data_source stringclasses 1
value | prompt listlengths 2 2 | ability stringclasses 1
value | reward_model dict | extra_info dict |
|---|---|---|---|---|
../dataset/DAPO-Math-17k | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{{}}.",
"role": "system"
},
{
"content": "\n\nIn 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 $\\angl... | MATH | {
"ground_truth": "34",
"style": "rule-lighteval/MATH_v2"
} | {
"index": 0
} |
../dataset/DAPO-Math-17k | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{{}}.",
"role": "system"
},
{
"content": "\n\nLet $ABCD$ 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 ... | MATH | {
"ground_truth": "113",
"style": "rule-lighteval/MATH_v2"
} | {
"index": 1
} |
../dataset/DAPO-Math-17k | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{{}}.",
"role": "system"
},
{
"content": "\n\nLet $a, b, c$ 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 + ... | MATH | {
"ground_truth": "-3",
"style": "rule-lighteval/MATH_v2"
} | {
"index": 2
} |
../dataset/DAPO-Math-17k | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{{}}.",
"role": "system"
},
{
"content": "\n\nThere 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 b... | MATH | {
"ground_truth": "3",
"style": "rule-lighteval/MATH_v2"
} | {
"index": 3
} |
../dataset/DAPO-Math-17k | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{{}}.",
"role": "system"
},
{
"content": "\n\nLet $S$ 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... | MATH | {
"ground_truth": "37",
"style": "rule-lighteval/MATH_v2"
} | {
"index": 4
} |
../dataset/DAPO-Math-17k | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{{}}.",
"role": "system"
},
{
"content": "\n\nFor which $n$ is $n^4 + 6n^3 + 11n^2 + 3n + 31$ a perfect square?\n\n",
"role": "user"
}
] | MATH | {
"ground_truth": "10",
"style": "rule-lighteval/MATH_v2"
} | {
"index": 5
} |
../dataset/DAPO-Math-17k | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{{}}.",
"role": "system"
},
{
"content": "\n\nFour 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 $a, b, ... | MATH | {
"ground_truth": "10",
"style": "rule-lighteval/MATH_v2"
} | {
"index": 6
} |
../dataset/DAPO-Math-17k | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{{}}.",
"role": "system"
},
{
"content": "\n\n$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 th... | MATH | {
"ground_truth": "2",
"style": "rule-lighteval/MATH_v2"
} | {
"index": 7
} |
../dataset/DAPO-Math-17k | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{{}}.",
"role": "system"
},
{
"content": "\n\nDetermine the smallest prime $p$ such that $2018!$ is divisible by $p^3$, but not divisible by $p^4$.\n\n",
"role": "user"
}
] | MATH | {
"ground_truth": "509",
"style": "rule-lighteval/MATH_v2"
} | {
"index": 8
} |
../dataset/DAPO-Math-17k | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{{}}.",
"role": "system"
},
{
"content": "\n\nSuppose 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 give... | MATH | {
"ground_truth": "3",
"style": "rule-lighteval/MATH_v2"
} | {
"index": 9
} |
../dataset/DAPO-Math-17k | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{{}}.",
"role": "system"
},
{
"content": "\n\nThere 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 woul... | MATH | {
"ground_truth": "1007",
"style": "rule-lighteval/MATH_v2"
} | {
"index": 10
} |
../dataset/DAPO-Math-17k | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{{}}.",
"role": "system"
},
{
"content": "\n\nRectangle $HOMF$ 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 $BC$ a... | MATH | {
"ground_truth": "28",
"style": "rule-lighteval/MATH_v2"
} | {
"index": 11
} |
../dataset/DAPO-Math-17k | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{{}}.",
"role": "system"
},
{
"content": "\n\nLet $a$, $b$, $c$ 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 $k$.\n\n",
... | MATH | {
"ground_truth": "5",
"style": "rule-lighteval/MATH_v2"
} | {
"index": 12
} |
../dataset/DAPO-Math-17k | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{{}}.",
"role": "system"
},
{
"content": "\n\nTwo 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 (... | MATH | {
"ground_truth": "5",
"style": "rule-lighteval/MATH_v2"
} | {
"index": 13
} |
../dataset/DAPO-Math-17k | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{{}}.",
"role": "system"
},
{
