data_source stringclasses 1
value | prompt listlengths 1 1 | ability stringclasses 1
value | reward_model dict | extra_info 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\n如图 1, 边长为 2 的正方形 $A B C D$ 和正方形 $A B E F$ 所在的面成 $60^{\\circ}$ 角， $M 、 N$ 分别是线段 $A C 、 B F$ 上的点, 且 $A M=F N$. 求线段 $M N$... | MATH | {
"ground_truth": "3",
"style": "rule-lighteval/MATH_v2"
} | {
"index": 0,
"original_index": "0eb1daf3-7afb-4c2a-af05-48480e518ed0",
"split": "train"
} |
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\nThree of the edges of a cube are $\\overline{AB}, \\overline{BC},$ and $\\overline{CD},$ and $\\overline{AD}$ is an in... | MATH | {
"ground_truth": "525",
"style": "rule-lighteval/MATH_v2"
} | {
"index": 1,
"original_index": "78dac33f-86d8-4aa3-a56b-59376d95fed0",
"split": "train"
} |
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 integer represented by $\\left[ \\sum_{n=1}^{10^9} n^{-2/3} \\right]$. Here $[x]$ denotes the greatest intege... | MATH | {
"ground_truth": "2997",
"style": "rule-lighteval/MATH_v2"
} | {
"index": 2,
"original_index": "4662c135-e0a5-4d89-9a16-73ce67f9d634",
"split": "train"
} |
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若非负数 $a, b, c$ 满足 $a+b+c=1$ ，则 $a^{2}(b-c)+b^{2}(c-a)+c^{2}(a-b)$ 的最大值是 $\\frac{\\sqrt{m}}{n}$ 的格式，请给出 $m + n$ 的值。\n\n... | MATH | {
"ground_truth": "21",
"style": "rule-lighteval/MATH_v2"
} | {
"index": 3,
"original_index": "0e9de14f-fa6a-4924-a2e8-b16a3eda608c",
"split": "train"
} |
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\nFour circles $\\omega,$ $\\omega_{A},$ $\\omega_{B},$ and $\\omega_{C}$ with the same radius are drawn in the interior... | MATH | {
"ground_truth": "389",
"style": "rule-lighteval/MATH_v2"
} | {
"index": 4,
"original_index": "99454afe-cdee-4f2b-b590-6751ca2a0442",
"split": "train"
} |
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 \\[2 \\times (2 \\times (2 \\times (2 \\times (2 \\times (2 \\times 2 - 2) - 2) - 2) - 2) - 2) - 2.\\]\n\nRem... | MATH | {
"ground_truth": "2",
"style": "rule-lighteval/MATH_v2"
} | {
"index": 5,
"original_index": "2ad05dc8-e170-4b65-833b-1a79fb243983",
"split": "train"
} |
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 $\\left\\{a_{n}\\right\\}$ 是公差不为 0 的等差数列, $\\left\\{b_{n}\\right\\}$ 是等比数列, 其 中 $a_{1}=3, b_{1}=1, a_{2}=b_{2}, 3 a... | MATH | {
"ground_truth": "3",
"style": "rule-lighteval/MATH_v2"
} | {
"index": 6,
"original_index": "9bdf520a-1a35-4828-b72c-a77f58f06840",
"split": "train"
} |
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 girl and a guy are going to arrive at a train station. If they arrive within 10 minutes of each other, they will ins... | MATH | {
"ground_truth": "10",
"style": "rule-lighteval/MATH_v2"
} | {
"index": 7,
"original_index": "61274a14-c2a2-4843-94bd-eced174f3d9f",
"split": "train"
} |
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\nThere are four entrances into Hades. Hermes brings you through one of them and drops you off at the shore of the river... | MATH | {
"ground_truth": "270",
"style": "rule-lighteval/MATH_v2"
} | {
"index": 8,
"original_index": "6d1ec9d9-0a06-4256-8c69-2b3695e7b1f6",
"split": "train"
} |
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 $\\mathcal{P}$ be a set of monic polynomials with integer coefficients of the least degree, with root $k \\cdot \\... | MATH | {
"ground_truth": "167",
"style": "rule-lighteval/MATH_v2"
} | {
"index": 9,
"original_index": "36de6be3-ec0d-4ab0-a39d-d6f8eb2fe51e",
"split": "train"
} |
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\nThere are $n$ players in a round-robin ping-pong tournament, meaning every two players will play exactly one game. Aft... | MATH | {
"ground_truth": "9",
"style": "rule-lighteval/MATH_v2"
} | {
"index": 10,
"original_index": "a6874e38-0c36-4399-ad09-f4eae26efcc9",
"split": "train"
} |
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\nCircle $B$, which has radius 2008, is tangent to horizontal line $A$ at point $P$. Circle $C_1$ has radius 1 and is ta... | MATH | {
"ground_truth": "45",
"style": "rule-lighteval/MATH_v2"
} | {
"index": 11,
"original_index": "3c2719eb-d362-46f9-9b66-5edc5395ad91",
"split": "train"
} |
