data_source stringclasses 1
value | prompt listlengths 1 1 | ability stringclasses 1
value | reward_model dict |
|---|---|---|---|
math_dapo | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nLet $m, n, p$ be fixed positive real numbers which satisfy $m n p=8$. Depending on these constants, find the minimum o... | MATH | {
"ground_truth": "36",
"style": "rule-lighteval/MATH_v2"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nIn rectangle $ADEH$, points $B$ and $C$ trisect $\\overline{AD}$, and points $G$ and $F$ trisect $\\overline{HE}$. In ... | MATH | {
"ground_truth": "3",
"style": "rule-lighteval/MATH_v2"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nA token is placed in the leftmost square in a strip of four squares. In each move, you are allowed to move the token l... | MATH | {
"ground_truth": "377",
"style": "rule-lighteval/MATH_v2"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\n设 f(x)\\in C^{\\infty}(\\bR)，满足 f''(x)=xf(x)，且 f(0)=18，f'(0)=3. 设 f(x) 的泰勒展开式为 \\ds{n=0}{\\infty}a_nx^n，求 \\left[\\df{... | MATH | {
"ground_truth": "21",
"style": "rule-lighteval/MATH_v2"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\n已知复数数列 $\\left\\{z_{n}\\right\\}$ 满足 $z_{1}=1, z_{n+1}=\\overline{z_{n}}+1+n \\mathrm{i}$ ，其中 $n=1,2, \\cdots$ ，其中 i 是... | MATH | {
"ground_truth": "2015",
"style": "rule-lighteval/MATH_v2"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\n对于每个自然数 \\(n\\)，抛物线 \\(y=\\left(n^{2}+n\\right) x^{2}-(2 n+1) x+1\\) 与 \\(x\\) 轴交于 \\(A_{n}, B_{n}\\)两点，以 \\(\\left|A_... | MATH | {
"ground_truth": "3985",
"style": "rule-lighteval/MATH_v2"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nLet $A$ be a real $4 \\times 2$ matrix and $B$ be a real $2 \\times 4$ matrix such that $$ AB=\\left(\\begin{array}{cc... | MATH | {
"ground_truth": "4",
"style": "rule-lighteval/MATH_v2"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nAlice is counting up by fives, starting with the number $3$. Meanwhile, Bob is counting down by fours, starting with t... | MATH | {
"ground_truth": "101",
"style": "rule-lighteval/MATH_v2"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nIn \\(\\triangle ABC\\), \\(AB=6\\), \\(AC=8\\), \\(BC=10\\), and \\(D\\) is the midpoint of \\(\\overline{BC}\\). Fin... | MATH | {
"ground_truth": "23",
"style": "rule-lighteval/MATH_v2"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\n对矩阵 P，定义 e^P=I+\\ds{m=1}{\\infty}\\df{1}{m!}P^m. 设 20 阶实矩阵 A 满足 e^A=I_{20}，且特征值的模长不超过 20，则这样的互不复相似的 A 有__________个.\n\... | MATH | {
"ground_truth": "286",
"style": "rule-lighteval/MATH_v2"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nSeven teams play a soccer tournament in which each team plays every other team exactly once. No ties occur, each team ... | MATH | {
"ground_truth": "831",
"style": "rule-lighteval/MATH_v2"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nFind the number of partitions of the set $\\{1,2,3,\\cdots ,11,12\\}$ into three nonempty subsets such that no subset ... | MATH | {
"ground_truth": "1023",
"style": "rule-lighteval/MATH_v2"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\n给定凸 20 边形 $P$ 。用 $P$ 的 17 条在内部不相交的对角线将 $P$ 分割成 18 个三角形。所得图形称为 $P$ 的一个三角剖分图。对 $P$ 的任意一个三角剖分图 $T, P$ 的 20 条边以及添加的 17 条对角... | MATH | {
"ground_truth": "89",
"style": "rule-lighteval/MATH_v2"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\n64 numbers (not necessarily distinct) are placed on the squares of a chessboard such that the sum of the numbers in ev... | MATH | {
"ground_truth": "7",
"style": "rule-lighteval/MATH_v2"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nA \"lame king\" is a chess piece that can move from a cell to any cell that shares at least one vertex with it, except... | MATH | {
"ground_truth": "25",
"style": "rule-lighteval/MATH_v2"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nA store offers packages of $12$ pens for $\\$10$ and packages of $20$ pens for $\\$15$. Using only these two types of ... | MATH | {
"ground_truth": "224",