"content": "\n\nBurrito 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.... | MATH | {
"ground_truth": "1",
"style": "rule-lighteval/MATH_v2"
} | {
"index": 14
} |
../dataset/DAPO-Math-17k | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{{}}.",
"role": "system"
},
{
"content": "\n\nDanial 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... | MATH | {
"ground_truth": "15",
"style": "rule-lighteval/MATH_v2"
} | {
"index": 15
} |
../dataset/DAPO-Math-17k | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{{}}.",
"role": "system"
},
{
"content": "\n\nSabrina 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 disca... | MATH | {
"ground_truth": "10",
"style": "rule-lighteval/MATH_v2"
} | {
"index": 16
} |
../dataset/DAPO-Math-17k | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{{}}.",
"role": "system"
},
{
"content": "\n\nDenote by $S(n)$ the sum of the digits of the positive integer $n$. Find all the solutions of the equation $n(S(n)-1)=2010.$\n\n",
"role": "user"
}
] | MATH | {
"ground_truth": "402",
"style": "rule-lighteval/MATH_v2"
} | {
"index": 17
} |
../dataset/DAPO-Math-17k | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{{}}.",
"role": "system"
},
{
"content": "\n\nFor 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... | MATH | {
"ground_truth": "7",
"style": "rule-lighteval/MATH_v2"
} | {
"index": 18
} |
../dataset/DAPO-Math-17k | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{{}}.",
"role": "system"
},
{
"content": "\n\nFind all integers $k$ such that all roots of the following polynomial are also integers:\n\n$$f(x) = x^3 - (k-3)x^2 - 11x + (4k-8).$$\n\n",
"role": "user"
}
] | MATH | {
"ground_truth": "5",
"style": "rule-lighteval/MATH_v2"
} | {
"index": 19
} |
../dataset/DAPO-Math-17k | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{{}}.",
"role": "system"
},
{
"content": "\n\nA 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 dis... | MATH | {
"ground_truth": "300",
"style": "rule-lighteval/MATH_v2"
} | {
"index": 20
} |
../dataset/DAPO-Math-17k | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{{}}.",
"role": "system"
},
{
"content": "\n\nIf $a, b$ are real numbers such that $a^3 + 12a^2 + 49a + 69 = 0$ and $b^3 - 9b^2 + 28b - 31 = 0$, find $a + b$.\n\n",
"role": "user"
}
] | MATH | {
"ground_truth": "1",
"style": "rule-lighteval/MATH_v2"
} | {
"index": 21
} |
../dataset/DAPO-Math-17k | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{{}}.",
"role": "system"
},
{
"content": "\n\nLet $S$ 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}\... | MATH | {
"ground_truth": "37",
"style": "rule-lighteval/MATH_v2"
} | {
"index": 22
} |
../dataset/DAPO-Math-17k | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{{}}.",
"role": "system"
},
{
"content": "\n\nSome 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 ... | MATH | {
"ground_truth": "-3",
"style": "rule-lighteval/MATH_v2"
} | {
"index": 23
} |
../dataset/DAPO-Math-17k | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{{}}.",
"role": "system"
},
{
"content": "\n\nFind all positive integers $n$ for which the largest prime divisor of $n^2 + 3$ is equal to the least prime divisor of $n^4 + 6$.\n\n",
"role": "user"
}
] | MATH | {
"ground_truth": "3",
"style": "rule-lighteval/MATH_v2"
} | {
"index": 24
} |
../dataset/DAPO-Math-17k | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{{}}.",
"role": "system"
},
{
"content": "\n\nCharlie 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 t... | MATH | {
"ground_truth": "8556",
"style": "rule-lighteval/MATH_v2"
} | {
"index": 25
} |
../dataset/DAPO-Math-17k | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{{}}.",
"role": "system"
},
{
"content": "\n\nThe 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. A... | MATH | {
"ground_truth": "14",
"style": "rule-lighteval/MATH_v2"
} | {
"index": 26
} |
../dataset/DAPO-Math-17k | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{{}}.",
"role": "system"
},
{
"content": "\n\nJoe 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... | MATH | {
"ground_truth": "7",
"style": "rule-lighteval/MATH_v2"
} | {
"index": 27
} |
../dataset/DAPO-Math-17k | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{{}}.",
"role": "system"
},
{
"content": "\n\nThe 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 t... | MATH | {
"ground_truth": "3",
