prompt listlengths 2 2 | data_source stringclasses 1
value | ability stringclasses 1
value | reward_model dict | extra_info dict | pass_at_1 float64 0 1 | pass_at_2 float64 0 1 | pass_at_3 float64 0 1 | pass_at_4 float64 0 1 | pass_at_5 float64 0 1 | pass_at_6 float64 0 1 | pass_at_7 float64 0 1 | pass_at_8 float64 0 1 | pass_at_9 float64 0 1 | pass_at_10 float64 0 1 | pass_at_11 float64 0 1 | pass_at_12 float64 0 1 | pass_at_13 float64 0 1 | pass_at_14 float64 0 1 | pass_at_15 float64 0 1 | pass_at_16 float64 0 1 | avg_response_length float64 146 12.9k | response_length_variance float64 13.3 24.8M | num_samples int64 32 32 | num_correct int64 0 32 | meta_stats_model stringclasses 1
value |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
[
{
"content": "You are a helpful assistant. You perform the given task by reasoning about it within <reasoning> ... </reasoning> tags. Then you give your final response to the task after that, with the final answer in \\boxed{}.",
"role": "system"
},
{
"content": "In triangle $ABC$, $\\sin \\angle A ... | open-r1/DAPO-Math-17k-Processed | math | {
"ground_truth": "34",
"style": "rule"
} | {
"answer": "34",
"index": 0,
"question": "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 $AB + AC$ ca... | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 12,632.5 | 945,393.75 | 32 | 0 | Qwen/Qwen3-4B-Instruct-2507 |
[
{
"content": "You are a helpful assistant. You perform the given task by reasoning about it within <reasoning> ... </reasoning> tags. Then you give your final response to the task after that, with the final answer in \\boxed{}.",
"role": "system"
},
{
"content": "Let $ABCD$ be a unit square in the p... | open-r1/DAPO-Math-17k-Processed | math | {
"ground_truth": "113",
"style": "rule"
} | {
"answer": "113",
"index": 1,
"question": "Let $ABCD$ be a unit square in the plane. Points $X$ and $Y$ are chosen independently and uniformly at random on the perimeter of $ABCD$. If the expected value of the area of triangle $\\triangle AXY$ can be expressed as $\\frac{m}{n}$ for relatively prime positive inte... | 0.125 | 0.237903 | 0.339516 | 0.430617 | 0.511958 | 0.58426 | 0.64822 | 0.704505 | 0.753754 | 0.79658 | 0.833565 | 0.865267 | 0.892214 | 0.914905 | 0.933815 | 0.949388 | 6,785.375 | 1,598,373.734375 | 32 | 4 | Qwen/Qwen3-4B-Instruct-2507 |
[
{
"content": "You are a helpful assistant. You perform the given task by reasoning about it within <reasoning> ... </reasoning> tags. Then you give your final response to the task after that, with the final answer in \\boxed{}.",
"role": "system"
},
{
"content": "Let $a, b, c$ be distinct numbers su... | open-r1/DAPO-Math-17k-Processed | math | {
"ground_truth": "-3",
"style": "rule"
} | {
"answer": "-3",
"index": 2,
"question": "Let $a, b, c$ be distinct numbers such that the equations $x^2 + ax + 1 = 0$ and $x^2 + bx + c = 0$ have a common real root, and the equations $x^2 + x + a = 0$ and $x^2 + cx + b = 0$ also have a common real root. Compute the sum $a + b + c$.",
"split": "train"
} | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 4,228.875 | 805,788.359375 | 32 | 32 | Qwen/Qwen3-4B-Instruct-2507 |
[
{
"content": "You are a helpful assistant. You perform the given task by reasoning about it within <reasoning> ... </reasoning> tags. Then you give your final response to the task after that, with the final answer in \\boxed{}.",
"role": "system"
},
{
"content": "There are $7$ boxes arranged in a ro... | open-r1/DAPO-Math-17k-Processed | math | {
"ground_truth": "3",
"style": "rule"
} | {
"answer": "3",
"index": 3,
"question": "There are $7$ boxes arranged in a row and numbered $1$ through $7$. You have a stack of $2015$ cards, which you place one by one in the boxes. The first card is placed in box $1$, the second in box $2$, and so forth up to the seventh card which is placed in box $7$. You t... | 0.875 | 0.987903 | 0.999194 | 0.999972 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 3,621.875 | 526,780.609375 | 32 | 28 | Qwen/Qwen3-4B-Instruct-2507 |
[
{
"content": "You are a helpful assistant. You perform the given task by reasoning about it within <reasoning> ... </reasoning> tags. Then you give your final response to the task after that, with the final answer in \\boxed{}.",
"role": "system"
},
{
"content": "Let $S$ be the set of triples $(a,b,... | open-r1/DAPO-Math-17k-Processed | math | {
"ground_truth": "37",
"style": "rule"
} | {
"answer": "37",
"index": 4,
"question": "Let $S$ be the set of triples $(a,b,c)$ of non-negative integers such that $a+b+c$ is even. The value of the sum\n\\[ \\sum_{(a,b,c) \\in S} \\frac{1}{2^a 3^b 5^c} \\]\ncan be expressed as $\\frac{m}{n}$, where $m$ and $n$ are relatively prime positive integers. Compute ... | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1,620.125 | 5,980.609375 | 32 | 32 | Qwen/Qwen3-4B-Instruct-2507 |
[
{
"content": "You are a helpful assistant. You perform the given task by reasoning about it within <reasoning> ... </reasoning> tags. Then you give your final response to the task after that, with the final answer in \\boxed{}.",
"role": "system"
},
{
"content": "For which $n$ is $n^4 + 6n^3 + 11n^2... | open-r1/DAPO-Math-17k-Processed | math | {
"ground_truth": "10",
"style": "rule"
} | {
"answer": "10",
"index": 5,
"question": "For which $n$ is $n^4 + 6n^3 + 11n^2 + 3n + 31$ a perfect square?",
"split": "train"
} | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 6,454.125 | 450,025.609375 | 32 | 32 | Qwen/Qwen3-4B-Instruct-2507 |
[
{
"content": "You are a helpful assistant. You perform the given task by reasoning about it within <reasoning> ... </reasoning> tags. Then you give your final response to the task after that, with the final answer in \\boxed{}.",
"role": "system"
},
{
"content": "Four positive integers $a, b, c, d$ ... | open-r1/DAPO-Math-17k-Processed | math | {
"ground_truth": "10",
"style": "rule"
} | {
"answer": "10",
"index": 6,
"question": "Four positive integers $a, b, c, d$ satisfy the condition $a < b < c < d$. Determine the smallest possible value of $d$ such that the arithmetic mean of the numbers $a, b, c$ is half of the arithmetic mean of the numbers $a, b, c, d$.",
"split": "train"
} | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1,965.75 | 41,204.4375 | 32 | 32 | Qwen/Qwen3-4B-Instruct-2507 |
[
{
"content": "You are a helpful assistant. You perform the given task by reasoning about it within <reasoning> ... </reasoning> tags. Then you give your final response to the task after that, with the final answer in \\boxed{}.",
"role": "system"
},
{
"content": "$n$ coins are arranged in a circle. ... | open-r1/DAPO-Math-17k-Processed | math | {
"ground_truth": "2",
"style": "rule"
} | {
"answer": "2",
"index": 7,
"question": "$n$ coins are arranged in a circle. If two neighboring coins both show heads or both show tails, you can flip both coins. How many distinct arrangements of the coins are there such that no arrangement can be transformed into another by performing these operations?",
"sp... | 0.625 | 0.866935 | 0.955645 | 0.986235 | 0.996067 | 0.99898 | 0.999765 | 0.999953 | 0.999992 | 0.999999 | 1 | 1 | 1 | 1 | 1 | 1 | 11,618.625 | 3,561,836.734375 | 32 | 20 | Qwen/Qwen3-4B-Instruct-2507 |
[
{
"content": "You are a helpful assistant. You perform the given task by reasoning about it within <reasoning> ... </reasoning> tags. Then you give your final response to the task after that, with the final answer in \\boxed{}.",
"role": "system"
},
{
"content": "Determine the smallest prime $p$ suc... | open-r1/DAPO-Math-17k-Processed | math | {
"ground_truth": "509",
"style": "rule"
} | {
"answer": "509",
"index": 8,
"question": "Determine the smallest prime $p$ such that $2018!$ is divisible by $p^3$, but not divisible by $p^4$.",
"split": "train"
} | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 4,892.625 | 1,327,407.734375 | 32 | 32 | Qwen/Qwen3-4B-Instruct-2507 |
[
{
"content": "You are a helpful assistant. You perform the given task by reasoning about it within <reasoning> ... </reasoning> tags. Then you give your final response to the task after that, with the final answer in \\boxed{}.",
"role": "system"
},
{
"content": "Suppose you have a sphere tangent to... | open-r1/DAPO-Math-17k-Processed | math | {
"ground_truth": "3",
"style": "rule"
} | {
"answer": "3",
"index": 9,
"question": "Suppose you have a sphere tangent to the $xy$-plane with its center having a positive $z$-coordinate. If it is projected from a point $P=(0,b,a)$ to the $xy$-plane, it gives the conic section $y=x^2$. If we write $a=\\frac{p}{q}$ where $p$ and $q$ are integers, find $p+q$... | 0.625 | 0.866935 | 0.955645 | 0.986235 | 0.996067 | 0.99898 | 0.999765 | 0.999953 | 0.999992 | 0.999999 | 1 | 1 | 1 | 1 | 1 | 1 | 10,420 | 4,152,934.75 | 32 | 20 | Qwen/Qwen3-4B-Instruct-2507 |
[
{
"content": "You are a helpful assistant. You perform the given task by reasoning about it within <reasoning> ... </reasoning> tags. Then you give your final response to the task after that, with the final answer in \\boxed{}.",
"role": "system"
},
{
"content": "There are $10^{2015}$ planets in an ... | open-r1/DAPO-Math-17k-Processed | math | {
"ground_truth": "1007",
"style": "rule"
} | {
"answer": "1007",
"index": 10,
"question": "There are $10^{2015}$ planets in an Intergalactic empire. Every two planets are connected by a two-way space line served by one of $2015$ travel companies. The Emperor would like to close $k$ of these companies such that it is still possible to reach any planet from a... | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 8,252.5 | 8,657,441.75 | 32 | 0 | Qwen/Qwen3-4B-Instruct-2507 |
[
{
"content": "You are a helpful assistant. You perform the given task by reasoning about it within <reasoning> ... </reasoning> tags. Then you give your final response to the task after that, with the final answer in \\boxed{}.",
"role": "system"
},
{
"content": "Rectangle $HOMF$ has $HO = 11$ and $... | open-r1/DAPO-Math-17k-Processed | math | {
"ground_truth": "28",
"style": "rule"
} | {
"answer": "28",
"index": 11,
"question": "Rectangle $HOMF$ has $HO = 11$ and $OM = 5$. Triangle $\\triangle ABC$ has orthocenter $H$ and circumcenter $O$. $M$ is the midpoint of $BC$, and altitude $AF$ meets $BC$ at $F$. Find the length of $BC$.",
"split": "train"
