node #0,3,0: 14:[12, 2] Operation: 66/33=2 Exploring Operation: 66-12=54, Resulting Numbers: [33, 54] Generated Node #0,3,1: 14:[33, 54] Operation: 66-12=54 Exploring Operation: 33-12=21, Resulting Numbers: [66, 21] Generated Node #0,3,2: 14:[66, 21] Operation: 33-12=21 Exploring Operation: 66-33=33, Resulting Numbers: [12, 33] Generated Node #0,3,3: 14:[12, 33] Operation: 66-33=33 Moving to Node #0,3,0 Current State: 14:[12, 2], Operations: ['61-28=33', '66/33=2'] Exploring Operation: 12-2=10, Resulting Numbers: [10] 10,14 unequal: No Solution Exploring Operation: 12*2=24, Resulting Numbers: [24] 24,14 unequal: No Solution Exploring Operation: 12/2=6, Resulting Numbers: [6] 6,14 unequal: No Solution Exploring Operation: 12+2=14, Resulting Numbers: [14] 14,14 equal: Goal Reached Moving to Node #0 Current State: 14:[12, 66, 61, 28], Operations: [] Exploring Operation: 61-28=33, Resulting Numbers: [12, 66, 33] Generated Node #0,3: 14:[12, 66, 33] Operation: 61-28=33 Moving to Node #0,3 Current State: 14:[12, 66, 33], Operations: ['61-28=33'] Exploring Operation: 66/33=2, Resulting Numbers: [12, 2] Generated Node #0,3,0: 14:[12, 2] Operation: 66/33=2 Moving to Node #0,3,0 Current State: 14:[12, 2], Operations: ['61-28=33', '66/33=2'] Exploring Operation: 12+2=14, Resulting Numbers: [14] 14,14 equal: Goal Reached Exit Sub Search at level 1
0.957465
hs_4
mult_heuristic
[ 72, 89, 14, 5 ]
71
[ "89-72=17", "5*17=85", "85-14=71" ]
Current State: 71:[72, 89, 14, 5], Operations: [] Exploring Operation: 89-72=17, Resulting Numbers: [14, 5, 17] Generated Node #2: [14, 5, 17] from Operation: 89-72=17 Current State: 71:[14, 5, 17], Operations: ['89-72=17'] Exploring Operation: 5*17=85, Resulting Numbers: [14, 85] Generated Node #3: [14, 85] from Operation: 5*17=85 Current State: 71:[14, 85], Operations: ['89-72=17', '5*17=85'] Exploring Operation: 85-14=71, Resulting Numbers: [71] 71,71 equal: Goal Reached
4
Current State: 71:[72, 89, 14, 5], Operations: [] Exploring Operation: 14*5=70, Resulting Numbers: [72, 89, 70] Generated Node #0,0: 71:[72, 89, 70] Operation: 14*5=70 Exploring Operation: 89-5=84, Resulting Numbers: [72, 14, 84] Generated Node #0,1: 71:[72, 14, 84] Operation: 89-5=84 Exploring Operation: 89-14=75, Resulting Numbers: [72, 5, 75] Generated Node #0,2: 71:[72, 5, 75] Operation: 89-14=75 Moving to Node #0,0 Current State: 71:[72, 89, 70], Operations: ['14*5=70'] Exploring Operation: 89-70=19, Resulting Numbers: [72, 19] Generated Node #0,0,0: 71:[72, 19] Operation: 89-70=19 Exploring Operation: 89-72=17, Resulting Numbers: [70, 17] Generated Node #0,0,1: 71:[70, 17] Operation: 89-72=17 Exploring Operation: 72-70=2, Resulting Numbers: [89, 2] Generated Node #0,0,2: 71:[89, 2] Operation: 72-70=2 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 71:[72, 19], Operations: ['14*5=70', '89-70=19'] Exploring Operation: 72-19=53, Resulting Numbers: [53] 53,71 unequal: No Solution Exploring Operation: 72*19=1368, Resulting Numbers: [1368] 1368,71 unequal: No Solution Exploring Operation: 72+19=91, Resulting Numbers: [91] 91,71 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 71:[70, 17], Operations: ['14*5=70', '89-72=17'] Exploring Operation: 70+17=87, Resulting Numbers: [87] 87,71 unequal: No Solution Exploring Operation: 70-17=53, Resulting Numbers: [53] 53,71 unequal: No Solution Exploring Operation: 70*17=1190, Resulting Numbers: [1190] 1190,71 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 71:[89, 2], Operations: ['14*5=70', '72-70=2'] Exploring Operation: 89+2=91, Resulting Numbers: [91] 91,71 unequal: No Solution Exploring Operation: 89-2=87, Resulting Numbers: [87] 87,71 unequal: No Solution Exploring Operation: 89*2=178, Resulting Numbers: [178] 178,71 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1 Current State: 71:[72, 14, 84], Operations: ['89-5=84'] Exploring Operation: 72+14=86, Resulting Numbers: [84, 86] Generated Node #0,1,0: 71:[84, 86] Operation: 72+14=86 Exploring Operation: 84-14=70, Resulting Numbers: [72, 70] Generated Node #0,1,1: 71:[72, 70] Operation: 84-14=70 Exploring Operation: 72-14=58, Resulting Numbers: [84, 58] Generated Node #0,1,2: 71:[84, 58] Operation: 72-14=58 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 71:[72, 70], Operations: ['89-5=84', '84-14=70'] Exploring Operation: 72+70=142, Resulting Numbers: [142] 142,71 unequal: No Solution Exploring Operation: 72*70=5040, Resulting Numbers: [5040] 5040,71 unequal: No Solution Exploring Operation: 72-70=2, Resulting Numbers: [2] 2,71 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 71:[84, 58], Operations: ['89-5=84', '72-14=58'] Exploring Operation: 84-58=26, Resulting Numbers: [26] 26,71 unequal: No Solution Exploring Operation: 84*58=4872, Resulting Numbers: [4872] 4872,71 unequal: No Solution Exploring Operation: 84+58=142, Resulting Numbers: [142] 142,71 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 71:[84, 86], Operations: ['89-5=84', '72+14=86'] Exploring Operation: 84+86=170, Resulting Numbers: [170] 170,71 unequal: No Solution Exploring Operation: 86-84=2, Resulting Numbers: [2] 2,71 unequal: No Solution Exploring Operation: 84*86=7224, Resulting Numbers: [7224] 7224,71 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,2 Current State: 71:[72, 5, 75], Operations: ['89-14=75'] Exploring Operation: 72-5=67, Resulting Numbers: [75, 67] Generated Node #0,2,0: 71:[75, 67] Operation: 72-5=67 Exploring Operation: 72+5=77, Resulting Numbers: [75, 77] Generated Node #0,2,1: 71:[75, 77] Operation: 72+5=77 Exploring Operation: 75-5=70, Resulting Numbers: [72, 70] Generated Node #0,2,2: 71:[72, 70] Operation: 75-5=70 Moving to Node #0,2,2 Current State: 71:[72, 70], Operations: ['89-14=75', '75-5=70'] Exploring Operation: 72+70=142, Resulting Numbers: [142] 142,71 unequal: No Solution Exploring Operation: 72*70=5040, Resulting Numbers: [5040] 5040,71 unequal: No Solution Exploring Operation: 72-70=2, Resulting Numbers: [2] 2,71 unequal: No Solution Moving to Node #0,2,0 Current State: 71:[75, 67], Operations: ['89-14=75', '72-5=67'] Exploring Operation: 75-67=8, Resulting Numbers: [8] 8,71 unequal: No Solution Exploring Operation: 75*67=5025, Resulting Numbers: [5025] 5025,71 unequal: No Solution Exploring Operation: 75+67=142, Resulting Numbers: [142] 142,71 unequal: No Solution Moving to Node #0,2,1 Current State: 71:[75, 77], Operations: ['89-14=75', '72+5=77'] Exploring Operation: 77-75=2, Resulting Numbers: [2] 2,71 unequal: No Solution Exploring Operation: 75*77=5775, Resulting Numbers: [5775] 5775,71 unequal: No Solution Exploring Operation: 75+77=152, Resulting Numbers: [152] 152,71 unequal: No Solution No solution found.
0
hs_3
mult_heuristic
[ 46, 20, 40, 1 ]
100
[ "46-40=6", "6-1=5", "20*5=100" ]
Current State: 100:[46, 20, 40, 1], Operations: [] Exploring Operation: 46-40=6, Resulting Numbers: [20, 1, 6] Generated Node #2: [20, 1, 6] from Operation: 46-40=6 Current State: 100:[20, 1, 6], Operations: ['46-40=6'] Exploring Operation: 6-1=5, Resulting Numbers: [20, 5] Generated Node #3: [20, 5] from Operation: 6-1=5 Current State: 100:[20, 5], Operations: ['46-40=6', '6-1=5'] Exploring Operation: 20*5=100, Resulting Numbers: [100] 100,100 equal: Goal Reached
4
Current State: 100:[46, 20, 40, 1], Operations: [] Exploring Operation: 40/20=2, Resulting Numbers: [46, 1, 2] Generated Node #0,0: 100:[46, 1, 2] Operation: 40/20=2 Exploring Operation: 46-20=26, Resulting Numbers: [40, 1, 26] Generated Node #0,1: 100:[40, 1, 26] Operation: 46-20=26 Exploring Operation: 40-20=20, Resulting Numbers: [46, 1, 20] Generated Node #0,2: 100:[46, 1, 20] Operation: 40-20=20 Exploring Operation: 46-40=6, Resulting Numbers: [20, 1, 6] Generated Node #0,3: 100:[20, 1, 6] Operation: 46-40=6 Start Sub Search at level 1: Moving to Node #0,3 Current State: 100:[20, 1, 6], Operations: ['46-40=6'] Exploring Operation: 20*1=20, Resulting Numbers: [6, 20] Generated Node #0,3,0: 100:[6, 20] Operation: 20*1=20 Exploring Operation: 6-1=5, Resulting Numbers: [20, 5] Generated Node #0,3,1: 100:[20, 5] Operation: 6-1=5 Exploring Operation: 20/1=20, Resulting Numbers: [6, 20] Generated Node #0,3,2: 100:[6, 20] Operation: 20/1=20 Exploring Operation: 1*6=6, Resulting Numbers: [20, 6] Generated Node #0,3,3: 100:[20, 6] Operation: 1*6=6 Moving to Node #0,3,1 Current State: 100:[20, 5], Operations: ['46-40=6', '6-1=5'] Exploring Operation: 20+5=25, Resulting Numbers: [25] 25,100 unequal: No Solution Exploring Operation: 20*5=100, Resulting Numbers: [100] 100,100 equal: Goal Reached Moving to Node #0 Current State: 100:[46, 20, 40, 1], Operations: [] Exploring Operation: 46-40=6, Resulting Numbers: [20, 1, 6] Generated Node #0,3: 100:[20, 1, 6] Operation: 46-40=6 Moving to Node #0,3 Current State: 100:[20, 1, 6], Operations: ['46-40=6'] Exploring Operation: 6-1=5, Resulting Numbers: [20, 5] Generated Node #0,3,1: 100:[20, 5] Operation: 6-1=5 Moving to Node #0,3,1 Current State: 100:[20, 5], Operations: ['46-40=6', '6-1=5'] Exploring Operation: 20*5=100, Resulting Numbers: [100] 100,100 equal: Goal Reached Exit Sub Search at level 1
0.987847
hs_4
sum_heuristic
[ 92, 11, 90, 47 ]
29
[ "92-90=2", "11+47=58", "58/2=29" ]
Current State: 29:[92, 11, 90, 47], Operations: [] Exploring Operation: 92-90=2, Resulting Numbers: [11, 47, 2] Generated Node #2: [11, 47, 2] from Operation: 92-90=2 Current State: 29:[11, 47, 2], Operations: ['92-90=2'] Exploring Operation: 11+47=58, Resulting Numbers: [2, 58] Generated Node #3: [2, 58] from Operation: 11+47=58 Current State: 29:[2, 58], Operations: ['92-90=2', '11+47=58'] Exploring Operation: 58/2=29, Resulting Numbers: [29] 29,29 equal: Goal Reached
4
Current State: 29:[92, 11, 90, 47], Operations: [] Exploring Operation: 92-90=2, Resulting Numbers: [11, 47, 2] Generated Node #0,0: 29:[11, 47, 2] Operation: 92-90=2 Exploring Operation: 92-47=45, Resulting Numbers: [11, 90, 45] Generated Node #0,1: 29:[11, 90, 45] Operation: 92-47=45 Moving to Node #0,0 Current State: 29:[11, 47, 2], Operations: ['92-90=2'] Exploring Operation: 47-11=36, Resulting Numbers: [2, 36] Generated Node #0,0,0: 29:[2, 36] Operation: 47-11=36 Exploring Operation: 11*2=22, Resulting Numbers: [47, 22] Generated Node #0,0,1: 29:[47, 22] Operation: 11*2=22 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 29:[47, 22], Operations: ['92-90=2', '11*2=22'] Exploring Operation: 47-22=25, Resulting Numbers: [25] 25,29 unequal: No Solution Exploring Operation: 47+22=69, Resulting Numbers: [69] 69,29 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 29:[2, 36], Operations: ['92-90=2', '47-11=36'] Exploring Operation: 36-2=34, Resulting Numbers: [34] 34,29 unequal: No Solution Exploring Operation: 2+36=38, Resulting Numbers: [38] 38,29 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1 Current State: 29:[11, 90, 45], Operations: ['92-47=45'] Exploring Operation: 90/45=2, Resulting Numbers: [11, 2] Generated Node #0,1,0: 29:[11, 2] Operation: 90/45=2 Exploring Operation: 90-45=45, Resulting Numbers: [11, 45] Generated Node #0,1,1: 29:[11, 45] Operation: 90-45=45 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 29:[11, 45], Operations: ['92-47=45', '90-45=45'] Exploring Operation: 11+45=56, Resulting Numbers: [56] 56,29 unequal: No Solution Exploring Operation: 45-11=34, Resulting Numbers: [34] 34,29 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 29:[11, 2], Operations: ['92-47=45', '90/45=2'] Exploring Operation: 11*2=22, Resulting Numbers: [22] 22,29 unequal: No Solution Exploring Operation: 11+2=13, Resulting Numbers: [13] 13,29 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_2
sum_heuristic
[ 25, 69, 13, 18 ]
64
[ "18-13=5", "25/5=5", "69-5=64" ]
Current State: 64:[25, 69, 13, 18], Operations: [] Exploring Operation: 18-13=5, Resulting Numbers: [25, 69, 5] Generated Node #2: [25, 69, 5] from Operation: 18-13=5 Current State: 64:[25, 69, 5], Operations: ['18-13=5'] Exploring Operation: 25/5=5, Resulting Numbers: [69, 5] Generated Node #3: [69, 5] from Operation: 25/5=5 Current State: 64:[69, 5], Operations: ['18-13=5', '25/5=5'] Exploring Operation: 69-5=64, Resulting Numbers: [64] 64,64 equal: Goal Reached
4
Current State: 64:[25, 69, 13, 18], Operations: [] Exploring Operation: 25-18=7, Resulting Numbers: [69, 13, 7] Generated Node #0,0: 64:[69, 13, 7] Operation: 25-18=7 Exploring Operation: 25-13=12, Resulting Numbers: [69, 18, 12] Generated Node #0,1: 64:[69, 18, 12] Operation: 25-13=12 Moving to Node #0,0 Current State: 64:[69, 13, 7], Operations: ['25-18=7'] Exploring Operation: 13-7=6, Resulting Numbers: [69, 6] Generated Node #0,0,0: 64:[69, 6] Operation: 13-7=6 Exploring Operation: 69-7=62, Resulting Numbers: [13, 62] Generated Node #0,0,1: 64:[13, 62] Operation: 69-7=62 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 64:[13, 62], Operations: ['25-18=7', '69-7=62'] Exploring Operation: 62-13=49, Resulting Numbers: [49] 49,64 unequal: No Solution Exploring Operation: 13+62=75, Resulting Numbers: [75] 75,64 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 64:[69, 6], Operations: ['25-18=7', '13-7=6'] Exploring Operation: 69+6=75, Resulting Numbers: [75] 75,64 unequal: No Solution Exploring Operation: 69-6=63, Resulting Numbers: [63] 63,64 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1 Current State: 64:[69, 18, 12], Operations: ['25-13=12'] Exploring Operation: 18-12=6, Resulting Numbers: [69, 6] Generated Node #0,1,0: 64:[69, 6] Operation: 18-12=6 Exploring Operation: 18+12=30, Resulting Numbers: [69, 30] Generated Node #0,1,1: 64:[69, 30] Operation: 18+12=30 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 64:[69, 6], Operations: ['25-13=12', '18-12=6'] Exploring Operation: 69-6=63, Resulting Numbers: [63] 63,64 unequal: No Solution Exploring Operation: 69+6=75, Resulting Numbers: [75] 75,64 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 64:[69, 30], Operations: ['25-13=12', '18+12=30'] Exploring Operation: 69-30=39, Resulting Numbers: [39] 39,64 unequal: No Solution Exploring Operation: 69+30=99, Resulting Numbers: [99] 99,64 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_2
mult_heuristic
[ 80, 67, 72, 64 ]
59
[ "80-72=8", "64/8=8", "67-8=59" ]
Current State: 59:[80, 67, 72, 64], Operations: [] Exploring Operation: 80-72=8, Resulting Numbers: [67, 64, 8] Generated Node #2: [67, 64, 8] from Operation: 80-72=8 Current State: 59:[67, 64, 8], Operations: ['80-72=8'] Exploring Operation: 64/8=8, Resulting Numbers: [67, 8] Generated Node #3: [67, 8] from Operation: 64/8=8 Current State: 59:[67, 8], Operations: ['80-72=8', '64/8=8'] Exploring Operation: 67-8=59, Resulting Numbers: [59] 59,59 equal: Goal Reached
4
Current State: 59:[80, 67, 72, 64], Operations: [] Exploring Operation: 80-64=16, Resulting Numbers: [67, 72, 16] Generated Node #0,0: 59:[67, 72, 16] Operation: 80-64=16 Exploring Operation: 80-72=8, Resulting Numbers: [67, 64, 8] Generated Node #0,1: 59:[67, 64, 8] Operation: 80-72=8 Exploring Operation: 80-67=13, Resulting Numbers: [72, 64, 13] Generated Node #0,2: 59:[72, 64, 13] Operation: 80-67=13 Exploring Operation: 72-67=5, Resulting Numbers: [80, 64, 5] Generated Node #0,3: 59:[80, 64, 5] Operation: 72-67=5 Exploring Operation: 72-64=8, Resulting Numbers: [80, 67, 8] Generated Node #0,4: 59:[80, 67, 8] Operation: 72-64=8 Moving to Node #0,0 Current State: 59:[67, 72, 16], Operations: ['80-64=16'] Exploring Operation: 67-16=51, Resulting Numbers: [72, 51] Generated Node #0,0,0: 59:[72, 51] Operation: 67-16=51 Exploring Operation: 72-67=5, Resulting Numbers: [16, 5] Generated Node #0,0,1: 59:[16, 5] Operation: 72-67=5 Exploring Operation: 67+16=83, Resulting Numbers: [72, 83] Generated Node #0,0,2: 59:[72, 83] Operation: 67+16=83 Exploring Operation: 72-16=56, Resulting Numbers: [67, 56] Generated Node #0,0,3: 59:[67, 56] Operation: 72-16=56 Exploring Operation: 72+16=88, Resulting Numbers: [67, 88] Generated Node #0,0,4: 59:[67, 88] Operation: 72+16=88 Moving to Node #0,2 Current State: 59:[72, 64, 13], Operations: ['80-67=13'] Exploring Operation: 72-13=59, Resulting Numbers: [64, 59] Generated Node #0,2,0: 59:[64, 59] Operation: 72-13=59 Exploring Operation: 72+13=85, Resulting Numbers: [64, 85] Generated Node #0,2,1: 59:[64, 85] Operation: 72+13=85 Exploring Operation: 64+13=77, Resulting Numbers: [72, 77] Generated Node #0,2,2: 59:[72, 77] Operation: 64+13=77 Exploring Operation: 64-13=51, Resulting Numbers: [72, 51] Generated Node #0,2,3: 59:[72, 51] Operation: 64-13=51 Exploring Operation: 72-64=8, Resulting Numbers: [13, 8] Generated Node #0,2,4: 59:[13, 8] Operation: 72-64=8 Moving to Node #0,1 Current State: 59:[67, 64, 8], Operations: ['80-72=8'] Exploring Operation: 64-8=56, Resulting Numbers: [67, 56] Generated Node #0,1,0: 59:[67, 56] Operation: 64-8=56 Exploring Operation: 67+8=75, Resulting Numbers: [64, 75] Generated Node #0,1,1: 59:[64, 75] Operation: 67+8=75 Exploring Operation: 67-8=59, Resulting Numbers: [64, 59] Generated Node #0,1,2: 59:[64, 59] Operation: 67-8=59 Exploring Operation: 64+8=72, Resulting Numbers: [67, 72] Generated Node #0,1,3: 59:[67, 72] Operation: 64+8=72 Exploring Operation: 64/8=8, Resulting Numbers: [67, 8] Generated Node #0,1,4: 59:[67, 8] Operation: 64/8=8 Moving to Node #0,3 Current State: 59:[80, 64, 5], Operations: ['72-67=5'] Exploring Operation: 64+5=69, Resulting Numbers: [80, 69] Generated Node #0,3,0: 59:[80, 69] Operation: 64+5=69 Exploring Operation: 80/5=16, Resulting Numbers: [64, 16] Generated Node #0,3,1: 59:[64, 16] Operation: 80/5=16 Exploring Operation: 80+5=85, Resulting Numbers: [64, 85] Generated Node #0,3,2: 59:[64, 85] Operation: 80+5=85 Exploring Operation: 64-5=59, Resulting Numbers: [80, 59] Generated Node #0,3,3: 59:[80, 59] Operation: 64-5=59 Exploring Operation: 80-5=75, Resulting Numbers: [64, 75] Generated Node #0,3,4: 59:[64, 75] Operation: 80-5=75 Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 59:[80, 59], Operations: ['72-67=5', '64-5=59'] Exploring Operation: 80*59=4720, Resulting Numbers: [4720] 4720,59 unequal: No Solution Exploring Operation: 80+59=139, Resulting Numbers: [139] 139,59 unequal: No Solution Exploring Operation: 80-59=21, Resulting Numbers: [21] 21,59 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,4 Current State: 59:[64, 75], Operations: ['72-67=5', '80-5=75'] Exploring Operation: 64+75=139, Resulting Numbers: [139] 139,59 unequal: No Solution Exploring Operation: 75-64=11, Resulting Numbers: [11] 11,59 unequal: No Solution Exploring Operation: 64*75=4800, Resulting Numbers: [4800] 4800,59 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 59:[80, 69], Operations: ['72-67=5', '64+5=69'] Exploring Operation: 80+69=149, Resulting Numbers: [149] 149,59 unequal: No Solution Exploring Operation: 80*69=5520, Resulting Numbers: [5520] 5520,59 unequal: No Solution Exploring Operation: 80-69=11, Resulting Numbers: [11] 11,59 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 59:[64, 85], Operations: ['72-67=5', '80+5=85'] Exploring Operation: 64*85=5440, Resulting Numbers: [5440] 5440,59 unequal: No Solution Exploring Operation: 64+85=149, Resulting Numbers: [149] 149,59 unequal: No Solution Exploring Operation: 85-64=21, Resulting Numbers: [21] 21,59 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 