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\nSuppose the side lengths of triangle $ABC$ are the roots of the polynomial $x^3 - 27x^2 + 222x - 540$. What is the pro... | MATH | {
"ground_truth": "10",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "d03c7b1d-1cf6-4c50-89cd-538408c05bec"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 $n$, let $S_n$ denote the set of positive integers $k$ such that $n^k - 1$ is divisible by $... | MATH | {
"ground_truth": "912",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "a3837244-b955-4eaa-9b8d-09eb72739338"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 reorderings of \\(2, 3, 4, 5, 6\\) have the property that every pair of adjacent numbers are relatively prime... | MATH | {
"ground_truth": "4",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "f253c5fd-0e19-4646-a94d-ef33372fe1c5"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 positive integers $m > n$, the quantities $a = \\text{lcm}(m, n)$ and $b = \\gcd(m, n)$ satisfy $a = 30b$. If... | MATH | {
"ground_truth": "11",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "1cd86045-bfd8-4525-99c6-bc88dd21265d"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 $x^3 - 3\\sqrt{3} x^2 + 9x - 3\\sqrt{3} - 64 = 0$, find the value of $x^6 - 8x^5 + 13x^4 - 5x^3 + 49x^2 - 137x + 20... | MATH | {
"ground_truth": "1898",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "80bcddcc-467e-4fb8-94af-571403611f0b"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 $ABCD$ is a rectangle whose diagonals meet at $E$. The perimeter of triangle $ABE$ is $10\\pi$ and the perimet... | MATH | {
"ground_truth": "47",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "fe59c2dd-355b-4f81-b5ea-c632a17baddb"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 numbers in the sequence 101, 104, 109, 116, $\\dots$ are of the form $a_n = 100 + n^2$, where $n = 1, 2, 3, \\dots... | MATH | {
"ground_truth": "401",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "152310db-3763-46c3-9326-b99c8cde1e74"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 $4 \\cos \\theta - 3 \\sin \\theta = \\frac{13}{3},$ it follows that $7 \\cos 2\\theta - 24 \\sin 2\\theta = \\fr... | MATH | {
"ground_truth": "122",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "5fbcedc6-142d-41d2-848a-e6a4b37375ae"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 $\\{a_n\\}$ satisfies the following conditions: \n- $a_0 = 0$ \n- $a_1 = a_2 = 1$ \n- $a_{3n} = a_n$ \n... | MATH | {
"ground_truth": "6",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "555d1ee5-1207-4f28-835e-cb45d4870de6"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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's formula states that for a convex polyhedron with $V$ vertices, $E$ edges, and $F$ faces, $V - E + F = 2$. A pa... | MATH | {
"ground_truth": "250",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "f7d305c1-82b2-4d2d-b6df-ae8452c1ccce"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 $f(x) = x^3 + 3x - 1$ have roots $a, b, c$. Given that \\(\\frac{1}{a^3 + b^3} + \\frac{1}{b^3 + c^3} + \\frac{1}{... | MATH | {
"ground_truth": "3989",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "5b37e3eb-028b-4721-be1d-02cbe2a691d0"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 George Washington Bridge is $2016$ meters long. Sally is standing on the bridge, $1010$ meters from its left end. ... | MATH | {
"ground_truth": "1016060",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "3e4b1e7d-8ddf-419a-923e-dbb4ef37a612"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 number of positive integers less than or equal to $10000$ which are relatively prime to $2014$.\n\nRemembe... | MATH | {
"ground_truth": "4648",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "221bacc0-4ea4-46e8-b14c-eabdcf20bde4"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 $2022$ stones on a table. At the start of the game, Teacher Tseng will choose a positive integer $m$ and let... | MATH | {
"ground_truth": "1",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "4219515a-888d-49df-91fd-931cf1e25d09"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nLet $a$, $b$, $c$ be the distinct roots of the polynomial $P(x) = x^3 - 10x^2 + x - 2015$. The cubic polynomial $Q(x)$... | MATH | {
"ground_truth": "2015000",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "1ff826fe-dacd-4e8d-b277-d9a8fbc1ba54"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 the equation: \n\n$$6\\{x\\}^3 + \\{x\\}^2 + \\{x\\} + 2x = 2018.$$ \n\nWith $\\{x\\}$... | MATH | {
"ground_truth": "5",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "f235f435-c352-4b0e-9b46-27d7b620a498"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nAlfred and Bonnie play a game where they take turns tossing a fair coin. The winner of the game is the first person to... | MATH | {