"style": "rule-lighteval/MATH_v2"
} | {
"index": 28
} |
../dataset/DAPO-Math-17k | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{{}}.",
"role": "system"
},
{
"content": "\n\nConsider two distinct positive integers $a$ and $b$ that have integer arithmetic, geometric, and harmonic means. Find the minimal value of $|a-b|$.\n\n",
"role": "user"... | MATH | {
"ground_truth": "30",
"style": "rule-lighteval/MATH_v2"
} | {
"index": 29
} |
../dataset/DAPO-Math-17k | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{{}}.",
"role": "system"
},
{
"content": "\n\nDexter 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 fro... | MATH | {
"ground_truth": "1010",
"style": "rule-lighteval/MATH_v2"
} | {
"index": 30
} |
../dataset/DAPO-Math-17k | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{{}}.",
"role": "system"
},
{
"content": "\n\nTriangle $\\triangle{ABC}$ 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 po... | MATH | {
"ground_truth": "40",
"style": "rule-lighteval/MATH_v2"
} | {
"index": 31
} |
../dataset/DAPO-Math-17k | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{{}}.",
"role": "system"
},
{
"content": "\n\nFind 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.\n\n",
"role": "user"
}
] | MATH | {
"ground_truth": "9",
"style": "rule-lighteval/MATH_v2"
} | {
"index": 32
} |
../dataset/DAPO-Math-17k | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{{}}.",
"role": "system"
},
{
"content": "\n\nLet $M$ be the set of those positive integers which are not divisible by $3$. The sum of $2n$ consecutive elements of $M$ is $300$. Determine $n$.\n\n",
"role": "user"
... | MATH | {
"ground_truth": "10",
"style": "rule-lighteval/MATH_v2"
} | {
"index": 33
} |
../dataset/DAPO-Math-17k | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{{}}.",
"role": "system"
},
{
"content": "\n\nPetya 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... | MATH | {
"ground_truth": "4",
"style": "rule-lighteval/MATH_v2"
} | {
"index": 34
} |
../dataset/DAPO-Math-17k | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{{}}.",
"role": "system"
},
{
"content": "\n\nDetermine the greatest power of $2$ that is a factor of $3^{15} + 3^{11} + 3^{6} + 1$.\n\n",
"role": "user"
}
] | MATH | {
"ground_truth": "64",
"style": "rule-lighteval/MATH_v2"
} | {
"index": 35
} |
../dataset/DAPO-Math-17k | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{{}}.",
"role": "system"
},
{
"content": "\n\nOn 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... | MATH | {
"ground_truth": "8",
"style": "rule-lighteval/MATH_v2"
} | {
"index": 36
} |
../dataset/DAPO-Math-17k | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{{}}.",
"role": "system"
},
{
"content": "\n\nFor 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 $\\frac{s(n)}{n}$?\... | MATH | {
"ground_truth": "1099",
"style": "rule-lighteval/MATH_v2"
} | {
"index": 37
} |
../dataset/DAPO-Math-17k | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{{}}.",
"role": "system"
},
{
"content": "\n\nSuppose 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 acquainta... | MATH | {
"ground_truth": "21",
"style": "rule-lighteval/MATH_v2"
} | {
"index": 38
} |
../dataset/DAPO-Math-17k | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{{}}.",
"role": "system"
},
{
"content": "\n\nHow 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... | MATH | {
"ground_truth": "40320",
"style": "rule-lighteval/MATH_v2"
} | {
"index": 39
} |
../dataset/DAPO-Math-17k | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{{}}.",
"role": "system"
},
{
"content": "\n\nFind 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.\n\n",
"role": "user"... | MATH | {
"ground_truth": "1",
"style": "rule-lighteval/MATH_v2"
} | {
"index": 40
} |
../dataset/DAPO-Math-17k | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{{}}.",
"role": "system"
},
{
"content": "\n\nLet $ABCDEFGHIJ$ 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 $... | MATH | {
"ground_truth": "5",
"style": "rule-lighteval/MATH_v2"
} | {
"index": 41
} |
../dataset/DAPO-Math-17k | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{{}}.",
"role": "system"
},
{
"content": "\n\nDetermine all integers $m$ for which all solutions of the equation $3x^3 - 3x^2 + m = 0$ are rational.\n\n",
"role": "user"
}
] | MATH | {
"ground_truth": "0",
"style": "rule-lighteval/MATH_v2"
