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\nFor how many values of $k$ is $12^{12}$ the least common multiple of the positive integers $6^6$ , $8^8$ , and $k$ ?\n... | MATH | {
"ground_truth": "25",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "c91159e1-d9f5-4929-a5fb-3a6148448b66"
} |
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 a given constant $b > 10,$ there are two possible triangles $ABC$ satisfying $AB = 10,$ $AC = b,$ and $\\sin B = \... | MATH | {
"ground_truth": "16",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "5d1cd258-c060-487a-b88a-ed7dbd87e5f3"
} |
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对实数 x，记 \\{x\\}=x-[x]. 令S=\\int_0^{2024}\\min\\left(\\left\\{\\df{x}{8}\\right\\},\\left\\{\\df{x}{4}\\right\\}\\right... | MATH | {
"ground_truth": "759",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "a5284710-432a-4b08-82d8-0d199634ea33"
} |
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 how many integers $n$ between $1$ and $50$, inclusive, is \n$$\\frac{(n^2-1)!}{(n!)^n}$$ \nan integer? (Recall th... | MATH | {
"ground_truth": "34",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "f58d6d54-f9ee-423a-a46c-d546e4b77d17"
} |
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 maximum possible value for the sum of the squares of the roots of \\(x^4 + ax^3 + bx^2 + cx + d\\) where \... | MATH | {
"ground_truth": "49",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "87125f5a-b1d7-47d0-a222-a85846c2f856"
} |
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 $T = \\{ 1, 2, 3, \\dots, 14, 15 \\}$. A subset $S$ of $T$ is defined as \\textit{handy} if the sum of all the ele... | MATH | {
"ground_truth": "6560",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "48b61bd5-8374-4873-a137-428c63de1890"
} |
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 $P_0(x) = x^3 + 313x^2 - 77x - 8$. For integers $n \\ge 1$, define $P_n(x) = P_{n - 1}(x - n)$. What is the coeffi... | MATH | {
"ground_truth": "763",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "2f2d0eb8-381d-4e81-a7ee-a47919ccb8a6"
} |
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 14-team baseball league, each team played every other team 10 times. At the end of the season, the number of game... | MATH | {
"ground_truth": "52",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "a41236bf-947c-490f-8d31-cb846fc3921f"
} |
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 largest integer that is a divisor of \\[\n(n+1)(n+3)(n+5)(n+7)(n+9)\n\\]for all positive even integers $n$... | MATH | {
"ground_truth": "15",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "e36d307f-6ea9-4355-bf38-68b941855cbd"
} |
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方程 $\\cos \\frac{X}{4}=\\cos x$ 的通解是 $\\qquad$ ，在 $(0,24 \\pi)$ 内不相同的解有多少个？请给出不相同解的个数。\n\nRemember to put your answer ... | MATH | {
"ground_truth": "20",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "28918e62-4ccc-4b2a-a9aa-4769597798f2"
} |
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 cyclic quadrilateral $ABCD$ has side lengths $AB = 3$, $BC = AD = 5$, and $CD = 8$. The radius of its circumcircle c... | MATH | {
"ground_truth": "13",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "31f55c2c-9c49-435d-a64c-82ac6d4dcb0a"
} |
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\nLines $l$ and $m$ are perpendicular. Line $l$ partitions a convex polygon into two parts of equal area, and partitions... | MATH | {
"ground_truth": "2141",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "882397ee-9dbc-4b0b-a393-bc3a493b11d4"
} |
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 four-digit solution to the following system of congruences. \\begin{align*}\n7x &\\equiv 21 \\... | MATH | {
"ground_truth": "1167",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "fee4b142-f611-42c9-af7f-12f7e8ec993e"
} |
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 largest integer $n$ such that $2^n + 65$ is equal to the square of an integer? Find the value of $n$.\n\nR... | MATH | {
"ground_truth": "10",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "c687b324-9900-4baf-9f82-20be38390bb9"
} |