"ground_truth": "93",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "597ea941-ab34-4463-bcaf-d2a27220c351"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nOne morning, each member of Manjul’s family drank an $8$-ounce mixture of coffee and milk. The amounts of coffee and m... | MATH | {
"ground_truth": "8",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "fe236e58-20e9-4908-a903-cfc3a64c5014"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nBob, a spherical person, is floating around peacefully when Dave the giant orange fish launches him straight up at 23 ... | MATH | {
"ground_truth": "3",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "3c28533b-e30a-4344-b324-b813608c861e"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 smallest positive integer $a$ such that $x^4 + a^2$ is not prime for any integer $x$.\n\nRemember to put your... | MATH | {
"ground_truth": "8",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "0b56196f-34f5-4ed4-89a1-03bcb92467e4"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nBroady The Boar is playing a board game consisting of a circle with $2021$ points on it, labeled $0$, $1$, $2$, \\ldot... | MATH | {
"ground_truth": "2021",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "309cebd3-b43e-42dd-b28b-cd47f2440b2b"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 positive integer $n$ such that $3^n$ divides $70! + 71! + 72!$.\n\nRemember to put your answer on it... | MATH | {
"ground_truth": "36",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "52a61377-fc5a-4c54-8a0d-eb7a976c704f"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 natural number $m$ such that for each non-negative real numbers $a_1 \\ge a_2 \\ge \\ldots \\ge ... | MATH | {
"ground_truth": "44",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "78f1171b-8e7b-4b72-906b-eb2f0bc010ca"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nCounting from the right end, what is the $2500$th digit of $10000!$?\n\nRemember to put your answer on its own line af... | MATH | {
"ground_truth": "2",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "86c1d506-b750-44fa-89ca-51c61d24bc57"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 last digit of $5^5 + 6^6 + 7^7 + 8^8 + 9^9$.\n\nRemember to put your answer on its own line after \"Answ... | MATH | {
"ground_truth": "9",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "0bfd0096-a286-4fa7-9c56-23522407f753"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nWhile there do not exist pairwise distinct real numbers $a,b,c$ satisfying $a^2+b^2+c^2 = ab+bc+ca$, there do exist co... | MATH | {
"ground_truth": "132",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "35079013-690d-4f80-ba33-36aed87d8936"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 last three digits of \n\\[2008^{2007^{\\cdot^{\\cdot^{\\cdot ^{2^1}}}}}.\\]\n\nRemember to put your answer on... | MATH | {
"ground_truth": "8",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "1b2ecb7b-bb05-48fc-9ef1-448b44a674b3"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nWu starts with exactly one coin. Each year, Wu flips every coin he has at once. For each heads he flips, Wu receives a... | MATH | {
"ground_truth": "71622400",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "13edd423-776e-4bda-bf67-d94644955772"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 non-zero real numbers $a$, $b$, and $c$ satisfy the conditions $a + b + c = 0$ and $a^4 + b^4 + c^4 = 128$. Dete... | MATH | {
"ground_truth": "-8",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "f1a74867-d4b7-4801-af44-7158a3fdea80"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nLet $a$, $b$, $c$ be positive real numbers for which:\n\\[\n \\frac{5}{a} = b+c, \\quad\n \\frac{10}{b} = c+a, \\qua... | MATH | {
"ground_truth": "55",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "be79dde1-cfaf-4a31-9a3e-2ff70b543deb"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 five dots arranged in a line from left to right. Each of the dots is colored from one of five colors such th... | MATH | {
"ground_truth": "2800",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "d3d2f935-b6c9-47f9-9c4b-94f42ea2ceaf"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nAn acute triangle $ABC$ has side lengths $a$, $b$, $c$ such that $a$, $b$, $c$ form an arithmetic sequence. Given that... | MATH | {
"ground_truth": "42",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "42198624-fca7-47cd-92e4-f7802258d96a"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 three-digit number $999$ has a special property: It is divisible by $27$, and its digit sum is also divisible by $... | MATH | {
"ground_truth": "75",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "456c2a13-2316-48c3-9d6a-081df4a1c9fa"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nLet $ABC$ be a triangle with side lengths $AB=6$, $AC=7$, and $BC=8$. Let $H$ be the orthocenter of $\\triangle ABC$ a... | MATH | {