} | {
"index": 42
} |
../dataset/DAPO-Math-17k | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{{}}.",
"role": "system"
},
{
"content": "\n\nThree 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 identi... | MATH | {
"ground_truth": "270901",
"style": "rule-lighteval/MATH_v2"
} | {
"index": 43
} |
../dataset/DAPO-Math-17k | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{{}}.",
"role": "system"
},
{
"content": "\n\nLet $A$, $B$, 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 measur... | MATH | {
"ground_truth": "12",
"style": "rule-lighteval/MATH_v2"
} | {
"index": 44
} |
../dataset/DAPO-Math-17k | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{{}}.",
"role": "system"
},
{
"content": "\n\nLet $A$, $B$, $C$, 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 $CQ = 7$. Th... | MATH | {
"ground_truth": "31",
"style": "rule-lighteval/MATH_v2"
} | {
"index": 45
} |
../dataset/DAPO-Math-17k | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{{}}.",
"role": "system"
},
{
"content": "\n\nFor 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 $|x^3 - y^3|$.\n\n",
"role": "user"
}
] | MATH | {
"ground_truth": "4375",
"style": "rule-lighteval/MATH_v2"
} | {
"index": 46
} |
../dataset/DAPO-Math-17k | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{{}}.",
"role": "system"
},
{
"content": "\n\nThere 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 w... | MATH | {
"ground_truth": "45",
"style": "rule-lighteval/MATH_v2"
} | {
"index": 47
} |
../dataset/DAPO-Math-17k | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{{}}.",
"role": "system"
},
{
"content": "\n\nFind 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 $m \\neq n$.\n... | MATH | {
"ground_truth": "2",
"style": "rule-lighteval/MATH_v2"
} | {
"index": 48
} |
../dataset/DAPO-Math-17k | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{{}}.",
"role": "system"
},
{
"content": "\n\nDetermine 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 eq... | MATH | {
"ground_truth": "1",
"style": "rule-lighteval/MATH_v2"
} | {
"index": 49
} |
../dataset/DAPO-Math-17k | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{{}}.",
"role": "system"
},
{
"content": "\n\nGiven 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 s... | MATH | {
"ground_truth": "3",
"style": "rule-lighteval/MATH_v2"
} | {
"index": 50
} |
../dataset/DAPO-Math-17k | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{{}}.",
"role": "system"
},
{
"content": "\n\nFor 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 ... | MATH | {
"ground_truth": "2021",
"style": "rule-lighteval/MATH_v2"
} | {
"index": 51
} |
../dataset/DAPO-Math-17k | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{{}}.",
"role": "system"
},
{
"content": "\n\nSuppose 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 $c$.\n\n",
"role": "user"
}... | MATH | {
"ground_truth": "37",
"style": "rule-lighteval/MATH_v2"
} | {
"index": 52
} |
../dataset/DAPO-Math-17k | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{{}}.",
"role": "system"
},
{
"content": "\n\nLet $a$, $b$, $c$ be real numbers such that $a^2 - 2 = 3b - c$, $b^2 + 4 = 3 + a$, and $c^2 + 4 = 3a - b$. Find $a^4 + b^4 + c^4$.\n\n",
"role": "user"
}
] | MATH | {
"ground_truth": "18",
"style": "rule-lighteval/MATH_v2"
} | {
"index": 53
} |
../dataset/DAPO-Math-17k | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{{}}.",
"role": "system"
},
{
"content": "\n\nFind the smallest natural number $n$ such that the expression $n^2 - n + 11$ has exactly four prime factors, which may not be distinct.\n\n",
"role": "user"
}
] | MATH | {
"ground_truth": "132",
"style": "rule-lighteval/MATH_v2"
} | {
"index": 54
} |
../dataset/DAPO-Math-17k | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{{}}.",
"role": "system"
},
{
"content": "\n\nLet $P$ 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... | MATH | {
"ground_truth": "1003",
"style": "rule-lighteval/MATH_v2"
} | {
"index": 55
} |
../dataset/DAPO-Math-17k | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{{}}.",
"role": "system"
},
{
"content": "\n\nByan 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 pas... | MATH | {
"ground_truth": "107",
"style": "rule-lighteval/MATH_v2"
} | {
"index": 56
} |
../dataset/DAPO-Math-17k | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{{}}.",