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 time is chosen randomly and uniformly in a 24-hour day. The probability that at that time, the non-reflex angle betw... | MATH | {
"ground_truth": "211",
"style": "rule-lighteval/MATH_v2"
} | {
"index": 12,
"original_index": "2cae6a18-2118-487d-a193-cccb7aca494e",
"split": "train"
} |
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 Mediterranean polynomial has only real roots and is of the form:\n\\[ P(x) = x^{10} - 20x^9 + 135x^8 + a_7x^7 + a_6x... | MATH | {
"ground_truth": "11",
"style": "rule-lighteval/MATH_v2"
} | {
"index": 13,
"original_index": "5d0926bc-3b41-4983-85ab-db098bb637d1",
"split": "train"
} |
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 $\\pi$ be a permutation of the numbers from $1$ through $2012$. What is the maximum possible number of integers $n... | MATH | {
"ground_truth": "1006",
"style": "rule-lighteval/MATH_v2"
} | {
"index": 14,
"original_index": "ed5f51a2-f4ee-4e2a-8e21-77d39b5fa1b3",
"split": "train"
} |
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 sequences of 10 letters where all the letters are either $A$ or $B$, the first letter is $A$, the l... | MATH | {
"ground_truth": "86",
"style": "rule-lighteval/MATH_v2"
} | {
"index": 15,
"original_index": "412af96a-3ea0-4575-b5ea-edd49fb972ce",
"split": "train"
} |
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 positive integers $n$ for which $|2^n + 5^n - 65|$ is a perfect square.\n\nRemember to put your an... | MATH | {
"ground_truth": "6",
"style": "rule-lighteval/MATH_v2"
} | {
"index": 16,
"original_index": "951d9a02-67f6-46ae-8d55-c2ad9a21931f",
"split": "train"
} |
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 the smallest positive integer $M$ such that there exists a positive integer $n$ for which:\n\n- $M$ is the sum... | MATH | {
"ground_truth": "4250",
"style": "rule-lighteval/MATH_v2"
} | {
"index": 17,
"original_index": "385a576c-9466-4e49-803c-ee894f7b815a",
"split": "train"
} |
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 P 是一个凸 2019 边形，任意三条对角线在形内不交于一点. 称 P 的对角线在形内的交点为\"结点\"，问：最多可以选取多少个结点，使得它们之间不存在一个圈？这里一个圈的任意两个相邻结点必须位于同一条对角线上，且在每条对角线上最... | MATH | {
"ground_truth": "2035151",
"style": "rule-lighteval/MATH_v2"
} | {
"index": 18,
"original_index": "659fd02c-3aa5-4b90-ae54-4c710e7973f4",
"split": "train"
} |
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 $Answer is the answer to the problem.\n\n在一个圆上随机取三点, 则以此三点为顶点的三角形是锐角三角形的概率为\n$\\qquad$.\n#*原始的答案是\\frac{m}{n}的形式，其中m、n是互质的。请给出最终m + n的值\n\nRemember to put your... | MATH | {
"ground_truth": "5",
"style": "rule-lighteval/MATH_v2"
} | {
"index": 19,
"original_index": "f20608e9-79cc-490e-ab84-8178da71d4d1",
"split": "train"
} |
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 largest positive integer $n$ such that $n\\varphi(n)$ is a perfect square. ($\\varphi(n)$ is the number of i... | MATH | {
"ground_truth": "1",
"style": "rule-lighteval/MATH_v2"
} | {
"index": 20,
"original_index": "81d89b64-ff5f-4cfb-aa2a-72481222f70f",
"split": "train"
} |
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已知集合 $A=\\{1,2, \\cdots, 6\\}$, 映射 $f: A \\rightarrow A$ 为一一映射,\n$$\n\\begin{aligned}\n& f^{(2)}(x)=f(f(x)), \\\\\n& f... | MATH | {
"ground_truth": "576",
"style": "rule-lighteval/MATH_v2"
} | {
"index": 21,
"original_index": "b9241322-9956-46cb-b0c3-6ab45c6d894f",
"split": "train"
} |
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\nCall a number unremarkable if, when written in base $10$, no two adjacent digits are equal. For example, $123$ is unre... | MATH | {
"ground_truth": "400185",
"style": "rule-lighteval/MATH_v2"
} | {
"index": 22,
"original_index": "f14dccc0-bb26-4b0c-aa33-0069ab603d15",
"split": "train"
} |
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$\\sum\\limits_{k=0}^{8}(-1)^{k}\\dbinom{8}{k} k^{8}$ 的值为_____.\n\nRemember to put your answer on its own line after \... | MATH | {
"ground_truth": "0",
"style": "rule-lighteval/MATH_v2"
} | {
"index": 23,
"original_index": "0c05f3f2-abe5-4d41-a99e-b71e9ffe81cb",
"split": "train"
} |
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 cone-shaped mountain has its base on the ocean floor and has a height of $8000$ feet. The top $\\frac{1}{8}$ of the ... | MATH | {
"ground_truth": "4000",