} | 0.75 | 0.943548 | 0.98871 | 0.998053 | 0.999722 | 0.999969 | 0.999998 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 6,654 | 6,296,851.25 | 32 | 24 | Qwen/Qwen3-4B-Instruct-2507 |
[
{
"content": "You are a helpful assistant. You perform the given task by reasoning about it within <reasoning> ... </reasoning> tags. Then you give your final response to the task after that, with the final answer in \\boxed{}.",
"role": "system"
},
{
"content": "Let $a$, $b$, $c$ be the three roots... | open-r1/DAPO-Math-17k-Processed | math | {
"ground_truth": "5",
"style": "rule"
} | {
"answer": "5",
"index": 12,
"question": "Let $a$, $b$, $c$ be the three roots of the equation $x^3-(k+1)x^2+kx+12=0$, where $k$ is a real number. If $(a-2)^3+(b-2)^3+(c-2)^3=-18$, find the value of $k$.",
"split": "train"
} | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 4,053.5 | 2,651,382.75 | 32 | 32 | Qwen/Qwen3-4B-Instruct-2507 |
[
{
"content": "You are a helpful assistant. You perform the given task by reasoning about it within <reasoning> ... </reasoning> tags. Then you give your final response to the task after that, with the final answer in \\boxed{}.",
"role": "system"
},
{
"content": "Two towns, $A$ and $B$, are $100$ mi... | open-r1/DAPO-Math-17k-Processed | math | {
"ground_truth": "5",
"style": "rule"
} | {
"answer": "5",
"index": 13,
"question": "Two towns, $A$ and $B$, are $100$ miles apart. Every $20$ minutes (starting at midnight), a bus traveling at $60$ mph leaves town $A$ for town $B$, and every $30$ minutes (starting at midnight), a bus traveling at $20$ mph leaves town $B$ for town $A$. Dirk starts in Tow... | 0.125 | 0.237903 | 0.339516 | 0.430617 | 0.511958 | 0.58426 | 0.64822 | 0.704505 | 0.753754 | 0.79658 | 0.833565 | 0.865267 | 0.892214 | 0.914905 | 0.933815 | 0.949388 | 10,419.125 | 7,103,186.859375 | 32 | 4 | Qwen/Qwen3-4B-Instruct-2507 |
[
{
"content": "You are a helpful assistant. You perform the given task by reasoning about it within <reasoning> ... </reasoning> tags. Then you give your final response to the task after that, with the final answer in \\boxed{}.",
"role": "system"
},
{
"content": "Burrito Bear has a white unit square... | open-r1/DAPO-Math-17k-Processed | math | {
"ground_truth": "1",
"style": "rule"
} | {
"answer": "1",
"index": 14,
"question": "Burrito Bear has a white unit square. She inscribes a circle inside the square and paints it black. She then inscribes a square inside the black circle and paints it white. Burrito repeats this process indefinitely. The total black area can be expressed as $\\frac{a\\pi+... | 0.5 | 0.758065 | 0.887097 | 0.949388 | 0.978309 | 0.991163 | 0.996601 | 0.998776 | 0.999592 | 0.999876 | 0.999966 | 0.999992 | 0.999998 | 1 | 1 | 1 | 7,050.75 | 4,582,975.4375 | 32 | 16 | Qwen/Qwen3-4B-Instruct-2507 |
[
{
"content": "You are a helpful assistant. You perform the given task by reasoning about it within <reasoning> ... </reasoning> tags. Then you give your final response to the task after that, with the final answer in \\boxed{}.",
"role": "system"
},
{
"content": "Danial went to a fruit stall that se... | open-r1/DAPO-Math-17k-Processed | math | {
"ground_truth": "15",
"style": "rule"
} | {
"answer": "15",
"index": 15,
"question": "Danial went to a fruit stall that sells apples, mangoes, and papayas. Each apple costs $3$ RM, each mango costs $4$ RM, and each papaya costs $5$ RM. He bought at least one of each fruit and paid exactly $50$ RM. What is the maximum number of fruits that he could have b... | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 3,556.625 | 1,633,333.984375 | 32 | 32 | Qwen/Qwen3-4B-Instruct-2507 |
[
{
"content": "You are a helpful assistant. You perform the given task by reasoning about it within <reasoning> ... </reasoning> tags. Then you give your final response to the task after that, with the final answer in \\boxed{}.",
"role": "system"
},
{
"content": "Sabrina has a fair tetrahedral die w... | open-r1/DAPO-Math-17k-Processed | math | {
"ground_truth": "10",
"style": "rule"
} | {
"answer": "10",
"index": 16,
"question": "Sabrina has a fair tetrahedral die with faces numbered 1, 2, 3, and 4. She rolls the die to create a sequence by recording the number on its bottom face. However, she discards any roll if appending its number to the sequence results in two consecutive terms that sum to ... | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 10,307.75 | 2,919,922.6875 | 32 | 0 | Qwen/Qwen3-4B-Instruct-2507 |
[
{
"content": "You are a helpful assistant. You perform the given task by reasoning about it within <reasoning> ... </reasoning> tags. Then you give your final response to the task after that, with the final answer in \\boxed{}.",
"role": "system"
},
{
"content": "Denote by $S(n)$ the sum of the digi... | open-r1/DAPO-Math-17k-Processed | math | {
"ground_truth": "402",
"style": "rule"
} | {
"answer": "402",
"index": 17,
"question": "Denote by $S(n)$ the sum of the digits of the positive integer $n$. Find all the solutions of the equation $n(S(n)-1)=2010.$",
"split": "train"
} | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1,922.5 | 47,872.75 | 32 | 32 | Qwen/Qwen3-4B-Instruct-2507 |
[
{
"content": "You are a helpful assistant. You perform the given task by reasoning about it within <reasoning> ... </reasoning> tags. Then you give your final response to the task after that, with the final answer in \\boxed{}.",
"role": "system"
},
{
"content": "For each positive integer $n$, let $... | open-r1/DAPO-Math-17k-Processed | math | {
"ground_truth": "7",
"style": "rule"
} | {
"answer": "7",
"index": 18,
"question": "For each positive integer $n$, let $S(n)$ be the sum of the digits of $n$. Determine the smallest positive integer $a$ such that there are infinitely many positive integers $n$ for which $S(n) - S(n + a) = 2018$.",
"split": "train"
} | 0.625 | 0.866935 | 0.955645 | 0.986235 | 0.996067 | 0.99898 | 0.999765 | 0.999953 | 0.999992 | 0.999999 | 1 | 1 | 1 | 1 | 1 | 1 | 8,618.625 | 4,301,256.234375 | 32 | 20 | Qwen/Qwen3-4B-Instruct-2507 |
[
{
"content": "You are a helpful assistant. You perform the given task by reasoning about it within <reasoning> ... </reasoning> tags. Then you give your final response to the task after that, with the final answer in \\boxed{}.",
"role": "system"
},
{
"content": "Find all integers $k$ such that all ... | open-r1/DAPO-Math-17k-Processed | math | {
"ground_truth": "5",
"style": "rule"
} | {
"answer": "5",
"index": 19,
"question": "Find all integers $k$ such that all roots of the following polynomial are also integers:\n\n$$f(x) = x^3 - (k-3)x^2 - 11x + (4k-8).$$",
"split": "train"
} | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 8,230.875 | 866,565.359375 | 32 | 32 | Qwen/Qwen3-4B-Instruct-2507 |
[
{
"content": "You are a helpful assistant. You perform the given task by reasoning about it within <reasoning> ... </reasoning> tags. Then you give your final response to the task after that, with the final answer in \\boxed{}.",
"role": "system"
},
{
"content": "A class has $25$ students. The teach... | open-r1/DAPO-Math-17k-Processed | math | {
"ground_truth": "300",
"style": "rule"
} | {
"answer": "300",
"index": 20,
"question": "A class has $25$ students. The teacher wants to stock $N$ candies and hold an Olympiad, distributing all $N$ candies based on student performance. The candies should be distributed such that students who solve the same number of tasks receive the same number of candies... | 0.875 | 0.987903 | 0.999194 | 0.999972 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 7,171.5 | 2,124,750.75 | 32 | 28 | Qwen/Qwen3-4B-Instruct-2507 |
[
{
"content": "You are a helpful assistant. You perform the given task by reasoning about it within <reasoning> ... </reasoning> tags. Then you give your final response to the task after that, with the final answer in \\boxed{}.",
"role": "system"
},
{
"content": "If $a, b$ are real numbers such that... | open-r1/DAPO-Math-17k-Processed | math | {
"ground_truth": "1",
"style": "rule"
} | {
"answer": "1",
"index": 21,
"question": "If $a, b$ are real numbers such that $a^3 + 12a^2 + 49a + 69 = 0$ and $b^3 - 9b^2 + 28b - 31 = 0$, find $a + b$.",
"split": "train"
} | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 4,738.75 | 7,495,486.9375 | 32 | 0 | Qwen/Qwen3-4B-Instruct-2507 |
[
{
"content": "You are a helpful assistant. You perform the given task by reasoning about it within <reasoning> ... </reasoning> tags. Then you give your final response to the task after that, with the final answer in \\boxed{}.",
"role": "system"
},
{
"content": "Let $S$ be the set of triples $(a,b,... | open-r1/DAPO-Math-17k-Processed | math | {
"ground_truth": "37",
"style": "rule"
} | {
"answer": "37",
"index": 22,
"question": "Let $S$ be the set of triples $(a,b,c)$ of non-negative integers such that $a+b+c$ is even. Determine the value of the sum:\n\\[\n\\sum_{(a,b,c)\\in S}\\frac{1}{2^a3^b5^c}\n\\]\nThis sum can be expressed as $\\frac{m}{n}$, where $m$ and $n$ are relatively prime positive... | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1,592 | 44,315.75 | 32 | 32 | Qwen/Qwen3-4B-Instruct-2507 |
[
{
"content": "You are a helpful assistant. You perform the given task by reasoning about it within <reasoning> ... </reasoning> tags. Then you give your final response to the task after that, with the final answer in \\boxed{}.",
"role": "system"
},
{
"content": "Some positive integers are initially... | open-r1/DAPO-Math-17k-Processed | math | {
"ground_truth": "-3",
"style": "rule"
} | {
"answer": "-3",
"index": 23,
"question": "Some positive integers are initially written on a board, where each 2 of them are different. Each time we can do the following moves: \n1. If there are 2 numbers (written on the board) in the form $n, n+1$, we can erase them and write down $n-2$. \n2. If there are 2 n... | 0.25 | 0.443548 | 0.591935 | 0.704505 | 0.788932 | 0.851471 | 0.897172 | 0.930077 | 0.953385 | 0.969599 | 0.980654 | 0.988024 | 0.992814 | 0.99584 | 0.997689 | 0.998776 | 8,068.875 | 401,259.109375 | 32 | 8 | Qwen/Qwen3-4B-Instruct-2507 |
[
{
"content": "You are a helpful assistant. You perform the given task by reasoning about it within <reasoning> ... </reasoning> tags. Then you give your final response to the task after that, with the final answer in \\boxed{}.",
"role": "system"
},
{
"content": "Find all positive integers $n$ for w... | open-r1/DAPO-Math-17k-Processed | math | {
"ground_truth": "3",
"style": "rule"
} | {