"role": "system"
},
{
"content": "\n\nFind 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 cont... | MATH | {
"ground_truth": "1",
"style": "rule-lighteval/MATH_v2"
} | {
"index": 57
} |
../dataset/DAPO-Math-17k | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{{}}.",
"role": "system"
},
{
"content": "\n\nOne day, students in school organized an exchange among themselves with the following rates:\n- $11$ strawberries exchange for $14$ raspberries.\n- $22$ cherries exchange f... | MATH | {
"ground_truth": "7",
"style": "rule-lighteval/MATH_v2"
} | {
"index": 58
} |
../dataset/DAPO-Math-17k | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{{}}.",
"role": "system"
},
{
"content": "\n\nIn 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 $BE = 5$.... | MATH | {
"ground_truth": "80",
"style": "rule-lighteval/MATH_v2"
} | {
"index": 59
} |
../dataset/DAPO-Math-17k | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{{}}.",
"role": "system"
},
{
"content": "\n\nFind all integers $n$ such that $\\frac{5^n - 1}{3}$ is a prime or a perfect square of an integer.\n\n",
"role": "user"
}
] | MATH | {
"ground_truth": "0",
"style": "rule-lighteval/MATH_v2"
} | {
"index": 60
} |
../dataset/DAPO-Math-17k | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{{}}.",
"role": "system"
},
{
"content": "\n\nFind the sum of all positive integers $x$ such that $|x^2-x-6|$ has exactly 4 positive integer divisors.\n\n",
"role": "user"
}
] | MATH | {
"ground_truth": "10",
"style": "rule-lighteval/MATH_v2"
} | {
"index": 61
} |
../dataset/DAPO-Math-17k | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{{}}.",
"role": "system"
},
{
"content": "\n\nThe 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 ... | MATH | {
"ground_truth": "50",
"style": "rule-lighteval/MATH_v2"
} | {
"index": 62
} |
../dataset/DAPO-Math-17k | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{{}}.",
"role": "system"
},
{
"content": "\n\nThe 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 sa... | MATH | {
"ground_truth": "152",
"style": "rule-lighteval/MATH_v2"
} | {
"index": 63
} |
../dataset/DAPO-Math-17k | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{{}}.",
"role": "system"
},
{
"content": "\n\nAn 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 o... | MATH | {
"ground_truth": "45",
"style": "rule-lighteval/MATH_v2"
} | {
"index": 64
} |
../dataset/DAPO-Math-17k | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{{}}.",
"role": "system"
},
{
"content": "\n\nFind 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 ... | MATH | {
"ground_truth": "9",
"style": "rule-lighteval/MATH_v2"
} | {
"index": 65
} |
../dataset/DAPO-Math-17k | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{{}}.",
"role": "system"
},
{
"content": "\n\nDetermine all natural numbers $n$ for which the number $A = n^4 + 4n^3 + 5n^2 + 6n$ is a perfect square of a natural number.\n\n",
"role": "user"
}
] | MATH | {
"ground_truth": "1",
"style": "rule-lighteval/MATH_v2"
} | {
"index": 66
} |
../dataset/DAPO-Math-17k | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{{}}.",
"role": "system"
},
{
"content": "\n\nLet'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 ... | MATH | {
"ground_truth": "200",
"style": "rule-lighteval/MATH_v2"
} | {
"index": 67
} |
../dataset/DAPO-Math-17k | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{{}}.",
"role": "system"
},
{
"content": "\n\nIt 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 $a < b < c$. Fin... | MATH | {
"ground_truth": "1987",
"style": "rule-lighteval/MATH_v2"
} | {
"index": 68
} |
../dataset/DAPO-Math-17k | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{{}}.",
"role": "system"
},
{
"content": "\n\nLet $f(x)$ 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 n... | MATH | {
"ground_truth": "3",
"style": "rule-lighteval/MATH_v2"
} | {
"index": 69
} |
../dataset/DAPO-Math-17k | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{{}}.",
"role": "system"
},
{
"content": "\n\nFind all natural numbers $a > 1$ with the property that every prime divisor of $a^6 - 1$ also divides at least one of the numbers $a^3 - 1$, $a^2 - 1$.\n\n",
"role": "u... | MATH | {
"ground_truth": "2",
"style": "rule-lighteval/MATH_v2"
} | {
"index": 70
} |
../dataset/DAPO-Math-17k | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{{}}.",