59:[64, 16], Operations: ['72-67=5', '80/5=16'] Exploring Operation: 64+16=80, Resulting Numbers: [80] 80,59 unequal: No Solution Exploring Operation: 64*16=1024, Resulting Numbers: [1024] 1024,59 unequal: No Solution Exploring Operation: 64/16=4, Resulting Numbers: [4] 4,59 unequal: No Solution Exploring Operation: 64-16=48, Resulting Numbers: [48] 48,59 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,4 Current State: 59:[80, 67, 8], Operations: ['72-64=8'] Exploring Operation: 80+8=88, Resulting Numbers: [67, 88] Generated Node #0,4,0: 59:[67, 88] Operation: 80+8=88 Exploring Operation: 80-8=72, Resulting Numbers: [67, 72] Generated Node #0,4,1: 59:[67, 72] Operation: 80-8=72 Exploring Operation: 80/8=10, Resulting Numbers: [67, 10] Generated Node #0,4,2: 59:[67, 10] Operation: 80/8=10 Exploring Operation: 67+8=75, Resulting Numbers: [80, 75] Generated Node #0,4,3: 59:[80, 75] Operation: 67+8=75 Exploring Operation: 67-8=59, Resulting Numbers: [80, 59] Generated Node #0,4,4: 59:[80, 59] Operation: 67-8=59 Start Sub Search at level 1: Moving to Node #0,4,1 Current State: 59:[67, 72], Operations: ['72-64=8', '80-8=72'] Exploring Operation: 67+72=139, Resulting Numbers: [139] 139,59 unequal: No Solution Exploring Operation: 67*72=4824, Resulting Numbers: [4824] 4824,59 unequal: No Solution Exploring Operation: 72-67=5, Resulting Numbers: [5] 5,59 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,4 Current State: 59:[80, 59], Operations: ['72-64=8', '67-8=59'] Exploring Operation: 80*59=4720, Resulting Numbers: [4720] 4720,59 unequal: No Solution Exploring Operation: 80-59=21, Resulting Numbers: [21] 21,59 unequal: No Solution Exploring Operation: 80+59=139, Resulting Numbers: [139] 139,59 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,0 Current State: 59:[67, 88], Operations: ['72-64=8', '80+8=88'] Exploring Operation: 67*88=5896, Resulting Numbers: [5896] 5896,59 unequal: No Solution Exploring Operation: 88-67=21, Resulting Numbers: [21] 21,59 unequal: No Solution Exploring Operation: 67+88=155, Resulting Numbers: [155] 155,59 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,3 Current State: 59:[80, 75], Operations: ['72-64=8', '67+8=75'] Exploring Operation: 80+75=155, Resulting Numbers: [155] 155,59 unequal: No Solution Exploring Operation: 80-75=5, Resulting Numbers: [5] 5,59 unequal: No Solution Exploring Operation: 80*75=6000, Resulting Numbers: [6000] 6000,59 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,2 Current State: 59:[67, 10], Operations: ['72-64=8', '80/8=10'] Exploring Operation: 67*10=670, Resulting Numbers: [670] 670,59 unequal: No Solution Exploring Operation: 67+10=77, Resulting Numbers: [77] 77,59 unequal: No Solution Exploring Operation: 67-10=57, Resulting Numbers: [57] 57,59 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,2,0 Current State: 59:[64, 59], Operations: ['80-67=13', '72-13=59'] Exploring Operation: 64-59=5, Resulting Numbers: [5] 5,59 unequal: No Solution Exploring Operation: 64+59=123, Resulting Numbers: [123] 123,59 unequal: No Solution Exploring Operation: 64*59=3776, Resulting Numbers: [3776] 3776,59 unequal: No Solution Moving to Node #0,1,2 Current State: 59:[64, 59], Operations: ['80-72=8', '67-8=59'] Exploring Operation: 64-59=5, Resulting Numbers: [5] 5,59 unequal: No Solution Exploring Operation: 64+59=123, Resulting Numbers: [123] 123,59 unequal: No Solution Exploring Operation: 64*59=3776, Resulting Numbers: [3776] 3776,59 unequal: No Solution Moving to Node #0,0,3 Current State: 59:[67, 56], Operations: ['80-64=16', '72-16=56'] Exploring Operation: 67*56=3752, Resulting Numbers: [3752] 3752,59 unequal: No Solution Exploring Operation: 67+56=123, Resulting Numbers: [123] 123,59 unequal: No Solution Exploring Operation: 67-56=11, Resulting Numbers: [11] 11,59 unequal: No Solution Moving to Node #0,1,0 Current State: 59:[67, 56], Operations: ['80-72=8', '64-8=56'] Exploring Operation: 67-56=11, Resulting Numbers: [11] 11,59 unequal: No Solution Exploring Operation: 67*56=3752, Resulting Numbers: [3752] 3752,59 unequal: No Solution Exploring Operation: 67+56=123, Resulting Numbers: [123] 123,59 unequal: No Solution Moving to Node #0,2,3 Current State: 59:[72, 51], Operations: ['80-67=13', '64-13=51'] Exploring Operation: 72-51=21, Resulting Numbers: [21] 21,59 unequal: No Solution Exploring Operation: 72+51=123, Resulting Numbers: [123] 123,59 unequal: No Solution Exploring Operation: 72*51=3672, Resulting Numbers: [3672] 3672,59 unequal: No Solution Moving to Node #0,1,3 Current State: 59:[67, 72], Operations: ['80-72=8', '64+8=72'] Exploring Operation: 72-67=5, Resulting Numbers: [5] 5,59 unequal: No Solution Exploring Operation: 67*72=4824, Resulting Numbers: [4824] 4824,59 unequal: No Solution Exploring Operation: 67+72=139, Resulting Numbers: [139] 139,59 unequal: No Solution Moving to Node #0,1,1 Current State: 59:[64, 75], Operations: ['80-72=8', '67+8=75'] Exploring Operation: 64+75=139, Resulting Numbers: [139] 139,59 unequal: No Solution Exploring Operation: 75-64=11, Resulting Numbers: [11] 11,59 unequal: No Solution Exploring Operation: 64*75=4800, Resulting Numbers: [4800] 4800,59 unequal: No Solution Moving to Node #0,0,0 Current State: 59:[72, 51], Operations: ['80-64=16', '67-16=51'] Exploring Operation: 72*51=3672, Resulting Numbers: [3672] 3672,59 unequal: No Solution Exploring Operation: 72+51=123, Resulting Numbers: [123] 123,59 unequal: No Solution Exploring Operation: 72-51=21, Resulting Numbers: [21] 21,59 unequal: No Solution Moving to Node #0,2,1 Current State: 59:[64, 85], Operations: ['80-67=13', '72+13=85'] Exploring Operation: 64*85=5440, Resulting Numbers: [5440] 5440,59 unequal: No Solution Exploring Operation: 85-64=21, Resulting Numbers: [21] 21,59 unequal: No Solution Exploring Operation: 64+85=149, Resulting Numbers: [149] 149,59 unequal: No Solution Moving to Node #0,2,2 Current State: 59:[72, 77], Operations: ['80-67=13', '64+13=77'] Exploring Operation: 72+77=149, Resulting Numbers: [149] 149,59 unequal: No Solution Exploring Operation: 77-72=5, Resulting Numbers: [5] 5,59 unequal: No Solution Exploring Operation: 72*77=5544, Resulting Numbers: [5544] 5544,59 unequal: No Solution Moving to Node #0,0,2 Current State: 59:[72, 83], Operations: ['80-64=16', '67+16=83'] Exploring Operation: 72*83=5976, Resulting Numbers: [5976] 5976,59 unequal: No Solution Exploring Operation: 72+83=155, Resulting Numbers: [155] 155,59 unequal: No Solution Exploring Operation: 83-72=11, Resulting Numbers: [11] 11,59 unequal: No Solution Moving to Node #0,0,4 Current State: 59:[67, 88], Operations: ['80-64=16', '72+16=88'] Exploring Operation: 67+88=155, Resulting Numbers: [155] 155,59 unequal: No Solution Exploring Operation: 88-67=21, Resulting Numbers: [21] 21,59 unequal: No Solution Exploring Operation: 67*88=5896, Resulting Numbers: [5896] 5896,59 unequal: No Solution Moving to Node #0,1,4 Current State: 59:[67, 8], Operations: ['80-72=8', '64/8=8'] Exploring Operation: 67*8=536, Resulting Numbers: [536] 536,59 unequal: No Solution Exploring Operation: 67+8=75, Resulting Numbers: [75] 75,59 unequal: No Solution Exploring Operation: 67-8=59, Resulting Numbers: [59] 59,59 equal: Goal Reached Moving to Node #0 Current State: 59:[80, 67, 72, 64], Operations: [] Exploring Operation: 80-72=8, Resulting Numbers: [67, 64, 8] Generated Node #0,1: 59:[67, 64, 8] Operation: 80-72=8 Moving to Node #0,1 Current State: 59:[67, 64, 8], Operations: ['80-72=8'] Exploring Operation: 64/8=8, Resulting Numbers: [67, 8] Generated Node #0,1,4: 59:[67, 8] Operation: 64/8=8 Moving to Node #0,1,4 Current State: 59:[67, 8], Operations: ['80-72=8', '64/8=8'] Exploring Operation: 67-8=59, Resulting Numbers: [59] 59,59 equal: Goal Reached
0.909722
hs_5
mult_heuristic
[ 48, 30, 22, 88 ]
84
[ "48-30=18", "88-22=66", "18+66=84" ]
Current State: 84:[48, 30, 22, 88], Operations: [] Exploring Operation: 48-30=18, Resulting Numbers: [22, 88, 18] Generated Node #2: [22, 88, 18] from Operation: 48-30=18 Current State: 84:[22, 88, 18], Operations: ['48-30=18'] Exploring Operation: 88-22=66, Resulting Numbers: [18, 66] Generated Node #3: [18, 66] from Operation: 88-22=66 Current State: 84:[18, 66], Operations: ['48-30=18', '88-22=66'] Exploring Operation: 18+66=84, Resulting Numbers: [84] 84,84 equal: Goal Reached
4
Current State: 84:[48, 30, 22, 88], Operations: [] Exploring Operation: 88/22=4, Resulting Numbers: [48, 30, 4] Generated Node #0,0: 84:[48, 30, 4] Operation: 88/22=4 Exploring Operation: 48-22=26, Resulting Numbers: [30, 88, 26] Generated Node #0,1: 84:[30, 88, 26] Operation: 48-22=26 Exploring Operation: 48-30=18, Resulting Numbers: [22, 88, 18] Generated Node #0,2: 84:[22, 88, 18] Operation: 48-30=18 Exploring Operation: 88-48=40, Resulting Numbers: [30, 22, 40] Generated Node #0,3: 84:[30, 22, 40] Operation: 88-48=40 Start Sub Search at level 1: Moving to Node #0,3 Current State: 84:[30, 22, 40], Operations: ['88-48=40'] Exploring Operation: 40-22=18, Resulting Numbers: [30, 18] Generated Node #0,3,0: 84:[30, 18] Operation: 40-22=18 Exploring Operation: 30-22=8, Resulting Numbers: [40, 8] Generated Node #0,3,1: 84:[40, 8] Operation: 30-22=8 Exploring Operation: 40-30=10, Resulting Numbers: [22, 10] Generated Node #0,3,2: 84:[22, 10] Operation: 40-30=10 Exploring Operation: 30+22=52, Resulting Numbers: [40, 52] Generated Node #0,3,3: 84:[40, 52] Operation: 30+22=52 Moving to Node #0,3,1 Current State: 84:[40, 8], Operations: ['88-48=40', '30-22=8'] Exploring Operation: 40-8=32, Resulting Numbers: [32] 32,84 unequal: No Solution Exploring Operation: 40+8=48, Resulting Numbers: [48] 48,84 unequal: No Solution Exploring Operation: 40/8=5, Resulting Numbers: [5] 5,84 unequal: No Solution Exploring Operation: 40*8=320, Resulting Numbers: [320] 320,84 unequal: No Solution Moving to Node #0,3,2 Current State: 84:[22, 10], Operations: ['88-48=40', '40-30=10'] Exploring Operation: 22+10=32, Resulting Numbers: [32] 32,84 unequal: No Solution Exploring Operation: 22*10=220, Resulting Numbers: [220] 220,84 unequal: No Solution Exploring Operation: 22-10=12, Resulting Numbers: [12] 12,84 unequal: No Solution Moving to Node #0,3,0 Current State: 84:[30, 18], Operations: ['88-48=40', '40-22=18'] Exploring Operation: 30-18=12, Resulting Numbers: [12] 12,84 unequal: No Solution Exploring Operation: 30*18=540, Resulting Numbers: [540] 540,84 unequal: No Solution Exploring Operation: 30+18=48, Resulting Numbers: [48] 48,84 unequal: No Solution Moving to Node #0,3,3 Current State: 84:[40, 52], Operations: ['88-48=40', '30+22=52'] Exploring Operation: 40*52=2080, Resulting Numbers: [2080] 2080,84 unequal: No Solution Exploring Operation: 40+52=92, Resulting Numbers: [92] 92,84 unequal: No Solution Exploring Operation: 52-40=12, Resulting Numbers: [12] 12,84 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 84:[48, 30, 4], Operations: ['88/22=4'] Exploring Operation: 48+30=78, Resulting Numbers: [4, 78] Generated Node #0,0,0: 84:[4, 78] Operation: 48+30=78 Exploring Operation: 48-4=44, Resulting Numbers: [30, 44] Generated Node #0,0,1: 84:[30, 44] Operation: 48-4=44 Exploring Operation: 48-30=18, Resulting Numbers: [4, 18] Generated Node #0,0,2: 84:[4, 18] Operation: 48-30=18 Exploring Operation: 48/4=12, Resulting Numbers: [30, 12] Generated Node #0,0,3: 84:[30, 12] Operation: 48/4=12 Start Sub Search at level 2: Moving to Node #0,0,3 Current State: 84:[30, 12], Operations: ['88/22=4', '48/4=12'] Exploring Operation: 30+12=42, Resulting Numbers: [42] 42,84 unequal: No Solution Exploring Operation: 30*12=360, Resulting Numbers: [360] 360,84 unequal: No Solution Exploring Operation: 30-12=18, Resulting Numbers: [18] 18,84 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 84:[4, 18], Operations: ['88/22=4', '48-30=18'] Exploring Operation: 4+18=22, Resulting Numbers: [22] 22,84 unequal: No Solution Exploring Operation: 18-4=14, Resulting Numbers: [14] 14,84 unequal: No Solution Exploring Operation: 4*18=72, Resulting Numbers: [72] 72,84 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 84:[30, 44], Operations: ['88/22=4', '48-4=44'] Exploring Operation: 30+44=74, Resulting Numbers: [74] 74,84 unequal: No Solution Exploring Operation: 30*44=1320, Resulting Numbers: [1320] 1320,84 unequal: No Solution Exploring Operation: 44-30=14, Resulting Numbers: [14] 14,84 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 84:[4, 78], Operations: ['88/22=4', '48+30=78'] Exploring Operation: 4*78=312, Resulting Numbers: [312] 312,84 unequal: No Solution Exploring Operation: 78-4=74, Resulting Numbers: [74] 74,84 unequal: No Solution Exploring Operation: 4+78=82, Resulting Numbers: [82] 82,84 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 84:[30, 88, 26], Operations: ['48-22=26'] Exploring Operation: 30-26=4, Resulting Numbers: [88, 4] Generated Node #0,1,0: 84:[88, 4] Operation: 30-26=4 Exploring Operation: 30+26=56, Resulting Numbers: [88, 56] Generated Node #0,1,1: 84:[88, 56] Operation: 30+26=56 Exploring Operation: 88-30=58, Resulting Numbers: [26, 58] Generated Node #0,1,2: 84:[26, 58] Operation: 88-30=58 Exploring Operation: 88-26=62, Resulting Numbers: [30, 62] Generated Node #0,1,3: 84:[30, 62] Operation: 88-26=62 Moving to Node #0,1,0 Current State: 84:[88, 4], Operations: ['48-22=26', '30-26=4'] Exploring Operation: 88/4=22, Resulting Numbers: [22] 22,84 unequal: No Solution Exploring Operation: 88*4=352, Resulting Numbers: [352] 352,84 unequal: No Solution Exploring Operation: 88+4=92, Resulting Numbers: [92] 92,84 unequal: No Solution Exploring Operation: 88-4=84, Resulting Numbers: [84] 84,84 equal: Goal Reached Moving to Node #0 Current State: 84:[48, 30, 22, 88], Operations: [] Exploring Operation: 48-22=26, Resulting Numbers: [30, 88, 26] Generated Node #0,1: 84:[30, 88, 26] Operation: 48-22=26 Moving to Node #0,1 Current State: 84:[30, 88, 26], Operations: ['48-22=26'] Exploring Operation: 30-26=4, Resulting Numbers: [88, 4] Generated Node #0,1,0: 84:[88, 4] Operation: 30-26=4 Moving to Node #0,1,0 Current State: 84:[88, 4], Operations: ['48-22=26', '30-26=4'] Exploring Operation: 88-4=84, Resulting Numbers: [84] 84,84 equal: Goal Reached Exit Sub Search at level 1
0.957465
hs_4
mult_heuristic
[ 24, 73, 19, 23 ]
92
[ "24-23=1", "73+19=92", "1*92=92" ]
Current State: 92:[24, 73, 19, 23], Operations: [] Exploring Operation: 24-23=1, Resulting Numbers: [73, 19, 1] Generated Node #2: [73, 19, 1] from Operation: 24-23=1 Current State: 92:[73, 19, 1], Operations: ['24-23=1'] Exploring Operation: 73+19=92, Resulting Numbers: [1, 92] Generated Node #3: [1, 92] from Operation: 73+19=92 Current State: 92:[1, 92], Operations: ['24-23=1', '73+19=92'] Exploring Operation: 1*92=92, Resulting Numbers: [92] 92,92 equal: Goal Reached
4
Current State: 92:[24, 73, 19, 23], Operations: [] Exploring Operation: 73-19=54, Resulting Numbers: [24, 23, 54] Generated Node #0,0: 92:[24, 23, 54] Operation: 73-19=54 Exploring Operation: 24+73=97, Resulting Numbers: [19, 23, 97] Generated Node #0,1: 92:[19, 23, 97] Operation: 24+73=97 Exploring Operation: 73-24=49, Resulting Numbers: [19, 23, 49] Generated Node #0,2: 92:[19, 23, 49] Operation: 73-24=49 Exploring Operation: 73+19=92, Resulting Numbers: [24, 23, 92] Generated Node #0,3: 92:[24, 23, 92] Operation: 73+19=92 Moving to Node #0,3 Current State: 92:[24, 23, 92], Operations: ['73+19=92'] Exploring Operation: 92-24=68, Resulting Numbers: [23, 68] Generated Node #0,3,0: 92:[23, 68] Operation: 92-24=68 Exploring Operation: 92/23=4, Resulting Numbers: [24, 4] Generated Node #0,3,1: 92:[24, 4] Operation: 92/23=4 Exploring Operation: 24-23=1, Resulting Numbers: [92, 1] Generated Node #0,3,2: 92:[92, 1] Operation: 24-23=1 Exploring Operation: 24+23=47, Resulting Numbers: [92, 47] Generated Node #0,3,3: 92:[92, 47] Operation: 24+23=47 Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 92:[24, 4], Operations: ['73+19=92', '92/23=4'] Exploring Operation: 24/4=6, Resulting Numbers: [6] 6,92 unequal: No Solution Exploring Operation: 24*4=96, Resulting Numbers: [96] 96,92 unequal: No Solution Exploring Operation: 24+4=28, Resulting Numbers: [28] 28,92 unequal: No Solution Exploring Operation: 24-4=20, Resulting Numbers: [20] 20,92 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 92:[92, 1], Operations: ['73+19=92', '24-23=1'] Exploring Operation: 92-1=91, Resulting Numbers: [91] 91,92 unequal: No Solution Exploring Operation: 92/1=92, Resulting Numbers: [92] 92,92 equal: Goal Reached Moving to Node #0 Current State: 92:[24, 73, 19, 23], Operations: [] Exploring Operation: 73+19=92, Resulting Numbers: [24, 23, 92] Generated Node #0,3: 92:[24, 23, 92] Operation: 73+19=92 Moving to Node #0,3 Current State: 92:[24, 23, 92], Operations: ['73+19=92'] Exploring Operation: 24-23=1, Resulting Numbers: [92, 1] Generated Node #0,3,2: 92:[92, 1] Operation: 24-23=1 Moving to Node #0,3,2 Current State: 92:[92, 1], Operations: ['73+19=92', '24-23=1'] Exploring Operation: 92/1=92, Resulting Numbers: [92] 92,92 equal: Goal Reached Exit Sub Search at level 1
0.984375
hs_4
mult_heuristic
[ 6, 90, 4, 20 ]
80
[ "6+90=96", "20-4=16", "96-16=80" ]
Current State: 80:[6, 90, 4, 20], Operations: [] Exploring Operation: 6+90=96, Resulting Numbers: [4, 20, 96] Generated Node #2: [4, 20, 96] from Operation: 6+90=96 Current State: 80:[4, 20, 96], Operations: ['6+90=96'] Exploring Operation: 20-4=16, Resulting Numbers: [96, 16] Generated Node #3: [96, 16] from Operation: 20-4=16 Current State: 80:[96, 16], Operations: ['6+90=96', '20-4=16'] Exploring Operation: 96-16=80, Resulting Numbers: [80] 80,80 equal: Goal Reached
4
Current State: 80:[6, 90, 4, 20], Operations: [] Exploring Operation: 90/6=15, Resulting Numbers: [4, 20, 15] Generated Node #0,0: 80:[4, 20, 15] Operation: 90/6=15 Moving to Node #0,0 Current State: 80:[4, 20, 15], Operations: ['90/6=15'] Exploring Operation: 20-15=5, Resulting Numbers: [4, 5] Generated Node #0,0,0: 80:[4, 5] Operation: 20-15=5 Moving to Node #0,0,0 Current State: 80:[4, 5], Operations: ['90/6=15', '20-15=5'] Exploring Operation: 4*5=20, Resulting Numbers: [20] 20,80 unequal: No Solution No solution found.
0
hs_1
mult_heuristic
[ 7, 8, 42, 7 ]
42
[ "7-7=0", "8*0=0", "42+0=42" ]
Current State: 42:[7, 8, 42, 7], Operations: [] Exploring Operation: 7-7=0, Resulting Numbers: [8, 42, 0] Generated Node #2: [8, 42, 0] from Operation: 7-7=0 Current State: 42:[8, 42, 0], Operations: ['7-7=0'] Exploring Operation: 8*0=0, Resulting Numbers: [42, 0] Generated Node #3: [42, 0] from Operation: 8*0=0 Current State: 42:[42, 0], Operations: ['7-7=0', '8*0=0'] Exploring Operation: 42+0=42, Resulting Numbers: [42] 42,42 equal: Goal Reached
4
Current State: 42:[7, 8, 42, 7], Operations: [] Exploring Operation: 7+8=15, Resulting Numbers: [42, 7, 15] Generated Node #0,0: 42:[42, 7, 15] Operation: 7+8=15 Moving to Node #0,0 Current State: 42:[42, 7, 15], Operations: ['7+8=15'] Exploring Operation: 42/7=6, Resulting Numbers: [15, 6] Generated Node #0,0,0: 42:[15, 6] Operation: 42/7=6 Moving to Node #0,0,0 Current State: 42:[15, 6], Operations: ['7+8=15', '42/7=6'] Exploring Operation: 15+6=21, Resulting Numbers: [21] 21,42 unequal: No Solution No solution found.