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 vertices of a cube are $P=(7,12,10)$, $Q=(8,8,1)$, and $R=(11,3,9)$. What is the side length of the cube?\n\nRem... | MATH | {
"ground_truth": "7",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "b3fcf40f-af44-4ea8-932b-dadafc470498"
} |
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 values of $x$ such that the area of the isosceles triangle with sides $x$, $65$, and $65$ is a posi... | MATH | {
"ground_truth": "4224",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "951597a2-c3c0-484c-8a9f-4131596939ac"
} |
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 functions $f(x)$ from $\\{1, 2, 3, 4, 5\\}$ to $\\{1, 2, 3, 4, 5\\}$ that satisfy $f(f(x)) = f(f(f(... | MATH | {
"ground_truth": "756",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "468deb46-2313-408c-b311-71738d332927"
} |
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\nJeffrey writes the numbers $1$ and $100000000 = 10^8$ on the blackboard. Every minute, if $x, y$ are on the board, Jef... | MATH | {
"ground_truth": "10000",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "ec572625-c31a-44fc-a9c2-2039d0b7b5b2"
} |
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设非负实数 a_1,a_2,\\cdots,a_{100} 满足对任意 2\\leq i\\leq 99，有 \\max\\{a_{i-1}+a_i,a_i+a_{i+1}\\}\\geq i. 求 a_1+a_2+\\cdots+a_... | MATH | {
"ground_truth": "1683",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "47eac659-5cbd-43c4-8045-fba955d4f475"
} |
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设正整数 $a, b, c$ 中任意两个数不互素，且 $a+b+c$ 为素数。求 $a+b+c$ 的最小值。\n\n\nRemember to put your answer on its own line after \"Answer... | MATH | {
"ground_truth": "31",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "1d35d78e-447d-4a1a-ad40-2ba922da4037"
} |
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 some matrix $\\mathbf{P} = \\begin{pmatrix} a & b \\\\ c & d \\end{pmatrix}$ with nonzero integer entries,\n\\[\\b... | MATH | {
"ground_truth": "6",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "2e625936-9873-406c-a380-4760c3a2d519"
} |
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 integers $0 \\le m,n \\le 2^{2017}-1$, let $\\alpha(m,n)$ be the number of nonnegative integers $k$ for which $\\l... | MATH | {
"ground_truth": "1382",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "062ca0e0-bda9-4b0b-ab46-b0529207261f"
} |
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\nDefine the sequences $a_n$ and $b_n$ as follows: $a_1 = 2017$ and $b_1 = 1$. \nFor $n > 1$, if there is a greatest int... | MATH | {
"ground_truth": "8002",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "005b07c9-79e5-4dc5-ad5c-b6a2ec724b00"
} |
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在正四面体 $A B C D$ 中, $E, F$ 分别在棱 $A B, A C$ 上,满足 $B E=3, E F=4$, 且 $E F$ 与面 $B C D$ 平行, 则 $\\triangle D E F$ 的面积为 $\\qqu... | MATH | {
"ground_truth": "35",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "2410cef2-e0a2-451f-9bcd-b53c5e109ea4"
} |
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 is a box containing $100$ balls, each of which is either orange or black. The box is equally likely to contain a... | MATH | {
"ground_truth": "5",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "6f7112a8-8477-4050-9e65-95def35413e4"
} |
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 digit in the number 2001 is placed on a different card. In how many ways can three different cards be selected so... | MATH | {
"ground_truth": "0",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "18d000b7-e571-4dd0-98e0-b39e22ea7eca"
} |
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 100\\times100 方格表的左上角小方格中有一只老鼠，右下角小方格中有一块奶酪. 老鼠希望移动到右下角小方格中吃奶酪，每次可以从一个小方格移动到相邻的小方格（两个小方格相邻指它们有公共边）. 现在在一些小方格的边上放置隔板... | MATH | {
"ground_truth": "2220",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "e11b1e41-6ec3-46d4-90d4-c43e3815abef"
} |
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 $m,$ define the polynomial $$P_m(z) = z^4-\\frac{2m^2}{m^2+1} z^3+\\frac{3m^2-2}{m^2+1}z^2-\\... | MATH | {
"ground_truth": "171",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "5ac92f1d-f1d1-4e8e-9565-cf22459a0629"
} |
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 base-10 positive integer greater than 5 that is a palindrome when written in both base 2 and 4.\n... | MATH | {
