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\nIs there a whole number that becomes exactly $57$ times less than itself when its first digit is crossed out?\n\nRemem... | MATH | {
"ground_truth": "7125",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "0ac48a29-2d49-4181-ba29-fa13f83ac5f8"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 prime factor of 8091?\n\nRemember to put your answer on its own line after \"Answer:\".",
"rol... | MATH | {
"ground_truth": "31",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "395e35a3-1e60-4398-a753-a06e1cc134fa"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 $k$ be an integer. If the equation $(x-1)\\left|x+1\\right|=x+\\frac{k}{2020}$ has three distinct real roots, how ... | MATH | {
"ground_truth": "4544",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "e4a9e622-5317-4378-8d7d-a78b5699d158"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 remainder when $98!$ is divided by $101$.\n\nRemember to put your answer on its own line after \"Answer:\"... | MATH | {
"ground_truth": "50",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "242fee3e-0c5d-4fab-9f07-cf4960389bce"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 $\\sum_{k \\in A} \\frac{1}{k-1}$ where $A= \\{ m^n : m,n \\in \\mathbb{Z}, m,n \\geq 2 \\}$.\n\nRemember to put ... | MATH | {
"ground_truth": "1",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "079e22d6-3431-45df-8153-12be136f87ab"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 remainder when $7^{7^7}$ is divided by $1000$.\n\nRemember to put your answer on its own line after \"Answer:... | MATH | {
"ground_truth": "343",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "6c441912-b35f-4158-b5d0-c7ac7d6470c6"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 $a_1, a_2, a_3, \\ldots$ be a non-decreasing sequence of positive integers. For $m \\ge 1$, define $b_m = \\min\\{... | MATH | {
"ground_truth": "1700",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "3974f8cc-945b-4f33-9d33-2ba397dafbae"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 integers $(x, y)$ satisfy $2 \\cdot |y| \\le x \\le 40$?\n\nRemember to put your answer on i... | MATH | {
"ground_truth": "841",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "d8437fd1-4381-4448-94a3-b17adcadf301"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 all positive integers $n > 1$, let $f(n)$ denote the largest odd proper divisor of $n$ (a proper divisor of $n$ is... | MATH | {
"ground_truth": "25",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "941f43b9-826f-4a5e-9f67-f1214d834296"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 $T_k = \\frac{k(k+1)}{2}$ be the $k$-th triangular number. The infinite series\n$$\\sum_{k=4}^{\\infty}\\frac{1}{(... | MATH | {
"ground_truth": "451",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "80b54b2b-45e3-4d4c-bbdb-c09bdc86c87a"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 trapezium in which $AB \\parallel CD$ and $AD \\perp AB$. Suppose $ABCD$ has an incircle which touches... | MATH | {
"ground_truth": "84",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "b64eda11-4b46-4474-90c6-bfa2ad3fa7b6"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nRecall that $[x]$ denotes the largest integer not exceeding $x$ for real $x$. For integers $a, b$ in the interval $1 \... | MATH | {
"ground_truth": "98",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "2dbd2451-9d3d-4d25-873e-db19c9db871a"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 number $\\lambda$, such that for any 12 points on the plane $P_1, P_2, \\ldots, P_{12}$ (po... | MATH | {
"ground_truth": "48",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "b9c2b1cf-15f8-414d-8b7b-a5ad78e8b155"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 integer side lengths has the property that its area minus $5$ times its perimeter equals $2023$. Find... | MATH | {
"ground_truth": "448",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "6cdcf169-1006-4714-866c-3c93803fc123"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 Fibonacci numbers are defined by $F_1 = F_2 = 1$ and $F_n = F_{n-1} + F_{n-2}$ for $n > 2$. It is well-known that ... | MATH | {
"ground_truth": "24",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "5926d7c7-8815-4936-9bd8-ca2d0498f03c"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 $f(x)$ is a polynomial with integer coefficients such that $f(0) = 11$ and $f(x_1) = f(x_2) = \\cdots = f(x_n)... | MATH | {
"ground_truth": "4",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "be437dee-6820-4af0-866a-4fa136709b88"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 $d_1, d_2, \\ldots, d_k$ be its divisors, such that $1 = d_1 < d_2 < \\ldots < d... | MATH | {