0
hs_1
sum_heuristic
[ 18, 42, 24, 62 ]
61
[ "42-18=24", "24/24=1", "62-1=61" ]
Current State: 61:[18, 42, 24, 62], Operations: [] Exploring Operation: 42-18=24, Resulting Numbers: [24, 62, 24] Generated Node #2: [24, 62, 24] from Operation: 42-18=24 Current State: 61:[24, 62, 24], Operations: ['42-18=24'] Exploring Operation: 24/24=1, Resulting Numbers: [62, 1] Generated Node #3: [62, 1] from Operation: 24/24=1 Current State: 61:[62, 1], Operations: ['42-18=24', '24/24=1'] Exploring Operation: 62-1=61, Resulting Numbers: [61] 61,61 equal: Goal Reached
4
Current State: 61:[18, 42, 24, 62], Operations: [] Exploring Operation: 18+24=42, Resulting Numbers: [42, 62, 42] Generated Node #0,0: 61:[42, 62, 42] Operation: 18+24=42 Exploring Operation: 42+24=66, Resulting Numbers: [18, 62, 66] Generated Node #0,1: 61:[18, 62, 66] Operation: 42+24=66 Exploring Operation: 62-18=44, Resulting Numbers: [42, 24, 44] Generated Node #0,2: 61:[42, 24, 44] Operation: 62-18=44 Exploring Operation: 18+42=60, Resulting Numbers: [24, 62, 60] Generated Node #0,3: 61:[24, 62, 60] Operation: 18+42=60 Moving to Node #0,0 Current State: 61:[42, 62, 42], Operations: ['18+24=42'] Exploring Operation: 62-42=20, Resulting Numbers: [42, 20] Generated Node #0,0,0: 61:[42, 20] Operation: 62-42=20 Exploring Operation: 42+42=84, Resulting Numbers: [62, 84] Generated Node #0,0,1: 61:[62, 84] Operation: 42+42=84 Exploring Operation: 62-42=20, Resulting Numbers: [42, 20] Generated Node #0,0,2: 61:[42, 20] Operation: 62-42=20 Exploring Operation: 42/42=1, Resulting Numbers: [62, 1] Generated Node #0,0,3: 61:[62, 1] Operation: 42/42=1 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 61:[62, 84], Operations: ['18+24=42', '42+42=84'] Exploring Operation: 62*84=5208, Resulting Numbers: [5208] 5208,61 unequal: No Solution Exploring Operation: 62+84=146, Resulting Numbers: [146] 146,61 unequal: No Solution Exploring Operation: 84-62=22, Resulting Numbers: [22] 22,61 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 61:[42, 20], Operations: ['18+24=42', '62-42=20'] Exploring Operation: 42+20=62, Resulting Numbers: [62] 62,61 unequal: No Solution Exploring Operation: 42-20=22, Resulting Numbers: [22] 22,61 unequal: No Solution Exploring Operation: 42*20=840, Resulting Numbers: [840] 840,61 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 61:[42, 20], Operations: ['18+24=42', '62-42=20'] Exploring Operation: 42*20=840, Resulting Numbers: [840] 840,61 unequal: No Solution Exploring Operation: 42+20=62, Resulting Numbers: [62] 62,61 unequal: No Solution Exploring Operation: 42-20=22, Resulting Numbers: [22] 22,61 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 61:[62, 1], Operations: ['18+24=42', '42/42=1'] Exploring Operation: 62/1=62, Resulting Numbers: [62] 62,61 unequal: No Solution Exploring Operation: 62-1=61, Resulting Numbers: [61] 61,61 equal: Goal Reached Moving to Node #0 Current State: 61:[18, 42, 24, 62], Operations: [] Exploring Operation: 18+24=42, Resulting Numbers: [42, 62, 42] Generated Node #0,0: 61:[42, 62, 42] Operation: 18+24=42 Moving to Node #0,0 Current State: 61:[42, 62, 42], Operations: ['18+24=42'] Exploring Operation: 42/42=1, Resulting Numbers: [62, 1] Generated Node #0,0,3: 61:[62, 1] Operation: 42/42=1 Moving to Node #0,0,3 Current State: 61:[62, 1], Operations: ['18+24=42', '42/42=1'] Exploring Operation: 62-1=61, Resulting Numbers: [61] 61,61 equal: Goal Reached Exit Sub Search at level 1
0.980035
hs_4
mult_heuristic
[ 19, 90, 30, 22 ]
45
[ "30-19=11", "90*11=990", "990/22=45" ]
Current State: 45:[19, 90, 30, 22], Operations: [] Exploring Operation: 30-19=11, Resulting Numbers: [90, 22, 11] Generated Node #2: [90, 22, 11] from Operation: 30-19=11 Current State: 45:[90, 22, 11], Operations: ['30-19=11'] Exploring Operation: 90*11=990, Resulting Numbers: [22, 990] Generated Node #3: [22, 990] from Operation: 90*11=990 Current State: 45:[22, 990], Operations: ['30-19=11', '90*11=990'] Exploring Operation: 990/22=45, Resulting Numbers: [45] 45,45 equal: Goal Reached
4
Current State: 45:[19, 90, 30, 22], Operations: [] Exploring Operation: 90/30=3, Resulting Numbers: [19, 22, 3] Generated Node #0,0: 45:[19, 22, 3] Operation: 90/30=3 Exploring Operation: 90-30=60, Resulting Numbers: [19, 22, 60] Generated Node #0,1: 45:[19, 22, 60] Operation: 90-30=60 Exploring Operation: 90-22=68, Resulting Numbers: [19, 30, 68] Generated Node #0,2: 45:[19, 30, 68] Operation: 90-22=68 Exploring Operation: 90-19=71, Resulting Numbers: [30, 22, 71] Generated Node #0,3: 45:[30, 22, 71] Operation: 90-19=71 Moving to Node #0,0 Current State: 45:[19, 22, 3], Operations: ['90/30=3'] Exploring Operation: 22-19=3, Resulting Numbers: [3, 3] Generated Node #0,0,0: 45:[3, 3] Operation: 22-19=3 Exploring Operation: 19-3=16, Resulting Numbers: [22, 16] Generated Node #0,0,1: 45:[22, 16] Operation: 19-3=16 Exploring Operation: 19+22=41, Resulting Numbers: [3, 41] Generated Node #0,0,2: 45:[3, 41] Operation: 19+22=41 Exploring Operation: 22-3=19, Resulting Numbers: [19, 19] Generated Node #0,0,3: 45:[19, 19] Operation: 22-3=19 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 45:[3, 3], Operations: ['90/30=3', '22-19=3'] Exploring Operation: 3/3=1, Resulting Numbers: [1] 1,45 unequal: No Solution Exploring Operation: 3-3=0, Resulting Numbers: [0] 0,45 unequal: No Solution Exploring Operation: 3+3=6, Resulting Numbers: [6] 6,45 unequal: No Solution Exploring Operation: 3*3=9, Resulting Numbers: [9] 9,45 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 45:[3, 41], Operations: ['90/30=3', '19+22=41'] Exploring Operation: 3+41=44, Resulting Numbers: [44] 44,45 unequal: No Solution Exploring Operation: 41-3=38, Resulting Numbers: [38] 38,45 unequal: No Solution Exploring Operation: 3*41=123, Resulting Numbers: [123] 123,45 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 45:[22, 16], Operations: ['90/30=3', '19-3=16'] Exploring Operation: 22+16=38, Resulting Numbers: [38] 38,45 unequal: No Solution Exploring Operation: 22*16=352, Resulting Numbers: [352] 352,45 unequal: No Solution Exploring Operation: 22-16=6, Resulting Numbers: [6] 6,45 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 45:[19, 19], Operations: ['90/30=3', '22-3=19'] Exploring Operation: 19/19=1, Resulting Numbers: [1] 1,45 unequal: No Solution Exploring Operation: 19*19=361, Resulting Numbers: [361] 361,45 unequal: No Solution Exploring Operation: 19-19=0, Resulting Numbers: [0] 0,45 unequal: No Solution Exploring Operation: 19+19=38, Resulting Numbers: [38] 38,45 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1 Current State: 45:[19, 22, 60], Operations: ['90-30=60'] Exploring Operation: 60-22=38, Resulting Numbers: [19, 38] Generated Node #0,1,0: 45:[19, 38] Operation: 60-22=38 Exploring Operation: 19+22=41, Resulting Numbers: [60, 41] Generated Node #0,1,1: 45:[60, 41] Operation: 19+22=41 Exploring Operation: 60-19=41, Resulting Numbers: [22, 41] Generated Node #0,1,2: 45:[22, 41] Operation: 60-19=41 Exploring Operation: 22-19=3, Resulting Numbers: [60, 3] Generated Node #0,1,3: 45:[60, 3] Operation: 22-19=3 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 45:[19, 38], Operations: ['90-30=60', '60-22=38'] Exploring Operation: 38-19=19, Resulting Numbers: [19] 19,45 unequal: No Solution Exploring Operation: 38/19=2, Resulting Numbers: [2] 2,45 unequal: No Solution Exploring Operation: 19+38=57, Resulting Numbers: [57] 57,45 unequal: No Solution Exploring Operation: 19*38=722, Resulting Numbers: [722] 722,45 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 45:[22, 41], Operations: ['90-30=60', '60-19=41'] Exploring Operation: 22+41=63, Resulting Numbers: [63] 63,45 unequal: No Solution Exploring Operation: 41-22=19, Resulting Numbers: [19] 19,45 unequal: No Solution Exploring Operation: 22*41=902, Resulting Numbers: [902] 902,45 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 45:[60, 3], Operations: ['90-30=60', '22-19=3'] Exploring Operation: 60-3=57, Resulting Numbers: [57] 57,45 unequal: No Solution Exploring Operation: 60*3=180, Resulting Numbers: [180] 180,45 unequal: No Solution Exploring Operation: 60+3=63, Resulting Numbers: [63] 63,45 unequal: No Solution Exploring Operation: 60/3=20, Resulting Numbers: [20] 20,45 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 45:[60, 41], Operations: ['90-30=60', '19+22=41'] Exploring Operation: 60*41=2460, Resulting Numbers: [2460] 2460,45 unequal: No Solution Exploring Operation: 60-41=19, Resulting Numbers: [19] 19,45 unequal: No Solution Exploring Operation: 60+41=101, Resulting Numbers: [101] 101,45 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,2 Current State: 45:[19, 30, 68], Operations: ['90-22=68'] Exploring Operation: 30-19=11, Resulting Numbers: [68, 11] Generated Node #0,2,0: 45:[68, 11] Operation: 30-19=11 Exploring Operation: 19+30=49, Resulting Numbers: [68, 49] Generated Node #0,2,1: 45:[68, 49] Operation: 19+30=49 Exploring Operation: 68-30=38, Resulting Numbers: [19, 38] Generated Node #0,2,2: 45:[19, 38] Operation: 68-30=38 Exploring Operation: 68-19=49, Resulting Numbers: [30, 49] Generated Node #0,2,3: 45:[30, 49] Operation: 68-19=49 Moving to Node #0,3 Current State: 45:[30, 22, 71], Operations: ['90-19=71'] Exploring Operation: 71-22=49, Resulting Numbers: [30, 49] Generated Node #0,3,0: 45:[30, 49] Operation: 71-22=49 Exploring Operation: 71-30=41, Resulting Numbers: [22, 41] Generated Node #0,3,1: 45:[22, 41] Operation: 71-30=41 Exploring Operation: 30-22=8, Resulting Numbers: [71, 8] Generated Node #0,3,2: 45:[71, 8] Operation: 30-22=8 Exploring Operation: 30+22=52, Resulting Numbers: [71, 52] Generated Node #0,3,3: 45:[71, 52] Operation: 30+22=52 Moving to Node #0,2,2 Current State: 45:[19, 38], Operations: ['90-22=68', '68-30=38'] Exploring Operation: 19*38=722, Resulting Numbers: [722] 722,45 unequal: No Solution Exploring Operation: 38-19=19, Resulting Numbers: [19] 19,45 unequal: No Solution Exploring Operation: 19+38=57, Resulting Numbers: [57] 57,45 unequal: No Solution Exploring Operation: 38/19=2, Resulting Numbers: [2] 2,45 unequal: No Solution Moving to Node #0,3,1 Current State: 45:[22, 41], Operations: ['90-19=71', '71-30=41'] Exploring Operation: 22*41=902, Resulting Numbers: [902] 902,45 unequal: No Solution Exploring Operation: 41-22=19, Resulting Numbers: [19] 19,45 unequal: No Solution Exploring Operation: 22+41=63, Resulting Numbers: [63] 63,45 unequal: No Solution Moving to Node #0,3,0 Current State: 45:[30, 49], Operations: ['90-19=71', '71-22=49'] Exploring Operation: 49-30=19, Resulting Numbers: [19] 19,45 unequal: No Solution Exploring Operation: 30*49=1470, Resulting Numbers: [1470] 1470,45 unequal: No Solution Exploring Operation: 30+49=79, Resulting Numbers: [79] 79,45 unequal: No Solution Moving to Node #0,2,3 Current State: 45:[30, 49], Operations: ['90-22=68', '68-19=49'] Exploring Operation: 49-30=19, Resulting Numbers: [19] 19,45 unequal: No Solution Exploring Operation: 30+49=79, Resulting Numbers: [79] 79,45 unequal: No Solution Exploring Operation: 30*49=1470, Resulting Numbers: [1470] 1470,45 unequal: No Solution Moving to Node #0,2,0 Current State: 45:[68, 11], Operations: ['90-22=68', '30-19=11'] Exploring Operation: 68+11=79, Resulting Numbers: [79] 79,45 unequal: No Solution Exploring Operation: 68-11=57, Resulting Numbers: [57] 57,45 unequal: No Solution Exploring Operation: 68*11=748, Resulting Numbers: [748] 748,45 unequal: No Solution Moving to Node #0,2,1 Current State: 45:[68, 49], Operations: ['90-22=68', '19+30=49'] Exploring Operation: 68*49=3332, Resulting Numbers: [3332] 3332,45 unequal: No Solution Exploring Operation: 68+49=117, Resulting Numbers: [117] 117,45 unequal: No Solution Exploring Operation: 68-49=19, Resulting Numbers: [19] 19,45 unequal: No Solution Moving to Node #0,3,2 Current State: 45:[71, 8], Operations: ['90-19=71', '30-22=8'] Exploring Operation: 71-8=63, Resulting Numbers: [63] 63,45 unequal: No Solution Exploring Operation: 71*8=568, Resulting Numbers: [568] 568,45 unequal: No Solution Exploring Operation: 71+8=79, Resulting Numbers: [79] 79,45 unequal: No Solution Moving to Node #0,3,3 Current State: 45:[71, 52], Operations: ['90-19=71', '30+22=52'] Exploring Operation: 71+52=123, Resulting Numbers: [123] 123,45 unequal: No Solution Exploring Operation: 71*52=3692, Resulting Numbers: [3692] 3692,45 unequal: No Solution Exploring Operation: 71-52=19, Resulting Numbers: [19] 19,45 unequal: No Solution No solution found.
0
hs_4
mult_heuristic
[ 5, 89, 21, 88 ]
16
[ "21-5=16", "89-88=1", "16*1=16" ]
Current State: 16:[5, 89, 21, 88], Operations: [] Exploring Operation: 21-5=16, Resulting Numbers: [89, 88, 16] Generated Node #2: [89, 88, 16] from Operation: 21-5=16 Current State: 16:[89, 88, 16], Operations: ['21-5=16'] Exploring Operation: 89-88=1, Resulting Numbers: [16, 1] Generated Node #3: [16, 1] from Operation: 89-88=1 Current State: 16:[16, 1], Operations: ['21-5=16', '89-88=1'] Exploring Operation: 16*1=16, Resulting Numbers: [16] 16,16 equal: Goal Reached
4
Current State: 16:[5, 89, 21, 88], Operations: [] Exploring Operation: 89-88=1, Resulting Numbers: [5, 21, 1] Generated Node #0,0: 16:[5, 21, 1] Operation: 89-88=1 Exploring Operation: 89-21=68, Resulting Numbers: [5, 88, 68] Generated Node #0,1: 16:[5, 88, 68] Operation: 89-21=68 Moving to Node #0,0 Current State: 16:[5, 21, 1], Operations: ['89-88=1'] Exploring Operation: 21-5=16, Resulting Numbers: [1, 16] Generated Node #0,0,0: 16:[1, 16] Operation: 21-5=16 Exploring Operation: 5-1=4, Resulting Numbers: [21, 4] Generated Node #0,0,1: 16:[21, 4] Operation: 5-1=4 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 16:[1, 16], Operations: ['89-88=1', '21-5=16'] Exploring Operation: 1*16=16, Resulting Numbers: [16] 16,16 equal: Goal Reached Moving to Node #0 Current State: 16:[5, 89, 21, 88], Operations: [] Exploring Operation: 89-88=1, Resulting Numbers: [5, 21, 1] Generated Node #0,0: 16:[5, 21, 1] Operation: 89-88=1 Moving to Node #0,0 Current State: 16:[5, 21, 1], Operations: ['89-88=1'] Exploring Operation: 21-5=16, Resulting Numbers: [1, 16] Generated Node #0,0,0: 16:[1, 16] Operation: 21-5=16 Moving to Node #0,0,0 Current State: 16:[1, 16], Operations: ['89-88=1', '21-5=16'] Exploring Operation: 1*16=16, Resulting Numbers: [16] 16,16 equal: Goal Reached Exit Sub Search at level 1
0.992188
hs_2
mult_heuristic
[ 37, 10, 25, 4 ]
58
[ "37-25=12", "4*12=48", "10+48=58" ]
Current State: 58:[37, 10, 25, 4], Operations: [] Exploring Operation: 37-25=12, Resulting Numbers: [10, 4, 12] Generated Node #2: [10, 4, 12] from Operation: 37-25=12 Current State: 58:[10, 4, 12], Operations: ['37-25=12'] Exploring Operation: 4*12=48, Resulting Numbers: [10, 48] Generated Node #3: [10, 48] from Operation: 4*12=48 Current State: 58:[10, 48], Operations: ['37-25=12', '4*12=48'] Exploring Operation: 10+48=58, Resulting Numbers: [58] 58,58 equal: Goal Reached
4
Current State: 58:[37, 10, 25, 4], Operations: [] Exploring Operation: 10+25=35, Resulting Numbers: [37, 4, 35] Generated Node #0,0: 58:[37, 4, 35] Operation: 10+25=35 Exploring Operation: 37-10=27, Resulting Numbers: [25, 4, 27] Generated Node #0,1: 58:[25, 4, 27] Operation: 37-10=27 Exploring Operation: 37-4=33, Resulting Numbers: [10, 25, 33] Generated Node #0,2: 58:[10, 25, 33] Operation: 37-4=33 Exploring Operation: 37+25=62, Resulting Numbers: [10, 4, 62] Generated Node #0,3: 58:[10, 4, 62] Operation: 37+25=62 Exploring Operation: 10-4=6, Resulting Numbers: [37, 25, 6] Generated Node #0,4: 58:[37, 25, 6] Operation: 10-4=6 Start Sub Search at level 1: Moving to Node #0,1 Current State: 58:[25, 4, 27], Operations: ['37-10=27'] Exploring Operation: 4+27=31, Resulting Numbers: [25, 31] Generated Node #0,1,0: 58:[25, 31] Operation: 4+27=31 Exploring Operation: 25-4=21, Resulting Numbers: [27, 21] Generated Node #0,1,1: 58:[27, 21] Operation: 25-4=21 Exploring Operation: 25+27=52, Resulting Numbers: [4, 52] Generated Node #0,1,2: 58:[4, 52] Operation: 25+27=52 Exploring Operation: 27-25=2, Resulting Numbers: [4, 2] Generated Node #0,1,3: 58:[4, 2] Operation: 27-25=2 Exploring Operation: 25+4=29, Resulting Numbers: [27, 29] Generated Node #0,1,4: 58:[27, 29] Operation: 25+4=29 Moving to Node #0,1,3 Current State: 58:[4, 2], Operations: ['37-10=27', '27-25=2'] Exploring Operation: 4-2=2, Resulting Numbers: [2] 2,58 unequal: No Solution Exploring Operation: 4/2=2, Resulting Numbers: [2] 2,58 unequal: No Solution Exploring Operation: 4+2=6, Resulting Numbers: [6] 6,58 unequal: No Solution Exploring Operation: 4*2=8, Resulting Numbers: [8] 8,58 unequal: No Solution Moving to Node #0,1,4 Current State: 58:[27, 29], Operations: ['37-10=27', '25+4=29'] Exploring Operation: 27+29=56, Resulting Numbers: [56] 56,58 unequal: No Solution Exploring Operation: 27*29=783, Resulting Numbers: [783] 783,58 unequal: No Solution Exploring Operation: 29-27=2, Resulting Numbers: [2] 2,58 unequal: No Solution Moving to Node #0,1,0 Current State: 58:[25, 31], Operations: ['37-10=27', '4+27=31'] Exploring Operation: 25+31=56, Resulting Numbers: [56] 56,58 unequal: No Solution Exploring Operation: 25*31=775, Resulting Numbers: [775] 775,58 unequal: No Solution Exploring Operation: 31-25=6, Resulting Numbers: [6] 6,58 unequal: No Solution Moving to Node #0,1,2 Current State: 58:[4, 52], Operations: ['37-10=27', '25+27=52'] Exploring Operation: 52-4=48, Resulting Numbers: [48] 48,58 unequal: No Solution Exploring Operation: 52/4=13, Resulting Numbers: [13] 13,58 unequal: No Solution Exploring Operation: 4+52=56, Resulting Numbers: [56] 56,58 unequal: No Solution Exploring Operation: 4*52=208, Resulting Numbers: [208] 208,58 unequal: No Solution Moving to Node #0,1,1 Current State: 58:[27, 21], Operations: ['37-10=27', '25-4=21'] Exploring Operation: 27+21=48, Resulting Numbers: [48] 48,58 unequal: No Solution Exploring Operation: 27-21=6, Resulting Numbers: [6] 6,58 unequal: No Solution Exploring Operation: 27*21=567, Resulting Numbers: [567] 567,58 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 58:[10, 4, 62], Operations: ['37+25=62'] Exploring Operation: 62-10=52, Resulting Numbers: [4, 52] Generated Node #0,3,0: 58:[4, 52] Operation: 62-10=52 Exploring Operation: 62-4=58, Resulting Numbers: [10, 58] Generated Node #0,3,1: 58:[10, 58] Operation: 62-4=58 Exploring Operation: 10*4=40, Resulting Numbers: [62, 40] Generated Node #0,3,2: 58:[62, 40] Operation: 10*4=40 Exploring Operation: 10-4=6, Resulting Numbers: [62, 6] Generated Node #0,3,3: 58:[62, 6] Operation: 10-4=6 Exploring Operation: 10+4=14, Resulting Numbers: [62, 14] Generated Node #0,3,4: 58:[62, 14] Operation: 10+4=14 Start Sub Search at level 2: Moving to Node #0,3,0 Current State: 58:[4, 52], Operations: ['37+25=62', '62-10=52'] Exploring Operation: 52-4=48, Resulting Numbers: [48] 48,58 unequal: No Solution Exploring Operation: 52/4=13, Resulting Numbers: [13] 13,58 unequal: No Solution Exploring Operation: 4*52=208, Resulting Numbers: [208] 208,58 unequal: No Solution Exploring Operation: 4+52=56, Resulting Numbers: [56] 56,58 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,1 Current State: 58:[10, 58], Operations: ['37+25=62', '62-4=58'] Exploring Operation: 10+58=68, Resulting Numbers: [68] 68,58 unequal: No Solution Exploring Operation: 10*58=580, Resulting Numbers: [580] 580,58 unequal: No Solution Exploring Operation: 58-10=48, Resulting Numbers: [48] 48,58 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,3 Current State: 58:[62, 6], Operations: ['37+25=62', '10-4=6'] Exploring Operation: 62-6=56, Resulting Numbers: [56] 56,58 unequal: No Solution Exploring Operation: 62+6=68, Resulting Numbers: [68] 68,58 unequal: No Solution Exploring Operation: 62*6=372, Resulting Numbers: [372] 372,58 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,2 Current State: 58:[62, 40], Operations: ['37+25=62', '10*4=40'] Exploring Operation: 62+40=102, Resulting Numbers: [102] 102,58 unequal: No Solution Exploring Operation: 62-40=22, Resulting Numbers: [22] 22,58 unequal: No Solution Exploring Operation: 62*40=2480, Resulting Numbers: [2480] 2480,58 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,4 Current State: 58:[62, 14], Operations: ['37+25=62', '10+4=14'] Exploring Operation: 62-14=48, Resulting Numbers: [48] 48,58 unequal: No Solution Exploring Operation: 62+14=76, Resulting Numbers: [76] 76,58 unequal: No Solution Exploring Operation: 62*14=868, Resulting Numbers: [868] 868,58 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 58:[37, 4, 35], Operations: ['10+25=35'] Exploring Operation: 37+4=41, Resulting Numbers: [35, 41] Generated Node #0,0,0: 58:[35, 41] Operation: 37+4=41 Exploring Operation: 37-35=2, Resulting Numbers: [4, 2] Generated Node #0,0,1: 58:[4, 2] Operation: 37-35=2 Exploring Operation: 37+35=72, Resulting Numbers: [4, 72] Generated Node #0,0,2: 58:[4, 72] Operation: 37+35=72 Exploring Operation: 37-4=33, Resulting Numbers: [35, 33] Generated Node #0,0,3: 58:[35, 33] Operation: 37-4=33 Exploring Operation: 35-4=31, Resulting Numbers: [37, 31] Generated Node #0,0,4: 58:[37, 31] Operation: 35-4=31 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 58:[4, 2], Operations: ['10+25=35', '37-35=2'] Exploring Operation: 4-2=2, Resulting Numbers: [2] 2,58 unequal: No Solution Exploring Operation: 4/2=2, Resulting Numbers: [2] 2,58 unequal: No Solution Exploring Operation: 4*2=8, Resulting Numbers: [8] 8,58 unequal: No Solution Exploring Operation: 4+2=6, Resulting Numbers: [6] 6,58 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,3 Current State: 58:[35, 33], Operations: ['10+25=35', '37-4=33'] Exploring Operation: 35+33=68, Resulting Numbers: [68] 68,58 unequal: No Solution Exploring Operation: 35-33=2, Resulting Numbers: [2] 2,58 unequal: No Solution Exploring Operation: 35*33=1155, Resulting Numbers: [1155] 1155,58 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,4 Current State: 58:[37, 31], Operations: ['10+25=35', '35-4=31'] Exploring Operation: 37-31=6, Resulting Numbers: [6] 6,58 unequal: No Solution Exploring Operation: 37*31=1147, Resulting Numbers: [1147] 1147,58 unequal: No Solution Exploring Operation: 37+31=68, Resulting Numbers: [68] 68,58 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 58:[4, 72], Operations: ['10+25=35', '37+35=72'] Exploring Operation: 4+72=76, Resulting Numbers: [76] 76,58 unequal: No Solution Exploring