data_source stringclasses 1
value | prompt listlengths 1 1 | ability stringclasses 1
value | reward_model dict | extra_info dict |
|---|---|---|---|---|
math_dapo | [
{
"role": "user",
"content": "Solve the following math problem step by step. 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 $ABC$, $\\sin \\angle A = \\frac{4}{5}$ and $\\angle A < 90^\\circ$. Let $D$ be a poin... | MATH | {
"style": "rule-lighteval/MATH_v2",
"ground_truth": "34"
} | {
"index": -1,
"repeat": 0,
"raw_problem": "",
"split": "",
"source": ""
} |
math_dapo | [
{
"role": "user",
"content": "Solve the following math problem step by step. 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 unit square in the plane. Points $X$ and $Y$ are chosen independently and uniforml... | MATH | {
"style": "rule-lighteval/MATH_v2",
"ground_truth": "113"
} | {
"index": -1,
"repeat": 0,
"raw_problem": "",
"split": "",
"source": ""
} |
math_dapo | [
{
"role": "user",
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nLet $a, b, c$ be distinct numbers such that the equations $x^2 + ax + 1 = 0$ and $x^2 + bx + c = 0... | MATH | {
"style": "rule-lighteval/MATH_v2",
"ground_truth": "-3"
} | {
"index": -1,
"repeat": 0,
"raw_problem": "",
"split": "",
"source": ""
} |
math_dapo | [
{
"role": "user",
"content": "Solve the following math problem step by step. 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 $7$ boxes arranged in a row and numbered $1$ through $7$. You have a stack of $2015$ car... | MATH | {
"style": "rule-lighteval/MATH_v2",
"ground_truth": "3"
} | {
"index": -1,
"repeat": 0,
"raw_problem": "",
"split": "",
"source": ""
} |
math_dapo | [
{
"role": "user",
"content": "Solve the following math problem step by step. 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 triples $(a,b,c)$ of non-negative integers such that $a+b+c$ is even. The va... | MATH | {
"style": "rule-lighteval/MATH_v2",
"ground_truth": "37"
} | {
"index": -1,
"repeat": 0,
"raw_problem": "",
"split": "",
"source": ""
} |
math_dapo | [
{
"role": "user",
"content": "Solve the following math problem step by step. 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 which $n$ is $n^4 + 6n^3 + 11n^2 + 3n + 31$ a perfect square?\n\nRemember to put your answer o... | MATH | {
"style": "rule-lighteval/MATH_v2",
"ground_truth": "10"
} | {
"index": -1,
"repeat": 0,
"raw_problem": "",
"split": "",
"source": ""
} |
math_dapo | [
{
"role": "user",
"content": "Solve the following math problem step by step. 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 positive integers $a, b, c, d$ satisfy the condition $a < b < c < d$. Determine the smallest ... | MATH | {
"style": "rule-lighteval/MATH_v2",
"ground_truth": "10"
} | {
"index": -1,
"repeat": 0,
"raw_problem": "",
"split": "",
"source": ""
} |
math_dapo | [
{
"role": "user",
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\n$n$ coins are arranged in a circle. If two neighboring coins both show heads or both show tails, y... | MATH | {
"style": "rule-lighteval/MATH_v2",
"ground_truth": "2"
} | {
"index": -1,
"repeat": 0,
"raw_problem": "",
"split": "",
"source": ""
} |
math_dapo | [
{
"role": "user",
"content": "Solve the following math problem step by step. 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 prime $p$ such that $2018!$ is divisible by $p^3$, but not divisible by $p^... | MATH | {
"style": "rule-lighteval/MATH_v2",
"ground_truth": "509"
} | {
"index": -1,
"repeat": 0,
"raw_problem": "",
"split": "",
"source": ""
} |
math_dapo | [
{
"role": "user",
"content": "Solve the following math problem step by step. 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 you have a sphere tangent to the $xy$-plane with its center having a positive $z$-coordina... | MATH | {
"style": "rule-lighteval/MATH_v2",
"ground_truth": "3"
} | {
"index": -1,
"repeat": 0,
"raw_problem": "",
"split": "",
"source": ""
} |
math_dapo | [
{
"role": "user",
"content": "Solve the following math problem step by step. 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 $10^{2015}$ planets in an Intergalactic empire. Every two planets are connected by a two... | MATH | {
"style": "rule-lighteval/MATH_v2",
"ground_truth": "1007"
} | {
"index": -1,
"repeat": 0,
"raw_problem": "",
"split": "",
"source": ""
} |
math_dapo | [
{
"role": "user",
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nRectangle $HOMF$ has $HO = 11$ and $OM = 5$. Triangle $\\triangle ABC$ has orthocenter $H$ and cir... | MATH | {
"style": "rule-lighteval/MATH_v2",
"ground_truth": "28"
} | {
"index": -1,
"repeat": 0,
"raw_problem": "",
"split": "",
"source": ""
} |
math_dapo | [
{
"role": "user",
"content": "Solve the following math problem step by step. 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 three roots of the equation $x^3-(k+1)x^2+kx+12=0$, where $k$ is a real n... | MATH | {
"style": "rule-lighteval/MATH_v2",
"ground_truth": "5"
} | {
"index": -1,
"repeat": 0,
"raw_problem": "",
"split": "",
"source": ""
} |