"ground_truth": "15",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "20699fd1-9a89-4c4d-9608-b983d9f721c4"
} |
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 \\(z, w\\) 满足: \\(|w+z|=1,\\left|w^{2}+z^{2}\\right|=4\\)，求 \\(|w z|\\) 的最小值。答案应以 \\(\\frac{k}{m}\\) 的形式给出，其中 \\(\... | MATH | {
"ground_truth": "5",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "405d798f-ed8a-4208-9cdf-4a36f5599845"
} |
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将编号为 $1,2,3, \\cdots, 9$ 的九个小球随机放置在圆周的九个等分点上，每个等分点上各放一个小球，设圆周上所有相邻两个球号码之差的绝对值之和为 $S$ ，求使 $S$ 达到最小值的放法的概率。（注：如果某种放法，经旋转... | MATH | {
"ground_truth": "316",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "727cbb16-e827-45b2-9802-0852cd7e4046"
} |
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 parallelepiped with side lengths $x$, $y$, and $z$. Suppose that the four space diagonals of $... | MATH | {
"ground_truth": "371",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "f346362b-79d3-4bf2-b225-18ac089ec9fa"
} |
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\nOf all the primes in the prime factorization of \\begin{align*}\\gcd(&2^23^35^57^711^{11}13^{13}17^{17}19^{19}23^{23},... | MATH | {
"ground_truth": "11",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "c44ca8fb-eef5-41c5-b6ed-9c38e94396de"
} |
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 have exactly three proper divisors (positive integral divisors excluding itself), each of w... | MATH | {
"ground_truth": "109",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "c250828c-11ce-4ff3-8f62-8bffe78218a0"
} |
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 house and a store were each sold for $\\$12000$. The house was sold at a loss of $20\\%$ of its cost, and the store ... | MATH | {
"ground_truth": "1000",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "77e46da8-59af-4554-b8d7-f17ad1a475b0"
} |
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 finite set $S \\subset \\mathbb{R}^3$, define $f(S)$ to be the minimum integer $k$ such that there exist $k$ p... | MATH | {
"ground_truth": "2189",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "f2ed6600-8e8c-4b1b-ab91-98894397f3f7"
} |
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 sequence \\((a_n)\\) of real numbers is defined by \\(a_0=1\\), \\(a_1=2015\\) and for all \\(n \\geq 1\\), we have:... | MATH | {
"ground_truth": "3021",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "608c574e-7777-4aa1-b583-0eaf63128b4d"
} |
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\\) and \\(b\\) be the roots of the equation \\(x^2-mx+2=0\\). Suppose that \\(a+\\frac{1}{b}\\) and \\(b+\\fr... | MATH | {
"ground_truth": "11",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "66d7c687-a852-4247-88cf-6543fe33a921"
} |
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 $ABC$ with $AC = 20$ is inscribed in a circle $\\omega$. A tangent $t$ to $\\omega$ is drawn through $B$. T... | MATH | {
"ground_truth": "10",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "24ee6a0a-5d77-4e8b-a3a5-b75d81273af4"
} |
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 zoo has a menagerie containing four pairs of different animals, one male and one female for each. The zookeeper wish... | MATH | {
"ground_truth": "144",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "f5649567-c70a-4a6a-a100-e413eb3e68df"
} |
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 $2^{-1} + 2^{-2} + 2^{-3} + 2^{-4} + 2^{-5} + 2^{-6} \\pmod{13}$?\n\nExpress your answer as an integer from $0... | MATH | {
"ground_truth": "2",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "8032cf62-417b-4f4b-b8e3-1b56aaf9081a"
} |
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 noncongruent integer-sided triangles with positive area and perimeter less than $15$ are neither equilateral,... | MATH | {
"ground_truth": "5",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "cdf9eb83-a5cb-4d0f-bfbb-61f4d1084a0c"
} |
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 the set of positive integers that are prime numbers. Find the number of subsets of $P$ that have the proper... | MATH | {
"ground_truth": "9",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "709a7396-7952-41ef-8f8a-6690ca165c03"