"style": "rule-lighteval/MATH_v2"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\n在直角坐标系 xoy 中，点 $A\\left(x_{1}, y_{1}\\right)$ 和点 $B\\left(x_{2}, y_{2}\\right)$ 的坐标均为一位的正整数。 $O A$ 与 $x$ 轴正方向的夹角大于 $45... | MATH | {
"ground_truth": "1985",
"style": "rule-lighteval/MATH_v2"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nGiven that the expected amount of $1$s in a randomly selected $2021$-digit number is $\\frac{m}{n}$, where $m$ and $n$... | MATH | {
"ground_truth": "1828",
"style": "rule-lighteval/MATH_v2"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nAlex, Mel, and Chelsea play a game that has $6$ rounds. In each round there is a single winner, and the outcomes of th... | MATH | {
"ground_truth": "41",
"style": "rule-lighteval/MATH_v2"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nLet $\\theta$ be the smallest acute angle for which $\\sin \\theta,$ $\\sin 2 \\theta,$ $\\sin 3 \\theta$ form an arit... | MATH | {
"ground_truth": "7",
"style": "rule-lighteval/MATH_v2"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nSuppose $z^{3}=2+2i$, where $i=\\sqrt{-1}$. The product of all possible values of the real part of $z$ can be written ... | MATH | {
"ground_truth": "3",
"style": "rule-lighteval/MATH_v2"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nHow many numbers $\\overline{abcd}$ with different digits satisfy the following property: if we replace the largest di... | MATH | {
"ground_truth": "162",
"style": "rule-lighteval/MATH_v2"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nA $20 \\times 20 \\times 20$ block is cut up into 8000 non-overlapping unit cubes, and a number is assigned to each cu... | MATH | {
"ground_truth": "333",
"style": "rule-lighteval/MATH_v2"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nA function $f(x)$ satisfies $f(x) = f\\left(\\frac{c}{x}\\right)$ for some real number $c > 1$ and all positive number... | MATH | {
"ground_truth": "6",
"style": "rule-lighteval/MATH_v2"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nTriangle $ABC$ has side lengths $AB = 13$, $AC = 14$, and $BC = 15$ and centroid $G$. What is the area of the triangle... | MATH | {
"ground_truth": "28",
"style": "rule-lighteval/MATH_v2"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nPaul and Sara are playing a game with integers on a whiteboard, with Paul going first. When it is Paul's turn, he can ... | MATH | {
"ground_truth": "3",
"style": "rule-lighteval/MATH_v2"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nFind the least natural number $n$, which has at least 6 different divisors $1 = d_1 < d_2 < d_3 < d_4 < d_5 < d_6 < \\... | MATH | {
"ground_truth": "494",
"style": "rule-lighteval/MATH_v2"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nSuppose that $3\\triangle_4=\\triangle2_{11}$, where $\\triangle$ represents a digit 0-9. What is the value of the mis... | MATH | {
"ground_truth": "1",
"style": "rule-lighteval/MATH_v2"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nA rectangular yard contains two flower beds in the shape of congruent isosceles right triangles. The remainder of the ... | MATH | {
"ground_truth": "6",
"style": "rule-lighteval/MATH_v2"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nA whole number is said to be ''9-heavy'' if the remainder when the number is divided by 9 is greater than 5. What is t... | MATH | {
"ground_truth": "105",
"style": "rule-lighteval/MATH_v2"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nFor any positive integer $n$, let $f(n)$ be the maximum number of groups formed by a total of $n$ people such that the... | MATH | {
"ground_truth": "242",
"style": "rule-lighteval/MATH_v2"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\n一颗质地均匀的正方体骰子，六个面上分别标有点数 $1,2,3,4,5,6$. 随机地抛掷该骰子三次 (各次抛掷结果相互独立), 所得的点数依次为 $a_{1}, a_{2}, a_{3}$, 则事件 \" $\\left|a_{1}-a... | MATH | {
"ground_truth": "5",
"style": "rule-lighteval/MATH_v2"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nFigure $ABCD$ is a square. Inside this square three smaller squares are drawn with side lengths as labeled. What is th... | MATH | {
"ground_truth": "7",