"answer": "3",
"index": 24,
"question": "Find all positive integers $n$ for which the largest prime divisor of $n^2 + 3$ is equal to the least prime divisor of $n^4 + 6$.",
"split": "train"
} | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 5,359.5 | 709,216.25 | 32 | 32 | Qwen/Qwen3-4B-Instruct-2507 |
[
{
"content": "You are a helpful assistant. You perform the given task by reasoning about it within <reasoning> ... </reasoning> tags. Then you give your final response to the task after that, with the final answer in \\boxed{}.",
"role": "system"
},
{
"content": "Charlie has a fair $n$-sided die (wi... | open-r1/DAPO-Math-17k-Processed | math | {
"ground_truth": "8556",
"style": "rule"
} | {
"answer": "8556",
"index": 25,
"question": "Charlie has a fair $n$-sided die (with each face showing a positive integer between $1$ and $n$ inclusive) and a list of $n$ consecutive positive integers. He first rolls the die, and if the number showing on top is $k$, he then uniformly and randomly selects a $k$-el... | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 5,878.625 | 1,916,165.234375 | 32 | 0 | Qwen/Qwen3-4B-Instruct-2507 |
[
{
"content": "You are a helpful assistant. You perform the given task by reasoning about it within <reasoning> ... </reasoning> tags. Then you give your final response to the task after that, with the final answer in \\boxed{}.",
"role": "system"
},
{
"content": "The integers from $1$ to $n$ are wri... | open-r1/DAPO-Math-17k-Processed | math | {
"ground_truth": "14",
"style": "rule"
} | {
"answer": "14",
"index": 26,
"question": "The integers from $1$ to $n$ are written, one on each of $n$ cards. The first player removes one card. Then the second player removes two cards with consecutive integers. After that, the first player removes three cards with consecutive integers. Finally, the second pla... | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 9,430.875 | 2,496,819.859375 | 32 | 0 | Qwen/Qwen3-4B-Instruct-2507 |
[
{
"content": "You are a helpful assistant. You perform the given task by reasoning about it within <reasoning> ... </reasoning> tags. Then you give your final response to the task after that, with the final answer in \\boxed{}.",
"role": "system"
},
{
"content": "Joe has $1729$ randomly oriented and... | open-r1/DAPO-Math-17k-Processed | math | {
"ground_truth": "7",
"style": "rule"
} | {
"answer": "7",
"index": 27,
"question": "Joe has $1729$ randomly oriented and randomly arranged unit cubes, which are initially unpainted. He makes two cubes of side lengths $9$ and $10$ or of side lengths $1$ and $12$ (randomly chosen). These cubes are dipped into white paint. Then two more cubes of side lengt... | 0.375 | 0.616935 | 0.770161 | 0.865267 | 0.92301 | 0.957228 | 0.976969 | 0.988024 | 0.994012 | 0.997136 | 0.998698 | 0.999442 | 0.999777 | 0.999918 | 0.999973 | 0.999992 | 8,744.875 | 783,938.859375 | 32 | 12 | Qwen/Qwen3-4B-Instruct-2507 |
[
{
"content": "You are a helpful assistant. You perform the given task by reasoning about it within <reasoning> ... </reasoning> tags. Then you give your final response to the task after that, with the final answer in \\boxed{}.",
"role": "system"
},
{
"content": "The circle $C_1$ is tangent to the c... | open-r1/DAPO-Math-17k-Processed | math | {
"ground_truth": "3",
"style": "rule"
} | {
"answer": "3",
"index": 28,
"question": "The circle $C_1$ is tangent to the circle $C_2$ internally at the point $A$. Let $O$ be the center of $C_2$. The point $P$ is on $C_1$, and the tangent line at $P$ passes through $O$. Let the ray $OP$ intersect with $C_2$ at $Q$, and let the tangent line of $C_1$ passing... | 0.875 | 0.987903 | 0.999194 | 0.999972 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 7,792.625 | 1,787,246.984375 | 32 | 28 | Qwen/Qwen3-4B-Instruct-2507 |
[
{
"content": "You are a helpful assistant. You perform the given task by reasoning about it within <reasoning> ... </reasoning> tags. Then you give your final response to the task after that, with the final answer in \\boxed{}.",
"role": "system"
},
{
"content": "Consider two distinct positive integ... | open-r1/DAPO-Math-17k-Processed | math | {
"ground_truth": "30",
"style": "rule"
} | {
"answer": "30",
"index": 29,
"question": "Consider two distinct positive integers $a$ and $b$ that have integer arithmetic, geometric, and harmonic means. Find the minimal value of $|a-b|$.",
"split": "train"
} | 0.75 | 0.943548 | 0.98871 | 0.998053 | 0.999722 | 0.999969 | 0.999998 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 7,777.625 | 519,568.484375 | 32 | 24 | Qwen/Qwen3-4B-Instruct-2507 |
[
{
"content": "You are a helpful assistant. You perform the given task by reasoning about it within <reasoning> ... </reasoning> tags. Then you give your final response to the task after that, with the final answer in \\boxed{}.",
"role": "system"
},
{
"content": "Dexter and Raquel are playing a game... | open-r1/DAPO-Math-17k-Processed | math | {
"ground_truth": "1010",
"style": "rule"
} | {
"answer": "1010",
"index": 30,
"question": "Dexter and Raquel are playing a game with $N$ stones. Dexter goes first and takes one stone from the pile. After that, the players alternate turns and can take anywhere from $1$ to $x + 1$ stones from the pile, where $x$ is the number of stones the other player took o... | 0.125 | 0.237903 | 0.339516 | 0.430617 | 0.511958 | 0.58426 | 0.64822 | 0.704505 | 0.753754 | 0.79658 | 0.833565 | 0.865267 | 0.892214 | 0.914905 | 0.933815 | 0.949388 | 10,282.125 | 5,246,823.859375 | 32 | 4 | Qwen/Qwen3-4B-Instruct-2507 |
[
{
"content": "You are a helpful assistant. You perform the given task by reasoning about it within <reasoning> ... </reasoning> tags. Then you give your final response to the task after that, with the final answer in \\boxed{}.",
"role": "system"
},
{
"content": "Triangle $\\triangle{ABC}$ is isosce... | open-r1/DAPO-Math-17k-Processed | math | {
"ground_truth": "40",
"style": "rule"
} | {
"answer": "40",
"index": 31,
"question": "Triangle $\\triangle{ABC}$ is isosceles with $AB = AC$. Let the incircle of $\\triangle{ABC}$ intersect $BC$ and $AC$ at $D$ and $E$ respectively. Let $F \\neq A$ be the point such that $DF = DA$ and $EF = EA$. If $AF = 8$ and the circumradius of $\\triangle{AED}$ is $5... | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 10,518.5 | 5,877,154 | 32 | 0 | Qwen/Qwen3-4B-Instruct-2507 |
[
{
"content": "You are a helpful assistant. You perform the given task by reasoning about it within <reasoning> ... </reasoning> tags. Then you give your final response to the task after that, with the final answer in \\boxed{}.",
"role": "system"
},
{
"content": "Find the sum of all possible values ... | open-r1/DAPO-Math-17k-Processed | math | {
"ground_truth": "9",
"style": "rule"
} | {
"answer": "9",
"index": 32,
"question": "Find the sum of all possible values of $a + b$ where $a$ and $b$ are nonnegative integers such that $4^a + 2^b + 5$ is a perfect square.",
"split": "train"
} | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 8,561.375 | 243,155.984375 | 32 | 32 | Qwen/Qwen3-4B-Instruct-2507 |
[
{
"content": "You are a helpful assistant. You perform the given task by reasoning about it within <reasoning> ... </reasoning> tags. Then you give your final response to the task after that, with the final answer in \\boxed{}.",
"role": "system"
},
{
"content": "Let $M$ be the set of those positive... | open-r1/DAPO-Math-17k-Processed | math | {
"ground_truth": "10",
"style": "rule"
} | {
"answer": "10",
"index": 33,
"question": "Let $M$ be the set of those positive integers which are not divisible by $3$. The sum of $2n$ consecutive elements of $M$ is $300$. Determine $n$.",
"split": "train"
} | 0.875 | 0.987903 | 0.999194 | 0.999972 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 5,369.375 | 8,148,662.484375 | 32 | 28 | Qwen/Qwen3-4B-Instruct-2507 |
[
{
"content": "You are a helpful assistant. You perform the given task by reasoning about it within <reasoning> ... </reasoning> tags. Then you give your final response to the task after that, with the final answer in \\boxed{}.",
"role": "system"
},
{
"content": "Petya and Vasya play the following g... | open-r1/DAPO-Math-17k-Processed | math | {
"ground_truth": "4",
"style": "rule"
} | {
"answer": "4",
"index": 34,
"question": "Petya and Vasya play the following game. Petya conceives a polynomial $P(x)$ with integer coefficients. On each move, Vasya pays him a ruble and calls an integer $a$ of his choice, which has not yet been called by him. Petya has to reply with the number of distinct integ... | 0.625 | 0.866935 | 0.955645 | 0.986235 | 0.996067 | 0.99898 | 0.999765 | 0.999953 | 0.999992 | 0.999999 | 1 | 1 | 1 | 1 | 1 | 1 | 8,132.5 | 686,395.25 | 32 | 20 | Qwen/Qwen3-4B-Instruct-2507 |
[
{
"content": "You are a helpful assistant. You perform the given task by reasoning about it within <reasoning> ... </reasoning> tags. Then you give your final response to the task after that, with the final answer in \\boxed{}.",
"role": "system"
},
{
"content": "Determine the greatest power of $2$ ... | open-r1/DAPO-Math-17k-Processed | math | {
"ground_truth": "64",
"style": "rule"
} | {
"answer": "64",
"index": 35,
"question": "Determine the greatest power of $2$ that is a factor of $3^{15} + 3^{11} + 3^{6} + 1$.",
"split": "train"
} | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 3,728.375 | 49,755.734375 | 32 | 32 | Qwen/Qwen3-4B-Instruct-2507 |
[
{
"content": "You are a helpful assistant. You perform the given task by reasoning about it within <reasoning> ... </reasoning> tags. Then you give your final response to the task after that, with the final answer in \\boxed{}.",
"role": "system"
},
{
"content": "On a board, the numbers from 1 to 20... | open-r1/DAPO-Math-17k-Processed | math | {
"ground_truth": "8",
"style": "rule"
} | {
"answer": "8",
"index": 36,
"question": "On a board, the numbers from 1 to 2009 are written. A couple of them are erased and instead of them, the remainder of the sum of the erased numbers divided by 13 is written on the board. After a few repetitions of this process, only three numbers are left, of which two a... | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 4,929.125 | 2,780,123.609375 | 32 | 32 | Qwen/Qwen3-4B-Instruct-2507 |
[
{