} |
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\nKelvin the Frog was bored in math class one day, so he wrote all ordered triples $(a, b, c)$ of positive integers such... | MATH | {
"ground_truth": "49140",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "34acdd92-1ba1-4788-8996-0b5f0b20219d"
} |
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 particle moves so that its speed for the second and subsequent miles varies inversely as the integral number of mile... | MATH | {
"ground_truth": "3",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "420ef8ac-18bd-480c-8268-9f221e45adc4"
} |
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 even three-digit integers have the property that their digits, read left to right, are in strictly increasin... | MATH | {
"ground_truth": "34",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "59c6f560-f863-4c01-b24f-79f39d5f06ff"
} |
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已知圆锥面 $x^{2}+y^{2}=\\frac{z^{2}}{3}$, 记沿该圆锥面从 $P(-\\sqrt{3}, 3,6)$ 到 $Q(\\sqrt{3}, 0,3)$ 的曲线长度的最小为值为 I, 则 $[10 I]=$ $\... | MATH | {
"ground_truth": "60",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "9c7747d0-7289-47db-8e26-43137045fe17"
} |
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, whose dimensions are $AB = 6, BC=5=DA,$ and $CD=4.$ Draw circles of radius $3$ c... | MATH | {
"ground_truth": "134",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "b584204a-0135-44e5-8169-dd14d8dd81c1"
} |
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 three standard, six-faced dice are rolled, what is the probability that the sum of the three numbers rolled is 9? E... | MATH | {
"ground_truth": "241",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "aa10fd31-97b1-4539-aef2-6effebcbc6d1"
} |
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>0$ ，满足：关于 $x$ 的方程 $\\sqrt{|x|}+\\sqrt{|x+a|}=b$ 恰有三个不同的实数解 $x_{1}, x_{2}, x_{3}$, 且 $x_{1}<x_{2}<x_{3}=b$, 则 $... | MATH | {
"ground_truth": "144",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "04056225-f6e2-4651-9502-f78d5ed1b6ab"
} |
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 minimum of \\( \\sum\\limits_{k=0}^{40} \\left(x+\\frac{k}{2}\\right)^2 \\) where \\( x \\) is a real number.... | MATH | {
"ground_truth": "1435",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "8973774b-9073-4d7e-bbbc-37c14a72a7f1"
} |
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 ordered pairs $(x,y)$ of real numbers that satisfy\n\\[x^2 + 2y^2 + \\frac{1}{2} \\le x(2y + 1).\\]... | MATH | {
"ground_truth": "1",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "47ede0e4-3356-479b-b2a8-e9766486c256"
} |
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方程 x^3-9x^2+8x+2=0 有 3 个实根 p,q,r，则 \\df{1}{p^2}+\\df{1}{q^2}+\\df{1}{r^2}=__________.\n\nRemember to put your answer o... | MATH | {
"ground_truth": "25",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "bfe7ce93-5585-4363-aabf-d6de22b6e9d4"
} |
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 $S = \\{1, \\cdots, 6\\}$ and $\\mathcal{P}$ be the set of all nonempty subsets of $S$. Let $N$ equal the number o... | MATH | {
"ground_truth": "9792",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "5fe15d3c-f590-4d18-a29a-7705df55e832"
} |
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 $n$ and $k$ are positive integers such that $5<\\frac nk<6$, then what is the smallest possible value of $\\frac{\\... | MATH | {
"ground_truth": "22",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "5916be78-314c-4913-b012-7b5075e744d0"
} |
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 sum of all the roots of \n\\((2x+3)(x-4)+(2x+3)(x-6)=0\\). \nExpress your answer as a fraction in simple... | MATH | {
"ground_truth": "9",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "35f0edbd-c5c1-4afd-afd2-918812c1ae4a"
} |
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设函数 f(x) 的定义域为 \\bR，且 f(x-1) 为偶函数，f(x-2) 为奇函数. 当 x\\in[1,2] 时，f(x)=ax^2+bx. 若 f(0)+f(3)=-1，则 f(\\df{9}{2})=__________.... | MATH | {
"ground_truth": "7",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "1d95e47e-c84f-4cdc-b424-3b28fb77ff48"
} |