"style": "rule-lighteval/MATH_v2"
} | {
"index": 24,
"original_index": "78e109bc-bfd1-401a-a126-4ab3f084696e",
"split": "train"
} |
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 Heidi's history class, the only grades that count toward the semester average are the $6$ tests she has already tak... | MATH | {
"ground_truth": "87",
"style": "rule-lighteval/MATH_v2"
} | {
"index": 25,
"original_index": "b3756554-8e02-41eb-80de-0b139515fbda",
"split": "train"
} |
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 digits are in the base-ten representation of $8^5 \\cdot 5^{10} \\cdot 15^5$?\n\nRemember to put your answer ... | MATH | {
"ground_truth": "18",
"style": "rule-lighteval/MATH_v2"
} | {
"index": 26,
"original_index": "16d60e70-f320-4b7b-9d3e-1ebb8b299d9f",
"split": "train"
} |
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 rectangle with sides $a$ and $b$ has an area of $24$ and a diagonal of length $11$. Find the perimeter of this recta... | MATH | {
"ground_truth": "26",
"style": "rule-lighteval/MATH_v2"
} | {
"index": 27,
"original_index": "2a8ce0db-ca38-489e-aa0f-913847af7c69",
"split": "train"
} |
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 basketball player has a constant probability of $.4$ of making any given shot, independent of previous shots. Let $a... | MATH | {
"ground_truth": "660",
"style": "rule-lighteval/MATH_v2"
} | {
"index": 28,
"original_index": "648399cf-03e2-478f-b803-d9a7368144bc",
"split": "train"
} |
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 real numbers which satisfy the equation $x|x-1|-4|x|+3=0$.\n\nRemember to put your answer on its ow... | MATH | {
"ground_truth": "3",
"style": "rule-lighteval/MATH_v2"
} | {
"index": 29,
"original_index": "867fc639-9a92-4779-a1ae-ba245ebffadd",
"split": "train"
} |
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\nOn a straight line $\\ell$, there are four points, $A$, $B$, $C$, and $D$ in that order, such that $AB = BC = CD$. A p... | MATH | {
"ground_truth": "30",
"style": "rule-lighteval/MATH_v2"
} | {
"index": 30,
"original_index": "1ffa0c8e-922f-4353-80af-9a84c8b802fd",
"split": "train"
} |
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 sum of the two three-digit integers, $6A2$ and $B34$, is divisible by $18$. What is the largest possible product o... | MATH | {
"ground_truth": "36",
"style": "rule-lighteval/MATH_v2"
} | {
"index": 31,
"original_index": "26f7bd44-047c-4a9d-9c0a-7ed7efb8b04a",
"split": "train"
} |
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 $ABCD$ be an isosceles trapezoid with $AD = BC = 15$ such that the distance between its bases $AB$ and $CD$ is $7$... | MATH | {
"ground_truth": "105",
"style": "rule-lighteval/MATH_v2"
} | {
"index": 32,
"original_index": "7238b73d-e1e5-4d71-8b87-b562e81039f2",
"split": "train"
} |
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\nOn the refrigerator, MATHCOUNTS is spelled out with 10 magnets, one letter per magnet. Two vowels and three consonants... | MATH | {
"ground_truth": "75",
"style": "rule-lighteval/MATH_v2"
} | {
"index": 33,
"original_index": "039cdbef-74bc-40a9-96d1-cacf487abf32",
"split": "train"
} |
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 \\( \\frac{1-4 \\sin \\alpha}{\\tan \\alpha}=\\sqrt{3}(\\alpha \\in\\left(0, \\frac{\\pi}{2}\\right)) \\). 原始答案为 \\... | MATH | {
"ground_truth": "19",
"style": "rule-lighteval/MATH_v2"
} | {
"index": 34,
"original_index": "9dfeea57-1c99-4b3d-b660-68eaaff5ea2c",
"split": "train"
} |
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 $f$ be a function from the non-negative integers to the non-negative integers such that $f(nm) = n f(m) + m f(n)$,... | MATH | {
"ground_truth": "36",
"style": "rule-lighteval/MATH_v2"
} | {
"index": 35,
"original_index": "c4881d73-6327-419b-8190-752b925b6f19",
"split": "train"
} |
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 $a, b$ 为不超过 12 的正整数，满足：存在常数 $C$ ，使得 $a^{n}+b^{n+9} \\equiv C(\\bmod 13)$ 对任意正整数 $n$ 成立. 求所有满足条件的有序数对 $(a, b)$. 请提供所有... | MATH | {
"ground_truth": "54",
"style": "rule-lighteval/MATH_v2"
} | {
"index": 36,
"original_index": "e92840b2-eba0-4b42-9e93-feba04ab44a8",
"split": "train"
} |