"style": "rule-lighteval/MATH_v2"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nLet $p$ be a polynomial with integer coefficients such that $p(15) = 6$, $p(22) = 1196$, and $p(35) = 26$. Find an int... | MATH | {
"ground_truth": "28",
"style": "rule-lighteval/MATH_v2"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nLet $ABC$ be a triangle with $AC = 28$, $BC = 33$, and $\\angle ABC = 2\\angle ACB$. Compute the length of side $AB$.\... | MATH | {
"ground_truth": "16",
"style": "rule-lighteval/MATH_v2"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nConsider the sequence given by $a_0 = 3$ and such that for $i \\ge 1$, we have $ai = 2^{a_{i-1}} + 1$. Let $m$ be the ... | MATH | {
"ground_truth": "35",
"style": "rule-lighteval/MATH_v2"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nA single section at a stadium can hold either $7$ adults or $11$ children. When $N$ sections are completely filled, an... | MATH | {
"ground_truth": "18",
"style": "rule-lighteval/MATH_v2"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nFind the sum of the four least positive integers each of whose digits add to $12$.\n\nRemember to put your answer on i... | MATH | {
"ground_truth": "210",
"style": "rule-lighteval/MATH_v2"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nTom, Dick, and Harry started out on a $100$-mile journey. Tom and Harry traveled by automobile at a speed of $25$ mph,... | MATH | {
"ground_truth": "8",
"style": "rule-lighteval/MATH_v2"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nGiven positive integers $x$ and $y$ such that $x\\neq y$ and $\\frac{1}{x} + \\frac{1}{y} = \\frac{1}{18}$, what is th... | MATH | {
"ground_truth": "75",
"style": "rule-lighteval/MATH_v2"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nSuppose that the angles of triangle $ABC$ satisfy\n\\[\\cos 3A + \\cos 3B + \\cos 3C = 1.\\]Two sides of the triangle ... | MATH | {
"ground_truth": "400",
"style": "rule-lighteval/MATH_v2"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nIf the six solutions of $x^6=-64$ are written in the form $a+bi$, where $a$ and $b$ are real, find the product of thos... | MATH | {
"ground_truth": "4",
"style": "rule-lighteval/MATH_v2"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nA total fixed amount of $N$ thousand rupees is given to $A$, $B$, and $C$ every year, each receiving an amount proport... | MATH | {
"ground_truth": "35",
"style": "rule-lighteval/MATH_v2"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nDoug can paint a room in $5$ hours. Dave can paint the same room in $7$ hours. Doug and Dave paint the room together a... | MATH | {
"ground_truth": "15",
"style": "rule-lighteval/MATH_v2"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\n数列 $\\left\\{a_{n}\\right\\}$ 满足: $a_{1}=\\frac{5}{2}, a_{n+1}=a_{n}^{2}-2$, 求 $\\left[a_{2023}\\right]$ 除以 7 的余数。\n\n... | MATH | {
"ground_truth": "2",
"style": "rule-lighteval/MATH_v2"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nIf \\[\\frac{1}{1+2} + \\frac{1}{1+2+3} + \\ldots + \\frac{1}{1+2 + \\ldots + 20} = \\frac{m}{n}\\]\nwhere $m$ and $n... | MATH | {
"ground_truth": "40",
"style": "rule-lighteval/MATH_v2"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nEach of the 2009 distinct points in the plane is colored either blue or red. On every blue-centered unit circle, there... | MATH | {
"ground_truth": "1964",
"style": "rule-lighteval/MATH_v2"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nSix congruent copies of the parabola $y = x^2$ are arranged in the plane so that each vertex is tangent to a circle, a... | MATH | {
"ground_truth": "7",
"style": "rule-lighteval/MATH_v2"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nEvaluate the integral: \n\n\\[ \\int_{\\frac{\\pi}{4}}^{\\frac{\\pi}{3}} \\frac{2\\sin^3 x}{\\cos^5 x} \\, dx. \\]\n\n... | MATH | {
"ground_truth": "4",
"style": "rule-lighteval/MATH_v2"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nEvaluate $2000^3-1999\\cdot 2000^2-1999^2\\cdot 2000+1999^3$\n\nRemember to put your answer on its own line after \"An... | MATH | {
"ground_truth": "3999",