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 $13^{-1} \\equiv 29 \\pmod{47}$, find $34^{-1} \\pmod{47}$, as a residue modulo 47. (Give a number between... | MATH | {
"ground_truth": "18",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "d37260c0-84f5-4fe3-9a59-acd95f63b84e"
} |
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 congruent equilateral triangles $\\triangle ABC$ and $\\triangle DEF$ lie on the same side of line $BC$ so that $B... | MATH | {
"ground_truth": "33",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "6d0b145b-d3bc-4855-b513-58047b718c69"
} |
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一个六面体的各个面和一个正八面体的各个面都是边长为 $a$ 的正三角形, 这样两个多面体的内切球的半径之比是一个既约分数 $\\frac{m}{n}$ 。那么, 积 $m \\cdot n$ 是\n$\\qquad$ $\\cdot$\... | MATH | {
"ground_truth": "6",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "f387fa35-ca89-409a-88ab-2f9a9657ff39"
} |
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 largest integer $n$ such that $7^{2048} - 1$ is divisible by $2^n$.\n\nRemember to put your answer on it... | MATH | {
"ground_truth": "14",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "b30444ad-ed14-47e0-8a5a-148e0017f3ac"
} |
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\n13 LHS Students attend the LHS Math Team tryouts. The students are numbered $1, 2, \\ldots, 13$. Their scores are $s_1... | MATH | {
"ground_truth": "78",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "3812d1fb-65f1-4ba8-8241-ece6766ae23f"
} |
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 concentric circles have radii $3,$ $4,$ and $5.$ An equilateral triangle with one vertex on each circle has side... | MATH | {
"ground_truth": "41",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "432d5a78-88b0-4716-adf1-0b8d6e188e99"
} |
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 diagram below shows a large square with each of its sides divided into four equal segments. The shaded square, who... | MATH | {
"ground_truth": "104",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "07e856a6-1edb-44f2-afec-ba56295cc2e1"
} |
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 $100$ people standing in a line from left to right. Half of them are randomly chosen to face right (with all... | MATH | {
"ground_truth": "50",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "fb913174-070a-4d16-8872-1db79e15825a"
} |
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 closest in value to\n\\[\\frac{1}{\\sqrt[4]{5^4+1}-\\sqrt[4]{5^4-1}}.\\]\n\nRemember to put your answ... | MATH | {
"ground_truth": "250",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "237e82fb-5fff-4bc9-b4de-7d3dd4f6aad3"
} |
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 face of a cube is given a single narrow stripe painted from the center of one edge to the center of the opposite ... | MATH | {
"ground_truth": "19",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "826f3e43-af7a-463c-965c-3cb416ba01b3"
} |
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\nMy clock chimes two times 15 minutes after the hour, four times 30 minutes after the hour and six times 45 minutes aft... | MATH | {
"ground_truth": "636",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "88eb27ad-2152-4d16-b7f0-67f018a940eb"
} |
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 $LMT$ represent a 3-digit positive integer where $L$ and $M$ are nonzero digits. Suppose that the 2-digit number $... | MATH | {
"ground_truth": "880",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "8fbf5877-b66b-43e5-aa77-d629df4c6022"
} |
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\nRobert tiles a $420 \\times 420$ square grid completely with $1 \\times 2$ blocks. He notices that the two diagonals o... | MATH | {
"ground_truth": "2517",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "d4f3093f-9129-47db-bf7e-749b4e5a3432"
} |
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 natural number $n$ is considered \\textit{good} if it can be expressed as the sum of $r$ consecutive positive intege... | MATH | {
"ground_truth": "93",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "208c62ec-e721-443d-a2c3-a117bab13aa0"
} |
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 has an area of $16$ and a perimeter of $18$. Determine the length of the diagonal of the rectangle.\n\nRem... | MATH | {