"content": "You are a helpful assistant. You perform the given task by reasoning about it within <reasoning> ... </reasoning> tags. Then you give your final response to the task after that, with the final answer in \\boxed{}.",
"role": "system"
},
{
"content": "For positive integers $n$, let $s(n)... | open-r1/DAPO-Math-17k-Processed | math | {
"ground_truth": "1099",
"style": "rule"
} | {
"answer": "1099",
"index": 37,
"question": "For positive integers $n$, let $s(n)$ be the sum of the digits of $n$. Over all four-digit positive integers $n$, which value of $n$ maximizes the ratio $\\frac{s(n)}{n}$?",
"split": "train"
} | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 6,737.625 | 804,217.484375 | 32 | 32 | Qwen/Qwen3-4B-Instruct-2507 |
[
{
"content": "You are a helpful assistant. You perform the given task by reasoning about it within <reasoning> ... </reasoning> tags. Then you give your final response to the task after that, with the final answer in \\boxed{}.",
"role": "system"
},
{
"content": "Suppose that $n$ persons meet in a m... | open-r1/DAPO-Math-17k-Processed | math | {
"ground_truth": "21",
"style": "rule"
} | {
"answer": "21",
"index": 38,
"question": "Suppose that $n$ persons meet in a meeting, and that each of the persons is acquainted with exactly $8$ others. Any two acquainted persons have exactly $4$ common acquaintances, and any two non-acquainted persons have exactly $2$ common acquaintances. Find all possible ... | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 6,804.375 | 696,179.734375 | 32 | 32 | Qwen/Qwen3-4B-Instruct-2507 |
[
{
"content": "You are a helpful assistant. You perform the given task by reasoning about it within <reasoning> ... </reasoning> tags. Then you give your final response to the task after that, with the final answer in \\boxed{}.",
"role": "system"
},
{
"content": "How many ways can $8$ mutually non-a... | open-r1/DAPO-Math-17k-Processed | math | {
"ground_truth": "40320",
"style": "rule"
} | {
"answer": "40320",
"index": 39,
"question": "How many ways can $8$ mutually non-attacking rooks be placed on a $9 \\times 9$ chessboard so that all $8$ rooks are on squares of the same color?\n\n(Two rooks are said to be attacking each other if they are placed in the same row or column of the board.)",
"split... | 0.75 | 0.943548 | 0.98871 | 0.998053 | 0.999722 | 0.999969 | 0.999998 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 4,638.5 | 229,209.5 | 32 | 24 | Qwen/Qwen3-4B-Instruct-2507 |
[
{
"content": "You are a helpful assistant. You perform the given task by reasoning about it within <reasoning> ... </reasoning> tags. Then you give your final response to the task after that, with the final answer in \\boxed{}.",
"role": "system"
},
{
"content": "Find a necessary and sufficient cond... | open-r1/DAPO-Math-17k-Processed | math | {
"ground_truth": "1",
"style": "rule"
} | {
"answer": "1",
"index": 40,
"question": "Find a necessary and sufficient condition on the positive integer $n$ such that the equation $x^n + (2 + x)^n + (2 - x)^n = 0$ has a rational root.",
"split": "train"
} | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 7,501.625 | 975,629.484375 | 32 | 32 | Qwen/Qwen3-4B-Instruct-2507 |
[
{
"content": "You are a helpful assistant. You perform the given task by reasoning about it within <reasoning> ... </reasoning> tags. Then you give your final response to the task after that, with the final answer in \\boxed{}.",
"role": "system"
},
{
"content": "Let $ABCDEFGHIJ$ be a regular 10-sid... | open-r1/DAPO-Math-17k-Processed | math | {
"ground_truth": "5",
"style": "rule"
} | {
"answer": "5",
"index": 41,
"question": "Let $ABCDEFGHIJ$ be a regular 10-sided polygon inscribed in a circle with center $O$ and radius $5$. The diagonals $AD$ and $BE$ intersect at point $P$, and the diagonals $AH$ and $BI$ intersect at point $Q$. Calculate the length of segment $PQ$.",
"split": "train"
} | 0.75 | 0.943548 | 0.98871 | 0.998053 | 0.999722 | 0.999969 | 0.999998 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 8,388.25 | 3,788,674.4375 | 32 | 24 | Qwen/Qwen3-4B-Instruct-2507 |
[
{
"content": "You are a helpful assistant. You perform the given task by reasoning about it within <reasoning> ... </reasoning> tags. Then you give your final response to the task after that, with the final answer in \\boxed{}.",
"role": "system"
},
{
"content": "Determine all integers $m$ for which... | open-r1/DAPO-Math-17k-Processed | math | {
"ground_truth": "0",
"style": "rule"
} | {
"answer": "0",
"index": 42,
"question": "Determine all integers $m$ for which all solutions of the equation $3x^3 - 3x^2 + m = 0$ are rational.",
"split": "train"
} | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 7,523.625 | 240,698.234375 | 32 | 32 | Qwen/Qwen3-4B-Instruct-2507 |
[
{
"content": "You are a helpful assistant. You perform the given task by reasoning about it within <reasoning> ... </reasoning> tags. Then you give your final response to the task after that, with the final answer in \\boxed{}.",
"role": "system"
},
{
"content": "Three boxes contain 600 balls each. ... | open-r1/DAPO-Math-17k-Processed | math | {
"ground_truth": "270901",
"style": "rule"
} | {
"answer": "270901",
"index": 43,
"question": "Three boxes contain 600 balls each. The first box contains 600 identical red balls, the second box contains 600 identical white balls, and the third box contains 600 identical blue balls. From these three boxes, 900 balls are chosen. In how many ways can the balls b... | 0.875 | 0.987903 | 0.999194 | 0.999972 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1,368.25 | 16,884.4375 | 32 | 28 | Qwen/Qwen3-4B-Instruct-2507 |
[
{
"content": "You are a helpful assistant. You perform the given task by reasoning about it within <reasoning> ... </reasoning> tags. Then you give your final response to the task after that, with the final answer in \\boxed{}.",
"role": "system"
},
{
"content": "Let $A$, $B$, and $C$ be three point... | open-r1/DAPO-Math-17k-Processed | math | {
"ground_truth": "12",
"style": "rule"
} | {
"answer": "12",
"index": 44,
"question": "Let $A$, $B$, and $C$ be three points on the edge of a circular chord such that $B$ is due west of $C$ and $\\triangle ABC$ is an equilateral triangle with each side measuring $86$ meters. A boy swam from $A$ directly towards $B$. After covering a distance of $x$ meters... | 0.75 | 0.943548 | 0.98871 | 0.998053 | 0.999722 | 0.999969 | 0.999998 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 8,822.875 | 3,092,783.109375 | 32 | 24 | Qwen/Qwen3-4B-Instruct-2507 |
[
{
"content": "You are a helpful assistant. You perform the given task by reasoning about it within <reasoning> ... </reasoning> tags. Then you give your final response to the task after that, with the final answer in \\boxed{}.",
"role": "system"
},
{
"content": "Let $A$, $B$, $C$, and $D$ be points... | open-r1/DAPO-Math-17k-Processed | math | {
"ground_truth": "31",
"style": "rule"
} | {
"answer": "31",
"index": 45,
"question": "Let $A$, $B$, $C$, and $D$ be points on a circle such that $AB = 11$ and $CD = 19$. Point $P$ is on segment $AB$ with $AP = 6$, and $Q$ is on segment $CD$ with $CQ = 7$. The line through $P$ and $Q$ intersects the circle at $X$ and $Y$. If $PQ = 27$, find $XY$.",
"spl... | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 5,579.125 | 9,710,337.359375 | 32 | 32 | Qwen/Qwen3-4B-Instruct-2507 |
[
{
"content": "You are a helpful assistant. You perform the given task by reasoning about it within <reasoning> ... </reasoning> tags. Then you give your final response to the task after that, with the final answer in \\boxed{}.",
"role": "system"
},
{
"content": "For any real numbers $x$ and $y$ tha... | open-r1/DAPO-Math-17k-Processed | math | {
"ground_truth": "4375",
"style": "rule"
} | {
"answer": "4375",
"index": 46,
"question": "For any real numbers $x$ and $y$ that satisfy the equations:\n\\[\nx + y - xy = 155\n\\]\nand\n\\[\nx^2 + y^2 = 325\n\\]\nFind $|x^3 - y^3|$.",
"split": "train"
} | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 5,682.875 | 180,181.109375 | 32 | 32 | Qwen/Qwen3-4B-Instruct-2507 |
[
{
"content": "You are a helpful assistant. You perform the given task by reasoning about it within <reasoning> ... </reasoning> tags. Then you give your final response to the task after that, with the final answer in \\boxed{}.",
"role": "system"
},
{
"content": "There are $2023$ distinct points on ... | open-r1/DAPO-Math-17k-Processed | math | {
"ground_truth": "45",
"style": "rule"
} | {
"answer": "45",
"index": 47,
"question": "There are $2023$ distinct points on a plane, which are colored either white or red. For each white point, there are exactly two red points such that the distance from the white point to each of these red points is $2023$. Find the minimum number of red points.",
"spli... | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 3,647.125 | 1,076,116.359375 | 32 | 32 | Qwen/Qwen3-4B-Instruct-2507 |
[
{
"content": "You are a helpful assistant. You perform the given task by reasoning about it within <reasoning> ... </reasoning> tags. Then you give your final response to the task after that, with the final answer in \\boxed{}.",
"role": "system"
},
{
"content": "Find all positive integers $k$ for w... | open-r1/DAPO-Math-17k-Processed | math | {
"ground_truth": "2",
"style": "rule"
} | {
"answer": "2",
"index": 48,
"question": "Find all positive integers $k$ for which the equation:\n$$ \\text{lcm}(m,n) - \\text{gcd}(m,n) = k(m-n) $$\nhas no solution in positive integers $(m,n)$ with $m \\neq n$.",
"split": "train"
} | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 6,370.375 | 367,507.484375 | 32 | 32 | Qwen/Qwen3-4B-Instruct-2507 |
[
{
"content": "You are a helpful assistant. You perform the given task by reasoning about it within <reasoning> ... </reasoning> tags. Then you give your final response to the task after that, with the final answer in \\boxed{}.",
"role": "system"
},
{
"content": "Determine the largest $k$ such that ... | open-r1/DAPO-Math-17k-Processed | math | {
"ground_truth": "1",
"style": "rule"
} | {
"answer": "1",
"index": 49,
"question": "Determine the largest $k$ such that for all competitive graphs with $2019$ vertices, if the difference between the in-degree and out-degree of any vertex is less than or equal to $k$, then this graph is strongly connected.",
"split": "train"