Operation: 72/4=18, Resulting Numbers: [18] 18,58 unequal: No Solution Exploring Operation: 4*72=288, Resulting Numbers: [288] 288,58 unequal: No Solution Exploring Operation: 72-4=68, Resulting Numbers: [68] 68,58 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 58:[35, 41], Operations: ['10+25=35', '37+4=41'] Exploring Operation: 35+41=76, Resulting Numbers: [76] 76,58 unequal: No Solution Exploring Operation: 35*41=1435, Resulting Numbers: [1435] 1435,58 unequal: No Solution Exploring Operation: 41-35=6, Resulting Numbers: [6] 6,58 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 58:[10, 25, 33], Operations: ['37-4=33'] Exploring Operation: 33-25=8, Resulting Numbers: [10, 8] Generated Node #0,2,0: 58:[10, 8] Operation: 33-25=8 Exploring Operation: 25-10=15, Resulting Numbers: [33, 15] Generated Node #0,2,1: 58:[33, 15] Operation: 25-10=15 Exploring Operation: 25+33=58, Resulting Numbers: [10, 58] Generated Node #0,2,2: 58:[10, 58] Operation: 25+33=58 Exploring Operation: 33-10=23, Resulting Numbers: [25, 23] Generated Node #0,2,3: 58:[25, 23] Operation: 33-10=23 Exploring Operation: 10+25=35, Resulting Numbers: [33, 35] Generated Node #0,2,4: 58:[33, 35] Operation: 10+25=35 Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 58:[10, 58], Operations: ['37-4=33', '25+33=58'] Exploring Operation: 10+58=68, Resulting Numbers: [68] 68,58 unequal: No Solution Exploring Operation: 58-10=48, Resulting Numbers: [48] 48,58 unequal: No Solution Exploring Operation: 10*58=580, Resulting Numbers: [580] 580,58 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,3 Current State: 58:[25, 23], Operations: ['37-4=33', '33-10=23'] Exploring Operation: 25-23=2, Resulting Numbers: [2] 2,58 unequal: No Solution Exploring Operation: 25+23=48, Resulting Numbers: [48] 48,58 unequal: No Solution Exploring Operation: 25*23=575, Resulting Numbers: [575] 575,58 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,4 Current State: 58:[33, 35], Operations: ['37-4=33', '10+25=35'] Exploring Operation: 33*35=1155, Resulting Numbers: [1155] 1155,58 unequal: No Solution Exploring Operation: 35-33=2, Resulting Numbers: [2] 2,58 unequal: No Solution Exploring Operation: 33+35=68, Resulting Numbers: [68] 68,58 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 58:[10, 8], Operations: ['37-4=33', '33-25=8'] Exploring Operation: 10-8=2, Resulting Numbers: [2] 2,58 unequal: No Solution Exploring Operation: 10+8=18, Resulting Numbers: [18] 18,58 unequal: No Solution Exploring Operation: 10*8=80, Resulting Numbers: [80] 80,58 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 58:[33, 15], Operations: ['37-4=33', '25-10=15'] Exploring Operation: 33+15=48, Resulting Numbers: [48] 48,58 unequal: No Solution Exploring Operation: 33*15=495, Resulting Numbers: [495] 495,58 unequal: No Solution Exploring Operation: 33-15=18, Resulting Numbers: [18] 18,58 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4 Current State: 58:[37, 25, 6], Operations: ['10-4=6'] Exploring Operation: 25+6=31, Resulting Numbers: [37, 31] Generated Node #0,4,0: 58:[37, 31] Operation: 25+6=31 Exploring Operation: 37-25=12, Resulting Numbers: [6, 12] Generated Node #0,4,1: 58:[6, 12] Operation: 37-25=12 Exploring Operation: 37+6=43, Resulting Numbers: [25, 43] Generated Node #0,4,2: 58:[25, 43] Operation: 37+6=43 Exploring Operation: 37+25=62, Resulting Numbers: [6, 62] Generated Node #0,4,3: 58:[6, 62] Operation: 37+25=62 Exploring Operation: 37-6=31, Resulting Numbers: [25, 31] Generated Node #0,4,4: 58:[25, 31] Operation: 37-6=31 Moving to Node #0,4,4 Current State: 58:[25, 31], Operations: ['10-4=6', '37-6=31'] Exploring Operation: 31-25=6, Resulting Numbers: [6] 6,58 unequal: No Solution Exploring Operation: 25+31=56, Resulting Numbers: [56] 56,58 unequal: No Solution Exploring Operation: 25*31=775, Resulting Numbers: [775] 775,58 unequal: No Solution Moving to Node #0,4,3 Current State: 58:[6, 62], Operations: ['10-4=6', '37+25=62'] Exploring Operation: 6*62=372, Resulting Numbers: [372] 372,58 unequal: No Solution Exploring Operation: 62-6=56, Resulting Numbers: [56] 56,58 unequal: No Solution Exploring Operation: 6+62=68, Resulting Numbers: [68] 68,58 unequal: No Solution Moving to Node #0,4,0 Current State: 58:[37, 31], Operations: ['10-4=6', '25+6=31'] Exploring Operation: 37*31=1147, Resulting Numbers: [1147] 1147,58 unequal: No Solution Exploring Operation: 37+31=68, Resulting Numbers: [68] 68,58 unequal: No Solution Exploring Operation: 37-31=6, Resulting Numbers: [6] 6,58 unequal: No Solution Moving to Node #0,4,1 Current State: 58:[6, 12], Operations: ['10-4=6', '37-25=12'] Exploring Operation: 12-6=6, Resulting Numbers: [6] 6,58 unequal: No Solution Exploring Operation: 6+12=18, Resulting Numbers: [18] 18,58 unequal: No Solution Exploring Operation: 12/6=2, Resulting Numbers: [2] 2,58 unequal: No Solution Exploring Operation: 6*12=72, Resulting Numbers: [72] 72,58 unequal: No Solution Moving to Node #0,4,2 Current State: 58:[25, 43], Operations: ['10-4=6', '37+6=43'] Exploring Operation: 43-25=18, Resulting Numbers: [18] 18,58 unequal: No Solution Exploring Operation: 25*43=1075, Resulting Numbers: [1075] 1075,58 unequal: No Solution Exploring Operation: 25+43=68, Resulting Numbers: [68] 68,58 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_5
mult_heuristic
[ 38, 66, 96, 75 ]
67
[ "38+66=104", "96+75=171", "171-104=67" ]
Current State: 67:[38, 66, 96, 75], Operations: [] Exploring Operation: 38+66=104, Resulting Numbers: [96, 75, 104] Generated Node #2: [96, 75, 104] from Operation: 38+66=104 Current State: 67:[96, 75, 104], Operations: ['38+66=104'] Exploring Operation: 96+75=171, Resulting Numbers: [104, 171] Generated Node #3: [104, 171] from Operation: 96+75=171 Current State: 67:[104, 171], Operations: ['38+66=104', '96+75=171'] Exploring Operation: 171-104=67, Resulting Numbers: [67] 67,67 equal: Goal Reached
4
Current State: 67:[38, 66, 96, 75], Operations: [] Exploring Operation: 96-38=58, Resulting Numbers: [66, 75, 58] Generated Node #0,0: 67:[66, 75, 58] Operation: 96-38=58 Exploring Operation: 66-38=28, Resulting Numbers: [96, 75, 28] Generated Node #0,1: 67:[96, 75, 28] Operation: 66-38=28 Exploring Operation: 38+66=104, Resulting Numbers: [96, 75, 104] Generated Node #0,2: 67:[96, 75, 104] Operation: 38+66=104 Exploring Operation: 96-66=30, Resulting Numbers: [38, 75, 30] Generated Node #0,3: 67:[38, 75, 30] Operation: 96-66=30 Exploring Operation: 75-38=37, Resulting Numbers: [66, 96, 37] Generated Node #0,4: 67:[66, 96, 37] Operation: 75-38=37 Moving to Node #0,0 Current State: 67:[66, 75, 58], Operations: ['96-38=58'] Exploring Operation: 75-58=17, Resulting Numbers: [66, 17] Generated Node #0,0,0: 67:[66, 17] Operation: 75-58=17 Exploring Operation: 66+58=124, Resulting Numbers: [75, 124] Generated Node #0,0,1: 67:[75, 124] Operation: 66+58=124 Exploring Operation: 75+58=133, Resulting Numbers: [66, 133] Generated Node #0,0,2: 67:[66, 133] Operation: 75+58=133 Exploring Operation: 75-66=9, Resulting Numbers: [58, 9] Generated Node #0,0,3: 67:[58, 9] Operation: 75-66=9 Exploring Operation: 66-58=8, Resulting Numbers: [75, 8] Generated Node #0,0,4: 67:[75, 8] Operation: 66-58=8 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 67:[66, 17], Operations: ['96-38=58', '75-58=17'] Exploring Operation: 66*17=1122, Resulting Numbers: [1122] 1122,67 unequal: No Solution Exploring Operation: 66-17=49, Resulting Numbers: [49] 49,67 unequal: No Solution Exploring Operation: 66+17=83, Resulting Numbers: [83] 83,67 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 67:[75, 124], Operations: ['96-38=58', '66+58=124'] Exploring Operation: 75+124=199, Resulting Numbers: [199] 199,67 unequal: No Solution Exploring Operation: 75*124=9300, Resulting Numbers: [9300] 9300,67 unequal: No Solution Exploring Operation: 124-75=49, Resulting Numbers: [49] 49,67 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 67:[66, 133], Operations: ['96-38=58', '75+58=133'] Exploring Operation: 66+133=199, Resulting Numbers: [199] 199,67 unequal: No Solution Exploring Operation: 133-66=67, Resulting Numbers: [67] 67,67 equal: Goal Reached Moving to Node #0 Current State: 67:[38, 66, 96, 75], Operations: [] Exploring Operation: 96-38=58, Resulting Numbers: [66, 75, 58] Generated Node #0,0: 67:[66, 75, 58] Operation: 96-38=58 Moving to Node #0,0 Current State: 67:[66, 75, 58], Operations: ['96-38=58'] Exploring Operation: 75+58=133, Resulting Numbers: [66, 133] Generated Node #0,0,2: 67:[66, 133] Operation: 75+58=133 Moving to Node #0,0,2 Current State: 67:[66, 133], Operations: ['96-38=58', '75+58=133'] Exploring Operation: 133-66=67, Resulting Numbers: [67] 67,67 equal: Goal Reached Exit Sub Search at level 1
0.980903
hs_5
mult_heuristic
[ 38, 70, 61, 65 ]
94
[ "70-38=32", "61+65=126", "126-32=94" ]
Current State: 94:[38, 70, 61, 65], Operations: [] Exploring Operation: 70-38=32, Resulting Numbers: [61, 65, 32] Generated Node #2: [61, 65, 32] from Operation: 70-38=32 Current State: 94:[61, 65, 32], Operations: ['70-38=32'] Exploring Operation: 61+65=126, Resulting Numbers: [32, 126] Generated Node #3: [32, 126] from Operation: 61+65=126 Current State: 94:[32, 126], Operations: ['70-38=32', '61+65=126'] Exploring Operation: 126-32=94, Resulting Numbers: [94] 94,94 equal: Goal Reached
4
Current State: 94:[38, 70, 61, 65], Operations: [] Exploring Operation: 70-65=5, Resulting Numbers: [38, 61, 5] Generated Node #0,0: 94:[38, 61, 5] Operation: 70-65=5 Moving to Node #0,0 Current State: 94:[38, 61, 5], Operations: ['70-65=5'] Exploring Operation: 38+61=99, Resulting Numbers: [5, 99] Generated Node #0,0,0: 94:[5, 99] Operation: 38+61=99 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 94:[5, 99], Operations: ['70-65=5', '38+61=99'] Exploring Operation: 99-5=94, Resulting Numbers: [94] 94,94 equal: Goal Reached Moving to Node #0 Current State: 94:[38, 70, 61, 65], Operations: [] Exploring Operation: 70-65=5, Resulting Numbers: [38, 61, 5] Generated Node #0,0: 94:[38, 61, 5] Operation: 70-65=5 Moving to Node #0,0 Current State: 94:[38, 61, 5], Operations: ['70-65=5'] Exploring Operation: 38+61=99, Resulting Numbers: [5, 99] Generated Node #0,0,0: 94:[5, 99] Operation: 38+61=99 Moving to Node #0,0,0 Current State: 94:[5, 99], Operations: ['70-65=5', '38+61=99'] Exploring Operation: 99-5=94, Resulting Numbers: [94] 94,94 equal: Goal Reached Exit Sub Search at level 1
0.993924
hs_1
mult_heuristic
[ 51, 54, 6, 21 ]
21
[ "51+54=105", "6*21=126", "126-105=21" ]
Current State: 21:[51, 54, 6, 21], Operations: [] Exploring Operation: 51+54=105, Resulting Numbers: [6, 21, 105] Generated Node #2: [6, 21, 105] from Operation: 51+54=105 Current State: 21:[6, 21, 105], Operations: ['51+54=105'] Exploring Operation: 6*21=126, Resulting Numbers: [105, 126] Generated Node #3: [105, 126] from Operation: 6*21=126 Current State: 21:[105, 126], Operations: ['51+54=105', '6*21=126'] Exploring Operation: 126-105=21, Resulting Numbers: [21] 21,21 equal: Goal Reached
4
Current State: 21:[51, 54, 6, 21], Operations: [] Exploring Operation: 54-51=3, Resulting Numbers: [6, 21, 3] Generated Node #0,0: 21:[6, 21, 3] Operation: 54-51=3 Exploring Operation: 54/6=9, Resulting Numbers: [51, 21, 9] Generated Node #0,1: 21:[51, 21, 9] Operation: 54/6=9 Start Sub Search at level 1: Moving to Node #0,0 Current State: 21:[6, 21, 3], Operations: ['54-51=3'] Exploring Operation: 6-3=3, Resulting Numbers: [21, 3] Generated Node #0,0,0: 21:[21, 3] Operation: 6-3=3 Exploring Operation: 6/3=2, Resulting Numbers: [21, 2] Generated Node #0,0,1: 21:[21, 2] Operation: 6/3=2 Moving to Node #0,0,0 Current State: 21:[21, 3], Operations: ['54-51=3', '6-3=3'] Exploring Operation: 21+3=24, Resulting Numbers: [24] 24,21 unequal: No Solution Exploring Operation: 21/3=7, Resulting Numbers: [7] 7,21 unequal: No Solution Moving to Node #0,0,1 Current State: 21:[21, 2], Operations: ['54-51=3', '6/3=2'] Exploring Operation: 21-2=19, Resulting Numbers: [19] 19,21 unequal: No Solution Exploring Operation: 21+2=23, Resulting Numbers: [23] 23,21 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 21:[51, 21, 9], Operations: ['54/6=9'] Exploring Operation: 51-21=30, Resulting Numbers: [9, 30] Generated Node #0,1,0: 21:[9, 30] Operation: 51-21=30 Exploring Operation: 51-9=42, Resulting Numbers: [21, 42] Generated Node #0,1,1: 21:[21, 42] Operation: 51-9=42 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 21:[9, 30], Operations: ['54/6=9', '51-21=30'] Exploring Operation: 30-9=21, Resulting Numbers: [21] 21,21 equal: Goal Reached Moving to Node #0 Current State: 21:[51, 54, 6, 21], Operations: [] Exploring Operation: 54/6=9, Resulting Numbers: [51, 21, 9] Generated Node #0,1: 21:[51, 21, 9] Operation: 54/6=9 Moving to Node #0,1 Current State: 21:[51, 21, 9], Operations: ['54/6=9'] Exploring Operation: 51-21=30, Resulting Numbers: [9, 30] Generated Node #0,1,0: 21:[9, 30] Operation: 51-21=30 Moving to Node #0,1,0 Current State: 21:[9, 30], Operations: ['54/6=9', '51-21=30'] Exploring Operation: 30-9=21, Resulting Numbers: [21] 21,21 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.986979
hs_2
sum_heuristic
[ 60, 96, 7, 68 ]
95
[ "60+96=156", "68-7=61", "156-61=95" ]
Current State: 95:[60, 96, 7, 68], Operations: [] Exploring Operation: 60+96=156, Resulting Numbers: [7, 68, 156] Generated Node #2: [7, 68, 156] from Operation: 60+96=156 Current State: 95:[7, 68, 156], Operations: ['60+96=156'] Exploring Operation: 68-7=61, Resulting Numbers: [156, 61] Generated Node #3: [156, 61] from Operation: 68-7=61 Current State: 95:[156, 61], Operations: ['60+96=156', '68-7=61'] Exploring Operation: 156-61=95, Resulting Numbers: [95] 95,95 equal: Goal Reached
4
Current State: 95:[60, 96, 7, 68], Operations: [] Exploring Operation: 60+68=128, Resulting Numbers: [96, 7, 128] Generated Node #0,0: 95:[96, 7, 128] Operation: 60+68=128 Exploring Operation: 68-60=8, Resulting Numbers: [96, 7, 8] Generated Node #0,1: 95:[96, 7, 8] Operation: 68-60=8 Start Sub Search at level 1: Moving to Node #0,1 Current State: 95:[96, 7, 8], Operations: ['68-60=8'] Exploring Operation: 8-7=1, Resulting Numbers: [96, 1] Generated Node #0,1,0: 95:[96, 1] Operation: 8-7=1 Exploring Operation: 7+8=15, Resulting Numbers: [96, 15] Generated Node #0,1,1: 95:[96, 15] Operation: 7+8=15 Moving to Node #0,1,0 Current State: 95:[96, 1], Operations: ['68-60=8', '8-7=1'] Exploring Operation: 96*1=96, Resulting Numbers: [96] 96,95 unequal: No Solution Exploring Operation: 96-1=95, Resulting Numbers: [95] 95,95 equal: Goal Reached Moving to Node #0 Current State: 95:[60, 96, 7, 68], Operations: [] Exploring Operation: 68-60=8, Resulting Numbers: [96, 7, 8] Generated Node #0,1: 95:[96, 7, 8] Operation: 68-60=8 Moving to Node #0,1 Current State: 95:[96, 7, 8], Operations: ['68-60=8'] Exploring Operation: 8-7=1, Resulting Numbers: [96, 1] Generated Node #0,1,0: 95:[96, 1] Operation: 8-7=1 Moving to Node #0,1,0 Current State: 95:[96, 1], Operations: ['68-60=8', '8-7=1'] Exploring Operation: 96-1=95, Resulting Numbers: [95] 95,95 equal: Goal Reached Exit Sub Search at level 1
0.991319
hs_2
sum_heuristic
[ 35, 83, 52, 9 ]
70
[ "52-35=17", "9*17=153", "153-83=70" ]
Current State: 70:[35, 83, 52, 9], Operations: [] Exploring Operation: 52-35=17, Resulting Numbers: [83, 9, 17] Generated Node #2: [83, 9, 17] from Operation: 52-35=17 Current State: 70:[83, 9, 17], Operations: ['52-35=17'] Exploring Operation: 9*17=153, Resulting Numbers: [83, 153] Generated Node #3: [83, 153] from Operation: 9*17=153 Current State: 70:[83, 153], Operations: ['52-35=17', '9*17=153'] Exploring Operation: 153-83=70, Resulting Numbers: [70] 70,70 equal: Goal Reached
4
Current State: 70:[35, 83, 52, 9], Operations: [] Exploring Operation: 52-9=43, Resulting Numbers: [35, 83, 43] Generated Node #0,0: 70:[35, 83, 43] Operation: 52-9=43 Exploring Operation: 83-9=74, Resulting Numbers: [35, 52, 74] Generated Node #0,1: 70:[35, 52, 74] Operation: 83-9=74 Exploring Operation: 52-35=17, Resulting Numbers: [83, 9, 17] Generated Node #0,2: 70:[83, 9, 17] Operation: 52-35=17 Exploring Operation: 52+9=61, Resulting Numbers: [35, 83, 61] Generated Node #0,3: 70:[35, 83, 61] Operation: 52+9=61 Exploring Operation: 83-52=31, Resulting Numbers: [35, 9, 31] Generated Node #0,4: 70:[35, 9, 31] Operation: 83-52=31 Start Sub Search at level 1: Moving to Node #0,4 Current State: 70:[35, 9, 31], Operations: ['83-52=31'] Exploring Operation: 35+31=66, Resulting Numbers: [9, 66] Generated Node #0,4,0: 70:[9, 66] Operation: 35+31=66 Exploring Operation: 31-9=22, Resulting Numbers: [35, 22] Generated Node #0,4,1: 70:[35, 22] Operation: 31-9=22 Exploring Operation: 35+9=44, Resulting Numbers: [31, 44] Generated Node #0,4,2: 70:[31, 44] Operation: 35+9=44 Exploring Operation: 9+31=40, Resulting Numbers: [35, 40] Generated Node #0,4,3: 70:[35, 40] Operation: 9+31=40 Exploring Operation: 35-31=4, Resulting Numbers: [9, 4] Generated Node #0,4,4: 70:[9, 4] Operation: 35-31=4 Moving to Node #0,4,4 Current State: 70:[9, 4], Operations: ['83-52=31', '35-31=4'] Exploring Operation: 9*4=36, Resulting Numbers: [36] 36,70 unequal: No Solution Exploring Operation: 9-4=5, Resulting Numbers: [5] 5,70 unequal: No Solution Exploring Operation: 9+4=13, Resulting Numbers: [13] 13,70 unequal: No Solution Moving to Node #0,4,3 Current State: 70:[35, 40], Operations: ['83-52=31', '9+31=40'] Exploring Operation: 35+40=75, Resulting Numbers: [75] 75,70 unequal: No Solution Exploring Operation: 35*40=1400, Resulting Numbers: [1400] 1400,70 unequal: No Solution Exploring Operation: 40-35=5, Resulting Numbers: [5] 5,70 unequal: No Solution Moving to Node #0,4,0 Current State: 70:[9, 66], Operations: ['83-52=31', '35+31=66'] Exploring Operation: 9*66=594, Resulting Numbers: [594] 594,70 unequal: No Solution Exploring Operation: 66-9=57, Resulting Numbers: [57] 57,70 unequal: No Solution Exploring Operation: 9+66=75, Resulting Numbers: [75] 75,70 unequal: No Solution Moving to Node #0,4,1 Current State: 70:[35, 22], Operations: ['83-52=31', '31-9=22'] Exploring Operation: 35+22=57, Resulting Numbers: [57] 57,70 unequal: No Solution Exploring Operation: 35*22=770, Resulting Numbers: [770] 770,70 unequal: No Solution Exploring Operation: 35-22=13, Resulting Numbers: [13] 13,70 unequal: No Solution Moving to Node #0,4,2 Current State: 70:[31, 44], Operations: ['83-52=31', '35+9=44'] Exploring Operation: 44-31=13, Resulting Numbers: [13] 13,70 unequal: No Solution Exploring Operation: 31*44=1364, Resulting Numbers: [1364] 1364,70 unequal: No Solution Exploring Operation: 31+44=75, Resulting Numbers: [75] 75,70 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 70:[83, 9, 17], Operations: ['52-35=17'] Exploring Operation: 83-17=66, Resulting Numbers: [9, 66] Generated Node #0,2,0: 70:[9, 66] Operation: 83-17=66 Exploring Operation: 83-9=74, Resulting Numbers: [17, 74] Generated Node #0,2,1: 70:[17, 74] Operation: 83-9=74 Exploring Operation: 83+9=92, Resulting Numbers: [17, 92] Generated Node #0,2,2: 70:[17, 92] Operation: 83+9=92 Exploring Operation: 9+17=26, Resulting Numbers: [83, 26] Generated Node #0,2,3: 70:[83, 26] Operation: 9+17=26 Exploring Operation: 17-9=8, Resulting Numbers: [83, 8] Generated Node #0,2,4: 70:[83, 8] Operation: 17-9=8 Moving to Node #0,2,0 Current State: 70:[9, 66], Operations: ['52-35=17', '83-17=66'] Exploring Operation: 9+66=75, Resulting Numbers: [75] 75,70 unequal: No Solution Exploring Operation: 9*66=594, Resulting Numbers: [594] 594,70 unequal: No Solution Exploring Operation: 66-9=57, Resulting Numbers: [57] 57,70 unequal: No Solution Moving to Node #0,2,1 Current State: 70:[17, 74], Operations: ['52-35=17', '83-9=74'] Exploring Operation: 17*74=1258, Resulting Numbers: [1258] 1258,70 unequal: No Solution Exploring Operation: 74-17=57, Resulting Numbers: [57] 57,70 unequal: No Solution Exploring Operation: 17+74=91, Resulting Numbers: [91] 91,70 unequal: No Solution Moving to Node #0,2,4 Current State: 70:[83, 8], Operations: ['52-35=17', '17-9=8'] Exploring Operation: 83*8=664, Resulting Numbers: [664] 664,70 unequal: No Solution Exploring Operation: 83+8=91, Resulting Numbers: [91] 91,70 unequal: No Solution Exploring Operation: 83-8=75, Resulting Numbers: [75] 75,70 unequal: No Solution Moving to Node #0,2,3 Current State: 70:[83, 26], Operations: ['52-35=17', '9+17=26'] Exploring Operation: 83*26=2158, Resulting Numbers: [2158] 2158,70 unequal: No Solution Exploring Operation: 83-26=57, Resulting Numbers: [57] 57,70 unequal: No Solution Exploring Operation: 83+26=109, Resulting Numbers: [109] 109,70 unequal: No Solution Moving to Node #0,2,2 Current State: 70:[17, 92], Operations: ['52-35=17', '83+9=92'] Exploring Operation: 17*92=1564, Resulting Numbers: [1564] 1564,70 unequal: No Solution Exploring Operation: 17+92=109, Resulting Numbers: [109] 109,70 unequal: No Solution Exploring Operation: 92-17=75, Resulting Numbers: [75] 75,70 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 70:[35, 83, 43], Operations: ['52-9=43'] Exploring Operation: 35+83=118, Resulting Numbers: [43, 118] Generated Node #0,0,0: 70:[43, 118] Operation: 35+83=118 Exploring Operation: 43-35=8, Resulting Numbers: [83, 8] Generated Node #0,0,1: 70:[83, 8] Operation: 43-35=8 Exploring Operation: 83-43=40, Resulting Numbers: [35, 40] Generated Node #0,0,2: 70:[35, 40] Operation: 83-43=40 Exploring Operation: 83-35=48, Resulting Numbers: [43, 48] Generated Node #0,0,3: 70:[43, 48] Operation: 83-35=48 Exploring Operation: 35+43=78, Resulting Numbers: [83, 78] Generated Node #0,0,4: 70:[83, 78] Operation: 35+43=78 Moving to Node #0,0,2 Current State: 70:[35, 40], Operations: ['52-9=43', '83-43=40'] Exploring Operation: 35+40=75, Resulting Numbers: [75] 75,70 unequal: No Solution Exploring Operation: 40-35=5, Resulting Numbers: [5] 5,70 unequal: No Solution Exploring Operation: 35*40=1400, Resulting Numbers: [1400] 1400,70 unequal: No Solution Moving to Node #0,0,1 Current State: 70:[83, 8], Operations: ['52-9=43', '43-35=8'] Exploring Operation: 83+8=91, Resulting Numbers: [91] 91,70 unequal: No Solution Exploring Operation: 83*8=664, Resulting Numbers: [664] 664,70 unequal: No Solution Exploring Operation: 83-8=75, Resulting Numbers: [75] 75,70 unequal: No Solution Moving to Node #0,0,3 Current State: 70:[43, 48], Operations: ['52-9=43', '83-35=48'] Exploring Operation: 