"ground_truth": "251",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "ef960371-7ff6-43e4-aa25-5af7aa51a1c5"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 triples of integers $(x, y, z)$ are there such that $x^2 + y^2 + z^2 = 34$?\n\nRemember to put your a... | MATH | {
"ground_truth": "48",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "9d259550-9d21-43a0-99ff-68027acd2d54"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 bijective function $g : \\mathbb{R} \\to \\mathbb{R}$, we say that a function $f : \\mathbb{R} \\to \\mathbb{R}$... | MATH | {
"ground_truth": "7",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "0395239f-9e86-4154-aad6-c40ca8044b9f"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 $\\triangle ABC$ has $\\angle{A}=90^\\circ$ with $BC=12$. Square $BCDE$ is drawn such that $A$ is in its inte... | MATH | {
"ground_truth": "149",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "822b2d99-412d-4d82-855c-1f3a313b0b1f"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nAt a recent math contest, Evan was asked to find $2^{2016} \\pmod{p}$ for a given prime number $p$ with $100 < p < 500... | MATH | {
"ground_truth": "211",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "137b6d74-aa4d-45d2-b388-a217e2c635f0"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nFarmer James invents a new currency such that for every positive integer $n \\leq 6$, there exists an $n$-coin worth $... | MATH | {
"ground_truth": "210",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "2e264ea1-1556-4eb6-90e3-79621f093671"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 board with dimensions $2018 \\times 2018$ is divided into unit cells of size $1 \\times 1$. In some cells of the boa... | MATH | {
"ground_truth": "1018081",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "4180cbec-a762-4723-a196-465d98a414ac"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 how many integer values $3 \\le n \\le 99$ satisfy that the polynomial $x^2 + x + 1$ divides $x^{2^n} + x + 1$.\n... | MATH | {
"ground_truth": "49",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "e8550eaf-2f1a-40e5-84cc-2a23276288af"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 chicken breeder went to check the price per chick he charged the previous year. He found an invoice, half erased, wh... | MATH | {
"ground_truth": "511",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "47590b4b-9f37-4571-9625-db852c1e559a"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nFind all positive integers $n$ such that $n$ is a perfect number and $\\varphi(n)$ is a power of $2$.\n\nRemember to p... | MATH | {
"ground_truth": "6",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "e50a8ba5-f107-4877-8b09-590807bf6e95"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 square with side length $2$. Let $M$ and $N$ be the midpoints of $\\overline{BC}$ and $\\overline{CD}$... | MATH | {
"ground_truth": "3225",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "94665fbe-83ae-485b-9cf7-4a1b88efb3aa"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 $S$ be the set of natural numbers that cannot be written as the sum of three squares. Legendre's three-square theo... | MATH | {
"ground_truth": "111",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "34184cdd-cb16-4e77-bb08-73687923d543"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 trapezoid has side lengths as indicated in the figure, with the sides of lengths $11$ and $36$ being parallel. Calcu... | MATH | {
"ground_truth": "564",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "64021516-9007-4747-a6e6-966aa5ba209d"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 friends purchased a ball. The first friend paid half of the ball's total price. The second friend contributed one... | MATH | {
"ground_truth": "100",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "4d71fa4d-3b97-47b4-82df-873be5cce7c7"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 last two digits of $\\binom{200}{100}$. Express the answer as an integer between $0$ and $99$. (e.g., if the ... | MATH | {
"ground_truth": "20",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "a65fce80-2b99-4ea0-906c-608bd2e998c0"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 value of \\( S = |x + 1| + |x + 5| + |x + 14| + |x + 97| + |x + 1920| \\).\n\nRemember to put your an... | MATH | {
"ground_truth": "2011",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "bb8c79a9-c506-4d86-9ef5-e53ef4ac7ad5"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 \\( \\sum_{i=1}^{2016} i(i+1)(i+2) \\pmod{2018} \\).\n\nRemember to put your answer on its own line after \"Answe... | MATH | {