} | 0.25 | 0.443548 | 0.591935 | 0.704505 | 0.788932 | 0.851471 | 0.897172 | 0.930077 | 0.953385 | 0.969599 | 0.980654 | 0.988024 | 0.992814 | 0.99584 | 0.997689 | 0.998776 | 6,438.625 | 1,193,226.984375 | 32 | 8 | Qwen/Qwen3-4B-Instruct-2507 |
[
{
"content": "You are a helpful assistant. You perform the given task by reasoning about it within <reasoning> ... </reasoning> tags. Then you give your final response to the task after that, with the final answer in \\boxed{}.",
"role": "system"
},
{
"content": "Given a regular tetrahedron with edg... | open-r1/DAPO-Math-17k-Processed | math | {
"ground_truth": "3",
"style": "rule"
} | {
"answer": "3",
"index": 50,
"question": "Given a regular tetrahedron with edge $a$, its edges are divided into $n$ equal segments, thus obtaining $n + 1$ points: $2$ at the ends and $n - 1$ inside. The following set of planes is considered:\n- Those that contain the faces of the tetrahedron, and\n- Each of the ... | 0.125 | 0.237903 | 0.339516 | 0.430617 | 0.511958 | 0.58426 | 0.64822 | 0.704505 | 0.753754 | 0.79658 | 0.833565 | 0.865267 | 0.892214 | 0.914905 | 0.933815 | 0.949388 | 9,406.375 | 1,083,523.234375 | 32 | 4 | Qwen/Qwen3-4B-Instruct-2507 |
[
{
"content": "You are a helpful assistant. You perform the given task by reasoning about it within <reasoning> ... </reasoning> tags. Then you give your final response to the task after that, with the final answer in \\boxed{}.",
"role": "system"
},
{
"content": "For some positive integer $n > m$, i... | open-r1/DAPO-Math-17k-Processed | math | {
"ground_truth": "2021",
"style": "rule"
} | {
"answer": "2021",
"index": 51,
"question": "For some positive integer $n > m$, it turns out that $n$ can be represented as a sum of $2021$ non-negative integer powers of $m$, and also as a sum of $2021$ non-negative integer powers of $m+1$. Find the maximal value of the positive integer $m$.",
"split": "train... | 0.375 | 0.616935 | 0.770161 | 0.865267 | 0.92301 | 0.957228 | 0.976969 | 0.988024 | 0.994012 | 0.997136 | 0.998698 | 0.999442 | 0.999777 | 0.999918 | 0.999973 | 0.999992 | 7,732.375 | 3,841,200.484375 | 32 | 12 | Qwen/Qwen3-4B-Instruct-2507 |
[
{
"content": "You are a helpful assistant. You perform the given task by reasoning about it within <reasoning> ... </reasoning> tags. Then you give your final response to the task after that, with the final answer in \\boxed{}.",
"role": "system"
},
{
"content": "Suppose integers $a < b < c$ satisfy... | open-r1/DAPO-Math-17k-Processed | math | {
"ground_truth": "37",
"style": "rule"
} | {
"answer": "37",
"index": 52,
"question": "Suppose integers $a < b < c$ satisfy the following conditions:\n\\[\n a + b + c = 95 \\\\\n a^2 + b^2 + c^2 = 3083\n\\]\nFind the value of $c$.",
"split": "train"
} | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 5,005.125 | 503,440.859375 | 32 | 32 | Qwen/Qwen3-4B-Instruct-2507 |
[
{
"content": "You are a helpful assistant. You perform the given task by reasoning about it within <reasoning> ... </reasoning> tags. Then you give your final response to the task after that, with the final answer in \\boxed{}.",
"role": "system"
},
{
"content": "Let $a$, $b$, $c$ be real numbers su... | open-r1/DAPO-Math-17k-Processed | math | {
"ground_truth": "18",
"style": "rule"
} | {
"answer": "18",
"index": 53,
"question": "Let $a$, $b$, $c$ be real numbers such that $a^2 - 2 = 3b - c$, $b^2 + 4 = 3 + a$, and $c^2 + 4 = 3a - b$. Find $a^4 + b^4 + c^4$.",
"split": "train"
} | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 4,594.875 | 2,018,655.609375 | 32 | 32 | Qwen/Qwen3-4B-Instruct-2507 |
[
{
"content": "You are a helpful assistant. You perform the given task by reasoning about it within <reasoning> ... </reasoning> tags. Then you give your final response to the task after that, with the final answer in \\boxed{}.",
"role": "system"
},
{
"content": "Find the smallest natural number $n$... | open-r1/DAPO-Math-17k-Processed | math | {
"ground_truth": "132",
"style": "rule"
} | {
"answer": "132",
"index": 54,
"question": "Find the smallest natural number $n$ such that the expression $n^2 - n + 11$ has exactly four prime factors, which may not be distinct.",
"split": "train"
} | 0.875 | 0.987903 | 0.999194 | 0.999972 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 10,860.125 | 1,250,263.859375 | 32 | 28 | Qwen/Qwen3-4B-Instruct-2507 |
[
{
"content": "You are a helpful assistant. You perform the given task by reasoning about it within <reasoning> ... </reasoning> tags. Then you give your final response to the task after that, with the final answer in \\boxed{}.",
"role": "system"
},
{
"content": "Let $P$ be a regular $2006$-gon. A d... | open-r1/DAPO-Math-17k-Processed | math | {
"ground_truth": "1003",
"style": "rule"
} | {
"answer": "1003",
"index": 55,
"question": "Let $P$ be a regular $2006$-gon. A diagonal is called *good* if its endpoints divide the boundary of $P$ into two parts, each composed of an odd number of sides of $P$. The sides of $P$ are also called *good*.\n\nSuppose $P$ has been dissected into triangles by $2003$... | 0.375 | 0.616935 | 0.770161 | 0.865267 | 0.92301 | 0.957228 | 0.976969 | 0.988024 | 0.994012 | 0.997136 | 0.998698 | 0.999442 | 0.999777 | 0.999918 | 0.999973 | 0.999992 | 9,403 | 286,168.75 | 32 | 12 | Qwen/Qwen3-4B-Instruct-2507 |
[
{
"content": "You are a helpful assistant. You perform the given task by reasoning about it within <reasoning> ... </reasoning> tags. Then you give your final response to the task after that, with the final answer in \\boxed{}.",
"role": "system"
},
{
"content": "Byan is playing a game called \"rave... | open-r1/DAPO-Math-17k-Processed | math | {
"ground_truth": "107",
"style": "rule"
} | {
"answer": "107",
"index": 56,
"question": "Byan is playing a game called \"raven, raven, falcon\" with his three friends. His friends sit in a circle, and Byan walks clockwise around them, tapping each friend he passes on the head and saying either \"raven\" or \"falcon,\" each with a probability of $\\frac{1}{... | 0.5 | 0.758065 | 0.887097 | 0.949388 | 0.978309 | 0.991163 | 0.996601 | 0.998776 | 0.999592 | 0.999876 | 0.999966 | 0.999992 | 0.999998 | 1 | 1 | 1 | 6,270.875 | 2,875,929.859375 | 32 | 16 | Qwen/Qwen3-4B-Instruct-2507 |
[
{
"content": "You are a helpful assistant. You perform the given task by reasoning about it within <reasoning> ... </reasoning> tags. Then you give your final response to the task after that, with the final answer in \\boxed{}.",
"role": "system"
},
{
"content": "Find all positive integers $n$ for w... | open-r1/DAPO-Math-17k-Processed | math | {
"ground_truth": "1",
"style": "rule"
} | {
"answer": "1",
"index": 57,
"question": "Find all positive integers $n$ for which all positive divisors of $n$ can be placed into the cells of a rectangular table under the following constraints:\n- Each cell contains a distinct divisor.\n- The sums of all rows are equal.\n- The sums of all columns are equal.",... | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 6,803 | 531,074.5 | 32 | 32 | Qwen/Qwen3-4B-Instruct-2507 |
[
{
"content": "You are a helpful assistant. You perform the given task by reasoning about it within <reasoning> ... </reasoning> tags. Then you give your final response to the task after that, with the final answer in \\boxed{}.",
"role": "system"
},
{
"content": "One day, students in school organize... | open-r1/DAPO-Math-17k-Processed | math | {
"ground_truth": "7",
"style": "rule"
} | {
"answer": "7",
"index": 58,
"question": "One day, students in school organized an exchange among themselves with the following rates:\n- $11$ strawberries exchange for $14$ raspberries.\n- $22$ cherries exchange for $21$ raspberries.\n- $10$ cherries exchange for $3$ bananas.\n- $5$ pears exchange for $2$ banan... | 0.75 | 0.943548 | 0.98871 | 0.998053 | 0.999722 | 0.999969 | 0.999998 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2,043.875 | 3,841,090.859375 | 32 | 24 | Qwen/Qwen3-4B-Instruct-2507 |
[
{
"content": "You are a helpful assistant. You perform the given task by reasoning about it within <reasoning> ... </reasoning> tags. Then you give your final response to the task after that, with the final answer in \\boxed{}.",
"role": "system"
},
{
"content": "In triangle $ABC$, let $D$ be the fo... | open-r1/DAPO-Math-17k-Processed | math | {
"ground_truth": "80",
"style": "rule"
} | {
"answer": "80",
"index": 59,
"question": "In triangle $ABC$, let $D$ be the foot of the altitude from $A$. Suppose that $AD = 4$, $BD = 3$, $CD = 2$, and $AB$ is extended past $B$ to a point $E$ such that $BE = 5$. Determine the value of $CE^2$.",
"split": "train"
} | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 966.75 | 36,649.9375 | 32 | 32 | Qwen/Qwen3-4B-Instruct-2507 |
[
{
"content": "You are a helpful assistant. You perform the given task by reasoning about it within <reasoning> ... </reasoning> tags. Then you give your final response to the task after that, with the final answer in \\boxed{}.",
"role": "system"
},
{
"content": "Find all integers $n$ such that $\\f... | open-r1/DAPO-Math-17k-Processed | math | {
"ground_truth": "0",
"style": "rule"
} | {
"answer": "0",
"index": 60,
"question": "Find all integers $n$ such that $\\frac{5^n - 1}{3}$ is a prime or a perfect square of an integer.",
"split": "train"
} | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 5,877 | 1,559,225 | 32 | 32 | Qwen/Qwen3-4B-Instruct-2507 |
[
{
"content": "You are a helpful assistant. You perform the given task by reasoning about it within <reasoning> ... </reasoning> tags. Then you give your final response to the task after that, with the final answer in \\boxed{}.",
"role": "system"
},
{
"content": "Find the sum of all positive integer... | open-r1/DAPO-Math-17k-Processed | math | {
"ground_truth": "10",
"style": "rule"
} | {
"answer": "10",
"index": 61,
"question": "Find the sum of all positive integers $x$ such that $|x^2-x-6|$ has exactly 4 positive integer divisors.",
"split": "train"
} | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 5,650.5 | 110,250.75 | 32 | 32 | Qwen/Qwen3-4B-Instruct-2507 |
[
{
"content": "You are a helpful assistant. You perform the given task by reasoning about it within <reasoning> ... </reasoning> tags. Then you give your final response to the task after that, with the final answer in \\boxed{}.",
"role": "system"
},
{
"content": "The numbers $1, 2, \\ldots, 10000$ a... | open-r1/DAPO-Math-17k-Processed | math | {
"ground_truth": "50",
"style": "rule"
} | {
"answer": "50",
"index": 62,