43*48=2064, Resulting Numbers: [2064] 2064,70 unequal: No Solution Exploring Operation: 48-43=5, Resulting Numbers: [5] 5,70 unequal: No Solution Exploring Operation: 43+48=91, Resulting Numbers: [91] 91,70 unequal: No Solution Moving to Node #0,0,4 Current State: 70:[83, 78], Operations: ['52-9=43', '35+43=78'] Exploring Operation: 83+78=161, Resulting Numbers: [161] 161,70 unequal: No Solution Exploring Operation: 83*78=6474, Resulting Numbers: [6474] 6474,70 unequal: No Solution Exploring Operation: 83-78=5, Resulting Numbers: [5] 5,70 unequal: No Solution Moving to Node #0,0,0 Current State: 70:[43, 118], Operations: ['52-9=43', '35+83=118'] Exploring Operation: 118-43=75, Resulting Numbers: [75] 75,70 unequal: No Solution Exploring Operation: 43+118=161, Resulting Numbers: [161] 161,70 unequal: No Solution Exploring Operation: 43*118=5074, Resulting Numbers: [5074] 5074,70 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 70:[35, 52, 74], Operations: ['83-9=74'] Exploring Operation: 35+74=109, Resulting Numbers: [52, 109] Generated Node #0,1,0: 70:[52, 109] Operation: 35+74=109 Exploring Operation: 74-52=22, Resulting Numbers: [35, 22] Generated Node #0,1,1: 70:[35, 22] Operation: 74-52=22 Exploring Operation: 35+52=87, Resulting Numbers: [74, 87] Generated Node #0,1,2: 70:[74, 87] Operation: 35+52=87 Exploring Operation: 74-35=39, Resulting Numbers: [52, 39] Generated Node #0,1,3: 70:[52, 39] Operation: 74-35=39 Exploring Operation: 52-35=17, Resulting Numbers: [74, 17] Generated Node #0,1,4: 70:[74, 17] Operation: 52-35=17 Moving to Node #0,1,4 Current State: 70:[74, 17], Operations: ['83-9=74', '52-35=17'] Exploring Operation: 74*17=1258, Resulting Numbers: [1258] 1258,70 unequal: No Solution Exploring Operation: 74-17=57, Resulting Numbers: [57] 57,70 unequal: No Solution Exploring Operation: 74+17=91, Resulting Numbers: [91] 91,70 unequal: No Solution Moving to Node #0,1,1 Current State: 70:[35, 22], Operations: ['83-9=74', '74-52=22'] Exploring Operation: 35*22=770, Resulting Numbers: [770] 770,70 unequal: No Solution Exploring Operation: 35+22=57, Resulting Numbers: [57] 57,70 unequal: No Solution Exploring Operation: 35-22=13, Resulting Numbers: [13] 13,70 unequal: No Solution Moving to Node #0,1,2 Current State: 70:[74, 87], Operations: ['83-9=74', '35+52=87'] Exploring Operation: 74+87=161, Resulting Numbers: [161] 161,70 unequal: No Solution Exploring Operation: 74*87=6438, Resulting Numbers: [6438] 6438,70 unequal: No Solution Exploring Operation: 87-74=13, Resulting Numbers: [13] 13,70 unequal: No Solution Moving to Node #0,1,3 Current State: 70:[52, 39], Operations: ['83-9=74', '74-35=39'] Exploring Operation: 52*39=2028, Resulting Numbers: [2028] 2028,70 unequal: No Solution Exploring Operation: 52-39=13, Resulting Numbers: [13] 13,70 unequal: No Solution Exploring Operation: 52+39=91, Resulting Numbers: [91] 91,70 unequal: No Solution Moving to Node #0,1,0 Current State: 70:[52, 109], Operations: ['83-9=74', '35+74=109'] Exploring Operation: 52+109=161, Resulting Numbers: [161] 161,70 unequal: No Solution Exploring Operation: 109-52=57, Resulting Numbers: [57] 57,70 unequal: No Solution Exploring Operation: 52*109=5668, Resulting Numbers: [5668] 5668,70 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 70:[35, 83, 61], Operations: ['52+9=61'] Exploring Operation: 35+83=118, Resulting Numbers: [61, 118] Generated Node #0,3,0: 70:[61, 118] Operation: 35+83=118 Exploring Operation: 61-35=26, Resulting Numbers: [83, 26] Generated Node #0,3,1: 70:[83, 26] Operation: 61-35=26 Exploring Operation: 83-61=22, Resulting Numbers: [35, 22] Generated Node #0,3,2: 70:[35, 22] Operation: 83-61=22 Exploring Operation: 83-35=48, Resulting Numbers: [61, 48] Generated Node #0,3,3: 70:[61, 48] Operation: 83-35=48 Exploring Operation: 35+61=96, Resulting Numbers: [83, 96] Generated Node #0,3,4: 70:[83, 96] Operation: 35+61=96 Start Sub Search at level 2: Moving to Node #0,3,2 Current State: 70:[35, 22], Operations: ['52+9=61', '83-61=22'] Exploring Operation: 35*22=770, Resulting Numbers: [770] 770,70 unequal: No Solution Exploring Operation: 35+22=57, Resulting Numbers: [57] 57,70 unequal: No Solution Exploring Operation: 35-22=13, Resulting Numbers: [13] 13,70 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,1 Current State: 70:[83, 26], Operations: ['52+9=61', '61-35=26'] Exploring Operation: 83-26=57, Resulting Numbers: [57] 57,70 unequal: No Solution Exploring Operation: 83*26=2158, Resulting Numbers: [2158] 2158,70 unequal: No Solution Exploring Operation: 83+26=109, Resulting Numbers: [109] 109,70 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,3 Current State: 70:[61, 48], Operations: ['52+9=61', '83-35=48'] Exploring Operation: 61*48=2928, Resulting Numbers: [2928] 2928,70 unequal: No Solution Exploring Operation: 61-48=13, Resulting Numbers: [13] 13,70 unequal: No Solution Exploring Operation: 61+48=109, Resulting Numbers: [109] 109,70 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,4 Current State: 70:[83, 96], Operations: ['52+9=61', '35+61=96'] Exploring Operation: 96-83=13, Resulting Numbers: [13] 13,70 unequal: No Solution Exploring Operation: 83+96=179, Resulting Numbers: [179] 179,70 unequal: No Solution Exploring Operation: 83*96=7968, Resulting Numbers: [7968] 7968,70 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,0 Current State: 70:[61, 118], Operations: ['52+9=61', '35+83=118'] Exploring Operation: 118-61=57, Resulting Numbers: [57] 57,70 unequal: No Solution Exploring Operation: 61*118=7198, Resulting Numbers: [7198] 7198,70 unequal: No Solution Exploring Operation: 61+118=179, Resulting Numbers: [179] 179,70 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_5
mult_heuristic
[ 77, 33, 12, 17 ]
39
[ "77-33=44", "17-12=5", "44-5=39" ]
Current State: 39:[77, 33, 12, 17], Operations: [] Exploring Operation: 77-33=44, Resulting Numbers: [12, 17, 44] Generated Node #2: [12, 17, 44] from Operation: 77-33=44 Current State: 39:[12, 17, 44], Operations: ['77-33=44'] Exploring Operation: 17-12=5, Resulting Numbers: [44, 5] Generated Node #3: [44, 5] from Operation: 17-12=5 Current State: 39:[44, 5], Operations: ['77-33=44', '17-12=5'] Exploring Operation: 44-5=39, Resulting Numbers: [39] 39,39 equal: Goal Reached
4
Current State: 39:[77, 33, 12, 17], Operations: [] Exploring Operation: 33-17=16, Resulting Numbers: [77, 12, 16] Generated Node #0,0: 39:[77, 12, 16] Operation: 33-17=16 Exploring Operation: 77-12=65, Resulting Numbers: [33, 17, 65] Generated Node #0,1: 39:[33, 17, 65] Operation: 77-12=65 Exploring Operation: 77-17=60, Resulting Numbers: [33, 12, 60] Generated Node #0,2: 39:[33, 12, 60] Operation: 77-17=60 Exploring Operation: 17-12=5, Resulting Numbers: [77, 33, 5] Generated Node #0,3: 39:[77, 33, 5] Operation: 17-12=5 Exploring Operation: 77-33=44, Resulting Numbers: [12, 17, 44] Generated Node #0,4: 39:[12, 17, 44] Operation: 77-33=44 Start Sub Search at level 1: Moving to Node #0,4 Current State: 39:[12, 17, 44], Operations: ['77-33=44'] Exploring Operation: 44-17=27, Resulting Numbers: [12, 27] Generated Node #0,4,0: 39:[12, 27] Operation: 44-17=27 Exploring Operation: 17-12=5, Resulting Numbers: [44, 5] Generated Node #0,4,1: 39:[44, 5] Operation: 17-12=5 Exploring Operation: 12+44=56, Resulting Numbers: [17, 56] Generated Node #0,4,2: 39:[17, 56] Operation: 12+44=56 Exploring Operation: 44-12=32, Resulting Numbers: [17, 32] Generated Node #0,4,3: 39:[17, 32] Operation: 44-12=32 Exploring Operation: 12+17=29, Resulting Numbers: [44, 29] Generated Node #0,4,4: 39:[44, 29] Operation: 12+17=29 Moving to Node #0,4,1 Current State: 39:[44, 5], Operations: ['77-33=44', '17-12=5'] Exploring Operation: 44-5=39, Resulting Numbers: [39] 39,39 equal: Goal Reached Moving to Node #0 Current State: 39:[77, 33, 12, 17], Operations: [] Exploring Operation: 77-33=44, Resulting Numbers: [12, 17, 44] Generated Node #0,4: 39:[12, 17, 44] Operation: 77-33=44 Moving to Node #0,4 Current State: 39:[12, 17, 44], Operations: ['77-33=44'] Exploring Operation: 17-12=5, Resulting Numbers: [44, 5] Generated Node #0,4,1: 39:[44, 5] Operation: 17-12=5 Moving to Node #0,4,1 Current State: 39:[44, 5], Operations: ['77-33=44', '17-12=5'] Exploring Operation: 44-5=39, Resulting Numbers: [39] 39,39 equal: Goal Reached Exit Sub Search at level 1
0.986979
hs_5
sum_heuristic
[ 22, 45, 78, 2 ]
53
[ "45-22=23", "78-2=76", "76-23=53" ]
Current State: 53:[22, 45, 78, 2], Operations: [] Exploring Operation: 45-22=23, Resulting Numbers: [78, 2, 23] Generated Node #2: [78, 2, 23] from Operation: 45-22=23 Current State: 53:[78, 2, 23], Operations: ['45-22=23'] Exploring Operation: 78-2=76, Resulting Numbers: [23, 76] Generated Node #3: [23, 76] from Operation: 78-2=76 Current State: 53:[23, 76], Operations: ['45-22=23', '78-2=76'] Exploring Operation: 76-23=53, Resulting Numbers: [53] 53,53 equal: Goal Reached
4
Current State: 53:[22, 45, 78, 2], Operations: [] Exploring Operation: 78/2=39, Resulting Numbers: [22, 45, 39] Generated Node #0,0: 53:[22, 45, 39] Operation: 78/2=39 Exploring Operation: 22*2=44, Resulting Numbers: [45, 78, 44] Generated Node #0,1: 53:[45, 78, 44] Operation: 22*2=44 Exploring Operation: 78-22=56, Resulting Numbers: [45, 2, 56] Generated Node #0,2: 53:[45, 2, 56] Operation: 78-22=56 Exploring Operation: 22+2=24, Resulting Numbers: [45, 78, 24] Generated Node #0,3: 53:[45, 78, 24] Operation: 22+2=24 Moving to Node #0,1 Current State: 53:[45, 78, 44], Operations: ['22*2=44'] Exploring Operation: 45-44=1, Resulting Numbers: [78, 1] Generated Node #0,1,0: 53:[78, 1] Operation: 45-44=1 Exploring Operation: 45+44=89, Resulting Numbers: [78, 89] Generated Node #0,1,1: 53:[78, 89] Operation: 45+44=89 Exploring Operation: 78-45=33, Resulting Numbers: [44, 33] Generated Node #0,1,2: 53:[44, 33] Operation: 78-45=33 Exploring Operation: 78-44=34, Resulting Numbers: [45, 34] Generated Node #0,1,3: 53:[45, 34] Operation: 78-44=34 Moving to Node #0,0 Current State: 53:[22, 45, 39], Operations: ['78/2=39'] Exploring Operation: 22+45=67, Resulting Numbers: [39, 67] Generated Node #0,0,0: 53:[39, 67] Operation: 22+45=67 Exploring Operation: 39-22=17, Resulting Numbers: [45, 17] Generated Node #0,0,1: 53:[45, 17] Operation: 39-22=17 Exploring Operation: 45-22=23, Resulting Numbers: [39, 23] Generated Node #0,0,2: 53:[39, 23] Operation: 45-22=23 Exploring Operation: 22+39=61, Resulting Numbers: [45, 61] Generated Node #0,0,3: 53:[45, 61] Operation: 22+39=61 Moving to Node #0,3 Current State: 53:[45, 78, 24], Operations: ['22+2=24'] Exploring Operation: 78-45=33, Resulting Numbers: [24, 33] Generated Node #0,3,0: 53:[24, 33] Operation: 78-45=33 Exploring Operation: 45+24=69, Resulting Numbers: [78, 69] Generated Node #0,3,1: 53:[78, 69] Operation: 45+24=69 Exploring Operation: 45-24=21, Resulting Numbers: [78, 21] Generated Node #0,3,2: 53:[78, 21] Operation: 45-24=21 Exploring Operation: 78-24=54, Resulting Numbers: [45, 54] Generated Node #0,3,3: 53:[45, 54] Operation: 78-24=54 Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 53:[45, 54], Operations: ['22+2=24', '78-24=54'] Exploring Operation: 45+54=99, Resulting Numbers: [99] 99,53 unequal: No Solution Exploring Operation: 54-45=9, Resulting Numbers: [9] 9,53 unequal: No Solution Exploring Operation: 45*54=2430, Resulting Numbers: [2430] 2430,53 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 53:[78, 69], Operations: ['22+2=24', '45+24=69'] Exploring Operation: 78-69=9, Resulting Numbers: [9] 9,53 unequal: No Solution Exploring Operation: 78*69=5382, Resulting Numbers: [5382] 5382,53 unequal: No Solution Exploring Operation: 78+69=147, Resulting Numbers: [147] 147,53 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 53:[24, 33], Operations: ['22+2=24', '78-45=33'] Exploring Operation: 24+33=57, Resulting Numbers: [57] 57,53 unequal: No Solution Exploring Operation: 24*33=792, Resulting Numbers: [792] 792,53 unequal: No Solution Exploring Operation: 33-24=9, Resulting Numbers: [9] 9,53 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 53:[78, 21], Operations: ['22+2=24', '45-24=21'] Exploring Operation: 78-21=57, Resulting Numbers: [57] 57,53 unequal: No Solution Exploring Operation: 78+21=99, Resulting Numbers: [99] 99,53 unequal: No Solution Exploring Operation: 78*21=1638, Resulting Numbers: [1638] 1638,53 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,2 Current State: 53:[45, 2, 56], Operations: ['78-22=56'] Exploring Operation: 56-2=54, Resulting Numbers: [45, 54] Generated Node #0,2,0: 53:[45, 54] Operation: 56-2=54 Exploring Operation: 2+56=58, Resulting Numbers: [45, 58] Generated Node #0,2,1: 53:[45, 58] Operation: 2+56=58 Exploring Operation: 45+2=47, Resulting Numbers: [56, 47] Generated Node #0,2,2: 53:[56, 47] Operation: 45+2=47 Exploring Operation: 45-2=43, Resulting Numbers: [56, 43] Generated Node #0,2,3: 53:[56, 43] Operation: 45-2=43 Moving to Node #0,2,0 Current State: 53:[45, 54], Operations: ['78-22=56', '56-2=54'] Exploring Operation: 45*54=2430, Resulting Numbers: [2430] 2430,53 unequal: No Solution Exploring Operation: 54-45=9, Resulting Numbers: [9] 9,53 unequal: No Solution Exploring Operation: 45+54=99, Resulting Numbers: [99] 99,53 unequal: No Solution Moving to Node #0,2,2 Current State: 53:[56, 47], Operations: ['78-22=56', '45+2=47'] Exploring Operation: 56-47=9, Resulting Numbers: [9] 9,53 unequal: No Solution Exploring Operation: 56+47=103, Resulting Numbers: [103] 103,53 unequal: No Solution Exploring Operation: 56*47=2632, Resulting Numbers: [2632] 2632,53 unequal: No Solution Moving to Node #0,2,3 Current State: 53:[56, 43], Operations: ['78-22=56', '45-2=43'] Exploring Operation: 56-43=13, Resulting Numbers: [13] 13,53 unequal: No Solution Exploring Operation: 56*43=2408, Resulting Numbers: [2408] 2408,53 unequal: No Solution Exploring Operation: 56+43=99, Resulting Numbers: [99] 99,53 unequal: No Solution Moving to Node #0,2,1 Current State: 53:[45, 58], Operations: ['78-22=56', '2+56=58'] Exploring Operation: 45*58=2610, Resulting Numbers: [2610] 2610,53 unequal: No Solution Exploring Operation: 58-45=13, Resulting Numbers: [13] 13,53 unequal: No Solution Exploring Operation: 45+58=103, Resulting Numbers: [103] 103,53 unequal: No Solution Moving to Node #0,0,3 Current State: 53:[45, 61], Operations: ['78/2=39', '22+39=61'] Exploring Operation: 45+61=106, Resulting Numbers: [106] 106,53 unequal: No Solution Exploring Operation: 45*61=2745, Resulting Numbers: [2745] 2745,53 unequal: No Solution Exploring Operation: 61-45=16, Resulting Numbers: [16] 16,53 unequal: No Solution Moving to Node #0,1,3 Current State: 53:[45, 34], Operations: ['22*2=44', '78-44=34'] Exploring Operation: 45+34=79, Resulting Numbers: [79] 79,53 unequal: No Solution Exploring Operation: 45*34=1530, Resulting Numbers: [1530] 1530,53 unequal: No Solution Exploring Operation: 45-34=11, Resulting Numbers: [11] 11,53 unequal: No Solution Moving to Node #0,0,0 Current State: 53:[39, 67], Operations: ['78/2=39', '22+45=67'] Exploring Operation: 39+67=106, Resulting Numbers: [106] 106,53 unequal: No Solution Exploring Operation: 67-39=28, Resulting Numbers: [28] 28,53 unequal: No Solution Exploring Operation: 39*67=2613, Resulting Numbers: [2613] 2613,53 unequal: No Solution Moving to Node #0,1,2 Current State: 53:[44, 33], Operations: ['22*2=44', '78-45=33'] Exploring Operation: 44*33=1452, Resulting Numbers: [1452] 1452,53 unequal: No Solution Exploring Operation: 44-33=11, Resulting Numbers: [11] 11,53 unequal: No Solution Exploring Operation: 44+33=77, Resulting Numbers: [77] 77,53 unequal: No Solution Moving to Node #0,0,1 Current State: 53:[45, 17], Operations: ['78/2=39', '39-22=17'] Exploring Operation: 45-17=28, Resulting Numbers: [28] 28,53 unequal: No Solution Exploring Operation: 45*17=765, Resulting Numbers: [765] 765,53 unequal: No Solution Exploring Operation: 45+17=62, Resulting Numbers: [62] 62,53 unequal: No Solution Moving to Node #0,0,2 Current State: 53:[39, 23], Operations: ['78/2=39', '45-22=23'] Exploring Operation: 39-23=16, Resulting Numbers: [16] 16,53 unequal: No Solution Exploring Operation: 39*23=897, Resulting Numbers: [897] 897,53 unequal: No Solution Exploring Operation: 39+23=62, Resulting Numbers: [62] 62,53 unequal: No Solution Moving to Node #0,1,1 Current State: 53:[78, 89], Operations: ['22*2=44', '45+44=89'] Exploring Operation: 89-78=11, Resulting Numbers: [11] 11,53 unequal: No Solution Exploring Operation: 78*89=6942, Resulting Numbers: [6942] 6942,53 unequal: No Solution Exploring Operation: 78+89=167, Resulting Numbers: [167] 167,53 unequal: No Solution Moving to Node #0,1,0 Current State: 53:[78, 1], Operations: ['22*2=44', '45-44=1'] Exploring Operation: 78+1=79, Resulting Numbers: [79] 79,53 unequal: No Solution Exploring Operation: 78-1=77, Resulting Numbers: [77] 77,53 unequal: No Solution Exploring Operation: 78/1=78, Resulting Numbers: [78] 78,53 unequal: No Solution Exploring Operation: 78*1=78, Resulting Numbers: [78] 78,53 unequal: No Solution No solution found.
0
hs_4
mult_heuristic
[ 81, 40, 42, 39 ]
13
[ "42-39=3", "81/3=27", "40-27=13" ]
Current State: 13:[81, 40, 42, 39], Operations: [] Exploring Operation: 42-39=3, Resulting Numbers: [81, 40, 3] Generated Node #2: [81, 40, 3] from Operation: 42-39=3 Current State: 13:[81, 40, 3], Operations: ['42-39=3'] Exploring Operation: 81/3=27, Resulting Numbers: [40, 27] Generated Node #3: [40, 27] from Operation: 81/3=27 Current State: 13:[40, 27], Operations: ['42-39=3', '81/3=27'] Exploring Operation: 40-27=13, Resulting Numbers: [13] 13,13 equal: Goal Reached
4
Current State: 13:[81, 40, 42, 39], Operations: [] Exploring Operation: 81-40=41, Resulting Numbers: [42, 39, 41] Generated Node #0,0: 13:[42, 39, 41] Operation: 81-40=41 Exploring Operation: 81-42=39, Resulting Numbers: [40, 39, 39] Generated Node #0,1: 13:[40, 39, 39] Operation: 81-42=39 Start Sub Search at level 1: Moving to Node #0,1 Current State: 13:[40, 39, 39], Operations: ['81-42=39'] Exploring Operation: 40-39=1, Resulting Numbers: [39, 1] Generated Node #0,1,0: 13:[39, 1] Operation: 40-39=1 Exploring Operation: 40-39=1, Resulting Numbers: [39, 1] Generated Node #0,1,1: 13:[39, 1] Operation: 40-39=1 Moving to Node #0,1,0 Current State: 13:[39, 1], Operations: ['81-42=39', '40-39=1'] Exploring Operation: 39*1=39, Resulting Numbers: [39] 39,13 unequal: No Solution Exploring Operation: 39-1=38, Resulting Numbers: [38] 38,13 unequal: No Solution Moving to Node #0,1,1 Current State: 13:[39, 1], Operations: ['81-42=39', '40-39=1'] Exploring Operation: 39*1=39, Resulting Numbers: [39] 39,13 unequal: No Solution Exploring Operation: 39-1=38, Resulting Numbers: [38] 38,13 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 13:[42, 39, 41], Operations: ['81-40=41'] Exploring Operation: 42-41=1, Resulting Numbers: [39, 1] Generated Node #0,0,0: 13:[39, 1] Operation: 42-41=1 Exploring Operation: 42-39=3, Resulting Numbers: [41, 3] Generated Node #0,0,1: 13:[41, 3] Operation: 42-39=3 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 13:[39, 1], Operations: ['81-40=41', '42-41=1'] Exploring Operation: 39-1=38, Resulting Numbers: [38] 38,13 unequal: No Solution Exploring Operation: 39*1=39, Resulting Numbers: [39] 39,13 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 13:[41, 3], Operations: ['81-40=41', '42-39=3'] Exploring Operation: 41-3=38, Resulting Numbers: [38] 38,13 unequal: No Solution Exploring Operation: 41+3=44, Resulting Numbers: [44] 44,13 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_2
mult_heuristic
[ 30, 45, 62, 74 ]
27
[ "45-30=15", "74-62=12", "15+12=27" ]
Current State: 27:[30, 45, 62, 74], Operations: [] Exploring Operation: 45-30=15, Resulting Numbers: [62, 74, 15] Generated Node #2: [62, 74, 15] from Operation: 45-30=15 Current State: 27:[62, 74, 15], Operations: ['45-30=15'] Exploring Operation: 74-62=12, Resulting Numbers: [15, 12] Generated Node #3: [15, 12] from Operation: 74-62=12 Current State: 27:[15, 12], Operations: ['45-30=15', '74-62=12'] Exploring Operation: 15+12=27, Resulting Numbers: [27] 27,27 equal: Goal Reached
4
Current State: 27:[30, 45, 62, 74], Operations: [] Exploring Operation: 74-62=12, Resulting Numbers: [30, 45, 12] Generated Node #0,0: 27:[30, 45, 12] Operation: 74-62=12 Moving to Node #0,0 Current State: 27:[30, 45, 12], Operations: ['74-62=12'] Exploring Operation: 45-30=15, Resulting Numbers: [12, 15] Generated Node #0,0,0: 27:[12, 15] Operation: 45-30=15 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 27:[12, 15], Operations: ['74-62=12', '45-30=15'] Exploring Operation: 12+15=27, Resulting Numbers: [27] 27,27 equal: Goal Reached Moving to Node #0 Current State: 27:[30, 45, 62, 74], Operations: [] Exploring Operation: 74-62=12, Resulting Numbers: [30, 45, 12] Generated Node #0,0: 27:[30, 45, 12] Operation: 74-62=12 Moving to Node #0,0 Current State: 27:[30, 45, 12], Operations: ['74-62=12'] Exploring Operation: 45-30=15, Resulting Numbers: [12, 15] Generated Node #0,0,0: 27:[12, 15] Operation: 45-30=15 Moving to Node #0,0,0 Current State: 27:[12, 15], Operations: ['74-62=12', '45-30=15'] Exploring Operation: 12+15=27, Resulting Numbers: [27] 27,27 equal: Goal Reached Exit Sub Search at level 1
0.993924
hs_1
mult_heuristic
[ 50, 95, 11, 81 ]
34
[ "95+81=176", "176/11=16", "50-16=34" ]
Current State: 34:[50, 95, 11, 81], Operations: [] Exploring Operation: 95+81=176, Resulting Numbers: [50, 11, 176] Generated Node #2: [50, 11, 176] from Operation: 95+81=176 Current State: 34:[50, 11, 176], Operations: ['95+81=176'] Exploring Operation: 176/11=16, Resulting Numbers: [50, 16] Generated Node #3: [50, 16] from Operation: 176/11=16 Current State: 34:[50, 16], Operations: ['95+81=176', '176/11=16'] Exploring Operation: 50-16=34, Resulting Numbers: [34] 34,34 equal: Goal Reached
4
Current State: 34:[50, 95, 11, 81], Operations: [] Exploring Operation: 95-81=14, Resulting Numbers: [50, 11, 14] Generated Node #0,0: 34:[50, 11, 14] Operation: 95-81=14 Moving to Node #0,0 Current State: 34:[50, 11, 14], Operations: ['95-81=14'] Exploring Operation: 50-11=39, Resulting Numbers: [14, 39] Generated Node #0,0,0: 34:[14, 39] Operation: 50-11=39 Moving to Node #0,0,0 Current State: 34:[14, 39], Operations: ['95-81=14', '50-11=39'] Exploring Operation: 39-14=25, Resulting Numbers: [25] 25,34 unequal: No Solution No solution found.