"role": "system"
},
{
"content": "\n\nGiven 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 $xy + \\frac{1}{xy}$.\n\n",
"role... | MATH | {
"ground_truth": "10",
"style": "rule-lighteval/MATH_v2"
} | {
"index": 71
} |
../dataset/DAPO-Math-17k | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{{}}.",
"role": "system"
},
{
"content": "\n\nFind the smallest positive integer $k$ such that $k + 25973$ is a palindrome, a number that reads the same forward and backward.\n\n",
"role": "user"
}
] | MATH | {
"ground_truth": "89",
"style": "rule-lighteval/MATH_v2"
} | {
"index": 72
} |
../dataset/DAPO-Math-17k | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{{}}.",
"role": "system"
},
{
"content": "\n\nFind 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 o... | MATH | {
"ground_truth": "1",
"style": "rule-lighteval/MATH_v2"
} | {
"index": 73
} |
../dataset/DAPO-Math-17k | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{{}}.",
"role": "system"
},
{
"content": "\n\nFind 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.\n\n",
"role": "user"
}
] | MATH | {
"ground_truth": "34",
"style": "rule-lighteval/MATH_v2"
} | {
"index": 74
} |
../dataset/DAPO-Math-17k | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{{}}.",
"role": "system"
},
{
"content": "\n\nLet 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 int... | MATH | {
"ground_truth": "4",
"style": "rule-lighteval/MATH_v2"
} | {
"index": 75
} |
../dataset/DAPO-Math-17k | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{{}}.",
"role": "system"
},
{
"content": "\n\n\\( \\triangle ABC \\) is an isosceles triangle with \\( AB = AC \\). Point \\( P \\) is located inside \\( \\triangle ABC \\) such that \\( \\angle BCP = 30^\\circ \\), \\... | MATH | {
"ground_truth": "13",
"style": "rule-lighteval/MATH_v2"
} | {
"index": 76
} |
../dataset/DAPO-Math-17k | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{{}}.",
"role": "system"
},
{
"content": "\n\nFive 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 othe... | MATH | {
"ground_truth": "720",
"style": "rule-lighteval/MATH_v2"
} | {
"index": 77
} |
../dataset/DAPO-Math-17k | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{{}}.",
"role": "system"
},
{
"content": "\n\nThe 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{... | MATH | {
"ground_truth": "2",
"style": "rule-lighteval/MATH_v2"
} | {
"index": 78
} |
../dataset/DAPO-Math-17k | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{{}}.",
"role": "system"
},
{
"content": "\n\nLet $f(n)$ 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)) = ... | MATH | {
"ground_truth": "3816",
"style": "rule-lighteval/MATH_v2"
} | {
"index": 79
} |
../dataset/DAPO-Math-17k | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{{}}.",
"role": "system"
},
{
"content": "\n\nLet $ABC$ 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... | MATH | {
"ground_truth": "40",
"style": "rule-lighteval/MATH_v2"
} | {
"index": 80
} |
../dataset/DAPO-Math-17k | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{{}}.",
"role": "system"
},
{
"content": "\n\nReal 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} + ... | MATH | {
"ground_truth": "-1",
"style": "rule-lighteval/MATH_v2"
} | {
"index": 81
} |
../dataset/DAPO-Math-17k | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{{}}.",
"role": "system"
},
{
"content": "\n\nFind all prime numbers $p$ such that $4p^2 + 1$ and $6p^2 + 1$ are also prime numbers.\n\n",
"role": "user"
}
] | MATH | {
"ground_truth": "5",
"style": "rule-lighteval/MATH_v2"
} | {
"index": 82
} |
../dataset/DAPO-Math-17k | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{{}}.",
"role": "system"
},
{
"content": "\n\nFind the sum of all positive integers $x$ such that $3 \\times 2^x = n^2 - 1$ for some positive integer $n$.\n\n",
"role": "user"
}
] | MATH | {
"ground_truth": "7",
"style": "rule-lighteval/MATH_v2"
} | {
"index": 83
} |
../dataset/DAPO-Math-17k | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{{}}.",
"role": "system"
},
{
"content": "\n\nLet $x$, $y$, $z$ 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... | MATH | {
"ground_truth": "31",
"style": "rule-lighteval/MATH_v2"
} | {
"index": 84
} |
../dataset/DAPO-Math-17k | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{{}}.",
"role": "system"
},
{
