prompt stringlengths 19 3.19k | solution stringlengths 1 23 | data_source stringclasses 1 value | source_prompt listlengths 1 1 | ability stringclasses 1 value | reward_model dict | extra_info dict | messages listlengths 1 1 | dataset stringclasses 1 value | ground_truth stringlengths 1 23 | frontier_id stringlengths 64 64 | olmo_completions listlengths 7 16 |
|---|---|---|---|---|---|---|---|---|---|---|---|
In triangle $ABC$, $\sin \angle A = \frac{4}{5}$ and $\angle A < 90^\circ$. Let $D$ be a point outside triangle $ABC$ such that $\angle BAD = \angle DAC$ and $\angle BDC = 90^\circ$. Suppose that $AD = 1$ and that $\frac{BD}{CD} = \frac{3}{2}$. If $AB + AC$ can be expressed in the form $\frac{a\sqrt{b}}{c}$ where $a, b, c$ are pairwise relatively prime integers, find $a + b + c$. | 34 | math_dapo | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nIn triangle $ABC$, $\\sin \\angle A = \\frac{4}{5}$ and $\\angle A < 90^\\circ$. Let $D$ be a point outside triangle $... | MATH | {
"ground_truth": "34",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "9a9b6eb4-a1cb-49d1-8c1e-62eaf2f74079"
} | [
{
"content": "In triangle $ABC$, $\\sin \\angle A = \\frac{4}{5}$ and $\\angle A < 90^\\circ$. Let $D$ be a point outside triangle $ABC$ such that $\\angle BAD = \\angle DAC$ and $\\angle BDC = 90^\\circ$. Suppose that $AD = 1$ and that $\\frac{BD}{CD} = \\frac{3}{2}$. If $AB + AC$ can be expressed in the form ... | math | 34 | 6b8246ed504c945d84c34bfae9e109c549d810864de2606b8013003087880973 | [
" but before your quote.\nI also recommend that you point out which objects are given in the problem and which were used to solve it, as in the following example.\n\nHere is the geometric problem and solution. \"\n\n[Your problem statement goes here.]\n\nEach part of the solution is preceded by a blank line\n[in La... |
"Let $ABCD$ be a unit square in the plane. Points $X$ and $Y$ are chosen independently and uniformly(...TRUNCATED) | 113 | math_dapo | [{"content":"Solve the following math problem step by step. The last line of your response should be(...TRUNCATED) | MATH | {
"ground_truth": "113",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "b426d104-244d-4831-a2c4-cd756b61700a"
} | [{"content":"Let $ABCD$ be a unit square in the plane. Points $X$ and $Y$ are chosen independently a(...TRUNCATED) | math | 113 | 892712fafe6ec94fad5d08cfca5509e26c0be630715db575628cf0321660ae97 | ["\n\n\nBoat races in Coinore Lake use 10-lap logarithmic courses with length $2400m$. The fastest b(...TRUNCATED) |
"Let $a, b, c$ be distinct numbers such that the equations $x^2 + ax + 1 = 0$ and $x^2 + bx + c = 0$(...TRUNCATED) | -3 | math_dapo | [{"content":"Solve the following math problem step by step. The last line of your response should be(...TRUNCATED) | MATH | {
"ground_truth": "-3",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "6ff0b17f-7e5c-4ae9-b5e9-63ebecd2b9f7"
} | [{"content":"Let $a, b, c$ be distinct numbers such that the equations $x^2 + ax + 1 = 0$ and $x^2 +(...TRUNCATED) | math | -3 | aa4f3e1b35fc6491be58f69ea06a2c0aae649ed1c90c7776fa84135f638e60f0 | [" and use the \\boxed{} button. Use the show 2 more hints button if you need two more hints.\n\n\nH(...TRUNCATED) |
"There are $7$ boxes arranged in a row and numbered $1$ through $7$. You have a stack of $2015$ card(...TRUNCATED) | 3 | math_dapo | [{"content":"Solve the following math problem step by step. The last line of your response should be(...TRUNCATED) | MATH | {
"ground_truth": "3",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "186c94eb-3f6a-43b1-b2a4-f7dec58b7318"
} | [{"content":"There are $7$ boxes arranged in a row and numbered $1$ through $7$. You have a stack of(...TRUNCATED) | math | 3 | 3806e1fb97e100b5f9b86380b1f3406420b843789bee1095e16e199145e63977 | [" We aim to minimize the difference between the highest number in a box ($\\max(V_k)$) and the lowe(...TRUNCATED) |