"style": "rule-lighteval/MATH_v2"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nFind the 2000th positive integer that is not the difference between any two integer squares.\n\nRemember to put your a... | MATH | {
"ground_truth": "7998",
"style": "rule-lighteval/MATH_v2"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nLet $ ABC$ be a triangle with $ BC \\equal{} 2007$, $ CA \\equal{} 2008$, $ AB \\equal{} 2009$. Let $ \\omega$ be an e... | MATH | {
"ground_truth": "2014024",
"style": "rule-lighteval/MATH_v2"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\n在集合$\\{0, 1, 2, \\ldots, 2014\\}$中，有多少个整数满足条件：$C^x_{2014} \\ge C^{999}_{2014}$？请计算满足该条件的整数个数。\n\nRemember to put your ... | MATH | {
"ground_truth": "17",
"style": "rule-lighteval/MATH_v2"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\n若方程 \\log_2\\left(k\\left(x-\\df{1}{2}\\right)\\right)=2\\log_2\\left(x+\\df{1}{2}\\right) 仅有一个实根，则满足条件的 k 的最大值等于_____... | MATH | {
"ground_truth": "4",
"style": "rule-lighteval/MATH_v2"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nLet $p(n) = n^4-6n^2-160$. If $a_n$ is the least odd prime dividing $q(n) = |p(n-30) \\cdot p(n+30)|$, find $\\sum_{n=... | MATH | {
"ground_truth": "7933",
"style": "rule-lighteval/MATH_v2"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nFind all positive integers $n$ such that $n^3 - 5n^2 + 9n - 6$ is a perfect square number.\n\nRemember to put your ans... | MATH | {
"ground_truth": "2",
"style": "rule-lighteval/MATH_v2"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nPam lists the four smallest positive prime numbers in increasing order. When she divides the positive integer $N$ by t... | MATH | {
"ground_truth": "53",
"style": "rule-lighteval/MATH_v2"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nIn pentagon $ABCDE$, $BC=CD=DE=2$ units, $\\angle E$ is a right angle and $m \\angle B = m \\angle C = m \\angle D = 1... | MATH | {
"ground_truth": "6",
"style": "rule-lighteval/MATH_v2"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nA word is an ordered, non-empty sequence of letters, such as $word$ or $wrod$. How many distinct $3$-letter words can ... | MATH | {
"ground_truth": "170",
"style": "rule-lighteval/MATH_v2"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nVertex \\(E\\) of equilateral \\(\\triangle{ABE}\\) is in the interior of unit square \\(ABCD\\). Let \\(R\\) be the r... | MATH | {
"ground_truth": "53",
"style": "rule-lighteval/MATH_v2"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nThe rectangle $ABCD^{}_{}$ below has dimensions $AB^{}_{} = 12 \\sqrt{3}$ and $BC^{}_{} = 13 \\sqrt{3}$. Diagonals $\... | MATH | {
"ground_truth": "594",
"style": "rule-lighteval/MATH_v2"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nLet $1,\\alpha_1,\\alpha_2,...,\\alpha_{10}$ be the roots of the polynomial $x^{11}-1$. It is a fact that there exists... | MATH | {
"ground_truth": "15",
"style": "rule-lighteval/MATH_v2"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nHow many whole numbers between $99$ and $999$ contain exactly one $0$? Provide your answer as an integer.\n\nRemember ... | MATH | {
"ground_truth": "162",
"style": "rule-lighteval/MATH_v2"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nPoint $P$ is in the interior of $\\triangle ABC$. The side lengths of $ABC$ are $AB = 7$, $BC = 8$, $CA = 9$. The thre... | MATH | {
"ground_truth": "600",
"style": "rule-lighteval/MATH_v2"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nLet $a,$ $b,$ $c$ be distinct complex numbers such that\n\\[\\frac{a}{1 - b} = \\frac{b}{1 - c} = \\frac{c}{1 - a} = k... | MATH | {
"ground_truth": "1",
"style": "rule-lighteval/MATH_v2"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nHow many positive integers $N$ satisfy all of the following three conditions?\n(i) $N$ is divisible by 2020 .\n(ii) $N... | MATH | {
"ground_truth": "508536",
"style": "rule-lighteval/MATH_v2"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\n已知点 $P$ 在椭圆 $\\frac{x^{2}}{2}+y^{2}=1$ 上, 记椭圆上顶点和右顶点分别为 $A$ 和 $B$. 则 $\\triangle A B P$ 面积的最大值的2倍减去$\\sqrt{2}$是 $\\qqu... | MATH | {