"ground_truth": "0",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "86a981e2-1520-4681-9239-d4c707ace66e"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 positive integer that is a divisor of all three of \\( A=2^{2010}\\times3^{2010} \\), \\( B=3^{2... | MATH | {
"ground_truth": "1",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "4ffe1ddc-165a-4eb6-a39e-2b117013442f"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\n$AB$ is the diameter of circle $O$. A random point $P$ is selected on $O$ such that $AP = 4$ and $BP = 3$. Points $C$ ... | MATH | {
"ground_truth": "90",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "66cc7cb4-174d-4291-87ae-582038c0fa38"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 \\((2^x - 4^x) + (2^{-x} - 4^{-x}) = 3\\), find the numerical value of the expression \n\\[\n(8^x + 3\\cdot 2^x) + ... | MATH | {
"ground_truth": "-1",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "f8dce418-73a2-4fcd-b805-884fcaa9da13"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nBeto plays the following game with his computer: initially, the computer randomly picks $30$ integers from $1$ to $201... | MATH | {
"ground_truth": "11",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "67143f48-0e7f-49be-8268-394f30ca82c9"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nSuppose that $a$, $b$, $c$, and $d$ are real numbers such that $a+b+c+d=8$. Compute the minimum possible value of \n\\... | MATH | {
"ground_truth": "112",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "d4d65683-d953-4e8d-aa81-7068abb7d612"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nXavier takes a permutation of the numbers $1$ through $2011$ at random, where each permutation has an equal probabilit... | MATH | {
"ground_truth": "1006",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "9249fd70-3d78-489b-bc69-892ca091cff0"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 lines $m$, $n$, and $\\ell$ lie in a plane such that no two are parallel. Lines $m$ and $n$ meet at an acute ang... | MATH | {
"ground_truth": "40",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "b9562435-e13c-41c3-8ebf-65e819198861"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 sequences of words (not necessarily grammatically correct) have the property that the first word has one lett... | MATH | {
"ground_truth": "60",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "1967755f-f45e-4cf4-8ebc-6891829d54ed"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 of the first $1000$ positive integers can be written as the sum of finitely many distinct numbers from the se... | MATH | {
"ground_truth": "105",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "fc23957b-a88a-4c54-81a5-07c82a6393d5"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 quadrilateral $ABCD$ is an isosceles trapezoid with $AB = CD = 1$, $BC = 2$, and $DA = 1 + \\sqrt{3}$. What is the... | MATH | {
"ground_truth": "90",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "27a5cff4-4060-4886-b92f-98c99e98c366"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 $pq$ for all pairs of prime numbers $p \\leq q$ such that $pq \\mid 15(p-1)(q-1)$.\n\nRemember to put ... | MATH | {
"ground_truth": "31",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "b23b2cee-3c2e-4e47-9d29-3fe1cb383149"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 there exists a polynomial \\[ P(x) = a_{2n}x^{2n} + a_{2n-1}x^{2n-1} + \... | MATH | {
"ground_truth": "2014",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "01109e3e-d9e4-4af6-8ce1-221a7b9b37ad"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 preparation for the family's upcoming vacation, Tony puts together five bags of jelly beans, one bag for each day o... | MATH | {
"ground_truth": "45",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "18aa1f84-ea33-4583-a57c-edf40e776080"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 $p$ and $q$ be positive integers such that $p$ is a prime, $p$ divides $q-1$, and $p+q$ divides $p^2+2020q^2$. Fin... | MATH | {
"ground_truth": "141",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "0828540c-adec-4e3d-9ff7-e9161f4e91db"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 whose prime factors add to $14$?\n\nRemember to put your answer on its own line after \"An... | MATH | {
"ground_truth": "162",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "ea80fbb7-d257-4255-b6a3-f121d80fb58a"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nLet $a$ be a number with $n$ digits ($n > 1$). A number $b$ with $2n$ digits is obtained by writing two copies of $a$ ... | MATH | {
"ground_truth": "7",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "705b01e0-51af-4714-ab66-27c053cc894e"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 pack of 27 distinct cards, and each card has three values on it. The first value is a shape from $\\{\\Delt... | MATH | {
