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 | completions listlengths 32 32 | pass_count int64 0 31 | pass_rate stringclasses 32
values | num_samples int64 32 32 | generator_model stringclasses 1
value | generator_chat_template stringclasses 1
value | generator_temperature float64 1 1 | generator_top_p float64 1 1 | generator_max_tokens int64 8.19k 8.19k | source_split stringclasses 1
value | difficulty dict |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
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... | 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 | [
"To find \\(AB + AC\\), we will proceed through a series of steps involving the use of the sine and cosine rules, as well as the given geometric conditions.\n\n1. **Determine the lengths and angles in \\( \\triangle ABC \\):**\n\nGiven \\(\\sin \\angle A = \\frac{4}{5}\\), we can determine \\(\\cos \\angle A\\) usi... | 0 | 0/32 | 32 | Qwen/Qwen3-4B-Base | qwen_instruct_user_boxed_math | 1 | 1 | 8,192 | train | {
"value": 0.9998824030015605,
"posterior_mean": 0.012690472884949308,
"posterior_lower_bound": 0.00011759699843950377,
"expected_quantile": 0.7053394355476582,
"bucket_index": 4,
"bucket_count": 5
} |
"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 | ["To find the expected value of the area of triangle \\(\\triangle AXY\\), we start by noting the pr(...TRUNCATED) | 0 | 0/32 | 32 | Qwen/Qwen3-4B-Base | qwen_instruct_user_boxed_math | 1 | 1 | 8,192 | train | {"value":0.9998824030015605,"posterior_mean":0.012690472884949308,"posterior_lower_bound":0.00011759(...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 | ["We are given the following system of equations:\n\n1. \\(x^2 + ax + 1 = 0\\) and \\(x^2 + bx + c =(...TRUNCATED) | 4 | 4/32 | 32 | Qwen/Qwen3-4B-Base | qwen_instruct_user_boxed_math | 1 | 1 | 8,192 | train | {"value":0.9377865556631289,"posterior_mean":0.128503202206495,"posterior_lower_bound":0.06221344433(...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 | ["ython 2, reasons step by step as required. If it's important, give the reasoning before the result(...TRUNCATED) | 1 | 1/32 | 32 | Qwen/Qwen3-4B-Base | qwen_instruct_user_boxed_math | 1 | 1 | 8,192 | train | {"value":0.9920557164040514,"posterior_mean":0.04164365521533573,"posterior_lower_bound":0.007944283(...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 | ["To find the sum of the series \\(\\sum_{(a,b,c) \\in S} \\frac{1}{2^a 3^b 5^c}\\) where \\(S\\) is(...TRUNCATED) | 2 | 2/32 | 32 | Qwen/Qwen3-4B-Base | qwen_instruct_user_boxed_math | 1 | 1 | 8,192 | train | {"value":0.9768059528333007,"posterior_mean":0.07059683754572216,"posterior_lower_bound":0.023194047(...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 | ["To find out the values of \\( n \\) for which \\( n^4 + 6n^3 + 11n^2 + 3n + 31 \\) is a perfect sq(...TRUNCATED) | 3 | 3/32 | 32 | Qwen/Qwen3-4B-Base | qwen_instruct_user_boxed_math | 1 | 1 | 8,192 | train | {"value":0.9582673368229699,"posterior_mean":0.09955001987610858,"posterior_lower_bound":0.041732663(...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 | ["To find the smallest possible value of \\(d\\), we need to follow these steps:\n\n1. Calculate the(...TRUNCATED) | 12 | 12/32 | 32 | Qwen/Qwen3-4B-Base | qwen_instruct_user_boxed_math | 1 | 1 | 8,192 | train | {"value":0.7420877487672262,"posterior_mean":0.36012866084958634,"posterior_lower_bound":0.257912251(...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 | ["To find the number of distinct arrangements of \\( n \\) coins such that no arrangement can be tra(...TRUNCATED) | 12 | 12/32 | 32 | Qwen/Qwen3-4B-Base | qwen_instruct_user_boxed_math | 1 | 1 | 8,192 | train | {"value":0.7420877487672262,"posterior_mean":0.36012866084958634,"posterior_lower_bound":0.257912251(...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 | ["To find the smallest prime \\( p \\) such that \\( 2018! \\) is divisible by \\( p^3 \\) but not b(...TRUNCATED) | 0 | 0/32 | 32 | Qwen/Qwen3-4B-Base | qwen_instruct_user_boxed_math | 1 | 1 | 8,192 | train | {"value":0.9998824030015605,"posterior_mean":0.012690472884949308,"posterior_lower_bound":0.00011759(...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 | ["To find the conic section equation after the projection, we need to establish the general form of (...TRUNCATED) | 3 | 3/32 | 32 | Qwen/Qwen3-4B-Base | qwen_instruct_user_boxed_math | 1 | 1 | 8,192 | train | {"value":0.9582673368229699,"posterior_mean":0.09955001987610858,"posterior_lower_bound":0.041732663(...TRUNCATED) |
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