"question": "The numbers $1, 2, \\ldots, 10000$ are placed in the cells of a $100 \\times 100$ square grid, each number appearing exactly once. In this arrangement, numbers that differ by $1$ are located in adjacent cells. We then calculate the distances between the centers of every... | 0.625 | 0.866935 | 0.955645 | 0.986235 | 0.996067 | 0.99898 | 0.999765 | 0.999953 | 0.999992 | 0.999999 | 1 | 1 | 1 | 1 | 1 | 1 | 8,625.5 | 286,667.25 | 32 | 20 | Qwen/Qwen3-4B-Instruct-2507 |
[
{
"content": "You are a helpful assistant. You perform the given task by reasoning about it within <reasoning> ... </reasoning> tags. Then you give your final response to the task after that, with the final answer in \\boxed{}.",
"role": "system"
},
{
"content": "The triangle $ABC$ has sides $AB = 1... | open-r1/DAPO-Math-17k-Processed | math | {
"ground_truth": "152",
"style": "rule"
} | {
"answer": "152",
"index": 63,
"question": "The triangle $ABC$ has sides $AB = 137$, $AC = 241$, and $BC = 200$. There is a point $D$ on $BC$ such that both incircles of triangles $ABD$ and $ACD$ touch $AD$ at the same point $E$. Determine the length of $CD$.",
"split": "train"
} | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1,162.875 | 27,548.359375 | 32 | 32 | Qwen/Qwen3-4B-Instruct-2507 |
[
{
"content": "You are a helpful assistant. You perform the given task by reasoning about it within <reasoning> ... </reasoning> tags. Then you give your final response to the task after that, with the final answer in \\boxed{}.",
"role": "system"
},
{
"content": "An arrangement of 12 real numbers in... | open-r1/DAPO-Math-17k-Processed | math | {
"ground_truth": "45",
"style": "rule"
} | {
"answer": "45",
"index": 64,
"question": "An arrangement of 12 real numbers in a row is called *good* if for any four consecutive numbers, the arithmetic mean of the first and last numbers is equal to the product of the two middle numbers. Determine how many good arrangements exist in which the first and last n... | 0.125 | 0.237903 | 0.339516 | 0.430617 | 0.511958 | 0.58426 | 0.64822 | 0.704505 | 0.753754 | 0.79658 | 0.833565 | 0.865267 | 0.892214 | 0.914905 | 0.933815 | 0.949388 | 8,765 | 955,360.75 | 32 | 4 | Qwen/Qwen3-4B-Instruct-2507 |
[
{
"content": "You are a helpful assistant. You perform the given task by reasoning about it within <reasoning> ... </reasoning> tags. Then you give your final response to the task after that, with the final answer in \\boxed{}.",
"role": "system"
},
{
"content": "Find all odd natural numbers $n$ suc... | open-r1/DAPO-Math-17k-Processed | math | {
"ground_truth": "9",
"style": "rule"
} | {
"answer": "9",
"index": 65,
"question": "Find all odd natural numbers $n$ such that $d(n)$ is the largest divisor of the number $n$ different from $n$. Here, $d(n)$ represents the number of divisors of the number $n$, including $1$ and $n$.",
"split": "train"
} | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 4,559 | 196,659.75 | 32 | 32 | Qwen/Qwen3-4B-Instruct-2507 |
[
{
"content": "You are a helpful assistant. You perform the given task by reasoning about it within <reasoning> ... </reasoning> tags. Then you give your final response to the task after that, with the final answer in \\boxed{}.",
"role": "system"
},
{
"content": "Determine all natural numbers $n$ fo... | open-r1/DAPO-Math-17k-Processed | math | {
"ground_truth": "1",
"style": "rule"
} | {
"answer": "1",
"index": 66,
"question": "Determine all natural numbers $n$ for which the number $A = n^4 + 4n^3 + 5n^2 + 6n$ is a perfect square of a natural number.",
"split": "train"
} | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 4,722.75 | 2,163,000.4375 | 32 | 32 | Qwen/Qwen3-4B-Instruct-2507 |
[
{
"content": "You are a helpful assistant. You perform the given task by reasoning about it within <reasoning> ... </reasoning> tags. Then you give your final response to the task after that, with the final answer in \\boxed{}.",
"role": "system"
},
{
"content": "Let's consider a set of distinct pos... | open-r1/DAPO-Math-17k-Processed | math | {
"ground_truth": "200",
"style": "rule"
} | {
"answer": "200",
"index": 67,
"question": "Let's consider a set of distinct positive integers with a sum equal to 2023. Among these integers, there are a total of $d$ even numbers and $m$ odd numbers. Determine the maximum possible value of $2d + 4m$.",
"split": "train"
} | 0.875 | 0.987903 | 0.999194 | 0.999972 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 5,808.75 | 510,919.9375 | 32 | 28 | Qwen/Qwen3-4B-Instruct-2507 |
[
{
"content": "You are a helpful assistant. You perform the given task by reasoning about it within <reasoning> ... </reasoning> tags. Then you give your final response to the task after that, with the final answer in \\boxed{}.",
"role": "system"
},
{
"content": "It is given that $x = -2272$, $y = 1... | open-r1/DAPO-Math-17k-Processed | math | {
"ground_truth": "1987",
"style": "rule"
} | {
"answer": "1987",
"index": 68,
"question": "It is given that $x = -2272$, $y = 10^3 + 10^2c + 10b + a$, and $z = 1$ satisfy the equation $ax + by + cz = 1$, where $a, b, c$ are positive integers with $a < b < c$. Find $y$.",
"split": "train"
} | 0.625 | 0.866935 | 0.955645 | 0.986235 | 0.996067 | 0.99898 | 0.999765 | 0.999953 | 0.999992 | 0.999999 | 1 | 1 | 1 | 1 | 1 | 1 | 9,195.375 | 9,122,968.234375 | 32 | 20 | Qwen/Qwen3-4B-Instruct-2507 |
[
{
"content": "You are a helpful assistant. You perform the given task by reasoning about it within <reasoning> ... </reasoning> tags. Then you give your final response to the task after that, with the final answer in \\boxed{}.",
"role": "system"
},
{
"content": "Let $f(x)$ be a quadratic polynomial... | open-r1/DAPO-Math-17k-Processed | math | {
"ground_truth": "3",
"style": "rule"
} | {
"answer": "3",
"index": 69,
"question": "Let $f(x)$ be a quadratic polynomial such that $f(f(1)) = f(-f(-1)) = 0$ and $f(1) \\neq -f(-1)$. Suppose furthermore that the quadratic $2f(x)$ has coefficients that are nonzero integers. Find $f(0)$.",
"split": "train"
} | 0.875 | 0.987903 | 0.999194 | 0.999972 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 7,296.875 | 5,307,156.609375 | 32 | 28 | Qwen/Qwen3-4B-Instruct-2507 |
[
{
"content": "You are a helpful assistant. You perform the given task by reasoning about it within <reasoning> ... </reasoning> tags. Then you give your final response to the task after that, with the final answer in \\boxed{}.",
"role": "system"
},
{
"content": "Find all natural numbers $a > 1$ wit... | open-r1/DAPO-Math-17k-Processed | math | {
"ground_truth": "2",
"style": "rule"
} | {
"answer": "2",
"index": 70,
"question": "Find all natural numbers $a > 1$ with the property that every prime divisor of $a^6 - 1$ also divides at least one of the numbers $a^3 - 1$, $a^2 - 1$.",
"split": "train"
} | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 6,449.5 | 792,990 | 32 | 32 | Qwen/Qwen3-4B-Instruct-2507 |
[
{
"content": "You are a helpful assistant. You perform the given task by reasoning about it within <reasoning> ... </reasoning> tags. Then you give your final response to the task after that, with the final answer in \\boxed{}.",
"role": "system"
},
{
"content": "Given that nonzero real numbers $x$ ... | open-r1/DAPO-Math-17k-Processed | math | {
"ground_truth": "10",
"style": "rule"
} | {
"answer": "10",
"index": 71,
"question": "Given that nonzero real numbers $x$ and $y$ satisfy the equations $x + \\frac{1}{y} = 3$ and $y + \\frac{1}{x} = 4$, find the value of $xy + \\frac{1}{xy}$.",
"split": "train"
} | 0.875 | 0.987903 | 0.999194 | 0.999972 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2,034.875 | 143,708.359375 | 32 | 28 | Qwen/Qwen3-4B-Instruct-2507 |
[
{
"content": "You are a helpful assistant. You perform the given task by reasoning about it within <reasoning> ... </reasoning> tags. Then you give your final response to the task after that, with the final answer in \\boxed{}.",
"role": "system"
},
{
"content": "Find the smallest positive integer $... | open-r1/DAPO-Math-17k-Processed | math | {
"ground_truth": "89",
"style": "rule"
} | {
"answer": "89",
"index": 72,
"question": "Find the smallest positive integer $k$ such that $k + 25973$ is a palindrome, a number that reads the same forward and backward.",
"split": "train"
} | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2,966 | 1,661,385.5 | 32 | 32 | Qwen/Qwen3-4B-Instruct-2507 |
[
{
"content": "You are a helpful assistant. You perform the given task by reasoning about it within <reasoning> ... </reasoning> tags. Then you give your final response to the task after that, with the final answer in \\boxed{}.",
"role": "system"
},
{
"content": "Find all values of the positive inte... | open-r1/DAPO-Math-17k-Processed | math | {
"ground_truth": "1",
"style": "rule"
} | {
"answer": "1",
"index": 73,
"question": "Find all values of the positive integer $m$ such that there exist polynomials $P(x)$, $Q(x)$, and $R(x,y)$ with real coefficients satisfying the condition: For every pair of real numbers $a$ and $b$ satisfying $a^m - b^2 = 0$, we always have $P(R(a,b)) = a$ and $Q(R(a,b)... | 0.875 | 0.987903 | 0.999194 | 0.999972 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 8,278.25 | 1,123,576.1875 | 32 | 28 | Qwen/Qwen3-4B-Instruct-2507 |
[
{
"content": "You are a helpful assistant. You perform the given task by reasoning about it within <reasoning> ... </reasoning> tags. Then you give your final response to the task after that, with the final answer in \\boxed{}.",
"role": "system"
},
{
"content": "Find the smallest positive integer $... | open-r1/DAPO-Math-17k-Processed | math | {
"ground_truth": "34",
"style": "rule"
} | {
"answer": "34",
"index": 74,
"question": "Find the smallest positive integer $n$ such that the decimal representation of $n!(n+1)!(2n+1)! - 1$ has its last 30 digits all equal to 9.",
"split": "train"
} | 0.625 | 0.866935 | 0.955645 | 0.986235 | 0.996067 | 0.99898 | 0.999765 | 0.999953 | 0.999992 | 0.999999 | 1 | 1 | 1 | 1 | 1 | 1 | 4,255 | 1,156,206.5 | 32 | 20 | Qwen/Qwen3-4B-Instruct-2507 |
[
{
"content": "You are a helpful assistant. You perform the given task by reasoning about it within <reasoning> ... </reasoning> tags. Then you give your final response to the task after that, with the final answer in \\boxed{}.",
"role": "system"
},
{
"content": "Let the number of ways for a rook to... | open-r1/DAPO-Math-17k-Processed | math | {