"ground_truth": "7",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "9192f0de-491f-430e-9037-3ed4de3821a9"
} |
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 prime number $p$ such that $p^3$ divides $$\\frac{122!}{121}+ 123!:$$\n\nRemember to put your answer... | MATH | {
"ground_truth": "61",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "3e21052c-f5e8-4bfb-976a-af89f3198f16"
} |
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 circles $\\omega_1$ and $\\omega_2$. They intersect in two points, one of which is the point $A$. Point $B$ ... | MATH | {
"ground_truth": "4",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "6f2e71b6-ee6e-4bcd-8da5-d8c1da23886d"
} |
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 $ABC$, where $AB = 28$, $AC = 36$, and $BC = 32$, let $D$ be the point on segment $BC$ such that $\\angle ... | MATH | {
"ground_truth": "18",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "15f84155-8516-4eba-8279-67c76d09415d"
} |
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\nPatrick started walking at a constant rate along a straight road from school to the park. One hour after Patrick left,... | MATH | {
"ground_truth": "277",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "a380db75-a4cc-484c-b235-fcce050b7516"
} |
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 $2022$ grids in a row. Two people, A and B, play a game with these grids. Initially, each odd-numbered grid ... | MATH | {
"ground_truth": "1011",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "d8ad1943-d93f-4d64-b717-57f63b554304"
} |
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已知函数 f:\\bR\\rightarrow\\bR，若对任意实数 x,y,z 都有\\df{1}{3}f(xy)+\\df{1}{3}f(xz)-f(x)f(yz)\\geq\\df{1}{9},求 \\ds{i=1}{100}[i... | MATH | {
"ground_truth": "1650",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "20247aa6-e432-4080-b98b-96013b760783"
} |
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 5x5x5 cube is formed by assembling 125 unit cubes. Nine unit squares are painted on each of the six faces of the cub... | MATH | {
"ground_truth": "83",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "b550cdfd-a2dd-4a0b-9aa1-026e12a063f0"
} |
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 square piece of paper is folded in half vertically. The folded paper is then cut in half along the dashed li... | MATH | {
"ground_truth": "11",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "bae9b795-e39f-4d24-8443-f2e48054bf1c"
} |
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 functions $f : \\{1,2,3,4,5,6\\} \\to \\{1,2,3,4,5,6\\}$ have the property that $f(f(x)) + f(x) + x$ is divis... | MATH | {
"ground_truth": "64",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "4ad3677e-50b8-4933-9114-c503e793aee6"
} |
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\n13. Let $\\triangle T B D$ be a triangle with $T B=6, B D=8$, and $D T=7$. Let $I$ be the incenter of $\\triangle T B ... | MATH | {
"ground_truth": "97",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "f01b9de6-b1a4-431d-b065-d08c251369fe"
} |
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求一切实数 $p$ ，使得三次方程 $5 x^{3}-5(p+1) x^{2}+(71 p-1) x+1=66 p$ 的三个根均为正整数。\n\nRemember to put your answer on its own line a... | MATH | {
"ground_truth": "76",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "bc6cffab-388d-49cb-9aa0-40eee922cf17"
} |
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 $AB=9^{}_{}$ and $BC: AC=40: 41^{}_{}$. What's the largest area that this triangle can have?\... | MATH | {
"ground_truth": "820",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "d5b84bf3-659e-4e79-aa49-c58cdd3ca6e8"
} |
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将一枚均匀的硬币连续抛掷 $n$ 次，以 $p_{n}$ 表示未出现连续 3 次正面的概率. 求数列 $\\left\\{p_{n}\\right\\}$ 的其极限.\n\nRemember to put your answer on ... | MATH | {
"ground_truth": "0",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "ecc6b85c-7e9f-43d0-b44a-626ba980b826"
} |
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设多项式 \\(f(x)\\) 的各项系数都是非负实数，且 \\(f(1)=f^{\\prime}(1)=f^{\\prime \\prime}(1)=f^{\\prime \\prime \\prime}(1)=1\\)。求 \\(f... | MATH | {