"ground_truth": "1278",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "4d9b704d-377e-4cf9-bb97-3cedf36e9528"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 $n$ for which there exists a sequence $(a_0, a_1, \\ldots, a_n)$ of non-zero digits such that, for ea... | MATH | {
"ground_truth": "4",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "255d1c07-7bca-4c6d-b8e2-6ac0e1871a59"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 number of two-digit numbers $\\overline{ab}$ with nonzero digits $a$ and $b$ such that $a$ and $b$ are bot... | MATH | {
"ground_truth": "14",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "39fd0404-f3df-4adb-9cba-006f00cc3420"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nFind the sum of the first $55$ terms of the sequence $\\binom{0}{0}, \\binom{1}{0}, \\binom{1}{1}, \\binom{2}{0}, \\bi... | MATH | {
"ground_truth": "1023",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "57e2d956-95ad-4f55-b7bf-9d4d5234f7e3"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 $S$ be the set of integers of the form $2^x + 2^y + 2^z$, where $x$, $y$, $z$ are pairwise distinct non-negative i... | MATH | {
"ground_truth": "577",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "4cfc73b0-924d-4ecf-a8e7-e15cfec9bbae"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 alphabet in its natural order $\\text{ABCDEFGHIJKLMNOPQRSTUVWXYZ}$ is $T_0$. We apply a permutation to $T_0$ to ge... | MATH | {
"ground_truth": "252",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "801723a0-cbc8-419f-adb2-5838f464ce3a"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 integers $n$ such that $1 \\leq n \\leq 2017$ and $(n-2)(n-0)(n-1)(n-7)$ is a multiple of $1001$.\n... | MATH | {
"ground_truth": "99",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "ca58a9e5-85b9-49f3-b772-9eb922178422"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nIt is given that there exists a unique triple of positive primes \\((p, q, r)\\) such that \\(p < q < r\\) and \n\\[\n... | MATH | {
"ground_truth": "19",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "319c453b-6c20-46fa-86f3-b3ab332824a7"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 blackboard, there are $25$ points arranged in a grid as shown in the figure below. Gastón needs to choose $4$ p... | MATH | {
"ground_truth": "50",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "80fe5248-7112-4dcb-90a6-2dfc4c8b8ab8"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nFind the sum of the decimal digits of \\[ \\left\\lfloor \\frac{51525354555657\\dots979899}{50} \\right\\rfloor. \\] H... | MATH | {
"ground_truth": "457",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "434f2876-b173-4828-b3c3-c20d3f1d53dc"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 want to paint some identically-sized cubes so that each face of each cube is painted a solid color, and each cube i... | MATH | {
"ground_truth": "210",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "d99a3a3c-4102-4c38-9f27-349a85955981"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 sets \\((A, B)\\) have the properties:\n\n1. \\( A \\subseteq \\{1, 2, 3, 4, 5, 6\\} \\)\n2.... | MATH | {
"ground_truth": "720",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "ace14ec8-7d35-42db-af5d-ce0b3a57b8e6"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 pairs of elements, from a group of order $2011$, such that the square of the first element of the p... | MATH | {
"ground_truth": "2011",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "34a8ea09-904b-4fcd-8cf8-101081d05535"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nLet $P$ be a point chosen on the interior of side $\\overline{BC}$ of triangle $\\triangle ABC$ with side lengths $\\o... | MATH | {
"ground_truth": "2365",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "13831a90-381c-4a9b-8c70-5ec2259b763e"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nLet $x$ be the minimal root of the equation $x^2 - 4x + 2 = 0$. Find the first two digits after the decimal point of t... | MATH | {
"ground_truth": "41",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "9ac0ba09-2496-46e6-b827-9174706faf76"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 polynomial $P(x)$ is a \\emph{base-$n$ polynomial} if it is of the form $a_d x^d + a_{d-1} x^{d-1} + \\cdots + a_1 x... | MATH | {
"ground_truth": "9",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "03ec6eaa-36a1-485d-a0f1-65431795a7ec"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 smallest value of the expression $$(x-1)(x-2)(x-3)(x-4) + 10$$.\n\nRemember to put your answer on its own lin... | MATH | {
"ground_truth": "9",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "33b523e9-e20c-4129-b837-aafd1cd28e9a"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 two-digit prime numbers whose digits are also both prime numbers.\n\nRemember to put your answer o... | MATH | {