"ground_truth": "4",
"style": "rule"
} | {
"answer": "4",
"index": 75,
"question": "Let the number of ways for a rook to return to its original square on a $4 \\times 4$ chessboard in 8 moves, starting from a corner, be $k$. Find the number of positive integers that are divisors of $k$. A \"move\" counts as shifting the rook by a positive number of squa... | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 9,440.75 | 4,680,184.9375 | 32 | 0 | Qwen/Qwen3-4B-Instruct-2507 |
[
{
"content": "You are a helpful assistant. You perform the given task by reasoning about it within <reasoning> ... </reasoning> tags. Then you give your final response to the task after that, with the final answer in \\boxed{}.",
"role": "system"
},
{
"content": "\\( \\triangle ABC \\) is an isoscel... | open-r1/DAPO-Math-17k-Processed | math | {
"ground_truth": "13",
"style": "rule"
} | {
"answer": "13",
"index": 76,
"question": "\\( \\triangle ABC \\) is an isosceles triangle with \\( AB = AC \\). Point \\( P \\) is located inside \\( \\triangle ABC \\) such that \\( \\angle BCP = 30^\\circ \\), \\( \\angle APB = 150^\\circ \\), and \\( \\angle CAP = 39^\\circ \\). Find \\( \\angle BAP \\).",
... | 0.375 | 0.616935 | 0.770161 | 0.865267 | 0.92301 | 0.957228 | 0.976969 | 0.988024 | 0.994012 | 0.997136 | 0.998698 | 0.999442 | 0.999777 | 0.999918 | 0.999973 | 0.999992 | 8,807.875 | 10,170,366.859375 | 32 | 12 | Qwen/Qwen3-4B-Instruct-2507 |
[
{
"content": "You are a helpful assistant. You perform the given task by reasoning about it within <reasoning> ... </reasoning> tags. Then you give your final response to the task after that, with the final answer in \\boxed{}.",
"role": "system"
},
{
"content": "Five congruent circles have centers ... | open-r1/DAPO-Math-17k-Processed | math | {
"ground_truth": "720",
"style": "rule"
} | {
"answer": "720",
"index": 77,
"question": "Five congruent circles have centers at the vertices of a regular pentagon so that each of the circles is tangent to its two neighbors. A sixth circle, congruent to the other five, is placed tangent to two of the five. If this sixth circle is allowed to roll without sli... | 0.25 | 0.443548 | 0.591935 | 0.704505 | 0.788932 | 0.851471 | 0.897172 | 0.930077 | 0.953385 | 0.969599 | 0.980654 | 0.988024 | 0.992814 | 0.99584 | 0.997689 | 0.998776 | 6,708 | 1,743,444 | 32 | 8 | Qwen/Qwen3-4B-Instruct-2507 |
[
{
"content": "You are a helpful assistant. You perform the given task by reasoning about it within <reasoning> ... </reasoning> tags. Then you give your final response to the task after that, with the final answer in \\boxed{}.",
"role": "system"
},
{
"content": "The thousands digit of a five-digit ... | open-r1/DAPO-Math-17k-Processed | math | {
"ground_truth": "2",
"style": "rule"
} | {
"answer": "2",
"index": 78,
"question": "The thousands digit of a five-digit number which is divisible by $37$ and $173$ is $3$. What is the hundreds digit of this number?\n\n\\[\n\\textbf{a)}\\ 0 \\quad \\textbf{b)}\\ 2 \\quad \\textbf{c)}\\ 4 \\quad \\textbf{d)}\\ 6 \\quad \\textbf{e)}\\ 8\n\\]",
"split": "... | 0.75 | 0.943548 | 0.98871 | 0.998053 | 0.999722 | 0.999969 | 0.999998 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2,812.5 | 641,693 | 32 | 24 | Qwen/Qwen3-4B-Instruct-2507 |
[
{
"content": "You are a helpful assistant. You perform the given task by reasoning about it within <reasoning> ... </reasoning> tags. Then you give your final response to the task after that, with the final answer in \\boxed{}.",
"role": "system"
},
{
"content": "Let $f(n)$ be a function satisfying ... | open-r1/DAPO-Math-17k-Processed | math | {
"ground_truth": "3816",
"style": "rule"
} | {
"answer": "3816",
"index": 79,
"question": "Let $f(n)$ be a function satisfying the following three conditions for all positive integers $n$:\n\n1. $f(n)$ is a positive integer.\n2. $f(n + 1) > f(n)$.\n3. $f(f(n)) = 3n$.\n\nFind $f(2001)$.",
"split": "train"
} | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 12,230.125 | 1,985,375.109375 | 32 | 0 | Qwen/Qwen3-4B-Instruct-2507 |
[
{
"content": "You are a helpful assistant. You perform the given task by reasoning about it within <reasoning> ... </reasoning> tags. Then you give your final response to the task after that, with the final answer in \\boxed{}.",
"role": "system"
},
{
"content": "Let $ABC$ be a triangle in the $xy$ ... | open-r1/DAPO-Math-17k-Processed | math | {
"ground_truth": "40",
"style": "rule"
} | {
"answer": "40",
"index": 80,
"question": "Let $ABC$ be a triangle in the $xy$ plane, where $B$ is at the origin $(0,0)$. Extend $BC$ to $D$ such that $BC: CD = 1:1$, extend $CA$ to $E$ such that $CA: AE = 1:2$, and extend $AB$ to $F$ such that $AB: BF = 1:3$. Let $G(32,24)$ be the centroid of the triangle $ABC$... | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 3,801.375 | 4,746,214.234375 | 32 | 32 | Qwen/Qwen3-4B-Instruct-2507 |
[
{
"content": "You are a helpful assistant. You perform the given task by reasoning about it within <reasoning> ... </reasoning> tags. Then you give your final response to the task after that, with the final answer in \\boxed{}.",
"role": "system"
},
{
"content": "Real nonzero numbers $x, y, z$ satis... | open-r1/DAPO-Math-17k-Processed | math | {
"ground_truth": "-1",
"style": "rule"
} | {
"answer": "-1",
"index": 81,
"question": "Real nonzero numbers $x, y, z$ satisfy $x + y + z = 0$. Furthermore, it is given that:\n\\[\nA = \\frac{x}{y} + \\frac{y}{z} + \\frac{z}{x} = \\frac{x}{z} + \\frac{z}{y} + \\frac{y}{x} + 1\n\\]\nDetermine the value of $A$.",
"split": "train"
} | 0.75 | 0.943548 | 0.98871 | 0.998053 | 0.999722 | 0.999969 | 0.999998 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 9,041.625 | 5,610,731.734375 | 32 | 24 | Qwen/Qwen3-4B-Instruct-2507 |
[
{
"content": "You are a helpful assistant. You perform the given task by reasoning about it within <reasoning> ... </reasoning> tags. Then you give your final response to the task after that, with the final answer in \\boxed{}.",
"role": "system"
},
{
"content": "Find all prime numbers $p$ such that... | open-r1/DAPO-Math-17k-Processed | math | {
"ground_truth": "5",
"style": "rule"
} | {
"answer": "5",
"index": 82,
"question": "Find all prime numbers $p$ such that $4p^2 + 1$ and $6p^2 + 1$ are also prime numbers.",
"split": "train"
} | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2,579.625 | 264,883.734375 | 32 | 32 | Qwen/Qwen3-4B-Instruct-2507 |
[
{
"content": "You are a helpful assistant. You perform the given task by reasoning about it within <reasoning> ... </reasoning> tags. Then you give your final response to the task after that, with the final answer in \\boxed{}.",
"role": "system"
},
{
"content": "Find the sum of all positive integer... | open-r1/DAPO-Math-17k-Processed | math | {
"ground_truth": "7",
"style": "rule"
} | {
"answer": "7",
"index": 83,
"question": "Find the sum of all positive integers $x$ such that $3 \\times 2^x = n^2 - 1$ for some positive integer $n$.",
"split": "train"
} | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 3,672.375 | 1,338,739.984375 | 32 | 32 | Qwen/Qwen3-4B-Instruct-2507 |
[
{
"content": "You are a helpful assistant. You perform the given task by reasoning about it within <reasoning> ... </reasoning> tags. Then you give your final response to the task after that, with the final answer in \\boxed{}.",
"role": "system"
},
{
"content": "Let $x$, $y$, $z$ be positive real n... | open-r1/DAPO-Math-17k-Processed | math | {
"ground_truth": "31",
"style": "rule"
} | {
"answer": "31",
"index": 84,
"question": "Let $x$, $y$, $z$ be positive real numbers satisfying the simultaneous equations:\n\\[\n\\begin{align*}\nx(y^2+yz+z^2)&=3y+10z,\\\\\ny(z^2+zx+x^2)&=21z+24x,\\\\\nz(x^2+xy+y^2)&=7x+28y.\n\\end{align*}\n\\]\nFind $xy+yz+zx$.",
"split": "train"
} | 0.5 | 0.758065 | 0.887097 | 0.949388 | 0.978309 | 0.991163 | 0.996601 | 0.998776 | 0.999592 | 0.999876 | 0.999966 | 0.999992 | 0.999998 | 1 | 1 | 1 | 9,515.625 | 5,448,546.484375 | 32 | 16 | Qwen/Qwen3-4B-Instruct-2507 |
[
{
"content": "You are a helpful assistant. You perform the given task by reasoning about it within <reasoning> ... </reasoning> tags. Then you give your final response to the task after that, with the final answer in \\boxed{}.",
"role": "system"
},
{
"content": "Given a pentagon $ABCDE$ with the fo... | open-r1/DAPO-Math-17k-Processed | math | {
"ground_truth": "90",
"style": "rule"
} | {
"answer": "90",
"index": 85,
"question": "Given a pentagon $ABCDE$ with the following properties:\n\n1. Angles $\\angle A$ and $\\angle C$ are right angles.\n2. The side lengths are $|AB| = 4$, $|BC| = 5$, $|CD| = 10$, and $|DE| = 6$.\n3. Point $C'$ is the reflection of point $C$ across line $BD$ and lies on li... | 0.75 | 0.943548 | 0.98871 | 0.998053 | 0.999722 | 0.999969 | 0.999998 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 9,764.25 | 5,157,329.6875 | 32 | 24 | Qwen/Qwen3-4B-Instruct-2507 |
[
{
"content": "You are a helpful assistant. You perform the given task by reasoning about it within <reasoning> ... </reasoning> tags. Then you give your final response to the task after that, with the final answer in \\boxed{}.",
"role": "system"
},
{
"content": "Let $f(x) = x^3 + ax^2 + bx + c$ hav... | open-r1/DAPO-Math-17k-Processed | math | {
"ground_truth": "1440",
"style": "rule"
} | {
"answer": "1440",
"index": 86,
"question": "Let $f(x) = x^3 + ax^2 + bx + c$ have solutions that are distinct negative integers. If $a+b+c = 2014$, find $c$.",
"split": "train"
} | 0.875 | 0.987903 | 0.999194 | 0.999972 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 4,247.125 | 13,673,837.609375 | 32 | 28 | Qwen/Qwen3-4B-Instruct-2507 |
[
{
"content": "You are a helpful assistant. You perform the given task by reasoning about it within <reasoning> ... </reasoning> tags. Then you give your final response to the task after that, with the final answer in \\boxed{}.",
"role": "system"
},
{
"content": "Let $\\triangle ABC$ have $AB=9$ and... | open-r1/DAPO-Math-17k-Processed | math | {
"ground_truth": "415",
"style": "rule"
} | {
"answer": "415",
"index": 87,
"question": "Let $\\triangle ABC$ have $AB=9$ and $AC=10$. A semicircle is inscribed in $\\triangle ABC$ with its center on segment $BC$ such that it is tangent to $AB$ at point $D$ and $AC$ at point $E$. If $AD=2DB$ and $r$ is the radius of the semicircle, $r^2$ can be expressed a... | 0.75 | 0.943548 | 0.98871 | 0.998053 | 0.999722 | 0.999969 | 0.999998 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 6,419.5 | 3,862,223.75 | 32 | 24 | Qwen/Qwen3-4B-Instruct-2507 |