"ground_truth": "4",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "f1c3e405-9b68-4d87-b387-2320daaf607d"
} |
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给定正整数 $k$. 若整数集 $\\mathbf{Z}$ 的子集序列 $I_{1} \\supseteq I_{2} \\supseteq \\cdots \\supseteq I_{k}$ 满足对 $i=1,2, \\cdots, ... | MATH | {
"ground_truth": "2016",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "942ed614-8671-4c08-9e4e-b61bb0e43585"
} |
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 $A \\subseteq \\{0,1,\\dots,29\\}$. It satisfies that for any integer $k$ and any two members $a,b \\in A$ (wh... | MATH | {
"ground_truth": "10",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "4aee130e-3ad9-4b51-ad95-bbdb3ee09045"
} |
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 $ABC$ have $\\angle A = 70^\\circ$, $\\angle B = 60^\\circ$, and $\\angle C = 50^\\circ$. Extend altitude... | MATH | {
"ground_truth": "50",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "1bebb179-426d-4dc6-998d-4e7015ffe72f"
} |
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 $m$ be a positive integer, and suppose that $9$ is its own inverse $\\pmod m$, but $3$ is $\\textbf{not}$ its own ... | MATH | {
"ground_truth": "6",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "0dcd19fb-cbfb-4504-a43f-95d96511d722"
} |
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 $a$ 为实数, 且对任意 $k \\in[-1,1]$, 当 $x \\in(0,6]$ 时, $6 \\ln x+x^{2}-8 x+a \\leqslant k x$ 恒成立, 则 $a$的最大值是 $\\qquad$.原始... | MATH | {
"ground_truth": "18",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "5ff8dd60-7af3-42b3-b87c-b695d50c05fb"
} |
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 xy 两项的系数相等，则 n 的值为________.\n\nRemember to put your answer on its own line ... | MATH | {
"ground_truth": "51",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "fc991e76-0963-4120-9b44-c27d8925bffb"
} |
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一个球与正四面体的六条棱都相切。若正四面体的棱长为 $a$，则这个球的体积的原始答案是\\frac{\\sqrt{a}\\pi a^b}{c}的格式，请给出a+b+c的值。\n\nRemember to put your answer ... | MATH | {
"ground_truth": "29",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "735f4fae-a20e-439a-bf35-673147771643"
} |
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定义在 \\(\\mathbf{R}\\) 上的函数 \\(f(x)\\) 满足 \\(f(0)=0\\), \\(f(x)+f(1-x)=1\\), \\(f\\left(\\frac{x}{5}\\right)=\\frac{1}{... | MATH | {
"ground_truth": "33",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "1765ca2d-2324-4e9d-b1b8-251de2864ae9"
} |
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 $z=(\\omega+2)^{3}(\\omega-3)^{2}$ 。求当 $\\omega$取遍所有模长为 1 的复数时, $z$ 的模长的最大值。原始答案为$m^{\\frac{p}{q}}$的形式，其中$p,q$互质，请... | MATH | {
"ground_truth": "14",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "e851ab41-50f9-440f-b5b1-802f43603b15"
} |
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 $\\triangle ABC$ be an isosceles triangle such that $BC = 30$ and $AB = AC.$ We have that $I$ is the incenter of $... | MATH | {
"ground_truth": "14",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "f094441d-2831-435c-b995-fb677f16b323"
} |
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 $a, b, c, d, e,$ and $f$ be real numbers. Define the polynomials: \n\\[ P(x) = 2x^4 - 26x^3 + ax^2 + bx + c \\] \n... | MATH | {
"ground_truth": "2400",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "54f4b5dd-619d-43d4-bab1-85cd48c23d87"
} |
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\nEuler discovered that the polynomial $p(n) = n^2 - n + 41$ yields prime numbers for many small positive integer values... | MATH | {
"ground_truth": "41",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "6e1c746c-6afa-4ac5-a97e-b00f005f6c3c"
} |
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\nEquilateral triangle $ABC$ has area $1$. $A'$, $B'$, and $C'$ are the midpoints of $BC$, $CA$, and $AB$, respectively.... | MATH | {
"ground_truth": "21",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "4436d9d8-0f11-4098-b3c6-2f45eaa02540"
} |
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 $m$ such that $2^m$ can be expressed as a sum of four factorials (of positive in... | MATH | {
"ground_truth": "21",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "3f0387a7-58b3-41a7-8613-c1442abe1d48"
} |
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