"ground_truth": "2",
"style": "rule-lighteval/MATH_v2"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nAn $m\\times n\\times p$ rectangular box has half the volume of an $(m + 2)\\times(n + 2)\\times(p + 2)$ rectangular b... | MATH | {
"ground_truth": "130",
"style": "rule-lighteval/MATH_v2"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nSuppose 2012 reals are selected independently and at random from the unit interval $[0,1]$, and then written in nondec... | MATH | {
"ground_truth": "601",
"style": "rule-lighteval/MATH_v2"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nCompute \\( \\sum_{k=1}^{420} \\gcd(k,420) \\).\n\nRemember to put your answer on its own line after \"Answer:\".",
... | MATH | {
"ground_truth": "4680",
"style": "rule-lighteval/MATH_v2"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nNebraska, the home of the AMC, changed its license plate scheme. Each old license plate consisted of a letter followed... | MATH | {
"ground_truth": "36",
"style": "rule-lighteval/MATH_v2"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nHow many polynomials of degree exactly $5$ with real coefficients send the set $\\{1, 2, 3, 4, 5, 6\\}$ to a permutati... | MATH | {
"ground_truth": "714",
"style": "rule-lighteval/MATH_v2"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\n某房间的室温 $T$ （单位：摄氏度）与时间 $t$ （单位：小时）的函数关系是： $T=$ $a \\sin t+b \\cos t, t \\in(0,+\\infty)$, 其中 $a, b$ 是正实数。如果该房间的最大温差为 ... | MATH | {
"ground_truth": "7",
"style": "rule-lighteval/MATH_v2"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nFind the maximal cardinality $|S|$ of the subset $S \\subset A=\\{1, 2, 3, \\dots, 9\\}$ given that no two sums $a+b$ ... | MATH | {
"ground_truth": "5",
"style": "rule-lighteval/MATH_v2"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nFind the least positive integer $n$ such that the prime factorizations of $n$, $n + 1$, and $n + 2$ each have exactly ... | MATH | {
"ground_truth": "33",
"style": "rule-lighteval/MATH_v2"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nEvaluate $$\\lim\\limits_{x\\to1^-}\\prod\\limits_{n=0}^\\infty\\left(\\frac{1+x^{n+1}}{1+x^n}\\right)^{x^n}.$$ Please... | MATH | {
"ground_truth": "1",
"style": "rule-lighteval/MATH_v2"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nNinety-four bricks, each measuring $4''\\times10''\\times19'',$ are to be stacked one on top of another to form a towe... | MATH | {
"ground_truth": "465",
"style": "rule-lighteval/MATH_v2"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nGiven points \\(P(-1,-2)\\) and \\(Q(4,2)\\) in the \\(xy\\)-plane; point \\(R(1,m)\\) is taken so that \\(PR+RQ\\) is... | MATH | {
"ground_truth": "7",
"style": "rule-lighteval/MATH_v2"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\n设整数 $n>4,(x+2 \\sqrt{y}-1)^{n}$ 的展开式中 $x^{n-4}$ 与 $x y$ 两项的系数相等, 则 $n$ 的值为 $\\qquad$.\n\nRemember to put your answer o... | MATH | {
"ground_truth": "51",
"style": "rule-lighteval/MATH_v2"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\n对于集合 $\\{x \\mid a \\leqslant x \\leqslant b\\}$ ，我们把 $b-a$ 称为它的长度.设集合 $A=\\{x \\mid a \\leqslant x \\leqslant$ $a+198... | MATH | {
"ground_truth": "983",
"style": "rule-lighteval/MATH_v2"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nIn real numbers, find the number of distinct pairs \\((x,y)\\) that satisfy the system of equations:\n\\[ x^2 = 4y + 1... | MATH | {
"ground_truth": "2",
"style": "rule-lighteval/MATH_v2"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nFind the product of all positive odd integers less than \\(10000\\). The original answer is in the format \\(\\frac{10... | MATH | {
"ground_truth": "10000",
"style": "rule-lighteval/MATH_v2"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nThe positive integer $8833$ has the property that $8833 = 88^2 + 33^2$. Find the unique other four-digit positive inte... | MATH | {
"ground_truth": "1233",
"style": "rule-lighteval/MATH_v2"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nTwo points $A$ and $B$ are randomly chosen on a circle with a radius of $100$. For a positive integer $x$, denote $P(x... | MATH | {