[
{
"content": "You are a helpful assistant. You perform the given task by reasoning about it within <reasoning> ... </reasoning> tags. Then you give your final response to the task after that, with the final answer in \\boxed{}.",
"role": "system"
},
{
"content": "Triangle $ABC$ is right-angled at $A... | open-r1/DAPO-Math-17k-Processed | math | {
"ground_truth": "936",
"style": "rule"
} | {
"answer": "936",
"index": 88,
"question": "Triangle $ABC$ is right-angled at $A$. The circle with center $A$ and radius $AB$ intersects $BC$ and $AC$ internally at points $D$ and $E$ respectively. Given that $BD = 20$ and $DC = 16$, determine $AC^2$.",
"split": "train"
} | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1,852.625 | 242,214.734375 | 32 | 32 | Qwen/Qwen3-4B-Instruct-2507 |
[
{
"content": "You are a helpful assistant. You perform the given task by reasoning about it within <reasoning> ... </reasoning> tags. Then you give your final response to the task after that, with the final answer in \\boxed{}.",
"role": "system"
},
{
"content": "Petya gave Vasya a number puzzle. Pe... | open-r1/DAPO-Math-17k-Processed | math | {
"ground_truth": "4",
"style": "rule"
} | {
"answer": "4",
"index": 89,
"question": "Petya gave Vasya a number puzzle. Petya chose a digit $X$ and said, \"I am thinking of a three-digit number that is divisible by 11. The hundreds digit is $X$ and the tens digit is 3. Find the units digit.\" Vasya was excited because he knew how to solve this problem, bu... | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1,709.75 | 181,253.4375 | 32 | 32 | Qwen/Qwen3-4B-Instruct-2507 |
[
{
"content": "You are a helpful assistant. You perform the given task by reasoning about it within <reasoning> ... </reasoning> tags. Then you give your final response to the task after that, with the final answer in \\boxed{}.",
"role": "system"
},
{
"content": "A Haiku is a Japanese poem of sevent... | open-r1/DAPO-Math-17k-Processed | math | {
"ground_truth": "4",
"style": "rule"
} | {
"answer": "4",
"index": 90,
"question": "A Haiku is a Japanese poem of seventeen syllables, in three lines of five, seven, and five.\n\nAda has been told to write down five haikus plus two more every hour. This means she needs to write down five in the first hour, seven in the second hour, nine in the third hou... | 0.5 | 0.758065 | 0.887097 | 0.949388 | 0.978309 | 0.991163 | 0.996601 | 0.998776 | 0.999592 | 0.999876 | 0.999966 | 0.999992 | 0.999998 | 1 | 1 | 1 | 5,012.125 | 856,523.859375 | 32 | 16 | Qwen/Qwen3-4B-Instruct-2507 |
[
{
"content": "You are a helpful assistant. You perform the given task by reasoning about it within <reasoning> ... </reasoning> tags. Then you give your final response to the task after that, with the final answer in \\boxed{}.",
"role": "system"
},
{
"content": "The quadrilateral $ABCD$ satisfies t... | open-r1/DAPO-Math-17k-Processed | math | {
"ground_truth": "10",
"style": "rule"
} | {
"answer": "10",
"index": 91,
"question": "The quadrilateral $ABCD$ satisfies the following conditions: \\( \\angle ABC = \\angle BCD = 150^{\\circ} \\). Additionally, \\( AB = 18 \\) and \\( BC = 24 \\). Equilateral triangles \\( \\triangle APB \\), \\( \\triangle BQC \\), and \\( \\triangle CRD \\) are constru... | 0.125 | 0.237903 | 0.339516 | 0.430617 | 0.511958 | 0.58426 | 0.64822 | 0.704505 | 0.753754 | 0.79658 | 0.833565 | 0.865267 | 0.892214 | 0.914905 | 0.933815 | 0.949388 | 11,945 | 2,375,677.75 | 32 | 4 | Qwen/Qwen3-4B-Instruct-2507 |
[
{
"content": "You are a helpful assistant. You perform the given task by reasoning about it within <reasoning> ... </reasoning> tags. Then you give your final response to the task after that, with the final answer in \\boxed{}.",
"role": "system"
},
{
"content": "We are given a coin of diameter $\\f... | open-r1/DAPO-Math-17k-Processed | math | {
"ground_truth": "6029",
"style": "rule"
} | {
"answer": "6029",
"index": 92,
"question": "We are given a coin of diameter $\\frac{1}{2}$ and a checkerboard of $1 \\times 1$ squares with an area of $2010 \\times 2010$. We toss the coin such that it lands completely on the checkerboard. If the probability that the coin doesn't touch any of the lattice lines ... | 0.875 | 0.987903 | 0.999194 | 0.999972 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2,461.25 | 846,245.9375 | 32 | 28 | Qwen/Qwen3-4B-Instruct-2507 |
[
{
"content": "You are a helpful assistant. You perform the given task by reasoning about it within <reasoning> ... </reasoning> tags. Then you give your final response to the task after that, with the final answer in \\boxed{}.",
"role": "system"
},
{
"content": "Graph $G_1$ of a quadratic trinomial... | open-r1/DAPO-Math-17k-Processed | math | {
"ground_truth": "2",
"style": "rule"
} | {
"answer": "2",
"index": 93,
"question": "Graph $G_1$ of a quadratic trinomial $y = px^2 + qx + r$ with real coefficients intersects the graph $G_2$ of a quadratic trinomial $y = x^2$ at points $A$ and $B$. The intersection of tangents to $G_2$ at points $A$ and $B$ is point $C$. If $C$ lies on $G_1$, find all p... | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 3,183 | 183,942 | 32 | 32 | Qwen/Qwen3-4B-Instruct-2507 |
[
{
"content": "You are a helpful assistant. You perform the given task by reasoning about it within <reasoning> ... </reasoning> tags. Then you give your final response to the task after that, with the final answer in \\boxed{}.",
"role": "system"
},
{
"content": "Let $ABC$ be an acute-angled triangl... | open-r1/DAPO-Math-17k-Processed | math | {
"ground_truth": "1",
"style": "rule"
} | {
"answer": "1",
"index": 94,
"question": "Let $ABC$ be an acute-angled triangle. Construct points $A'$, $B'$, $C'$ on its sides $BC$, $CA$, $AB$ such that:\n- $A'B' \\parallel AB$, \n- $C'C$ is the bisector of angle $A'C'B'$, \n- $A'C' + B'C' = AB$.",
"split": "train"
} | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 5,134.75 | 1,566,368.4375 | 32 | 0 | Qwen/Qwen3-4B-Instruct-2507 |
[
{
"content": "You are a helpful assistant. You perform the given task by reasoning about it within <reasoning> ... </reasoning> tags. Then you give your final response to the task after that, with the final answer in \\boxed{}.",
"role": "system"
},
{
"content": "The radius $r$ of a circle with cent... | open-r1/DAPO-Math-17k-Processed | math | {
"ground_truth": "5",
"style": "rule"
} | {
"answer": "5",
"index": 95,
"question": "The radius $r$ of a circle with center at the origin is an odd integer. There is a point $(p^m, q^n)$ on the circle, with $p, q$ being prime numbers and $m, n$ being positive integers. Determine $r$.",
"split": "train"
} | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 4,074.875 | 884,666.109375 | 32 | 32 | Qwen/Qwen3-4B-Instruct-2507 |
[
{
"content": "You are a helpful assistant. You perform the given task by reasoning about it within <reasoning> ... </reasoning> tags. Then you give your final response to the task after that, with the final answer in \\boxed{}.",
"role": "system"
},
{
"content": "Using each of the digits $1, 2, 3, \... | open-r1/DAPO-Math-17k-Processed | math | {
"ground_truth": "8",
"style": "rule"
} | {
"answer": "8",
"index": 96,
"question": "Using each of the digits $1, 2, 3, \\ldots, 8, 9$ exactly once, we form nine, not necessarily distinct, nine-digit numbers. Their sum ends in $n$ zeroes, where $n$ is a non-negative integer. Determine the maximum possible value of $n$.",
"split": "train"
} | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 10,261 | 894,108 | 32 | 0 | Qwen/Qwen3-4B-Instruct-2507 |
[
{
"content": "You are a helpful assistant. You perform the given task by reasoning about it within <reasoning> ... </reasoning> tags. Then you give your final response to the task after that, with the final answer in \\boxed{}.",
"role": "system"
},
{
"content": "Determine the largest positive integ... | open-r1/DAPO-Math-17k-Processed | math | {
"ground_truth": "107",
"style": "rule"
} | {
"answer": "107",
"index": 97,
"question": "Determine the largest positive integer $n$ such that the following statement holds:\n\nIf $a_1, a_2, a_3, a_4, a_5, a_6$ are six distinct positive integers less than or equal to $n$, then there exist three distinct positive integers from these six, say $a$, $b$, and $c... | 0.375 | 0.616935 | 0.770161 | 0.865267 | 0.92301 | 0.957228 | 0.976969 | 0.988024 | 0.994012 | 0.997136 | 0.998698 | 0.999442 | 0.999777 | 0.999918 | 0.999973 | 0.999992 | 7,233.125 | 1,540,473.109375 | 32 | 12 | Qwen/Qwen3-4B-Instruct-2507 |
[
{
"content": "You are a helpful assistant. You perform the given task by reasoning about it within <reasoning> ... </reasoning> tags. Then you give your final response to the task after that, with the final answer in \\boxed{}.",
"role": "system"
},
{
"content": "Solve for $x$:\n\\[\nv - w + x - y +... | open-r1/DAPO-Math-17k-Processed | math | {
"ground_truth": "24",
"style": "rule"
} | {
"answer": "24",
"index": 98,
"question": "Solve for $x$:\n\\[\nv - w + x - y + z = 79 \\\\\nv + w + x + y + z = -1 \\\\\nv + 2w + 4x + 8y + 16z = -2 \\\\\nv + 3w + 9x + 27y + 81z = -1 \\\\\nv + 5w + 25x + 125y + 625z = 79.\n\\]",
"split": "train"
} | 0.875 | 0.987903 | 0.999194 | 0.999972 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 3,733.375 | 907,712.984375 | 32 | 28 | Qwen/Qwen3-4B-Instruct-2507 |
[
{
"content": "You are a helpful assistant. You perform the given task by reasoning about it within <reasoning> ... </reasoning> tags. Then you give your final response to the task after that, with the final answer in \\boxed{}.",
"role": "system"
},
{
"content": "You have a 4-digit whole number that... | open-r1/DAPO-Math-17k-Processed | math | {
"ground_truth": "3025",
"style": "rule"
} | {
"answer": "3025",
"index": 99,
"question": "You have a 4-digit whole number that is a perfect square. Another number is constructed by making the following changes to the digits of the original number:\n\n1. Add 1 to the unit's digit.\n2. Subtract 1 from the ten's digit.\n3. Add 1 to the hundred's digit.\n4. Su... | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 5,261.625 | 9,497,481.234375 | 32 | 32 | Qwen/Qwen3-4B-Instruct-2507 |
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