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已知正方体 $A B C D-A^{\\prime} B^{\\prime} C^{\\prime} D^{\\prime}$ 的棱长为 1, 点 $M, N$ 分别为线段 $A B^{\\prime}, A C$ 上的动点, 点 $T... | MATH | {
"ground_truth": "8",
"style": "rule-lighteval/MATH_v2"
} | {
"index": 37,
"original_index": "76c03a72-598b-4e70-bee7-5b17c75b3759",
"split": "train"
} |
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\nJonah recently harvested a large number of lychees and wants to split them into groups. Unfortunately, for all $n$ whe... | MATH | {
"ground_truth": "839",
"style": "rule-lighteval/MATH_v2"
} | {
"index": 38,
"original_index": "1b7e532c-88c2-4ab1-a69f-3ec0e287b53f",
"split": "train"
} |
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 solutions to $\\cos \\frac{x}{4} = \\cos x$ in the interval $0 < x < 24 \\pi.$\n\nRemember to put y... | MATH | {
"ground_truth": "20",
"style": "rule-lighteval/MATH_v2"
} | {
"index": 39,
"original_index": "1b4b4d4a-8714-44c0-956a-5539db88a3b9",
"split": "train"
} |
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\nWhen Eva counts, she skips all numbers containing a digit divisible by 3. For example, the first ten numbers she count... | MATH | {
"ground_truth": "255",
"style": "rule-lighteval/MATH_v2"
} | {
"index": 40,
"original_index": "88cb5074-bcf2-44ef-b11d-0f331e59e843",
"split": "train"
} |
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\nSam spends his days walking around the following $2 \\times 2$ grid of squares:\n\\[\n\\begin{array}{|c|c|}\n\\hline\n... | MATH | {
"ground_truth": "167",
"style": "rule-lighteval/MATH_v2"
} | {
"index": 41,
"original_index": "b2ef73d0-2462-4e1b-b18e-8e3ba46b3a99",
"split": "train"
} |
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 a parlor game, the magician asks one of the participants to think of a three digit number $(abc)$ where $a$, $b$, a... | MATH | {
"ground_truth": "358",
"style": "rule-lighteval/MATH_v2"
} | {
"index": 42,
"original_index": "91e3a9de-570f-47cd-9ffc-f198c1b2edab",
"split": "train"
} |
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 PQR$ , $PR=15$ , $QR=20$ , and $PQ=25$ . Points $A$ and $B$ lie on $\\overline{PQ}$ , points $C$ and $D... | MATH | {
"ground_truth": "120",
"style": "rule-lighteval/MATH_v2"
} | {
"index": 43,
"original_index": "182263c3-7897-41fa-826d-56483b0504b0",
"split": "train"
} |
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 $0<x<\\frac{\\pi}{2}$, 且 $\\frac{\\sin ^{4} x}{9}+\\frac{\\cos ^{4} x}{4}=\\frac{1}{13}$, 则 $\\tan x$ 的值可以表示为\\frac{... | MATH | {
"ground_truth": "5",
"style": "rule-lighteval/MATH_v2"
} | {
"index": 44,
"original_index": "2658c4f0-018e-491b-9258-bd62d6b805d1",
"split": "train"
} |
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 integer factors of $2020$ have more than $3$ factors? (As an example, $12$ has $6$ factors, namely $... | MATH | {
"ground_truth": "7",
"style": "rule-lighteval/MATH_v2"
} | {
"index": 45,
"original_index": "662c1d31-49ca-4bde-b1e9-57b030536b95",
"split": "train"
} |
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 arithmetic mean of the nine numbers in the set $\\{9, 99, 999, 9999, \\ldots, 999999999\\}$ is a $9$-digit number ... | MATH | {
"ground_truth": "0",
"style": "rule-lighteval/MATH_v2"
} | {
"index": 46,
"original_index": "319939d7-226d-4972-872e-c4d98efc4653",
"split": "train"
} |
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 solid in the shape of a right circular cone is 4 inches tall and its base has a 3-inch radius. The entire surface of... | MATH | {
"ground_truth": "512",
"style": "rule-lighteval/MATH_v2"
} | {
"index": 47,
"original_index": "d057bdda-f1b8-4823-84b6-0e194d8b3432",
"split": "train"
} |
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 fair, six-sided dice are rolled. What is the probability that the sum of the two numbers showing is between 3 and... | MATH | {
"ground_truth": "35",
"style": "rule-lighteval/MATH_v2"
} | {
"index": 48,
"original_index": "4269c7ae-8705-488a-b81a-26786e406d1d",
"split": "train"
} |
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 positive integers less than $2018$ that are divisible by $6$ but are not divisible by at least one ... | MATH | {
"ground_truth": "280",
"style": "rule-lighteval/MATH_v2"
} | {
"index": 49,