"ground_truth": "174",
"style": "rule-lighteval/MATH_v2"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nLet $A$, $B$, $C$ and $D$ be the vertices of a regular tetrahedron, each of whose edges measures $1$ meter. A bug, sta... | MATH | {
"ground_truth": "182",
"style": "rule-lighteval/MATH_v2"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nLet $a$ be the sum of the numbers:\n\n$99 \\times 0.9$\n\n$999 \\times 0.9$\n\n$9999 \\times 0.9$\n\n$\\vdots$\n\n$999... | MATH | {
"ground_truth": "891",
"style": "rule-lighteval/MATH_v2"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nFor real numbers $a,$ $b,$ and $c,$ the matrix\n\\[\\begin{pmatrix} a & b & c \\\\ b & c & a \\\\ c & a & b \\end{pmat... | MATH | {
"ground_truth": "-3",
"style": "rule-lighteval/MATH_v2"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\n在平面直角坐标系 $x O y$ 中, 点集 $K=\\{(x, y) \\mid x, y=-1,0,1\\}$. 在 $K$ 中随机取出三个点, 则这三点中存在两点之间距离为 $\\sqrt{5}$ 的概率为 $\\qquad$.原... | MATH | {
"ground_truth": "11",
"style": "rule-lighteval/MATH_v2"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\n对正整数 n，记 g(n) 为 n 与 2015 的最大公约数. 求满足下列条件的有序三元数组 (a,b,c) 的个数：(1) a,b,c\\in\\{1,2,\\cdots,2015\\}；(2) g(a), g(b), g(c), ... | MATH | {
"ground_truth": "138240",
"style": "rule-lighteval/MATH_v2"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nA triangle has an area of 114 square units and sides of integer length. What is the perimeter of the triangle?\n\nReme... | MATH | {
"ground_truth": "76",
"style": "rule-lighteval/MATH_v2"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\n设 3 阶实对称矩阵 $A$ 的三个特征值分别为 $-1,-1,2$, 且 $(1,1,-1)^{T}$ 是特征值 2所对应的特征向量。记 $A$ 中所有元素的平方之和为 $I$, 则 $[I]=$ $\\qquad$.\n\nReme... | MATH | {
"ground_truth": "6",
"style": "rule-lighteval/MATH_v2"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nFind the sum of all the rational terms in the expansion of\n\\[(\\sqrt{2} + \\sqrt[3]{3})^{12}.\\]\n\nRemember to put ... | MATH | {
"ground_truth": "66673",
"style": "rule-lighteval/MATH_v2"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\n在 $5 \\times 5$ 矩阵中, 每个元素都为 0 或 1, 且满足：五行的元素之和都相等,但五列的元素之和两两不等。这样的矩阵的个数为 $\\qquad$ \n\nRemember to put your answer on ... | MATH | {
"ground_truth": "26400",
"style": "rule-lighteval/MATH_v2"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nRecall that an integer $d$ is said to be a divisor of an integer $a$ if $a/d$ is also an integer. For how many integer... | MATH | {
"ground_truth": "14",
"style": "rule-lighteval/MATH_v2"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nLet $\\triangle PQR$ be a triangle in the plane, and let $S$ be a point outside the plane of $\\triangle PQR$, so that... | MATH | {
"ground_truth": "1440",
"style": "rule-lighteval/MATH_v2"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\n已知 f:\\bZ\\rightarrow\\bZ 为偶函数，且 f(1)=1, f(2017)\\neq1. 若对任意整数 x, y，均有2f(x+y)-f(x)-f(y)\\leq |f(x)-f(y)|,求 f(2018) 的所有... | MATH | {
"ground_truth": "1",
"style": "rule-lighteval/MATH_v2"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nA mason has bricks with dimensions $2 \\times 5 \\times 8$ and other bricks with dimensions $2 \\times 3 \\times 7$. S... | MATH | {
"ground_truth": "24",
"style": "rule-lighteval/MATH_v2"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\n设 V 为关于 x 的次数小于或等于 10 的实多项式构成的集合, 且 a为实数。定义 $V$ 到 V 的线性映射 F 为 $F(f)=\\left(x^{2} f\\right)^{\\prime \\prime}+f^{\\prim... | MATH | {
"ground_truth": "572",
"style": "rule-lighteval/MATH_v2"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\n设复数 $w=\\left(\\frac{a+\\mathrm{i}}{1+\\mathrm{i}}\\right)^{2}$, 其中 $a$ 为实数, 若 $w$ 的实部为 2, 求 $w$ 的虚部。答案的形式为$\\frac{k}{... | MATH | {
"ground_truth": "-1",
"style": "rule-lighteval/MATH_v2"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nLet $x$ and $y$ be integers satisfying both $x^2 - 16x + 3y = 20$ and $y^2 + 4y - x = -12$. Find $x + y$.\n\nRemember ... | MATH | {
"ground_truth": "18",
"style": "rule-lighteval/MATH_v2"
} |
End of preview. Expand in Data Studio
No dataset card yet
- Downloads last month
- 1