0
hs_1
mult_heuristic
[ 1, 40, 24, 8 ]
36
[ "40-1=39", "24/8=3", "39-3=36" ]
Current State: 36:[1, 40, 24, 8], Operations: [] Exploring Operation: 40-1=39, Resulting Numbers: [24, 8, 39] Generated Node #2: [24, 8, 39] from Operation: 40-1=39 Current State: 36:[24, 8, 39], Operations: ['40-1=39'] Exploring Operation: 24/8=3, Resulting Numbers: [39, 3] Generated Node #3: [39, 3] from Operation: 24/8=3 Current State: 36:[39, 3], Operations: ['40-1=39', '24/8=3'] Exploring Operation: 39-3=36, Resulting Numbers: [36] 36,36 equal: Goal Reached
4
Current State: 36:[1, 40, 24, 8], Operations: [] Exploring Operation: 40-24=16, Resulting Numbers: [1, 8, 16] Generated Node #0,0: 36:[1, 8, 16] Operation: 40-24=16 Exploring Operation: 24/8=3, Resulting Numbers: [1, 40, 3] Generated Node #0,1: 36:[1, 40, 3] Operation: 24/8=3 Moving to Node #0,0 Current State: 36:[1, 8, 16], Operations: ['40-24=16'] Exploring Operation: 1+8=9, Resulting Numbers: [16, 9] Generated Node #0,0,0: 36:[16, 9] Operation: 1+8=9 Exploring Operation: 16/8=2, Resulting Numbers: [1, 2] Generated Node #0,0,1: 36:[1, 2] Operation: 16/8=2 Moving to Node #0,1 Current State: 36:[1, 40, 3], Operations: ['24/8=3'] Exploring Operation: 40-3=37, Resulting Numbers: [1, 37] Generated Node #0,1,0: 36:[1, 37] Operation: 40-3=37 Exploring Operation: 40-1=39, Resulting Numbers: [3, 39] Generated Node #0,1,1: 36:[3, 39] Operation: 40-1=39 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 36:[1, 37], Operations: ['24/8=3', '40-3=37'] Exploring Operation: 1*37=37, Resulting Numbers: [37] 37,36 unequal: No Solution Exploring Operation: 37-1=36, Resulting Numbers: [36] 36,36 equal: Goal Reached Moving to Node #0 Current State: 36:[1, 40, 24, 8], Operations: [] Exploring Operation: 24/8=3, Resulting Numbers: [1, 40, 3] Generated Node #0,1: 36:[1, 40, 3] Operation: 24/8=3 Moving to Node #0,1 Current State: 36:[1, 40, 3], Operations: ['24/8=3'] Exploring Operation: 40-3=37, Resulting Numbers: [1, 37] Generated Node #0,1,0: 36:[1, 37] Operation: 40-3=37 Moving to Node #0,1,0 Current State: 36:[1, 37], Operations: ['24/8=3', '40-3=37'] Exploring Operation: 37-1=36, Resulting Numbers: [36] 36,36 equal: Goal Reached Exit Sub Search at level 1
0.989583
hs_2
mult_heuristic
[ 13, 43, 11, 2 ]
17
[ "13+43=56", "56/2=28", "28-11=17" ]
Current State: 17:[13, 43, 11, 2], Operations: [] Exploring Operation: 13+43=56, Resulting Numbers: [11, 2, 56] Generated Node #2: [11, 2, 56] from Operation: 13+43=56 Current State: 17:[11, 2, 56], Operations: ['13+43=56'] Exploring Operation: 56/2=28, Resulting Numbers: [11, 28] Generated Node #3: [11, 28] from Operation: 56/2=28 Current State: 17:[11, 28], Operations: ['13+43=56', '56/2=28'] Exploring Operation: 28-11=17, Resulting Numbers: [17] 17,17 equal: Goal Reached
4
Current State: 17:[13, 43, 11, 2], Operations: [] Exploring Operation: 13+2=15, Resulting Numbers: [43, 11, 15] Generated Node #0,0: 17:[43, 11, 15] Operation: 13+2=15 Exploring Operation: 43-13=30, Resulting Numbers: [11, 2, 30] Generated Node #0,1: 17:[11, 2, 30] Operation: 43-13=30 Moving to Node #0,0 Current State: 17:[43, 11, 15], Operations: ['13+2=15'] Exploring Operation: 43-15=28, Resulting Numbers: [11, 28] Generated Node #0,0,0: 17:[11, 28] Operation: 43-15=28 Exploring Operation: 43-11=32, Resulting Numbers: [15, 32] Generated Node #0,0,1: 17:[15, 32] Operation: 43-11=32 Moving to Node #0,1 Current State: 17:[11, 2, 30], Operations: ['43-13=30'] Exploring Operation: 11+2=13, Resulting Numbers: [30, 13] Generated Node #0,1,0: 17:[30, 13] Operation: 11+2=13 Exploring Operation: 30/2=15, Resulting Numbers: [11, 15] Generated Node #0,1,1: 17:[11, 15] Operation: 30/2=15 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 17:[11, 15], Operations: ['43-13=30', '30/2=15'] Exploring Operation: 11+15=26, Resulting Numbers: [26] 26,17 unequal: No Solution Exploring Operation: 15-11=4, Resulting Numbers: [4] 4,17 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 17:[30, 13], Operations: ['43-13=30', '11+2=13'] Exploring Operation: 30+13=43, Resulting Numbers: [43] 43,17 unequal: No Solution Exploring Operation: 30-13=17, Resulting Numbers: [17] 17,17 equal: Goal Reached Moving to Node #0 Current State: 17:[13, 43, 11, 2], Operations: [] Exploring Operation: 43-13=30, Resulting Numbers: [11, 2, 30] Generated Node #0,1: 17:[11, 2, 30] Operation: 43-13=30 Moving to Node #0,1 Current State: 17:[11, 2, 30], Operations: ['43-13=30'] Exploring Operation: 11+2=13, Resulting Numbers: [30, 13] Generated Node #0,1,0: 17:[30, 13] Operation: 11+2=13 Moving to Node #0,1,0 Current State: 17:[30, 13], Operations: ['43-13=30', '11+2=13'] Exploring Operation: 30-13=17, Resulting Numbers: [17] 17,17 equal: Goal Reached Exit Sub Search at level 1
0.987847
hs_2
mult_heuristic
[ 26, 23, 44, 19 ]
75
[ "26-23=3", "44-19=25", "3*25=75" ]
Current State: 75:[26, 23, 44, 19], Operations: [] Exploring Operation: 26-23=3, Resulting Numbers: [44, 19, 3] Generated Node #2: [44, 19, 3] from Operation: 26-23=3 Current State: 75:[44, 19, 3], Operations: ['26-23=3'] Exploring Operation: 44-19=25, Resulting Numbers: [3, 25] Generated Node #3: [3, 25] from Operation: 44-19=25 Current State: 75:[3, 25], Operations: ['26-23=3', '44-19=25'] Exploring Operation: 3*25=75, Resulting Numbers: [75] 75,75 equal: Goal Reached
4
Current State: 75:[26, 23, 44, 19], Operations: [] Exploring Operation: 44-19=25, Resulting Numbers: [26, 23, 25] Generated Node #0,0: 75:[26, 23, 25] Operation: 44-19=25 Moving to Node #0,0 Current State: 75:[26, 23, 25], Operations: ['44-19=25'] Exploring Operation: 26-23=3, Resulting Numbers: [25, 3] Generated Node #0,0,0: 75:[25, 3] Operation: 26-23=3 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 75:[25, 3], Operations: ['44-19=25', '26-23=3'] Exploring Operation: 25*3=75, Resulting Numbers: [75] 75,75 equal: Goal Reached Moving to Node #0 Current State: 75:[26, 23, 44, 19], Operations: [] Exploring Operation: 44-19=25, Resulting Numbers: [26, 23, 25] Generated Node #0,0: 75:[26, 23, 25] Operation: 44-19=25 Moving to Node #0,0 Current State: 75:[26, 23, 25], Operations: ['44-19=25'] Exploring Operation: 26-23=3, Resulting Numbers: [25, 3] Generated Node #0,0,0: 75:[25, 3] Operation: 26-23=3 Moving to Node #0,0,0 Current State: 75:[25, 3], Operations: ['44-19=25', '26-23=3'] Exploring Operation: 25*3=75, Resulting Numbers: [75] 75,75 equal: Goal Reached Exit Sub Search at level 1
0.993924
hs_1
sum_heuristic
[ 17, 90, 3, 44 ]
60
[ "17+90=107", "3+44=47", "107-47=60" ]
Current State: 60:[17, 90, 3, 44], Operations: [] Exploring Operation: 17+90=107, Resulting Numbers: [3, 44, 107] Generated Node #2: [3, 44, 107] from Operation: 17+90=107 Current State: 60:[3, 44, 107], Operations: ['17+90=107'] Exploring Operation: 3+44=47, Resulting Numbers: [107, 47] Generated Node #3: [107, 47] from Operation: 3+44=47 Current State: 60:[107, 47], Operations: ['17+90=107', '3+44=47'] Exploring Operation: 107-47=60, Resulting Numbers: [60] 60,60 equal: Goal Reached
4
Current State: 60:[17, 90, 3, 44], Operations: [] Exploring Operation: 90/3=30, Resulting Numbers: [17, 44, 30] Generated Node #0,0: 60:[17, 44, 30] Operation: 90/3=30 Exploring Operation: 90-44=46, Resulting Numbers: [17, 3, 46] Generated Node #0,1: 60:[17, 3, 46] Operation: 90-44=46 Moving to Node #0,0 Current State: 60:[17, 44, 30], Operations: ['90/3=30'] Exploring Operation: 17+44=61, Resulting Numbers: [30, 61] Generated Node #0,0,0: 60:[30, 61] Operation: 17+44=61 Exploring Operation: 44-17=27, Resulting Numbers: [30, 27] Generated Node #0,0,1: 60:[30, 27] Operation: 44-17=27 Moving to Node #0,1 Current State: 60:[17, 3, 46], Operations: ['90-44=46'] Exploring Operation: 17+46=63, Resulting Numbers: [3, 63] Generated Node #0,1,0: 60:[3, 63] Operation: 17+46=63 Exploring Operation: 46-17=29, Resulting Numbers: [3, 29] Generated Node #0,1,1: 60:[3, 29] Operation: 46-17=29 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 60:[3, 29], Operations: ['90-44=46', '46-17=29'] Exploring Operation: 3+29=32, Resulting Numbers: [32] 32,60 unequal: No Solution Exploring Operation: 29-3=26, Resulting Numbers: [26] 26,60 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 60:[3, 63], Operations: ['90-44=46', '17+46=63'] Exploring Operation: 63/3=21, Resulting Numbers: [21] 21,60 unequal: No Solution Exploring Operation: 63-3=60, Resulting Numbers: [60] 60,60 equal: Goal Reached Moving to Node #0 Current State: 60:[17, 90, 3, 44], Operations: [] Exploring Operation: 90-44=46, Resulting Numbers: [17, 3, 46] Generated Node #0,1: 60:[17, 3, 46] Operation: 90-44=46 Moving to Node #0,1 Current State: 60:[17, 3, 46], Operations: ['90-44=46'] Exploring Operation: 17+46=63, Resulting Numbers: [3, 63] Generated Node #0,1,0: 60:[3, 63] Operation: 17+46=63 Moving to Node #0,1,0 Current State: 60:[3, 63], Operations: ['90-44=46', '17+46=63'] Exploring Operation: 63-3=60, Resulting Numbers: [60] 60,60 equal: Goal Reached Exit Sub Search at level 1
0.987847
hs_2
sum_heuristic
[ 28, 28, 48, 16 ]
53
[ "28+28=56", "48/16=3", "56-3=53" ]
Current State: 53:[28, 28, 48, 16], Operations: [] Exploring Operation: 28+28=56, Resulting Numbers: [48, 16, 56] Generated Node #2: [48, 16, 56] from Operation: 28+28=56 Current State: 53:[48, 16, 56], Operations: ['28+28=56'] Exploring Operation: 48/16=3, Resulting Numbers: [56, 3] Generated Node #3: [56, 3] from Operation: 48/16=3 Current State: 53:[56, 3], Operations: ['28+28=56', '48/16=3'] Exploring Operation: 56-3=53, Resulting Numbers: [53] 53,53 equal: Goal Reached
4
Current State: 53:[28, 28, 48, 16], Operations: [] Exploring Operation: 28+28=56, Resulting Numbers: [48, 16, 56] Generated Node #0,0: 53:[48, 16, 56] Operation: 28+28=56 Exploring Operation: 48+16=64, Resulting Numbers: [28, 28, 64] Generated Node #0,1: 53:[28, 28, 64] Operation: 48+16=64 Exploring Operation: 28-16=12, Resulting Numbers: [28, 48, 12] Generated Node #0,2: 53:[28, 48, 12] Operation: 28-16=12 Exploring Operation: 28+16=44, Resulting Numbers: [28, 48, 44] Generated Node #0,3: 53:[28, 48, 44] Operation: 28+16=44 Exploring Operation: 28+16=44, Resulting Numbers: [28, 48, 44] Generated Node #0,4: 53:[28, 48, 44] Operation: 28+16=44 Start Sub Search at level 1: Moving to Node #0,3 Current State: 53:[28, 48, 44], Operations: ['28+16=44'] Exploring Operation: 28+48=76, Resulting Numbers: [44, 76] Generated Node #0,3,0: 53:[44, 76] Operation: 28+48=76 Exploring Operation: 44-28=16, Resulting Numbers: [48, 16] Generated Node #0,3,1: 53:[48, 16] Operation: 44-28=16 Exploring Operation: 48-28=20, Resulting Numbers: [44, 20] Generated Node #0,3,2: 53:[44, 20] Operation: 48-28=20 Exploring Operation: 48+44=92, Resulting Numbers: [28, 92] Generated Node #0,3,3: 53:[28, 92] Operation: 48+44=92 Exploring Operation: 28+44=72, Resulting Numbers: [48, 72] Generated Node #0,3,4: 53:[48, 72] Operation: 28+44=72 Moving to Node #0,3,4 Current State: 53:[48, 72], Operations: ['28+16=44', '28+44=72'] Exploring Operation: 48+72=120, Resulting Numbers: [120] 120,53 unequal: No Solution Exploring Operation: 72-48=24, Resulting Numbers: [24] 24,53 unequal: No Solution Exploring Operation: 48*72=3456, Resulting Numbers: [3456] 3456,53 unequal: No Solution Moving to Node #0,3,0 Current State: 53:[44, 76], Operations: ['28+16=44', '28+48=76'] Exploring Operation: 44+76=120, Resulting Numbers: [120] 120,53 unequal: No Solution Exploring Operation: 76-44=32, Resulting Numbers: [32] 32,53 unequal: No Solution Exploring Operation: 44*76=3344, Resulting Numbers: [3344] 3344,53 unequal: No Solution Moving to Node #0,3,1 Current State: 53:[48, 16], Operations: ['28+16=44', '44-28=16'] Exploring Operation: 48-16=32, Resulting Numbers: [32] 32,53 unequal: No Solution Exploring Operation: 48/16=3, Resulting Numbers: [3] 3,53 unequal: No Solution Exploring Operation: 48+16=64, Resulting Numbers: [64] 64,53 unequal: No Solution Exploring Operation: 48*16=768, Resulting Numbers: [768] 768,53 unequal: No Solution Moving to Node #0,3,2 Current State: 53:[44, 20], Operations: ['28+16=44', '48-28=20'] Exploring Operation: 44-20=24, Resulting Numbers: [24] 24,53 unequal: No Solution Exploring Operation: 44+20=64, Resulting Numbers: [64] 64,53 unequal: No Solution Exploring Operation: 44*20=880, Resulting Numbers: [880] 880,53 unequal: No Solution Moving to Node #0,3,3 Current State: 53:[28, 92], Operations: ['28+16=44', '48+44=92'] Exploring Operation: 92-28=64, Resulting Numbers: [64] 64,53 unequal: No Solution Exploring Operation: 28*92=2576, Resulting Numbers: [2576] 2576,53 unequal: No Solution Exploring Operation: 28+92=120, Resulting Numbers: [120] 120,53 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4 Current State: 53:[28, 48, 44], Operations: ['28+16=44'] Exploring Operation: 48+44=92, Resulting Numbers: [28, 92] Generated Node #0,4,0: 53:[28, 92] Operation: 48+44=92 Exploring Operation: 28+44=72, Resulting Numbers: [48, 72] Generated Node #0,4,1: 53:[48, 72] Operation: 28+44=72 Exploring Operation: 44-28=16, Resulting Numbers: [48, 16] Generated Node #0,4,2: 53:[48, 16] Operation: 44-28=16 Exploring Operation: 48-28=20, Resulting Numbers: [44, 20] Generated Node #0,4,3: 53:[44, 20] Operation: 48-28=20 Exploring Operation: 28+48=76, Resulting Numbers: [44, 76] Generated Node #0,4,4: 53:[44, 76] Operation: 28+48=76 Moving to Node #0,4,1 Current State: 53:[48, 72], Operations: ['28+16=44', '28+44=72'] Exploring Operation: 48+72=120, Resulting Numbers: [120] 120,53 unequal: No Solution Exploring Operation: 48*72=3456, Resulting Numbers: [3456] 3456,53 unequal: No Solution Exploring Operation: 72-48=24, Resulting Numbers: [24] 24,53 unequal: No Solution Moving to Node #0,4,4 Current State: 53:[44, 76], Operations: ['28+16=44', '28+48=76'] Exploring Operation: 76-44=32, Resulting Numbers: [32] 32,53 unequal: No Solution Exploring Operation: 44*76=3344, Resulting Numbers: [3344] 3344,53 unequal: No Solution Exploring Operation: 44+76=120, Resulting Numbers: [120] 120,53 unequal: No Solution Moving to Node #0,4,2 Current State: 53:[48, 16], Operations: ['28+16=44', '44-28=16'] Exploring Operation: 48-16=32, Resulting Numbers: [32] 32,53 unequal: No Solution Exploring Operation: 48*16=768, Resulting Numbers: [768] 768,53 unequal: No Solution Exploring Operation: 48+16=64, Resulting Numbers: [64] 64,53 unequal: No Solution Exploring Operation: 48/16=3, Resulting Numbers: [3] 3,53 unequal: No Solution Moving to Node #0,4,3 Current State: 53:[44, 20], Operations: ['28+16=44', '48-28=20'] Exploring Operation: 44*20=880, Resulting Numbers: [880] 880,53 unequal: No Solution Exploring Operation: 44-20=24, Resulting Numbers: [24] 24,53 unequal: No Solution Exploring Operation: 44+20=64, Resulting Numbers: [64] 64,53 unequal: No Solution Moving to Node #0,4,0 Current State: 53:[28, 92], Operations: ['28+16=44', '48+44=92'] Exploring Operation: 28+92=120, Resulting Numbers: [120] 120,53 unequal: No Solution Exploring Operation: 92-28=64, Resulting Numbers: [64] 64,53 unequal: No Solution Exploring Operation: 28*92=2576, Resulting Numbers: [2576] 2576,53 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 53:[48, 16, 56], Operations: ['28+28=56'] Exploring Operation: 48+16=64, Resulting Numbers: [56, 64] Generated Node #0,0,0: 53:[56, 64] Operation: 48+16=64 Exploring Operation: 48/16=3, Resulting Numbers: [56, 3] Generated Node #0,0,1: 53:[56, 3] Operation: 48/16=3 Exploring Operation: 16+56=72, Resulting Numbers: [48, 72] Generated Node #0,0,2: 53:[48, 72] Operation: 16+56=72 Exploring Operation: 48-16=32, Resulting Numbers: [56, 32] Generated Node #0,0,3: 53:[56, 32] Operation: 48-16=32 Exploring Operation: 56-16=40, Resulting Numbers: [48, 40] Generated Node #0,0,4: 53:[48, 40] Operation: 56-16=40 Moving to Node #0,0,0 Current State: 53:[56, 64], Operations: ['28+28=56', '48+16=64'] Exploring Operation: 56+64=120, Resulting Numbers: [120] 120,53 unequal: No Solution Exploring Operation: 56*64=3584, Resulting Numbers: [3584] 3584,53 unequal: No Solution Exploring Operation: 64-56=8, Resulting Numbers: [8] 8,53 unequal: No Solution Moving to Node #0,0,4 Current State: 53:[48, 40], Operations: ['28+28=56', '56-16=40'] Exploring Operation: 48*40=1920, Resulting Numbers: [1920] 1920,53 unequal: No Solution Exploring Operation: 48-40=8, Resulting Numbers: [8] 8,53 unequal: No Solution Exploring Operation: 48+40=88, Resulting Numbers: [88] 88,53 unequal: No Solution Moving to Node #0,0,2 Current State: 53:[48, 72], Operations: ['28+28=56', '16+56=72'] Exploring Operation: 48*72=3456, Resulting Numbers: [3456] 3456,53 unequal: No Solution Exploring Operation: 48+72=120, Resulting Numbers: [120] 120,53 unequal: No Solution Exploring Operation: 72-48=24, Resulting Numbers: [24] 24,53 unequal: No Solution Moving to Node #0,0,3 Current State: 53:[56, 32], Operations: ['28+28=56', '48-16=32'] Exploring Operation: 56+32=88, Resulting Numbers: [88] 88,53 unequal: No Solution Exploring Operation: 56-32=24, Resulting Numbers: [24] 24,53 unequal: No Solution Exploring Operation: 56*32=1792, Resulting Numbers: [1792] 1792,53 unequal: No Solution Moving to Node #0,0,1 Current State: 53:[56, 3], Operations: ['28+28=56', '48/16=3'] Exploring Operation: 56*3=168, Resulting Numbers: [168] 168,53 unequal: No Solution Exploring Operation: 56+3=59, Resulting Numbers: [59] 59,53 unequal: No Solution Exploring Operation: 56-3=53, Resulting Numbers: [53] 53,53 equal: Goal Reached Moving to Node #0 Current State: 53:[28, 28, 48, 16], Operations: [] Exploring Operation: 28+28=56, Resulting Numbers: [48, 16, 56] Generated Node #0,0: 53:[48, 16, 56] Operation: 28+28=56 Moving to Node #0,0 Current State: 53:[48, 16, 56], Operations: ['28+28=56'] Exploring Operation: 48/16=3, Resulting Numbers: [56, 3] Generated Node #0,0,1: 53:[56, 3] Operation: 48/16=3 Moving to Node #0,0,1 Current State: 53:[56, 3], Operations: ['28+28=56', '48/16=3'] Exploring Operation: 56-3=53, Resulting Numbers: [53] 53,53 equal: Goal Reached Exit Sub Search at level 1
0.938368
hs_5
mult_heuristic
[ 90, 25, 69, 50 ]
46
[ "90-25=65", "69-50=19", "65-19=46" ]
Current State: 46:[90, 25, 69, 50], Operations: [] Exploring Operation: 90-25=65, Resulting Numbers: [69, 50, 65] Generated Node #2: [69, 50, 65] from Operation: 90-25=65 Current State: 46:[69, 50, 65], Operations: ['90-25=65'] Exploring Operation: 69-50=19, Resulting Numbers: [65, 19] Generated Node #3: [65, 19] from Operation: 69-50=19 Current State: 46:[65, 19], Operations: ['90-25=65', '69-50=19'] Exploring Operation: 65-19=46, Resulting Numbers: [46] 46,46 equal: Goal Reached
4
Current State: 46:[90, 25, 69, 50], Operations: [] Exploring Operation: 90-50=40, Resulting Numbers: [25, 69, 40] Generated Node #0,0: 46:[25, 69, 40] Operation: 90-50=40 Exploring Operation: 90-25=65, Resulting Numbers: [69, 50, 65] Generated Node #0,1: 46:[69, 50, 65] Operation: 90-25=65 Exploring Operation: 90-69=21, Resulting Numbers: [25, 50, 21] Generated Node #0,2: 46:[25, 50, 21] Operation: 90-69=21 Exploring Operation: 69-50=19, Resulting Numbers: [90, 25, 19] Generated Node #0,3: 46:[90, 25, 19] Operation: 69-50=19 Exploring Operation: 69-25=44, Resulting Numbers: [90, 50, 44] Generated Node #0,4: 46:[90, 50, 44] Operation: 69-25=44 Moving to Node #0,2 Current State: 46:[25, 50, 21], Operations: ['90-69=21'] Exploring Operation: 25-21=4, Resulting Numbers: [50, 4] Generated Node #0,2,0: 46:[50, 4] Operation: 25-21=4 Exploring Operation: 50/25=2, Resulting Numbers: [21, 2] Generated Node #0,2,1: 46:[21, 2] Operation: 50/25=2 Exploring Operation: 25+21=46, Resulting Numbers: [50, 46] Generated Node #0,2,2: 46:[50, 46] Operation: 25+21=46 Exploring Operation: 50-25=25, Resulting Numbers: [21, 25] Generated Node #0,2,3: 46:[21, 25] Operation: 50-25=25 Exploring Operation: 50-21=29, Resulting Numbers: [25, 29] Generated Node #0,2,4: 46:[25, 29] Operation: 50-21=29 Moving to Node #0,0 Current State: 46:[25, 69, 40], Operations: ['90-50=40'] Exploring Operation: 40-25=15, Resulting Numbers: [69, 15] Generated Node #0,0,0: 46:[69, 15] Operation: 40-25=15 Exploring Operation: 69-25=44, Resulting Numbers: [40, 44] Generated Node #0,0,1: 46:[40, 44] Operation: 69-25=44 Exploring Operation: 25+69=94, Resulting Numbers: [40, 94] Generated Node #0,0,2: 46:[40, 94] Operation: 25+69=94 Exploring Operation: 25+40=65, Resulting Numbers: [69, 65] Generated Node #0,0,3: 46:[69, 65] Operation: 25+40=65 Exploring Operation: 69-40=29, Resulting Numbers: [25, 29] Generated Node #0,0,4: 46:[25, 29] Operation: 69-40=29 Moving to Node #0,1 Current State: 46:[69, 50, 65], Operations: ['90-25=65'] Exploring Operation: 69-65=4, Resulting Numbers: [50, 4] Generated Node #0,1,0: 46:[50, 4] Operation: 69-65=4 Exploring Operation: 69+65=134, Resulting Numbers: [50, 134] Generated Node #0,1,1: 46:[50, 134] Operation: 69+65=134 Exploring Operation: 65-50=15, Resulting Numbers: [69, 15] Generated Node #0,1,2: 46:[69, 15] Operation: 65-50=15 Exploring Operation: 69+50=119, Resulting Numbers: [65, 119] Generated Node #0,1,3: 46:[65, 119] Operation: 69+50=119 Exploring Operation: 69-50=19, Resulting Numbers: [65, 19] Generated Node #0,1,4: 46:[65, 19] Operation: 69-50=19 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 46:[50, 4], Operations: ['90-25=65', '69-65=4'] Exploring Operation: 50*4=200, Resulting Numbers: [200] 200,46 unequal: No Solution Exploring Operation: 50+4=54, Resulting Numbers: [54] 54,46 unequal: No Solution Exploring Operation: 50-4=46, Resulting Numbers: [46] 46,46 equal: Goal Reached Moving to Node #0 Current State: 46:[90, 25, 69, 50], Operations: [] Exploring Operation: 90-25=65, Resulting Numbers: [69, 50, 65] Generated Node #0,1: 46:[69, 50, 65] Operation: 90-25=65 Moving to Node #0,1 Current State: 46:[69, 50, 65], Operations: ['90-25=65'] Exploring Operation: 69-65=4, Resulting Numbers: [50, 4] Generated Node #0,1,0: 46:[50, 4] Operation: 69-65=4 Moving to Node #0,1,0 Current State: 46:[50, 4], Operations: ['90-25=65', '69-65=4'] Exploring Operation: 50-4=46, Resulting Numbers: [46] 46,46 equal: Goal Reached Exit Sub Search at level 1