"original_index": "ea47e174-747b-4165-9c70-024cc6e1dbf1",
"split": "train"
} |
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 $B = (20, 14)$ and $C = (18, 0)$ be two points in the plane. For every line $\\ell$ passing through $B$, we color ... | MATH | {
"ground_truth": "157",
"style": "rule-lighteval/MATH_v2"
} | {
"index": 50,
"original_index": "2c557f8d-1f97-4480-a4cc-8e37b371b849",
"split": "train"
} |
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=\\sqrt{30}$, $AC=\\sqrt{6}$, and $BC=\\sqrt{15}$. There is a point $D$ for which $\\overline{AD... | MATH | {
"ground_truth": "65",
"style": "rule-lighteval/MATH_v2"
} | {
"index": 51,
"original_index": "2b6b274d-340c-406f-83df-f4c2986765f0",
"split": "train"
} |
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\nDetermine the greatest possible value of $\\sum_{i=1}^{10}\\cos(3x_i)$ for real numbers $x_1,x_2,\\ldots,x_{10}$ satis... | MATH | {
"ground_truth": "529",
"style": "rule-lighteval/MATH_v2"
} | {
"index": 52,
"original_index": "7235ddb1-8f5b-4089-b8a6-0b9c7f12e971",
"split": "train"
} |
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 $\\sigma_1 : \\mathbb{N} \\to \\mathbb{N}$ be a function that takes a natural number $n$, and returns the sum of t... | MATH | {
"ground_truth": "1234",
"style": "rule-lighteval/MATH_v2"
} | {
"index": 53,
"original_index": "fe940806-f964-45ea-bad0-9ef8fdf11b8a",
"split": "train"
} |
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 you flip a fair coin four times, what is the probability of flipping at least three heads in a row? Express your an... | MATH | {
"ground_truth": "19",
"style": "rule-lighteval/MATH_v2"
} | {
"index": 54,
"original_index": "e1ad9680-bada-4132-94fd-49a6cdd19098",
"split": "train"
} |
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 $N$ be the number of $2015$-tuples of (not necessarily distinct) subsets $(S_1, S_2, \\dots, S_{2015})$ of $\\{1, ... | MATH | {
"ground_truth": "2030612",
"style": "rule-lighteval/MATH_v2"
} | {
"index": 55,
"original_index": "cdbbfbbc-3060-49fc-812d-22609b7f22a2",
"split": "train"
} |
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\nSvitlana writes the number $147$ on a blackboard. Then, at any point, if the number on the blackboard is $n$, she can ... | MATH | {
"ground_truth": "163",
"style": "rule-lighteval/MATH_v2"
} | {
"index": 56,
"original_index": "e7f589d5-4bf9-432b-9849-361c5e37fa6d",
"split": "train"
} |
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\nSeveral players try out for the USAMTS basketball team, and they all have integer heights and weights when measured in... | MATH | {
"ground_truth": "128",
"style": "rule-lighteval/MATH_v2"
} | {
"index": 57,
"original_index": "5ffb3608-a061-4bc5-bacd-82df2bf7b64d",
"split": "train"
} |
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点集 $S=\\left\\{(x, y) \\mid x \\leq 5, y \\leq 4, x, y \\in \\mathrm{~N}^{*}\\right\\}$, 则由 $S$ 中的点可组成 $\\qquad$个不同的三角... | MATH | {
"ground_truth": "1056",
"style": "rule-lighteval/MATH_v2"
} | {
"index": 58,
"original_index": "4cb66c62-3689-46a2-bbaf-9ffe41a01451",
"split": "train"
} |
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\nWhen we say that Ray is climbing up the stairs $m$ at a time, we mean that he starts on the floor (step $0$) then jump... | MATH | {
"ground_truth": "27",
"style": "rule-lighteval/MATH_v2"
} | {
"index": 59,
"original_index": "b207a3aa-b145-46e1-a041-96c84238e970",
"split": "train"
} |
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 decimal representation of the binomial coefficient $\\dbinom{2n}{n}$... | MATH | {
"ground_truth": "313",
"style": "rule-lighteval/MATH_v2"
} | {
"index": 60,
"original_index": "9a902e94-2c12-455c-8be8-74173be05db2",
"split": "train"
} |
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 greatest integer $n < 1000$ for which $4n^3 - 3n$ is the product of two consecutive odd integers.\n\nRemember... | MATH | {
"ground_truth": "899",
"style": "rule-lighteval/MATH_v2"
} | {
"index": 61,
"original_index": "85354bcd-4b6c-4924-974f-52a3dabccc95",
"split": "train"
} |
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\nColour a $20000 \\times 20000$ square grid using 2000 different colours, with one colour per square. Two squares are c... | MATH | {