"ground_truth": "186",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "25b2b538-8a3e-4c09-ba0e-5e8d022058f6"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 $10$ horses, named Horse 1, Horse 2, $\\ldots$, Horse 10. They get their names from how many minutes it take... | MATH | {
"ground_truth": "3",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "647cb40c-db24-45c2-9752-810674bbed46"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 smallest natural number that divides $2^n + 15$ for some natural number $n$ and can be expressed in the form ... | MATH | {
"ground_truth": "23",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "7e7fc5f4-c096-4e65-a493-656c505b6183"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 sum of the two largest prime factors of the integer $89! + 90!$.\n\nRemember to put your answer on its o... | MATH | {
"ground_truth": "172",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "c19a16cb-4d85-4990-bf82-2e2beab5a9cc"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 ducks, Wat and Q, are taking a math test with $1022$ other ducklings. The test consists of $30$ questions, and the... | MATH | {
"ground_truth": "1020",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "265cbf27-dff8-4f91-bda8-03df129f4e42"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nFind the product of all possible real values for $k$ such that the system of equations\n$$x^2 + y^2 = 80$$\n$$x^2 + y^... | MATH | {
"ground_truth": "960",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "70496b8c-7cb4-4185-a686-cf23fdcc8ed3"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 $a$, $b$, and $c$ be the 3 roots of the equation $x^3 - x + 1 = 0$. Find the value of $\\frac{1}{a+1} + \\frac{1}{... | MATH | {
"ground_truth": "-2",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "2ce2cec1-8061-4431-a3a2-e6164618e795"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 this problem, the symbol $0$ represents the number zero, the symbol $1$ represents the number seven, the symbol $2$... | MATH | {
"ground_truth": "90",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "0f7f2051-701d-424f-a2b2-50dcadc70bcf"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nAlbert rolls a fair six-sided die thirteen times. For each roll, if the number is strictly greater than the previous r... | MATH | {
"ground_truth": "5",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "53f6d64a-7c8b-4446-a3a0-ab7cdb76990f"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 Thursday, January 1, 2015, Anna buys one book and one shelf. For the next two years, she buys one book every day an... | MATH | {
"ground_truth": "89",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "e9f39ad8-dfb0-4ecb-aeab-f240fb2315c2"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 every integer $a > 1$, an infinite list of integers is constructed $L(a)$, as follows:\n\n1. $a$ is the first numb... | MATH | {
"ground_truth": "2002",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "8983853b-284a-4f56-8c2f-4476280b56c3"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 the students attending a school athletic event, $80\\%$ of the boys were dressed in the school colors, $60\\%$ of t... | MATH | {
"ground_truth": "71",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "d1c0ea26-9a50-493a-bb21-2c83c500afa6"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nReimu has a wooden cube. In each step, she creates a new polyhedron from the previous one by cutting off a pyramid fro... | MATH | {
"ground_truth": "974",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "071b97cd-e516-4f1f-8d42-d2daf82a2a95"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nJonathan has a magical coin machine that accepts coins in amounts of $7$, $8$, and $9$. If he puts in $7$ coins, he ge... | MATH | {
"ground_truth": "4",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "4022d28d-e65a-4e19-8e3c-2a780a4f8054"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 every positive integer $k$, let $\\mathbf{T}_k = (k(k+1), 0)$, and define $\\mathcal{H}_k$ as the homothety center... | MATH | {
"ground_truth": "256",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "6be576a1-cb79-4524-974c-5fe1eacc38a0"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 set of three elements is called arithmetic if one of its elements is the arithmetic mean of the other two. Likewise,... | MATH | {
"ground_truth": "1004",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "c465b4af-080a-4013-a43f-75062a7aa147"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nJerry and Hannah Kubik live in Jupiter Falls with their five children. Jerry works as a Renewable Energy Engineer for ... | MATH | {
"ground_truth": "56",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "ab55c0fa-8ffe-4771-885e-d5e3213bffdb"
} |
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