"ground_truth": "130",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "16771d40-3e91-4b2e-bff9-84cbbaa8d702"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 all natural numbers with the property: the sum of the largest three divisors of a number $n$, ex... | MATH | {
"ground_truth": "6",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "24488eff-a4cc-4941-a7cf-eae3cb28ab53"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 least positive integer $n$ for which the following statement is true: the product of any $n$ odd consecu... | MATH | {
"ground_truth": "6",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "11bb3d5e-0a22-44e9-8fbd-e8c644a04df6"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 subset \\( T \\) of \\(\\{1, 2, \\dots, 2024\\}\\) is **kawaii** if \\( T \\) has the following properti... | MATH | {
"ground_truth": "675",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "4a984d7d-2191-4561-8712-4b1208db28f8"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 NIMO problem writers have invented a new chess piece called the *Oriented Knight*. This new chess piece has a limi... | MATH | {
"ground_truth": "252",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "fd1f8bf0-2bc5-4cb2-a438-dac493c6c548"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 cyclic quadrilateral with side lengths $1$, $4$, $8$, $7$ in that order. What is its circumdiameter? Let ... | MATH | {
"ground_truth": "66",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "05d59f38-1926-4160-b40a-42cd2fcdb999"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 probability that the sum of three distinct integers between $16$ and $30$ (inclusive) is even can be written as... | MATH | {
"ground_truth": "97",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "56db629c-c989-453f-964f-c21c9fbd8a84"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 $n$-sided regular polygon with side length $1$ is rotated by $\\frac{180^\\circ}{n}$ about its center. The intersec... | MATH | {
"ground_truth": "9",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "cd833912-394c-4bc0-b2e7-2280078c7215"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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$ is isosceles with $AB = AC$. The bisectors of angles $\\angle ABC$ and $\\angle ACB$ meet at point $I$.... | MATH | {
"ground_truth": "20",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "f7d3337b-3c8e-47d7-b9e8-0b636739a75e"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 parallel to the sides of an equilateral triangle are drawn such that they divide each side into $10$ equal segme... | MATH | {
"ground_truth": "10",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "b758fafb-bf07-47e7-8ef7-016edc96f2a3"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 mahogany bookshelf has four identical-looking books which are $200$, $400$, $600$, and $800$ pages long. Velma picks... | MATH | {
"ground_truth": "6425",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "84c8145c-0e2d-4ec5-a0a1-f520bb05bc33"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 product \n$$\\frac{1}{2} \\cdot \\frac{2}{4} \\cdot \\frac{3}{8} \\cdot \\frac{4}{16} \\cdot \\ldots \\cdot \\frac... | MATH | {
"ground_truth": "2",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "cda8b493-bf74-4264-bc1e-a7fe79ae3fff"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nEdward had to escape from prison to work in the grading room today. He stopped to rest at a place $1,875$ feet from th... | MATH | {
"ground_truth": "75",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "8019fbbc-7e53-4675-b4bb-8f10e11e7e23"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 remainder when the number of positive divisors of the value $$(3^{2020}+3^{2021})(3^{2021}+3^{2022})(3^{2022}... | MATH | {
"ground_truth": "783",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "19b53d14-d677-4466-89df-24efd8dc9bbf"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nSay that a polynomial with real coefficients in two variables, $x, y$, is balanced if the average value of the polynom... | MATH | {
"ground_truth": "2020050",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "07973cac-2f89-4bf4-850d-408738326402"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 + y^{-99} = 3$ and $x + y = -2$, find the sum of all possible values of $x$.\n\nRemember to put your answer on i... | MATH | {
"ground_truth": "-195",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "4754301e-a6e6-4bf0-9db8-ea754486d32f"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\n480 one-centimeter unit cubes are used to build a block measuring 6 cm by 8 cm by 10 cm. A tiny ant then chews its way... | MATH | {
"ground_truth": "20",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "77a83369-9b69-4d41-ad64-229402af0726"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 $\\phi = \\frac{1+\\sqrt{5}}{2}$. A base-$\\phi$ number $(a_n a_{n-1} \\ldots a_1 a_0)_{\\phi}$, where $0 \\le a_n... | MATH | {