0.976563
hs_5
sum_heuristic
[ 94, 29, 16, 82 ]
57
[ "94+29=123", "82-16=66", "123-66=57" ]
Current State: 57:[94, 29, 16, 82], Operations: [] Exploring Operation: 94+29=123, Resulting Numbers: [16, 82, 123] Generated Node #2: [16, 82, 123] from Operation: 94+29=123 Current State: 57:[16, 82, 123], Operations: ['94+29=123'] Exploring Operation: 82-16=66, Resulting Numbers: [123, 66] Generated Node #3: [123, 66] from Operation: 82-16=66 Current State: 57:[123, 66], Operations: ['94+29=123', '82-16=66'] Exploring Operation: 123-66=57, Resulting Numbers: [57] 57,57 equal: Goal Reached
4
Current State: 57:[94, 29, 16, 82], Operations: [] Exploring Operation: 94-82=12, Resulting Numbers: [29, 16, 12] Generated Node #0,0: 57:[29, 16, 12] Operation: 94-82=12 Exploring Operation: 82-29=53, Resulting Numbers: [94, 16, 53] Generated Node #0,1: 57:[94, 16, 53] Operation: 82-29=53 Exploring Operation: 94-29=65, Resulting Numbers: [16, 82, 65] Generated Node #0,2: 57:[16, 82, 65] Operation: 94-29=65 Start Sub Search at level 1: Moving to Node #0,0 Current State: 57:[29, 16, 12], Operations: ['94-82=12'] Exploring Operation: 29-12=17, Resulting Numbers: [16, 17] Generated Node #0,0,0: 57:[16, 17] Operation: 29-12=17 Exploring Operation: 16-12=4, Resulting Numbers: [29, 4] Generated Node #0,0,1: 57:[29, 4] Operation: 16-12=4 Exploring Operation: 29-16=13, Resulting Numbers: [12, 13] Generated Node #0,0,2: 57:[12, 13] Operation: 29-16=13 Moving to Node #0,0,0 Current State: 57:[16, 17], Operations: ['94-82=12', '29-12=17'] Exploring Operation: 16*17=272, Resulting Numbers: [272] 272,57 unequal: No Solution Exploring Operation: 16+17=33, Resulting Numbers: [33] 33,57 unequal: No Solution Exploring Operation: 17-16=1, Resulting Numbers: [1] 1,57 unequal: No Solution Moving to Node #0,0,1 Current State: 57:[29, 4], Operations: ['94-82=12', '16-12=4'] Exploring Operation: 29+4=33, Resulting Numbers: [33] 33,57 unequal: No Solution Exploring Operation: 29-4=25, Resulting Numbers: [25] 25,57 unequal: No Solution Exploring Operation: 29*4=116, Resulting Numbers: [116] 116,57 unequal: No Solution Moving to Node #0,0,2 Current State: 57:[12, 13], Operations: ['94-82=12', '29-16=13'] Exploring Operation: 13-12=1, Resulting Numbers: [1] 1,57 unequal: No Solution Exploring Operation: 12+13=25, Resulting Numbers: [25] 25,57 unequal: No Solution Exploring Operation: 12*13=156, Resulting Numbers: [156] 156,57 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 57:[16, 82, 65], Operations: ['94-29=65'] Exploring Operation: 65-16=49, Resulting Numbers: [82, 49] Generated Node #0,2,0: 57:[82, 49] Operation: 65-16=49 Exploring Operation: 82-16=66, Resulting Numbers: [65, 66] Generated Node #0,2,1: 57:[65, 66] Operation: 82-16=66 Exploring Operation: 82-65=17, Resulting Numbers: [16, 17] Generated Node #0,2,2: 57:[16, 17] Operation: 82-65=17 Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 57:[16, 17], Operations: ['94-29=65', '82-65=17'] Exploring Operation: 17-16=1, Resulting Numbers: [1] 1,57 unequal: No Solution Exploring Operation: 16+17=33, Resulting Numbers: [33] 33,57 unequal: No Solution Exploring Operation: 16*17=272, Resulting Numbers: [272] 272,57 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 57:[65, 66], Operations: ['94-29=65', '82-16=66'] Exploring Operation: 65+66=131, Resulting Numbers: [131] 131,57 unequal: No Solution Exploring Operation: 65*66=4290, Resulting Numbers: [4290] 4290,57 unequal: No Solution Exploring Operation: 66-65=1, Resulting Numbers: [1] 1,57 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 57:[82, 49], Operations: ['94-29=65', '65-16=49'] Exploring Operation: 82*49=4018, Resulting Numbers: [4018] 4018,57 unequal: No Solution Exploring Operation: 82+49=131, Resulting Numbers: [131] 131,57 unequal: No Solution Exploring Operation: 82-49=33, Resulting Numbers: [33] 33,57 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 57:[94, 16, 53], Operations: ['82-29=53'] Exploring Operation: 16+53=69, Resulting Numbers: [94, 69] Generated Node #0,1,0: 57:[94, 69] Operation: 16+53=69 Exploring Operation: 94-16=78, Resulting Numbers: [53, 78] Generated Node #0,1,1: 57:[53, 78] Operation: 94-16=78 Exploring Operation: 94-53=41, Resulting Numbers: [16, 41] Generated Node #0,1,2: 57:[16, 41] Operation: 94-53=41 Moving to Node #0,1,2 Current State: 57:[16, 41], Operations: ['82-29=53', '94-53=41'] Exploring Operation: 16*41=656, Resulting Numbers: [656] 656,57 unequal: No Solution Exploring Operation: 16+41=57, Resulting Numbers: [57] 57,57 equal: Goal Reached Moving to Node #0 Current State: 57:[94, 29, 16, 82], Operations: [] Exploring Operation: 82-29=53, Resulting Numbers: [94, 16, 53] Generated Node #0,1: 57:[94, 16, 53] Operation: 82-29=53 Moving to Node #0,1 Current State: 57:[94, 16, 53], Operations: ['82-29=53'] Exploring Operation: 94-53=41, Resulting Numbers: [16, 41] Generated Node #0,1,2: 57:[16, 41] Operation: 94-53=41 Moving to Node #0,1,2 Current State: 57:[16, 41], Operations: ['82-29=53', '94-53=41'] Exploring Operation: 16+41=57, Resulting Numbers: [57] 57,57 equal: Goal Reached Exit Sub Search at level 1
0.96875
hs_3
sum_heuristic
[ 26, 5, 43, 12 ]
52
[ "26-5=21", "43-12=31", "21+31=52" ]
Current State: 52:[26, 5, 43, 12], Operations: [] Exploring Operation: 26-5=21, Resulting Numbers: [43, 12, 21] Generated Node #2: [43, 12, 21] from Operation: 26-5=21 Current State: 52:[43, 12, 21], Operations: ['26-5=21'] Exploring Operation: 43-12=31, Resulting Numbers: [21, 31] Generated Node #3: [21, 31] from Operation: 43-12=31 Current State: 52:[21, 31], Operations: ['26-5=21', '43-12=31'] Exploring Operation: 21+31=52, Resulting Numbers: [52] 52,52 equal: Goal Reached
4
Current State: 52:[26, 5, 43, 12], Operations: [] Exploring Operation: 5+43=48, Resulting Numbers: [26, 12, 48] Generated Node #0,0: 52:[26, 12, 48] Operation: 5+43=48 Exploring Operation: 43-26=17, Resulting Numbers: [5, 12, 17] Generated Node #0,1: 52:[5, 12, 17] Operation: 43-26=17 Exploring Operation: 43+12=55, Resulting Numbers: [26, 5, 55] Generated Node #0,2: 52:[26, 5, 55] Operation: 43+12=55 Exploring Operation: 43-12=31, Resulting Numbers: [26, 5, 31] Generated Node #0,3: 52:[26, 5, 31] Operation: 43-12=31 Start Sub Search at level 1: Moving to Node #0,2 Current State: 52:[26, 5, 55], Operations: ['43+12=55'] Exploring Operation: 55-26=29, Resulting Numbers: [5, 29] Generated Node #0,2,0: 52:[5, 29] Operation: 55-26=29 Exploring Operation: 55-5=50, Resulting Numbers: [26, 50] Generated Node #0,2,1: 52:[26, 50] Operation: 55-5=50 Exploring Operation: 55/5=11, Resulting Numbers: [26, 11] Generated Node #0,2,2: 52:[26, 11] Operation: 55/5=11 Exploring Operation: 26+5=31, Resulting Numbers: [55, 31] Generated Node #0,2,3: 52:[55, 31] Operation: 26+5=31 Moving to Node #0,2,1 Current State: 52:[26, 50], Operations: ['43+12=55', '55-5=50'] Exploring Operation: 50-26=24, Resulting Numbers: [24] 24,52 unequal: No Solution Exploring Operation: 26*50=1300, Resulting Numbers: [1300] 1300,52 unequal: No Solution Exploring Operation: 26+50=76, Resulting Numbers: [76] 76,52 unequal: No Solution Moving to Node #0,2,2 Current State: 52:[26, 11], Operations: ['43+12=55', '55/5=11'] Exploring Operation: 26-11=15, Resulting Numbers: [15] 15,52 unequal: No Solution Exploring Operation: 26+11=37, Resulting Numbers: [37] 37,52 unequal: No Solution Exploring Operation: 26*11=286, Resulting Numbers: [286] 286,52 unequal: No Solution Moving to Node #0,2,0 Current State: 52:[5, 29], Operations: ['43+12=55', '55-26=29'] Exploring Operation: 5*29=145, Resulting Numbers: [145] 145,52 unequal: No Solution Exploring Operation: 5+29=34, Resulting Numbers: [34] 34,52 unequal: No Solution Exploring Operation: 29-5=24, Resulting Numbers: [24] 24,52 unequal: No Solution Moving to Node #0,2,3 Current State: 52:[55, 31], Operations: ['43+12=55', '26+5=31'] Exploring Operation: 55+31=86, Resulting Numbers: [86] 86,52 unequal: No Solution Exploring Operation: 55*31=1705, Resulting Numbers: [1705] 1705,52 unequal: No Solution Exploring Operation: 55-31=24, Resulting Numbers: [24] 24,52 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 52:[26, 12, 48], Operations: ['5+43=48'] Exploring Operation: 48/12=4, Resulting Numbers: [26, 4] Generated Node #0,0,0: 52:[26, 4] Operation: 48/12=4 Exploring Operation: 26-12=14, Resulting Numbers: [48, 14] Generated Node #0,0,1: 52:[48, 14] Operation: 26-12=14 Exploring Operation: 12+48=60, Resulting Numbers: [26, 60] Generated Node #0,0,2: 52:[26, 60] Operation: 12+48=60 Exploring Operation: 48-26=22, Resulting Numbers: [12, 22] Generated Node #0,0,3: 52:[12, 22] Operation: 48-26=22 Moving to Node #0,0,0 Current State: 52:[26, 4], Operations: ['5+43=48', '48/12=4'] Exploring Operation: 26*4=104, Resulting Numbers: [104] 104,52 unequal: No Solution Exploring Operation: 26-4=22, Resulting Numbers: [22] 22,52 unequal: No Solution Exploring Operation: 26+4=30, Resulting Numbers: [30] 30,52 unequal: No Solution Moving to Node #0,0,3 Current State: 52:[12, 22], Operations: ['5+43=48', '48-26=22'] Exploring Operation: 12+22=34, Resulting Numbers: [34] 34,52 unequal: No Solution Exploring Operation: 12*22=264, Resulting Numbers: [264] 264,52 unequal: No Solution Exploring Operation: 22-12=10, Resulting Numbers: [10] 10,52 unequal: No Solution Moving to Node #0,0,1 Current State: 52:[48, 14], Operations: ['5+43=48', '26-12=14'] Exploring Operation: 48*14=672, Resulting Numbers: [672] 672,52 unequal: No Solution Exploring Operation: 48-14=34, Resulting Numbers: [34] 34,52 unequal: No Solution Exploring Operation: 48+14=62, Resulting Numbers: [62] 62,52 unequal: No Solution Moving to Node #0,0,2 Current State: 52:[26, 60], Operations: ['5+43=48', '12+48=60'] Exploring Operation: 60-26=34, Resulting Numbers: [34] 34,52 unequal: No Solution Exploring Operation: 26*60=1560, Resulting Numbers: [1560] 1560,52 unequal: No Solution Exploring Operation: 26+60=86, Resulting Numbers: [86] 86,52 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 52:[5, 12, 17], Operations: ['43-26=17'] Exploring Operation: 17-12=5, Resulting Numbers: [5, 5] Generated Node #0,1,0: 52:[5, 5] Operation: 17-12=5 Exploring Operation: 17-5=12, Resulting Numbers: [12, 12] Generated Node #0,1,1: 52:[12, 12] Operation: 17-5=12 Exploring Operation: 12+17=29, Resulting Numbers: [5, 29] Generated Node #0,1,2: 52:[5, 29] Operation: 12+17=29 Exploring Operation: 5+17=22, Resulting Numbers: [12, 22] Generated Node #0,1,3: 52:[12, 22] Operation: 5+17=22 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 52:[5, 5], Operations: ['43-26=17', '17-12=5'] Exploring Operation: 5+5=10, Resulting Numbers: [10] 10,52 unequal: No Solution Exploring Operation: 5/5=1, Resulting Numbers: [1] 1,52 unequal: No Solution Exploring Operation: 5*5=25, Resulting Numbers: [25] 25,52 unequal: No Solution Exploring Operation: 5-5=0, Resulting Numbers: [0] 0,52 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 52:[12, 12], Operations: ['43-26=17', '17-5=12'] Exploring Operation: 12+12=24, Resulting Numbers: [24] 24,52 unequal: No Solution Exploring Operation: 12/12=1, Resulting Numbers: [1] 1,52 unequal: No Solution Exploring Operation: 12*12=144, Resulting Numbers: [144] 144,52 unequal: No Solution Exploring Operation: 12-12=0, Resulting Numbers: [0] 0,52 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 52:[5, 29], Operations: ['43-26=17', '12+17=29'] Exploring Operation: 5+29=34, Resulting Numbers: [34] 34,52 unequal: No Solution Exploring Operation: 29-5=24, Resulting Numbers: [24] 24,52 unequal: No Solution Exploring Operation: 5*29=145, Resulting Numbers: [145] 145,52 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,3 Current State: 52:[12, 22], Operations: ['43-26=17', '5+17=22'] Exploring Operation: 12+22=34, Resulting Numbers: [34] 34,52 unequal: No Solution Exploring Operation: 12*22=264, Resulting Numbers: [264] 264,52 unequal: No Solution Exploring Operation: 22-12=10, Resulting Numbers: [10] 10,52 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 52:[26, 5, 31], Operations: ['43-12=31'] Exploring Operation: 31-26=5, Resulting Numbers: [5, 5] Generated Node #0,3,0: 52:[5, 5] Operation: 31-26=5 Exploring Operation: 26+31=57, Resulting Numbers: [5, 57] Generated Node #0,3,1: 52:[5, 57] Operation: 26+31=57 Exploring Operation: 31-5=26, Resulting Numbers: [26, 26] Generated Node #0,3,2: 52:[26, 26] Operation: 31-5=26 Exploring Operation: 26+5=31, Resulting Numbers: [31, 31] Generated Node #0,3,3: 52:[31, 31] Operation: 26+5=31 Start Sub Search at level 2: Moving to Node #0,3,2 Current State: 52:[26, 26], Operations: ['43-12=31', '31-5=26'] Exploring Operation: 26-26=0, Resulting Numbers: [0] 0,52 unequal: No Solution Exploring Operation: 26+26=52, Resulting Numbers: [52] 52,52 equal: Goal Reached Moving to Node #0 Current State: 52:[26, 5, 43, 12], Operations: [] Exploring Operation: 43-12=31, Resulting Numbers: [26, 5, 31] Generated Node #0,3: 52:[26, 5, 31] Operation: 43-12=31 Moving to Node #0,3 Current State: 52:[26, 5, 31], Operations: ['43-12=31'] Exploring Operation: 31-5=26, Resulting Numbers: [26, 26] Generated Node #0,3,2: 52:[26, 26] Operation: 31-5=26 Moving to Node #0,3,2 Current State: 52:[26, 26], Operations: ['43-12=31', '31-5=26'] Exploring Operation: 26+26=52, Resulting Numbers: [52] 52,52 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.944444
hs_4
mult_heuristic
[ 57, 92, 55, 76 ]
30
[ "57-55=2", "92/2=46", "76-46=30" ]
Current State: 30:[57, 92, 55, 76], Operations: [] Exploring Operation: 57-55=2, Resulting Numbers: [92, 76, 2] Generated Node #2: [92, 76, 2] from Operation: 57-55=2 Current State: 30:[92, 76, 2], Operations: ['57-55=2'] Exploring Operation: 92/2=46, Resulting Numbers: [76, 46] Generated Node #3: [76, 46] from Operation: 92/2=46 Current State: 30:[76, 46], Operations: ['57-55=2', '92/2=46'] Exploring Operation: 76-46=30, Resulting Numbers: [30] 30,30 equal: Goal Reached
4
Current State: 30:[57, 92, 55, 76], Operations: [] Exploring Operation: 92-76=16, Resulting Numbers: [57, 55, 16] Generated Node #0,0: 30:[57, 55, 16] Operation: 92-76=16 Start Sub Search at level 1: Moving to Node #0,0 Current State: 30:[57, 55, 16], Operations: ['92-76=16'] Exploring Operation: 57-55=2, Resulting Numbers: [16, 2] Generated Node #0,0,0: 30:[16, 2] Operation: 57-55=2 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 30:[16, 2], Operations: ['92-76=16', '57-55=2'] Exploring Operation: 16-2=14, Resulting Numbers: [14] 14,30 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
sum_heuristic
[ 15, 45, 96, 36 ]
44
[ "45/15=3", "96+36=132", "132/3=44" ]
Current State: 44:[15, 45, 96, 36], Operations: [] Exploring Operation: 45/15=3, Resulting Numbers: [96, 36, 3] Generated Node #2: [96, 36, 3] from Operation: 45/15=3 Current State: 44:[96, 36, 3], Operations: ['45/15=3'] Exploring Operation: 96+36=132, Resulting Numbers: [3, 132] Generated Node #3: [3, 132] from Operation: 96+36=132 Current State: 44:[3, 132], Operations: ['45/15=3', '96+36=132'] Exploring Operation: 132/3=44, Resulting Numbers: [44] 44,44 equal: Goal Reached
4
Current State: 44:[15, 45, 96, 36], Operations: [] Exploring Operation: 96-45=51, Resulting Numbers: [15, 36, 51] Generated Node #0,0: 44:[15, 36, 51] Operation: 96-45=51 Start Sub Search at level 1: Moving to Node #0,0 Current State: 44:[15, 36, 51], Operations: ['96-45=51'] Exploring Operation: 36-15=21, Resulting Numbers: [51, 21] Generated Node #0,0,0: 44:[51, 21] Operation: 36-15=21 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 44:[51, 21], Operations: ['96-45=51', '36-15=21'] Exploring Operation: 51-21=30, Resulting Numbers: [30] 30,44 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
mult_heuristic
[ 69, 25, 6, 75 ]
25
[ "69+25=94", "75-6=69", "94-69=25" ]
Current State: 25:[69, 25, 6, 75], Operations: [] Exploring Operation: 69+25=94, Resulting Numbers: [6, 75, 94] Generated Node #2: [6, 75, 94] from Operation: 69+25=94 Current State: 25:[6, 75, 94], Operations: ['69+25=94'] Exploring Operation: 75-6=69, Resulting Numbers: [94, 69] Generated Node #3: [94, 69] from Operation: 75-6=69 Current State: 25:[94, 69], Operations: ['69+25=94', '75-6=69'] Exploring Operation: 94-69=25, Resulting Numbers: [25] 25,25 equal: Goal Reached
4
Current State: 25:[69, 25, 6, 75], Operations: [] Exploring Operation: 75/25=3, Resulting Numbers: [69, 6, 3] Generated Node #0,0: 25:[69, 6, 3] Operation: 75/25=3 Exploring Operation: 75-69=6, Resulting Numbers: [25, 6, 6] Generated Node #0,1: 25:[25, 6, 6] Operation: 75-69=6 Exploring Operation: 69-25=44, Resulting Numbers: [6, 75, 44] Generated Node #0,2: 25:[6, 75, 44] Operation: 69-25=44 Moving to Node #0,1 Current State: 25:[25, 6, 6], Operations: ['75-69=6'] Exploring Operation: 25+6=31, Resulting Numbers: [6, 31] Generated Node #0,1,0: 25:[6, 31] Operation: 25+6=31 Exploring Operation: 6-6=0, Resulting Numbers: [25, 0] Generated Node #0,1,1: 25:[25, 0] Operation: 6-6=0 Exploring Operation: 6/6=1, Resulting Numbers: [25, 1] Generated Node #0,1,2: 25:[25, 1] Operation: 6/6=1 Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 25:[25, 1], Operations: ['75-69=6', '6/6=1'] Exploring Operation: 25+1=26, Resulting Numbers: [26] 26,25 unequal: No Solution Exploring Operation: 25*1=25, Resulting Numbers: [25] 25,25 equal: Goal Reached Moving to Node #0 Current State: 25:[69, 25, 6, 75], Operations: [] Exploring Operation: 75-69=6, Resulting Numbers: [25, 6, 6] Generated Node #0,1: 25:[25, 6, 6] Operation: 75-69=6 Moving to Node #0,1 Current State: 25:[25, 6, 6], Operations: ['75-69=6'] Exploring Operation: 6/6=1, Resulting Numbers: [25, 1] Generated Node #0,1,2: 25:[25, 1] Operation: 6/6=1 Moving to Node #0,1,2 Current State: 25:[25, 1], Operations: ['75-69=6', '6/6=1'] Exploring Operation: 25*1=25, Resulting Numbers: [25] 25,25 equal: Goal Reached Exit Sub Search at level 1
0.989583
hs_3
sum_heuristic
[ 49, 93, 19, 99 ]
74
[ "93-49=44", "19+99=118", "118-44=74" ]
Current State: 74:[49, 93, 19, 99], Operations: [] Exploring Operation: 93-49=44, Resulting Numbers: [19, 99, 44] Generated Node #2: [19, 99, 44] from Operation: 93-49=44 Current State: 74:[19, 99, 44], Operations: ['93-49=44'] Exploring Operation: 19+99=118, Resulting Numbers: [44, 118] Generated Node #3: [44, 118] from Operation: 19+99=118 Current State: 74:[44, 118], Operations: ['93-49=44', '19+99=118'] Exploring Operation: 118-44=74, Resulting Numbers: [74] 74,74 equal: Goal Reached
4
Current State: 74:[49, 93, 19, 99], Operations: [] Exploring Operation: 99-93=6, Resulting Numbers: [49, 19, 6] Generated Node #0,0: 74:[49, 19, 6] Operation: 99-93=6 Exploring Operation: 99-19=80, Resulting Numbers: [49, 93, 80] Generated Node #0,1: 74:[49, 93, 80] Operation: 99-19=80 Exploring Operation: 93-19=74, Resulting Numbers: [49, 99, 74] Generated Node #0,2: 74:[49, 99, 74] Operation: 93-19=74 Moving to Node #0,0 Current State: 74:[49, 19, 6], Operations: ['99-93=6'] Exploring Operation: 49-19=30, Resulting Numbers: [6, 30] Generated Node #0,0,0: 74:[6, 30] Operation: 49-19=30 Exploring Operation: 49-6=43, Resulting Numbers: [19, 43] Generated Node #0,0,1: 74:[19, 43] Operation: 49-6=43 Exploring Operation: 49+19=68, Resulting Numbers: [6, 68] Generated Node #0,0,2: 74:[6, 68] Operation: 49+19=68 Moving to Node #0,1 Current State: 74:[49, 93, 80], Operations: ['99-19=80'] Exploring Operation: 80-49=31, Resulting Numbers: [93, 31] Generated Node #0,1,0: 74:[93, 31] Operation: 80-49=31 Exploring Operation: 93-49=44, Resulting Numbers: [80, 44] Generated Node #0,1,1: 74:[80, 44] Operation: 93-49=44 Exploring Operation: 93-80=13, Resulting Numbers: [49, 13] Generated Node #0,1,2: 74:[49, 13] Operation: 93-80=13 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 74:[80, 44], Operations: ['99-19=80', '93-49=44'] Exploring Operation: 80+44=124, Resulting Numbers: [124] 124,74 unequal: No Solution Exploring Operation: 80-44=36, Resulting Numbers: [36] 36,74 unequal: No Solution Exploring Operation: 80*44=3520, Resulting Numbers: [3520] 3520,74 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 74:[49, 13], Operations: ['99-19=80', '93-80=13'] Exploring Operation: 49-13=36, Resulting Numbers: [36] 36,74 unequal: No Solution Exploring Operation: 49*13=637, Resulting Numbers: [637] 637,74 unequal: No Solution Exploring Operation: 49+13=62, Resulting Numbers: [62] 62,74 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 74:[93, 31], Operations: ['99-19=80', '80-49=31'] Exploring Operation: 93-31=62, Resulting Numbers: [62] 62,74 unequal: No Solution Exploring Operation: 93+31=124, Resulting Numbers: [124] 124,74 unequal: No Solution Exploring Operation: 93/31=3, Resulting Numbers: [3] 3,74 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,2 Current State: 74:[49, 99, 74], Operations: ['93-19=74'] Exploring Operation: 74-49=25, Resulting Numbers: [99, 25] Generated Node #0,2,0: 74:[99, 25] Operation: 74-49=25 Exploring Operation: 99-74=25, Resulting Numbers: [49, 25] Generated Node #0,2,1: 74:[49, 25] Operation: 99-74=25 Exploring Operation: 99-49=50, Resulting Numbers: [74, 50] Generated Node #0,2,2: 74:[74, 50] Operation: 99-49=50 Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 74:[74, 50], Operations: ['93-19=74', '99-49=50'] Exploring Operation: 74-50=24, Resulting Numbers: [24] 24,74 unequal: No Solution Exploring Operation: 74*50=3700, Resulting Numbers: [3700] 3700,74 unequal: No Solution Exploring Operation: 74+50=124, Resulting Numbers: [124] 124,74 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 74:[49, 25], Operations: ['93-19=74', '99-74=25'] Exploring Operation: 49+25=74, Resulting Numbers: [74] 74,74 equal: Goal Reached Moving to Node #0 Current State: 74:[49, 93, 19, 99], Operations: [] Exploring Operation: 93-19=74, Resulting Numbers: [49, 99, 74] Generated Node #0,2: 74:[49, 99, 74] Operation: 93-19=74 Moving to Node #0,2 Current State: 74:[49, 99, 74], Operations: ['93-19=74'] Exploring Operation: 99-74=25, Resulting Numbers: [49, 25] Generated Node #0,2,1: 74:[49, 25] Operation: 99-74=25 Moving to Node #0,2,1 Current State: 74:[49, 25], Operations: ['93-19=74', '99-74=25'] Exploring Operation: 49+25=74, Resulting Numbers: [74] 74,74 equal: Goal Reached Exit Sub Search at level 1