"Let $S$ be the set of triples $(a,b,c)$ of non-negative integers such that $a+b+c$ is even. The val(...TRUNCATED) | 37 | math_dapo | [{"content":"Solve the following math problem step by step. The last line of your response should be(...TRUNCATED) | MATH | {
"ground_truth": "37",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "485b39f5-e71b-42b3-931f-219becbee2a3"
} | [{"content":"Let $S$ be the set of triples $(a,b,c)$ of non-negative integers such that $a+b+c$ is e(...TRUNCATED) | math | 37 | 62461912b50b8e4f29316c6da06a8dbf0fd2203d0530faa296ac857b8943d8a3 | ["\fAnswer: The final answer is 7.\nHere is a concise derivation:\n\n\n1. Write the sum over all $(a(...TRUNCATED) |
For which $n$ is $n^4 + 6n^3 + 11n^2 + 3n + 31$ a perfect square? | 10 | math_dapo | [{"content":"Solve the following math problem step by step. The last line of your response should be(...TRUNCATED) | MATH | {
"ground_truth": "10",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "96bd487f-c324-41b4-8015-f8234fe31bb4"
} | [
{
"content": "For which $n$ is $n^4 + 6n^3 + 11n^2 + 3n + 31$ a perfect square?",
"role": "user"
}
] | math | 10 | 98ce0926efe04451b7779132e3111a3e09a239b0b94f0200e4fc6f39abeffddc | [" (do not put the bit after this that says \"Answer: \" in your answer because that is my instructi(...TRUNCATED) |
"Four positive integers $a, b, c, d$ satisfy the condition $a < b < c < d$. Determine the smallest p(...TRUNCATED) | 10 | math_dapo | [{"content":"Solve the following math problem step by step. The last line of your response should be(...TRUNCATED) | MATH | {
"ground_truth": "10",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "b9fe2231-060d-4b0a-bf73-7d4cfc8b7dd0"
} | [{"content":"Four positive integers $a, b, c, d$ satisfy the condition $a < b < c < d$. Determine th(...TRUNCATED) | math | 10 | 5b983c5dc71c65e064f1091c593a3eb68f44f5e1dd4895df78b106a754209546 | ["\n\n\n\nAlright, so I need to find four positive integers a, b, c, d where a < b < c < d. The cond(...TRUNCATED) |
"$n$ coins are arranged in a circle. If two neighboring coins both show heads or both show tails, yo(...TRUNCATED) | 2 | math_dapo | [{"content":"Solve the following math problem step by step. The last line of your response should be(...TRUNCATED) | MATH | {
"ground_truth": "2",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "29f6a98f-0730-48f6-b637-2e902c24d9bd"
} | [{"content":"$n$ coins are arranged in a circle. If two neighboring coins both show heads or both sh(...TRUNCATED) | math | 2 | 9ce3c8e802e097f0b94f1e8cc5c6c347d3b9b19b1bc157c66502caa6b2dcb74f | [" 4. 3\n\nOkay, so I have this problem here about coins arranged in a circle. The question is askin(...TRUNCATED) |
"Determine the smallest prime $p$ such that $2018!$ is divisible by $p^3$, but not divisible by $p^4(...TRUNCATED) | 509 | math_dapo | [{"content":"Solve the following math problem step by step. The last line of your response should be(...TRUNCATED) | MATH | {
"ground_truth": "509",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "4c4f3cb8-c7ae-4f8e-b9eb-d2fcfc2dd442"
} | [{"content":"Determine the smallest prime $p$ such that $2018!$ is divisible by $p^3$, but not divis(...TRUNCATED) | math | 509 | 82732d61f519f5f89b971d132c6704b1b2b94899f9bd03272aefdad31397382d | ["\n\n\n\nAnswer: 7"," and without putting the answer in a box.\n\nWhat is the answer to the problem(...TRUNCATED) |
"Suppose you have a sphere tangent to the $xy$-plane with its center having a positive $z$-coordinat(...TRUNCATED) | 3 | math_dapo | [{"content":"Solve the following math problem step by step. The last line of your response should be(...TRUNCATED) | MATH | {
"ground_truth": "3",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "e4eede97-5bed-4a2a-9b64-5de4e8cde3e8"
} | [{"content":"Suppose you have a sphere tangent to the $xy$-plane with its center having a positive $(...TRUNCATED) | math | 3 | 84d73fd80422d0d73ecae1660afbccd9c6467db1265ad81e6536182f3c9777cd | [" Remember: There is 1 point (and a half point) for the mathematical description of the box dimensi(...TRUNCATED) |
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