"ground_truth": "1048576",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "f2c0adee-ea2b-4ad9-a74a-fdfdf5b02802"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 sides of triangles $ABC$ and $ACD$ satisfy the following conditions: $AB = AD = 3$ cm, $BC = 7$ cm, $DC = 11$ cm. ... | MATH | {
"ground_truth": "9",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "4b0a7507-5b53-428d-922c-c1b7c2b3bc95"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nTwo points $A$ and $B$ are selected independently and uniformly at random along the perimeter of a unit square with ve... | MATH | {
"ground_truth": "716",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "9b7bca5e-07ec-4b1c-bc84-537be917e3da"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 < 2018$ such that $25^n + 9^n$ is divisible by $13$.\n\nRemember to put your a... | MATH | {
"ground_truth": "336",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "59959acf-ca8b-4fb5-87e7-398b6b3306c7"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 relatively prime positive integers $p$ and $q$ such that $\\frac{p}{q} = \\sum_{n=3}^{\\infty} \\frac{1}{n^5... | MATH | {
"ground_truth": "97",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "3c64e181-9ffe-4c1f-9521-b9bd9c8f4615"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nJuan wrote a natural number. Maria then added a digit $1$ to the left and a digit $1$ to the right of Juan's number. A... | MATH | {
"ground_truth": "532",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "c6fc994b-3a37-404c-8896-632b131e340e"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 tournament with $8$ players, each pair of players played exactly one match. Each match ended either with a win fo... | MATH | {
"ground_truth": "4",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "4c3a44db-da3d-4e20-a76d-9d0b0568982c"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 less than or equal to $\\sum_{k=1}^{2^{1983}} k^{\\frac{1}{1983} -1}$.\n\nRemember to put yo... | MATH | {
"ground_truth": "1983",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "501ddeee-9873-45c3-8d12-748d00b311af"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 *form* is the union of squared rectangles whose bases are consecutive unitary segments in a horizontal line that lea... | MATH | {
"ground_truth": "36",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "b24d7802-05c1-49d3-b76a-fbd8615291af"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nAlex launches his boat into a river and heads upstream at a constant speed. At the same time, at a point $8$ miles ups... | MATH | {
"ground_truth": "52",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "7a608c50-8cff-4fbe-b87a-2567d1926997"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 $k$ such that when $\\frac{k}{2023}$ is written in simplest form, the sum of the numer... | MATH | {
"ground_truth": "35",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "cbd4f2a0-e688-44e4-8b40-b5276a12674a"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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$ is a positive number such that $x^{x^{x^{x}}} = ((x^{x})^{x})^{x}$, find $(x^{x})^{(x^{x})}$.\n\nRemember to pu... | MATH | {
"ground_truth": "27",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "5482bade-3d27-4db1-b6e1-cbab54d0fa9a"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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, 2, 3, \\ldots, 280\\}$. Find the smallest integer $n$ such that each $n$-element subset of $S$ contains... | MATH | {
"ground_truth": "217",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "85a6f999-c9ff-4325-8593-d4e70fb8011b"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 $(a, b)$ are there such that a right triangle with legs of length $a, b$ h... | MATH | {
"ground_truth": "99",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "140a2781-070d-48d8-b4d0-7e6e888e1f3f"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 $H_n = \\frac{1}{1} + \\frac{1}{2} + \\cdots + \\frac{1}{n}$. If \\[ \\sum_{n=4}^{\... | MATH | {
"ground_truth": "611",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "7e1a306e-733d-49fd-bd06-42af28864ecf"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 random permutation on $\\{1, 2, \\dots, 100\\}$ satisfying $f(1) > f(4)$ and $f(9) > f(16)$. The probabil... | MATH | {
"ground_truth": "730",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "ebad5bd1-d83d-4d9d-a546-f47642b010ac"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nSiva has the following expression, which is missing operations:\n$$\\frac{1}{2} \\_ \\frac{1}{4} \\_ \\frac{1}{8} \\_ ... | MATH | {