"ground_truth": "2000",
"style": "rule-lighteval/MATH_v2"
} | {
"index": 62,
"original_index": "a3a8b897-cc33-4dd0-8dbe-7d4907b7cb6e",
"split": "train"
} |
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 ordered pairs of positive integers $(m,n)$ satisfy $\\gcd(m,n) = 2$ and $\\mathop{\\text{lcm}}[m,n] = 108$?\n... | MATH | {
"ground_truth": "4",
"style": "rule-lighteval/MATH_v2"
} | {
"index": 63,
"original_index": "9c2536f7-6bee-4b7d-af08-764d343a2246",
"split": "train"
} |
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设正数列 $x_{1}, x_{2}, \\cdots, x_{n}, \\cdots$ 满足\n$(8 x_{2}-7 x_{1}) x_{1}^{7}=8$\n及 $x_{k+1} x_{k-1}-x_{k}^{2}=\\frac{... | MATH | {
"ground_truth": "9",
"style": "rule-lighteval/MATH_v2"
} | {
"index": 64,
"original_index": "7ffb2ec0-dedd-4602-80f4-bb76ec20f1e1",
"split": "train"
} |
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\nMenkara has a $4 \\times 6$ index card. If she shortens the length of one side of this card by $1$ inch, the card woul... | MATH | {
"ground_truth": "20",
"style": "rule-lighteval/MATH_v2"
} | {
"index": 65,
"original_index": "58c8a5b7-ba91-453f-b6db-51b27784bd73",
"split": "train"
} |
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\nWhat is the least positive integer $m$ such that $m\\cdot2!\\cdot3!\\cdot4!\\cdot5!\\cdots16!$ is a perfect square? Fi... | MATH | {
"ground_truth": "70",
"style": "rule-lighteval/MATH_v2"
} | {
"index": 66,
"original_index": "53fa9f22-a44f-44f0-a4e8-ef1ddd301468",
"split": "train"
} |
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已知数列 $\\left\\{a_{n}\\right\\}$ 满足 $a_{n}=(\\sqrt{2}+1)^{n}-(\\sqrt{2}-1)^{n}(n \\in \\mathbf{N})$ ，用 $[x]$ 表示不超过实数 $x... | MATH | {
"ground_truth": "2",
"style": "rule-lighteval/MATH_v2"
} | {
"index": 67,
"original_index": "927b6861-ff9c-4702-a149-beadc95df443",
"split": "train"
} |
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已知定义在 $\\mathbf{R}^{+}$上的函数 $f(x)=\\left\\{\\begin{array}{ll}\\left|\\log _{3} x-1\\right|, & 0<x \\leqslant 9, \\\\ 4... | MATH | {
"ground_truth": "225",
"style": "rule-lighteval/MATH_v2"
} | {
"index": 68,
"original_index": "ab1a4900-b1ed-491d-a661-7bb7244ea159",
"split": "train"
} |
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\nEight people are sitting around a circular table, each holding a fair coin. All eight people flip their coins and thos... | MATH | {
"ground_truth": "303",
"style": "rule-lighteval/MATH_v2"
} | {
"index": 69,
"original_index": "0b3b1875-ffea-4d7a-aba2-3ef3ea4cf39b",
"split": "train"
} |
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一个盒中有 9 个正品和 3 个废品，每次取一个产品，取出后不再放回. 则在取出 2 个正品前已取出 3 个废品的概率为__________.原始的答案是\\frac{m}{n}的形式，其中m、n是互质的。请给出最终m + n的值\n\... | MATH | {
"ground_truth": "56",
"style": "rule-lighteval/MATH_v2"
} | {
"index": 70,
"original_index": "f9ed4fc6-6b98-43d1-938c-21140d8a6f94",
"split": "train"
} |
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 $ABCD$ be a quadrilateral such that $\\angle ABC = \\angle CDA = 90^o$, and $BC = 7$. Let $E$ and $F$ be on $BD$ ... | MATH | {
"ground_truth": "9",
"style": "rule-lighteval/MATH_v2"
} | {
"index": 71,
"original_index": "87c2bf19-841d-4598-ad2c-4415301880ce",
"split": "train"
} |
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 each positive integer $k$, let $S_k$ denote the increasing arithmetic sequence of integers whose first term is $1... | MATH | {
"ground_truth": "12",
"style": "rule-lighteval/MATH_v2"
} | {
"index": 72,
"original_index": "33b07191-12e8-47bf-8017-668f4dc9b275",
"split": "train"
} |
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 $T_k$ be the transformation of the coordinate plane that first rotates the plane $k$ degrees counterclockwise arou... | MATH | {
"ground_truth": "359",
"style": "rule-lighteval/MATH_v2"
} | {
"index": 73,
"original_index": "7a2ffca2-216e-4c1a-a40d-eda1f57379ff",
"split": "train"
} |
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 $f: \\mathbb{R}^+ \\to \\mathbb{R}^+$ be a function such that for all $x,y \\in \\mathbb{R}^+$, $f(x)f(y) = f(xy) ... | MATH | {
"ground_truth": "47",
"style": "rule-lighteval/MATH_v2"
} | {
"index": 74,
"original_index": "dd38204c-b841-49c5-b37b-d5159d9fa574",