"content": "\n\nGiven 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| = ... | MATH | {
"ground_truth": "90",
"style": "rule-lighteval/MATH_v2"
} | {
"index": 85
} |
../dataset/DAPO-Math-17k | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{{}}.",
"role": "system"
},
{
"content": "\n\nLet $f(x) = x^3 + ax^2 + bx + c$ have solutions that are distinct negative integers. If $a+b+c = 2014$, find $c$.\n\n",
"role": "user"
}
] | MATH | {
"ground_truth": "1440",
"style": "rule-lighteval/MATH_v2"
} | {
"index": 86
} |
../dataset/DAPO-Math-17k | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{{}}.",
"role": "system"
},
{
"content": "\n\nLet $\\triangle ABC$ 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... | MATH | {
"ground_truth": "415",
"style": "rule-lighteval/MATH_v2"
} | {
"index": 87
} |
../dataset/DAPO-Math-17k | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{{}}.",
"role": "system"
},
{
"content": "\n\nTriangle $ABC$ 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 = 2... | MATH | {
"ground_truth": "936",
"style": "rule-lighteval/MATH_v2"
} | {
"index": 88
} |
../dataset/DAPO-Math-17k | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{{}}.",
"role": "system"
},
{
"content": "\n\nPetya 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 ... | MATH | {
"ground_truth": "4",
"style": "rule-lighteval/MATH_v2"
} | {
"index": 89
} |
../dataset/DAPO-Math-17k | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{{}}.",
"role": "system"
},
{
"content": "\n\nA 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 me... | MATH | {
"ground_truth": "4",
"style": "rule-lighteval/MATH_v2"
} | {
"index": 90
} |
../dataset/DAPO-Math-17k | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{{}}.",
"role": "system"
},
{
"content": "\n\nThe quadrilateral $ABCD$ satisfies the following conditions: \\( \\angle ABC = \\angle BCD = 150^{\\circ} \\). Additionally, \\( AB = 18 \\) and \\( BC = 24 \\). Equilatera... | MATH | {
"ground_truth": "10",
"style": "rule-lighteval/MATH_v2"
} | {
"index": 91
} |
../dataset/DAPO-Math-17k | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{{}}.",
"role": "system"
},
{
"content": "\n\nWe 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 complete... | MATH | {
"ground_truth": "6029",
"style": "rule-lighteval/MATH_v2"
} | {
"index": 92
} |
../dataset/DAPO-Math-17k | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{{}}.",
"role": "system"
},
{
"content": "\n\nGraph $G_1$ 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 int... | MATH | {
"ground_truth": "2",
"style": "rule-lighteval/MATH_v2"
} | {
"index": 93
} |
../dataset/DAPO-Math-17k | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{{}}.",
"role": "system"
},
{
"content": "\n\nLet $ABC$ 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 angl... | MATH | {
"ground_truth": "1",
"style": "rule-lighteval/MATH_v2"
} | {
"index": 94
} |
../dataset/DAPO-Math-17k | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{{}}.",
"role": "system"
},
{
"content": "\n\nThe 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 positi... | MATH | {
"ground_truth": "5",
"style": "rule-lighteval/MATH_v2"
} | {
"index": 95
} |
../dataset/DAPO-Math-17k | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{{}}.",
"role": "system"
},
{
"content": "\n\nUsing 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... | MATH | {
"ground_truth": "8",
"style": "rule-lighteval/MATH_v2"
} | {
"index": 96
} |
../dataset/DAPO-Math-17k | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{{}}.",
"role": "system"
},
{
"content": "\n\nDetermine 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 equ... | MATH | {
"ground_truth": "107",
"style": "rule-lighteval/MATH_v2"
} | {
"index": 97
} |
../dataset/DAPO-Math-17k | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{{}}.",
"role": "system"
},
{
"content": "\n\nSolve 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 + 62... | MATH | {
"ground_truth": "24",
"style": "rule-lighteval/MATH_v2"
} | {
"index": 98
} |
../dataset/DAPO-Math-17k | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{{}}.",
"role": "system"
},
{
"content": "\n\nYou 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... | MATH | {
"ground_truth": "3025",
"style": "rule-lighteval/MATH_v2"
} | {
"index": 99
} |
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