"ground_truth": "39",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "4eb166bb-e741-4493-8e59-15349538ad25"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 smallest positive integer $n$ such that there exist positive integers $x_1, x_2, \\ldots, x_n$ so that e... | MATH | {
"ground_truth": "11",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "fb464299-f245-462b-8fc1-4925992b38dc"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 sequence $a_0, a_1, \\ldots$ of real numbers is defined by $a_0=1$ and \\[a_n=\\begin{cases}a_{n-1}a_0+... | MATH | {
"ground_truth": "1923",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "a956c4e9-bcdc-430d-af04-b01d1dde3f12"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 an integer $x \\in \\{1, \\dots, 102\\}$ is \\textit{square-ish} if there exists some integer $n$ such tha... | MATH | {
"ground_truth": "52",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "04de73fb-3870-44c1-993d-e031595c5c16"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 palindrome number is a positive integer that reads the same forward and backward. For example, $1221$ and $8$ are pa... | MATH | {
"ground_truth": "121",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "1e72172f-59aa-422f-bdd0-e18ffe49a87f"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 $m = 30030$ and let $M$ be the set of its positive divisors which have exactly $2$ prime factors. Determine the sm... | MATH | {
"ground_truth": "11",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "2afed460-9a73-4798-9a38-c73a5bf08a9f"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 Purple Comet! Math Meet runs from April 27 through May 3, so the sum of the calendar dates for these seven days is... | MATH | {
"ground_truth": "142",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "00ed6eef-afb2-477e-a128-e078111aaaa8"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 ways are there to create two 3-digit numbers $m$ and $n$ such that $n = 3m$? Each of the digits $1$, $2$, $3$... | MATH | {
"ground_truth": "2",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "ab9383eb-d636-4b77-960a-2da12744e4dd"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 integer closest to $\\pi^{\\pi}$?\n\nRemember to put your answer on its own line after \"Answer:\".",
... | MATH | {
"ground_truth": "36",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "6cfb04ae-7584-46c2-a4bc-04f885f2fba2"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 positive real numbers such that $\\log_{43}{a} = \\log_{47} (3a + 4b) = \\log_{2021}b^2$. Then, the... | MATH | {
"ground_truth": "123",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "4f92b57d-922f-4adb-999c-d418af68d0a3"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 square has vertices $(0,10)$, $(0, 0)$, $(10, 0)$, and $(10,10)$ on the $x-y$ coordinate plane. A second quadrilater... | MATH | {
"ground_truth": "50",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "886b6423-287c-49fb-a347-22b67ef5b308"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 largest prime factor of $199^4 + 4$ has four digits. Compute the second largest prime factor.\n\nRemember to put y... | MATH | {
"ground_truth": "181",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "2c8634db-3516-4e5a-85dd-5b5bab9d43f5"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 permutations $p(n)$ of the set $\\{1, 2, \\dots, 35\\}$ satisfy the condition that if $a \\mid b$ (where $a$ ... | MATH | {
"ground_truth": "48",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "5eaeeb6e-236a-4e4d-9038-931dd0062504"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 ways can you arrange $3$ Alice's, $1$ Bob, $3$ Chad's, and $1$ David in a line if the Alice's are all indisti... | MATH | {
"ground_truth": "280",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "4700094f-81f7-40c3-8be5-c96df0a75257"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 $a, b, c, d$ be real numbers satisfying the system of equations:\n\\[\n\\begin{align*}\n(a+b)(c+d) &= 2, \\\\\n(a+... | MATH | {
"ground_truth": "7",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "d982cf50-e702-498e-af91-8724e5a52a58"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 $AB = 5$, $AC = 8$, and $BC = 7$. Let $D$ be on side $AC$ such that $AD = 5$ and $CD = 3$... | MATH | {
"ground_truth": "13",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "e36d234d-eb14-4ff4-9d7f-31157a798ad8"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nEvin and Jerry are playing a game with a pile of marbles. On each player's turn, they can remove $2$, $3$, $7$, or $8$... | MATH | {
"ground_truth": "573",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "20fff7e4-2bbd-45c3-a243-9e9602d6fc48"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 persons will play exactly one game. Aft... | MATH | {