"split": "train"
} |
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 product $\\left(4^5\\right)\\left(5^{13}\\right)$ is written as an integer, how many digits are in this integer... | MATH | {
"ground_truth": "13",
"style": "rule-lighteval/MATH_v2"
} | {
"index": 75,
"original_index": "6dbe18ca-9ab9-4782-9b9a-248791c37380",
"split": "train"
} |
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 $n$ be a positive integer and let $k$ be the number of positive integers less than $2^n$ that are invertible modul... | MATH | {
"ground_truth": "8",
"style": "rule-lighteval/MATH_v2"
} | {
"index": 76,
"original_index": "22f5b8aa-8420-4f39-8dc2-101111904790",
"split": "train"
} |
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 you continue this pattern in which each line-segment extremity is replaced by a gradually smaller Y in the next fig... | MATH | {
"ground_truth": "48",
"style": "rule-lighteval/MATH_v2"
} | {
"index": 77,
"original_index": "4f122bff-0536-4cd4-a8d2-814ed88daf53",
"split": "train"
} |
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 interior diagonals does an icosahedron have? (An $\\emph{icosahedron}$ is a 3-dimensional figure with 20 tri... | MATH | {
"ground_truth": "36",
"style": "rule-lighteval/MATH_v2"
} | {
"index": 78,
"original_index": "c573ab66-0d0b-42fa-a41e-774c1cc4103f",
"split": "train"
} |
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_{1}, F_{2}$ 为椭圆 $\\frac{x^{2}}{a^{2}}+\\frac{y^{2}}{b^{2}}=1(a>b>0)$ 的左、右焦点，该椭圆上存在两点 $A, B$ ，使得 $\\overrightarro... | MATH | {
"ground_truth": "3",
"style": "rule-lighteval/MATH_v2"
} | {
"index": 79,
"original_index": "2879b860-f669-4274-bd64-4f4ef762d2e8",
"split": "train"
} |
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 the function $f$ has all real numbers in its domain and range and is invertible. Some values of $f$ are given ... | MATH | {
"ground_truth": "14",
"style": "rule-lighteval/MATH_v2"
} | {
"index": 80,
"original_index": "1486938c-6215-4397-ad17-e925958e2fd5",
"split": "train"
} |
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 traffic light runs repeatedly through the following cycle: green for \\(30\\) seconds, then yellow for \\(3\\) secon... | MATH | {
"ground_truth": "8",
"style": "rule-lighteval/MATH_v2"
} | {
"index": 81,
"original_index": "f795e745-0c50-4800-af3e-cb571a2616c2",
"split": "train"
} |
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 $B(0,1), P 、 Q$ 为椭圆 $\\frac{x^{2}}{4}+y^{2}=1$上异于点 $B$ 的任意两点, 且 $B P \\perp B Q$.\\n(1) 若点 $B$ 在线段 $P Q$ 上的射影为 $M$... | MATH | {
"ground_truth": "16",
"style": "rule-lighteval/MATH_v2"
} | {
"index": 82,
"original_index": "8d02a1d4-36d6-4538-aa50-537981c2279b",
"split": "train"
} |
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 $\\overline{CH}$ be an altitude of $\\triangle ABC$. Let $R\\,$ and $S\\,$ be the points where the circles inscrib... | MATH | {
"ground_truth": "997",
"style": "rule-lighteval/MATH_v2"
} | {
"index": 83,
"original_index": "8b3d0490-f534-43c7-adb3-ded11ec247fd",
"split": "train"
} |
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实数 $x 、 y$ 满足 $4 x^{2}-5 x y+4 y^{2}=5$ ，设 $S=x^{2}+y^{2}$ ，则 $\\frac{1}{S_{\\max }}+\\frac{1}{S_{\\min }}$ 的值为$\\qqua... | MATH | {
"ground_truth": "13",
"style": "rule-lighteval/MATH_v2"
} | {
"index": 84,
"original_index": "fb77d01e-61e3-423b-b82b-859ff0d46cc0",
"split": "train"
} |
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\nWe say that a positive integer $n$ is [i]divable [/i] if there exist positive integers $1 < a < b < n$ such that, if t... | MATH | {
"ground_truth": "27",
"style": "rule-lighteval/MATH_v2"
} | {
"index": 85,
"original_index": "f1317461-76c4-49cb-9f29-b01c3edef708",
"split": "train"
} |
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 ball bounces back up $\\frac{2}{3}$ of the height from which it falls. If the ball is dropped from a height of $243$... | MATH | {
"ground_truth": "6",
"style": "rule-lighteval/MATH_v2"
} | {
"index": 86,
"original_index": "0084d749-54e6-4601-9a28-538eb8ed129a",
"split": "train"
} |
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若函数$f(x)$满足$\\forall x\\in\\mathbf{R}$，$f(x)+f(1-x)=1$，$f(x)=2f\\left(\\frac{x}{5}\\right)$，且当$0\\leqslant x_{1}\\leqs... | MATH | {