0.974826
hs_3
mult_heuristic
[ 33, 8, 39, 24 ]
15
[ "33+39=72", "72/8=9", "24-9=15" ]
Current State: 15:[33, 8, 39, 24], Operations: [] Exploring Operation: 33+39=72, Resulting Numbers: [8, 24, 72] Generated Node #2: [8, 24, 72] from Operation: 33+39=72 Current State: 15:[8, 24, 72], Operations: ['33+39=72'] Exploring Operation: 72/8=9, Resulting Numbers: [24, 9] Generated Node #3: [24, 9] from Operation: 72/8=9 Current State: 15:[24, 9], Operations: ['33+39=72', '72/8=9'] Exploring Operation: 24-9=15, Resulting Numbers: [15] 15,15 equal: Goal Reached
4
Current State: 15:[33, 8, 39, 24], Operations: [] Exploring Operation: 24/8=3, Resulting Numbers: [33, 39, 3] Generated Node #0,0: 15:[33, 39, 3] Operation: 24/8=3 Exploring Operation: 33-24=9, Resulting Numbers: [8, 39, 9] Generated Node #0,1: 15:[8, 39, 9] Operation: 33-24=9 Exploring Operation: 39-33=6, Resulting Numbers: [8, 24, 6] Generated Node #0,2: 15:[8, 24, 6] Operation: 39-33=6 Exploring Operation: 39-24=15, Resulting Numbers: [33, 8, 15] Generated Node #0,3: 15:[33, 8, 15] Operation: 39-24=15 Exploring Operation: 33-8=25, Resulting Numbers: [39, 24, 25] Generated Node #0,4: 15:[39, 24, 25] Operation: 33-8=25 Moving to Node #0,2 Current State: 15:[8, 24, 6], Operations: ['39-33=6'] Exploring Operation: 24-6=18, Resulting Numbers: [8, 18] Generated Node #0,2,0: 15:[8, 18] Operation: 24-6=18 Exploring Operation: 24-8=16, Resulting Numbers: [6, 16] Generated Node #0,2,1: 15:[6, 16] Operation: 24-8=16 Exploring Operation: 8+6=14, Resulting Numbers: [24, 14] Generated Node #0,2,2: 15:[24, 14] Operation: 8+6=14 Exploring Operation: 24/6=4, Resulting Numbers: [8, 4] Generated Node #0,2,3: 15:[8, 4] Operation: 24/6=4 Exploring Operation: 24/8=3, Resulting Numbers: [6, 3] Generated Node #0,2,4: 15:[6, 3] Operation: 24/8=3 Start Sub Search at level 1: Moving to Node #0,2,4 Current State: 15:[6, 3], Operations: ['39-33=6', '24/8=3'] Exploring Operation: 6-3=3, Resulting Numbers: [3] 3,15 unequal: No Solution Exploring Operation: 6/3=2, Resulting Numbers: [2] 2,15 unequal: No Solution Exploring Operation: 6*3=18, Resulting Numbers: [18] 18,15 unequal: No Solution Exploring Operation: 6+3=9, Resulting Numbers: [9] 9,15 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 15:[6, 16], Operations: ['39-33=6', '24-8=16'] Exploring Operation: 6+16=22, Resulting Numbers: [22] 22,15 unequal: No Solution Exploring Operation: 16-6=10, Resulting Numbers: [10] 10,15 unequal: No Solution Exploring Operation: 6*16=96, Resulting Numbers: [96] 96,15 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 15:[8, 4], Operations: ['39-33=6', '24/6=4'] Exploring Operation: 8+4=12, Resulting Numbers: [12] 12,15 unequal: No Solution Exploring Operation: 8-4=4, Resulting Numbers: [4] 4,15 unequal: No Solution Exploring Operation: 8*4=32, Resulting Numbers: [32] 32,15 unequal: No Solution Exploring Operation: 8/4=2, Resulting Numbers: [2] 2,15 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 15:[8, 18], Operations: ['39-33=6', '24-6=18'] Exploring Operation: 18-8=10, Resulting Numbers: [10] 10,15 unequal: No Solution Exploring Operation: 8*18=144, Resulting Numbers: [144] 144,15 unequal: No Solution Exploring Operation: 8+18=26, Resulting Numbers: [26] 26,15 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 15:[24, 14], Operations: ['39-33=6', '8+6=14'] Exploring Operation: 24+14=38, Resulting Numbers: [38] 38,15 unequal: No Solution Exploring Operation: 24*14=336, Resulting Numbers: [336] 336,15 unequal: No Solution Exploring Operation: 24-14=10, Resulting Numbers: [10] 10,15 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,3 Current State: 15:[33, 8, 15], Operations: ['39-24=15'] Exploring Operation: 33+8=41, Resulting Numbers: [15, 41] Generated Node #0,3,0: 15:[15, 41] Operation: 33+8=41 Exploring Operation: 33-8=25, Resulting Numbers: [15, 25] Generated Node #0,3,1: 15:[15, 25] Operation: 33-8=25 Exploring Operation: 15-8=7, Resulting Numbers: [33, 7] Generated Node #0,3,2: 15:[33, 7] Operation: 15-8=7 Exploring Operation: 33-15=18, Resulting Numbers: [8, 18] Generated Node #0,3,3: 15:[8, 18] Operation: 33-15=18 Exploring Operation: 8+15=23, Resulting Numbers: [33, 23] Generated Node #0,3,4: 15:[33, 23] Operation: 8+15=23 Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 15:[8, 18], Operations: ['39-24=15', '33-15=18'] Exploring Operation: 8*18=144, Resulting Numbers: [144] 144,15 unequal: No Solution Exploring Operation: 18-8=10, Resulting Numbers: [10] 10,15 unequal: No Solution Exploring Operation: 8+18=26, Resulting Numbers: [26] 26,15 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 15:[15, 25], Operations: ['39-24=15', '33-8=25'] Exploring Operation: 15*25=375, Resulting Numbers: [375] 375,15 unequal: No Solution Exploring Operation: 15+25=40, Resulting Numbers: [40] 40,15 unequal: No Solution Exploring Operation: 25-15=10, Resulting Numbers: [10] 10,15 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 15:[33, 7], Operations: ['39-24=15', '15-8=7'] Exploring Operation: 33+7=40, Resulting Numbers: [40] 40,15 unequal: No Solution Exploring Operation: 33-7=26, Resulting Numbers: [26] 26,15 unequal: No Solution Exploring Operation: 33*7=231, Resulting Numbers: [231] 231,15 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 15:[15, 41], Operations: ['39-24=15', '33+8=41'] Exploring Operation: 15+41=56, Resulting Numbers: [56] 56,15 unequal: No Solution Exploring Operation: 15*41=615, Resulting Numbers: [615] 615,15 unequal: No Solution Exploring Operation: 41-15=26, Resulting Numbers: [26] 26,15 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,4 Current State: 15:[33, 23], Operations: ['39-24=15', '8+15=23'] Exploring Operation: 33*23=759, Resulting Numbers: [759] 759,15 unequal: No Solution Exploring Operation: 33-23=10, Resulting Numbers: [10] 10,15 unequal: No Solution Exploring Operation: 33+23=56, Resulting Numbers: [56] 56,15 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1 Current State: 15:[8, 39, 9], Operations: ['33-24=9'] Exploring Operation: 39-8=31, Resulting Numbers: [9, 31] Generated Node #0,1,0: 15:[9, 31] Operation: 39-8=31 Exploring Operation: 39-9=30, Resulting Numbers: [8, 30] Generated Node #0,1,1: 15:[8, 30] Operation: 39-9=30 Exploring Operation: 8+9=17, Resulting Numbers: [39, 17] Generated Node #0,1,2: 15:[39, 17] Operation: 8+9=17 Exploring Operation: 9-8=1, Resulting Numbers: [39, 1] Generated Node #0,1,3: 15:[39, 1] Operation: 9-8=1 Exploring Operation: 8+39=47, Resulting Numbers: [9, 47] Generated Node #0,1,4: 15:[9, 47] Operation: 8+39=47 Moving to Node #0,0 Current State: 15:[33, 39, 3], Operations: ['24/8=3'] Exploring Operation: 39-33=6, Resulting Numbers: [3, 6] Generated Node #0,0,0: 15:[3, 6] Operation: 39-33=6 Exploring Operation: 39/3=13, Resulting Numbers: [33, 13] Generated Node #0,0,1: 15:[33, 13] Operation: 39/3=13 Exploring Operation: 33/3=11, Resulting Numbers: [39, 11] Generated Node #0,0,2: 15:[39, 11] Operation: 33/3=11 Exploring Operation: 39-3=36, Resulting Numbers: [33, 36] Generated Node #0,0,3: 15:[33, 36] Operation: 39-3=36 Exploring Operation: 33-3=30, Resulting Numbers: [39, 30] Generated Node #0,0,4: 15:[39, 30] Operation: 33-3=30 Moving to Node #0,4 Current State: 15:[39, 24, 25], Operations: ['33-8=25'] Exploring Operation: 25-24=1, Resulting Numbers: [39, 1] Generated Node #0,4,0: 15:[39, 1] Operation: 25-24=1 Exploring Operation: 39-24=15, Resulting Numbers: [25, 15] Generated Node #0,4,1: 15:[25, 15] Operation: 39-24=15 Exploring Operation: 39+24=63, Resulting Numbers: [25, 63] Generated Node #0,4,2: 15:[25, 63] Operation: 39+24=63 Exploring Operation: 39+25=64, Resulting Numbers: [24, 64] Generated Node #0,4,3: 15:[24, 64] Operation: 39+25=64 Exploring Operation: 39-25=14, Resulting Numbers: [24, 14] Generated Node #0,4,4: 15:[24, 14] Operation: 39-25=14 Start Sub Search at level 1: Moving to Node #0,4,1 Current State: 15:[25, 15], Operations: ['33-8=25', '39-24=15'] Exploring Operation: 25*15=375, Resulting Numbers: [375] 375,15 unequal: No Solution Exploring Operation: 25+15=40, Resulting Numbers: [40] 40,15 unequal: No Solution Exploring Operation: 25-15=10, Resulting Numbers: [10] 10,15 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,4 Current State: 15:[24, 14], Operations: ['33-8=25', '39-25=14'] Exploring Operation: 24-14=10, Resulting Numbers: [10] 10,15 unequal: No Solution Exploring Operation: 24+14=38, Resulting Numbers: [38] 38,15 unequal: No Solution Exploring Operation: 24*14=336, Resulting Numbers: [336] 336,15 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,0 Current State: 15:[39, 1], Operations: ['33-8=25', '25-24=1'] Exploring Operation: 39*1=39, Resulting Numbers: [39] 39,15 unequal: No Solution Exploring Operation: 39/1=39, Resulting Numbers: [39] 39,15 unequal: No Solution Exploring Operation: 39-1=38, Resulting Numbers: [38] 38,15 unequal: No Solution Exploring Operation: 39+1=40, Resulting Numbers: [40] 40,15 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,2 Current State: 15:[25, 63], Operations: ['33-8=25', '39+24=63'] Exploring Operation: 25+63=88, Resulting Numbers: [88] 88,15 unequal: No Solution Exploring Operation: 63-25=38, Resulting Numbers: [38] 38,15 unequal: No Solution Exploring Operation: 25*63=1575, Resulting Numbers: [1575] 1575,15 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,3 Current State: 15:[24, 64], Operations: ['33-8=25', '39+25=64'] Exploring Operation: 24+64=88, Resulting Numbers: [88] 88,15 unequal: No Solution Exploring Operation: 24*64=1536, Resulting Numbers: [1536] 1536,15 unequal: No Solution Exploring Operation: 64-24=40, Resulting Numbers: [40] 40,15 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,0,0 Current State: 15:[3, 6], Operations: ['24/8=3', '39-33=6'] Exploring Operation: 6/3=2, Resulting Numbers: [2] 2,15 unequal: No Solution Exploring Operation: 3+6=9, Resulting Numbers: [9] 9,15 unequal: No Solution Exploring Operation: 3*6=18, Resulting Numbers: [18] 18,15 unequal: No Solution Exploring Operation: 6-3=3, Resulting Numbers: [3] 3,15 unequal: No Solution Moving to Node #0,1,1 Current State: 15:[8, 30], Operations: ['33-24=9', '39-9=30'] Exploring Operation: 8*30=240, Resulting Numbers: [240] 240,15 unequal: No Solution Exploring Operation: 30-8=22, Resulting Numbers: [22] 22,15 unequal: No Solution Exploring Operation: 8+30=38, Resulting Numbers: [38] 38,15 unequal: No Solution Moving to Node #0,0,1 Current State: 15:[33, 13], Operations: ['24/8=3', '39/3=13'] Exploring Operation: 33-13=20, Resulting Numbers: [20] 20,15 unequal: No Solution Exploring Operation: 33+13=46, Resulting Numbers: [46] 46,15 unequal: No Solution Exploring Operation: 33*13=429, Resulting Numbers: [429] 429,15 unequal: No Solution Moving to Node #0,1,0 Current State: 15:[9, 31], Operations: ['33-24=9', '39-8=31'] Exploring Operation: 31-9=22, Resulting Numbers: [22] 22,15 unequal: No Solution Exploring Operation: 9*31=279, Resulting Numbers: [279] 279,15 unequal: No Solution Exploring Operation: 9+31=40, Resulting Numbers: [40] 40,15 unequal: No Solution Moving to Node #0,1,2 Current State: 15:[39, 17], Operations: ['33-24=9', '8+9=17'] Exploring Operation: 39+17=56, Resulting Numbers: [56] 56,15 unequal: No Solution Exploring Operation: 39-17=22, Resulting Numbers: [22] 22,15 unequal: No Solution Exploring Operation: 39*17=663, Resulting Numbers: [663] 663,15 unequal: No Solution Moving to Node #0,1,3 Current State: 15:[39, 1], Operations: ['33-24=9', '9-8=1'] Exploring Operation: 39/1=39, Resulting Numbers: [39] 39,15 unequal: No Solution Exploring Operation: 39-1=38, Resulting Numbers: [38] 38,15 unequal: No Solution Exploring Operation: 39+1=40, Resulting Numbers: [40] 40,15 unequal: No Solution Exploring Operation: 39*1=39, Resulting Numbers: [39] 39,15 unequal: No Solution Moving to Node #0,0,2 Current State: 15:[39, 11], Operations: ['24/8=3', '33/3=11'] Exploring Operation: 39*11=429, Resulting Numbers: [429] 429,15 unequal: No Solution Exploring Operation: 39+11=50, Resulting Numbers: [50] 50,15 unequal: No Solution Exploring Operation: 39-11=28, Resulting Numbers: [28] 28,15 unequal: No Solution Moving to Node #0,1,4 Current State: 15:[9, 47], Operations: ['33-24=9', '8+39=47'] Exploring Operation: 47-9=38, Resulting Numbers: [38] 38,15 unequal: No Solution Exploring Operation: 9*47=423, Resulting Numbers: [423] 423,15 unequal: No Solution Exploring Operation: 9+47=56, Resulting Numbers: [56] 56,15 unequal: No Solution Moving to Node #0,0,4 Current State: 15:[39, 30], Operations: ['24/8=3', '33-3=30'] Exploring Operation: 39+30=69, Resulting Numbers: [69] 69,15 unequal: No Solution Exploring Operation: 39*30=1170, Resulting Numbers: [1170] 1170,15 unequal: No Solution Exploring Operation: 39-30=9, Resulting Numbers: [9] 9,15 unequal: No Solution Moving to Node #0,0,3 Current State: 15:[33, 36], Operations: ['24/8=3', '39-3=36'] Exploring Operation: 36-33=3, Resulting Numbers: [3] 3,15 unequal: No Solution Exploring Operation: 33*36=1188, Resulting Numbers: [1188] 1188,15 unequal: No Solution Exploring Operation: 33+36=69, Resulting Numbers: [69] 69,15 unequal: No Solution No solution found.
0
hs_5
mult_heuristic
[ 45, 75, 14, 61 ]
17
[ "75-45=30", "61-14=47", "47-30=17" ]
Current State: 17:[45, 75, 14, 61], Operations: [] Exploring Operation: 75-45=30, Resulting Numbers: [14, 61, 30] Generated Node #2: [14, 61, 30] from Operation: 75-45=30 Current State: 17:[14, 61, 30], Operations: ['75-45=30'] Exploring Operation: 61-14=47, Resulting Numbers: [30, 47] Generated Node #3: [30, 47] from Operation: 61-14=47 Current State: 17:[30, 47], Operations: ['75-45=30', '61-14=47'] Exploring Operation: 47-30=17, Resulting Numbers: [17] 17,17 equal: Goal Reached
4
Current State: 17:[45, 75, 14, 61], Operations: [] Exploring Operation: 61-45=16, Resulting Numbers: [75, 14, 16] Generated Node #0,0: 17:[75, 14, 16] Operation: 61-45=16 Exploring Operation: 45-14=31, Resulting Numbers: [75, 61, 31] Generated Node #0,1: 17:[75, 61, 31] Operation: 45-14=31 Exploring Operation: 75-14=61, Resulting Numbers: [45, 61, 61] Generated Node #0,2: 17:[45, 61, 61] Operation: 75-14=61 Exploring Operation: 75-45=30, Resulting Numbers: [14, 61, 30] Generated Node #0,3: 17:[14, 61, 30] Operation: 75-45=30 Exploring Operation: 75-61=14, Resulting Numbers: [45, 14, 14] Generated Node #0,4: 17:[45, 14, 14] Operation: 75-61=14 Start Sub Search at level 1: Moving to Node #0,4 Current State: 17:[45, 14, 14], Operations: ['75-61=14'] Exploring Operation: 14/14=1, Resulting Numbers: [45, 1] Generated Node #0,4,0: 17:[45, 1] Operation: 14/14=1 Exploring Operation: 14+14=28, Resulting Numbers: [45, 28] Generated Node #0,4,1: 17:[45, 28] Operation: 14+14=28 Exploring Operation: 45+14=59, Resulting Numbers: [14, 59] Generated Node #0,4,2: 17:[14, 59] Operation: 45+14=59 Exploring Operation: 45-14=31, Resulting Numbers: [14, 31] Generated Node #0,4,3: 17:[14, 31] Operation: 45-14=31 Exploring Operation: 45-14=31, Resulting Numbers: [14, 31] Generated Node #0,4,4: 17:[14, 31] Operation: 45-14=31 Moving to Node #0,4,3 Current State: 17:[14, 31], Operations: ['75-61=14', '45-14=31'] Exploring Operation: 31-14=17, Resulting Numbers: [17] 17,17 equal: Goal Reached Moving to Node #0 Current State: 17:[45, 75, 14, 61], Operations: [] Exploring Operation: 75-61=14, Resulting Numbers: [45, 14, 14] Generated Node #0,4: 17:[45, 14, 14] Operation: 75-61=14 Moving to Node #0,4 Current State: 17:[45, 14, 14], Operations: ['75-61=14'] Exploring Operation: 45-14=31, Resulting Numbers: [14, 31] Generated Node #0,4,3: 17:[14, 31] Operation: 45-14=31 Moving to Node #0,4,3 Current State: 17:[14, 31], Operations: ['75-61=14', '45-14=31'] Exploring Operation: 31-14=17, Resulting Numbers: [17] 17,17 equal: Goal Reached Exit Sub Search at level 1
0.986979
hs_5
sum_heuristic
[ 3, 22, 99, 27 ]
18
[ "3*22=66", "27*66=1782", "1782/99=18" ]
Current State: 18:[3, 22, 99, 27], Operations: [] Exploring Operation: 3*22=66, Resulting Numbers: [99, 27, 66] Generated Node #2: [99, 27, 66] from Operation: 3*22=66 Current State: 18:[99, 27, 66], Operations: ['3*22=66'] Exploring Operation: 27*66=1782, Resulting Numbers: [99, 1782] Generated Node #3: [99, 1782] from Operation: 27*66=1782 Current State: 18:[99, 1782], Operations: ['3*22=66', '27*66=1782'] Exploring Operation: 1782/99=18, Resulting Numbers: [18] 18,18 equal: Goal Reached
4
Current State: 18:[3, 22, 99, 27], Operations: [] Exploring Operation: 99-27=72, Resulting Numbers: [3, 22, 72] Generated Node #0,0: 18:[3, 22, 72] Operation: 99-27=72 Exploring Operation: 99/3=33, Resulting Numbers: [22, 27, 33] Generated Node #0,1: 18:[22, 27, 33] Operation: 99/3=33 Start Sub Search at level 1: Moving to Node #0,1 Current State: 18:[22, 27, 33], Operations: ['99/3=33'] Exploring Operation: 33-22=11, Resulting Numbers: [27, 11] Generated Node #0,1,0: 18:[27, 11] Operation: 33-22=11 Exploring Operation: 33-27=6, Resulting Numbers: [22, 6] Generated Node #0,1,1: 18:[22, 6] Operation: 33-27=6 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 18:[22, 6], Operations: ['99/3=33', '33-27=6'] Exploring Operation: 22-6=16, Resulting Numbers: [16] 16,18 unequal: No Solution Exploring Operation: 22+6=28, Resulting Numbers: [28] 28,18 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 18:[27, 11], Operations: ['99/3=33', '33-22=11'] Exploring Operation: 27+11=38, Resulting Numbers: [38] 38,18 unequal: No Solution Exploring Operation: 27-11=16, Resulting Numbers: [16] 16,18 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 18:[3, 22, 72], Operations: ['99-27=72'] Exploring Operation: 72-22=50, Resulting Numbers: [3, 50] Generated Node #0,0,0: 18:[3, 50] Operation: 72-22=50 Exploring Operation: 72/3=24, Resulting Numbers: [22, 24] Generated Node #0,0,1: 18:[22, 24] Operation: 72/3=24 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 18:[22, 24], Operations: ['99-27=72', '72/3=24'] Exploring Operation: 22+24=46, Resulting Numbers: [46] 46,18 unequal: No Solution Exploring Operation: 24-22=2, Resulting Numbers: [2] 2,18 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 18:[3, 50], Operations: ['99-27=72', '72-22=50'] Exploring Operation: 3+50=53, Resulting Numbers: [53] 53,18 unequal: No Solution Exploring Operation: 50-3=47, Resulting Numbers: [47] 47,18 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_2
sum_heuristic
[ 80, 27, 14, 2 ]
60
[ "80-27=53", "14/2=7", "53+7=60" ]
Current State: 60:[80, 27, 14, 2], Operations: [] Exploring Operation: 80-27=53, Resulting Numbers: [14, 2, 53] Generated Node #2: [14, 2, 53] from Operation: 80-27=53 Current State: 60:[14, 2, 53], Operations: ['80-27=53'] Exploring Operation: 14/2=7, Resulting Numbers: [53, 7] Generated Node #3: [53, 7] from Operation: 14/2=7 Current State: 60:[53, 7], Operations: ['80-27=53', '14/2=7'] Exploring Operation: 53+7=60, Resulting Numbers: [60] 60,60 equal: Goal Reached
4
Current State: 60:[80, 27, 14, 2], Operations: [] Exploring Operation: 80-27=53, Resulting Numbers: [14, 2, 53] Generated Node #0,0: 60:[14, 2, 53] Operation: 80-27=53 Start Sub Search at level 1: Moving to Node #0,0 Current State: 60:[14, 2, 53], Operations: ['80-27=53'] Exploring Operation: 2+53=55, Resulting Numbers: [14, 55] Generated Node #0,0,0: 60:[14, 55] Operation: 2+53=55 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 60:[14, 55], Operations: ['80-27=53', '2+53=55'] Exploring Operation: 14+55=69, Resulting Numbers: [69] 69,60 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
sum_heuristic