"ground_truth": "9",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "73911982-0e3c-4c7b-b2d8-86d663268707"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 four-digit natural numbers $\\overline{xyzw}$ such that the sum of the number and the sum of its digits equal... | MATH | {
"ground_truth": "1978",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "72eede9e-7567-4ac3-b66a-c4b06f2a91c0"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 the set of all integers from $1$ to $2013$. Each subset of $M$ is assigned one of $k$ available colors. The... | MATH | {
"ground_truth": "2014",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "09996c17-f9bd-4a8b-937a-bc4704f5fac5"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 $\\mathcal{S}$ be the set of all positive integers which are both a multiple of $3$ and have at least one digit th... | MATH | {
"ground_truth": "197",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "546b6a07-6803-439e-b693-1fa998ad211c"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nCaroline wants to plant 10 trees in her orchard. Planting $n$ apple trees requires $n^2$ square meters, planting $n$ a... | MATH | {
"ground_truth": "40",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "0def1791-c7e2-4e2c-8a0f-ea2d7807bcd8"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 angles $A$, $B$, and $C$. Suppose $\\tan A$, $\\tan B$, $\\tan C$ form a geometric sequen... | MATH | {
"ground_truth": "11",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "d4096537-33dd-449b-97e1-4524e2c73220"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nPål has more chickens than he can manage to keep track of. Therefore, he keeps an index card for each chicken. He keep... | MATH | {
"ground_truth": "5052",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "512523f7-cdcb-443d-bbca-a7eab362944f"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 the parallelogram $ABCD$, we are given that $AC = 10$ and $BD = 28$. The points $K$ and $L$ are such that they move... | MATH | {
"ground_truth": "2",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "ec17d15d-eecb-4343-bca2-fa6ee4841f1a"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 circle is inscribed in a regular octagon with area $2024$. A second regular octagon is inscribed in the circle, and ... | MATH | {
"ground_truth": "1520",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "4378c3cd-cd34-4139-b7b9-52ec21a246c7"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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\\uparrow\\uparrow b = a^{a^{\\cdots^{a}}} \\), where there are \\( b \\) instances of \\( a \\). The operati... | MATH | {
"ground_truth": "27",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "74819e2f-feec-41c5-954f-83cc1f3244e4"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 date \\( mm/dd/yy \\) \\textit{multiplicative} if its month number times its day number is a two-digit integer ... | MATH | {
"ground_truth": "29",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "eb6c1c90-5c67-45b5-9f7b-761969132dde"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 the plane, there are $2020$ points, some of which are black and the rest are green. For every black point, the foll... | MATH | {
"ground_truth": "45",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "04b59d01-0ef5-41cc-938e-3105ce23713a"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 John has $5$ cows, $4$ pigs, and $7$ horses. How many ways can he pair up the animals so that every pair consis... | MATH | {
"ground_truth": "100800",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "d5a17182-b7df-4620-b9e1-ada7eefa3336"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nEva draws an equilateral triangle and its altitudes. In the first step, she draws the center triangle of the equilater... | MATH | {
"ground_truth": "7",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "c3a67386-142b-4c41-b58e-1030480f6abc"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 $24$ participants who attended a meeting. Each pair of them either shook hands once or did not. A total of $... | MATH | {
"ground_truth": "864",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "89d07d6f-0b10-4a77-b5e5-2649728770ff"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 $2(\\sin 2^{\\circ} \\tan 1^{\\circ} + \\sin 4^{\\circ} \\tan 1^{\\circ} + \\cdots + \\sin 178^{\\ci... | MATH | {
"ground_truth": "2",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "64670946-dff7-4cd5-af37-a4d495ce898b"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 bag contains $8$ green candies and $4$ red candies. You randomly select one candy at a time to eat. If you eat five ... | MATH | {
"ground_truth": "6",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "3985f030-650b-4916-9642-0479b30c1c49"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 with the first term $a_0$ is defined such that $a_{n+1} = 2a_n^2 - 1$ for $n \\geq 0$. Let $N$ denote the n... | MATH | {