"ground_truth": "33",
"style": "rule-lighteval/MATH_v2"
} | {
"index": 87,
"original_index": "0f85b9d2-6b25-4515-bb84-f0e5eaf902ea",
"split": "train"
} |
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 circles form a ring with each circle externally tangent to the two circles adjacent to it. All six circ... | MATH | {
"ground_truth": "942",
"style": "rule-lighteval/MATH_v2"
} | {
"index": 88,
"original_index": "8928998d-0896-4024-bf5d-31944b7bf796",
"split": "train"
} |
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 $a, b$ are positive real numbers such that $a\\sqrt{a} + b\\sqrt{b} = 183$ and $a\\sqrt{b} + b\\sqrt{a} = 182$... | MATH | {
"ground_truth": "73",
"style": "rule-lighteval/MATH_v2"
} | {
"index": 89,
"original_index": "26a8e0fe-1d35-4bbd-93c4-4aff7313dffa",
"split": "train"
} |
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 value of $x$ between 0 and 180 such that\n\\[\\tan (120^\\circ - x^\\circ) = \\frac{\\sin 120^\\circ - \\sin ... | MATH | {
"ground_truth": "100",
"style": "rule-lighteval/MATH_v2"
} | {
"index": 90,
"original_index": "91dc61fd-6339-4c08-8a97-3cb21721547c",
"split": "train"
} |
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 lines \\begin{align*}\ny&=3x+5 \\\\ 2y&=4x+5 \\\\ 3y&=9x-2 \\\\ 2y&=x-3 \\\\ 4y&=x-5.\n\\end{align*}Let's... | MATH | {
"ground_truth": "1",
"style": "rule-lighteval/MATH_v2"
} | {
"index": 91,
"original_index": "ecfc842c-a878-4b2c-9864-7ac53e47b1e4",
"split": "train"
} |
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 positive integers $n,$ $1 \\le n \\le 1000,$ for which the polynomial $x^2 + x - n$ can be factored... | MATH | {
"ground_truth": "31",
"style": "rule-lighteval/MATH_v2"
} | {
"index": 92,
"original_index": "83c8f91a-7740-43b5-b1e6-ecf4aa444f1a",
"split": "train"
} |
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 Prime Land, there are seven major cities, labeled $C_0$, $C_1$, \\dots, $C_6$. For convenience, we let $C_{n+7} = C... | MATH | {
"ground_truth": "147",
"style": "rule-lighteval/MATH_v2"
} | {
"index": 93,
"original_index": "64b3c5b6-0f00-450b-9586-98aaefe86671",
"split": "train"
} |
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 a positive integer $k$, let $||k||$ denote the absolute difference between $k$ and the nearest perfect square. F... | MATH | {
"ground_truth": "89800",
"style": "rule-lighteval/MATH_v2"
} | {
"index": 94,
"original_index": "29014c43-0acd-480f-a472-ed4386a8db94",
"split": "train"
} |
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 an integer $a_0$, we define a sequence of real numbers $a_0, a_1, . . .$ using the relation $$a^2_i = 1 + ia^2_{... | MATH | {
"ground_truth": "4946",
"style": "rule-lighteval/MATH_v2"
} | {
"index": 95,
"original_index": "bcc40c20-6fca-437d-b54d-35544475fddd",
"split": "train"
} |
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 rectangle that is inscribed in a larger rectangle (with one vertex on each side) is called unstuck if it is possible... | MATH | {
"ground_truth": "448",
"style": "rule-lighteval/MATH_v2"
} | {
"index": 96,
"original_index": "33271436-b8d4-47ad-80ca-0cdd3f22b4d7",
"split": "train"
} |
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 2023 可以拆分为几个正整数之和，所有整数中的最大值和最小值相差不超过 1。有多少种可能？\n\nRemember to put your answer on its own line after \"Answer:\".",
... | MATH | {
"ground_truth": "2023",
"style": "rule-lighteval/MATH_v2"
} | {
"index": 97,
"original_index": "433d2f28-71c3-4162-b4e8-b74f7d077dcd",
"split": "train"
} |
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\nFour people were guessing the number, $N$, of jellybeans in a jar. No two guesses were equally close to $N$. The close... | MATH | {
"ground_truth": "1256",
"style": "rule-lighteval/MATH_v2"
} | {
"index": 98,
"original_index": "957fbf4a-0447-453f-b429-3e05fb613ffc",
"split": "train"
} |
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\nWhat is the area in square units of the convex quadrilateral with vertices $(-1, 0)$, $(0, 1)$, $(2, 0)$ and $(0, -3)$... | MATH | {
"ground_truth": "6",
"style": "rule-lighteval/MATH_v2"
} | {
"index": 99,
"original_index": "2a6098af-9253-4ee0-b736-9b2d70628e2f",
"split": "train"
} |
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