"ground_truth": "4",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "160d74f7-d105-4d6b-9856-0a683443b323"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nBen flips a coin 10 times and records the absolute difference between the total number of heads and tails. He then fli... | MATH | {
"ground_truth": "831",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "6012c3a7-f329-4da7-810d-21c4e593be42"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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": "ea47e174-747b-4165-9c70-024cc6e1dbf1"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 how many ways can you divide the set of eight numbers $\\{2, 3, \\ldots, 9\\}$ into $4$ pairs such that no pair of ... | MATH | {
"ground_truth": "36",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "f7e0e685-4077-41a3-82e6-3d46408a90a5"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 $x$ such that \n\\[2010^{\\log_{10}x} = 11^{\\log_{10}(1+3+5+\\cdots +4019)}.\\]\n\nRemember to put your answer o... | MATH | {
"ground_truth": "121",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "99fd0f52-0d59-46c8-92da-e08b950a5a1b"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 $6$-digit integers such that the sum of their digits is $9$, and four of its digits are $2... | MATH | {
"ground_truth": "180",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "444dee5d-22eb-40b0-ba5d-e731aeedea11"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 natural number. A cube of edge $n$ may be divided into 1996 smaller cubes, each having edge lengths that ... | MATH | {
"ground_truth": "13",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "4d32e9e9-9e26-4e65-a918-c62aaf4f0ba3"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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_n)\\) be a sequence of positive integers defined as follows: \\(x_1\\) is a fixed six-digit number and for a... | MATH | {
"ground_truth": "5",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "b03b9b20-075c-410f-b702-eabc1501a626"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 real roots of the polynomial:\n\\[\n\\prod_{k=1}^{100} \\left( x^2-11x+k \\right) = \\left( x^2-11... | MATH | {
"ground_truth": "330",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "ca041568-a5fb-436e-a34d-23951e5525d3"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 how many permutations of the numbers $1, 2, \\dots, 8$ have no adjacent numbers that sum to $9$.\n\nRemember t... | MATH | {
"ground_truth": "13824",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "6c495044-1dcd-4522-be4b-40f1400970ad"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 nonempty word is called pronounceable if it alternates between vowels (A, E, I, O, U) and consonants (all other lett... | MATH | {
"ground_truth": "68",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "7a7e5fa1-1be7-487f-b6b7-573d85df69ed"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 $B$, $M$, and $T$ be the three roots of the equation $x^3 + 20x^2 - 18x - 19 = 0$. What is the value of $|(B + 1)(... | MATH | {
"ground_truth": "18",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "e67a27ce-535c-4a8f-be09-9b0e3ec908dd"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 smallest perfect square that ends in \\( 9009 \\)?\n\nRemember to put your answer on its own line after \"... | MATH | {
"ground_truth": "1503",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "5ec1e7b6-c438-4f69-a5a3-ec2d1ae5d15e"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 number line, consider the point $x$ that corresponds to the value $10$. Consider $24$ distinct integer points $... | MATH | {
"ground_truth": "494",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "1744a664-442e-45f3-a38b-1d08d998a034"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nWilliam is biking from his home to his school and back, using the same route. When he travels to school, there is an i... | MATH | {
"ground_truth": "31",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "d6f1991f-b390-4b02-a4c7-90c925683e17"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 integers $n$ are there such that $(n+1!)(n+2!)(n+3!)\\cdots(n+2013!)$ is divisible by $210$ and $1 \\le n \\l... | MATH | {
"ground_truth": "120",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "75287c31-7601-4e11-93d7-675a8b57f439"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 the beginning of a game, the numbers $1, 2, \\ldots, 2004$ are written on a desk. A move consists of:\n\n1. Selecti... | MATH | {
"ground_truth": "4",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "16b41f71-546a-4d93-bdbc-8163a083e3c5"
} |
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