math_dapo | [
{
"role": "user",
"content": "Solve the following math problem step by step. 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 towns, $A$ and $B$, are $100$ miles apart. Every $20$ minutes (starting at midnight), a bus tr... | MATH | {
"style": "rule-lighteval/MATH_v2",
"ground_truth": "5"
} | {
"index": -1,
"repeat": 0,
"raw_problem": "",
"split": "",
"source": ""
} |
math_dapo | [
{
"role": "user",
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nBurrito Bear has a white unit square. She inscribes a circle inside the square and paints it black... | MATH | {
"style": "rule-lighteval/MATH_v2",
"ground_truth": "1"
} | {
"index": -1,
"repeat": 0,
"raw_problem": "",
"split": "",
"source": ""
} |
math_dapo | [
{
"role": "user",
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nDanial went to a fruit stall that sells apples, mangoes, and papayas. Each apple costs $3$ RM, eac... | MATH | {
"style": "rule-lighteval/MATH_v2",
"ground_truth": "15"
} | {
"index": -1,
"repeat": 0,
"raw_problem": "",
"split": "",
"source": ""
} |
math_dapo | [
{
"role": "user",
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nSabrina has a fair tetrahedral die with faces numbered 1, 2, 3, and 4. She rolls the die to create... | MATH | {
"style": "rule-lighteval/MATH_v2",
"ground_truth": "10"
} | {
"index": -1,
"repeat": 0,
"raw_problem": "",
"split": "",
"source": ""
} |
math_dapo | [
{
"role": "user",
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nDenote by $S(n)$ the sum of the digits of the positive integer $n$. Find all the solutions of the ... | MATH | {
"style": "rule-lighteval/MATH_v2",
"ground_truth": "402"
} | {
"index": -1,
"repeat": 0,
"raw_problem": "",
"split": "",
"source": ""
} |
math_dapo | [
{
"role": "user",
"content": "Solve the following math problem step by step. 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 $S(n)$ be the sum of the digits of $n$. Determine the smallest ... | MATH | {
"style": "rule-lighteval/MATH_v2",
"ground_truth": "7"
} | {
"index": -1,
"repeat": 0,
"raw_problem": "",
"split": "",
"source": ""
} |
math_dapo | [
{
"role": "user",
"content": "Solve the following math problem step by step. 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 integers $k$ such that all roots of the following polynomial are also integers:\n\n$$f(x)... | MATH | {
"style": "rule-lighteval/MATH_v2",
"ground_truth": "5"
} | {
"index": -1,
"repeat": 0,
"raw_problem": "",
"split": "",
"source": ""
} |
math_dapo | [
{
"role": "user",
"content": "Solve the following math problem step by step. 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 class has $25$ students. The teacher wants to stock $N$ candies and hold an Olympiad, distributi... | MATH | {
"style": "rule-lighteval/MATH_v2",
"ground_truth": "300"
} | {
"index": -1,
"repeat": 0,
"raw_problem": "",
"split": "",
"source": ""
} |
math_dapo | [
{
"role": "user",
"content": "Solve the following math problem step by step. 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 $a, b$ are real numbers such that $a^3 + 12a^2 + 49a + 69 = 0$ and $b^3 - 9b^2 + 28b - 31 = 0$,... | MATH | {
"style": "rule-lighteval/MATH_v2",
"ground_truth": "1"
} | {
"index": -1,
"repeat": 0,
"raw_problem": "",
"split": "",
"source": ""
} |
math_dapo | [
{
"role": "user",
"content": "Solve the following math problem step by step. 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 triples $(a,b,c)$ of non-negative integers such that $a+b+c$ is even. Determ... | MATH | {
"style": "rule-lighteval/MATH_v2",
"ground_truth": "37"
} | {
"index": -1,
"repeat": 0,
"raw_problem": "",
"split": "",
"source": ""
} |
math_dapo | [
{
"role": "user",
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nSome positive integers are initially written on a board, where each 2 of them are different. Each ... | MATH | {
"style": "rule-lighteval/MATH_v2",
"ground_truth": "-3"
} | {
"index": -1,
"repeat": 0,
"raw_problem": "",
"split": "",
"source": ""
} |
math_dapo | [
{
"role": "user",
"content": "Solve the following math problem step by step. 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$ for which the largest prime divisor of $n^2 + 3$ is equal to the le... | MATH | {
"style": "rule-lighteval/MATH_v2",
"ground_truth": "3"
} | {
"index": -1,
"repeat": 0,
"raw_problem": "",
"split": "",
"source": ""
} |
math_dapo | [
{
"role": "user",
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nCharlie has a fair $n$-sided die (with each face showing a positive integer between $1$ and $n$ in... | MATH | {
"style": "rule-lighteval/MATH_v2",
"ground_truth": "8556"
} | {
"index": -1,
"repeat": 0,
"raw_problem": "",
"split": "",
"source": ""
} |
math_dapo | [
{
"role": "user",
"content": "Solve the following math problem step by step. 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 integers from $1$ to $n$ are written, one on each of $n$ cards. The first player removes one c... | MATH | {
"style": "rule-lighteval/MATH_v2",
"ground_truth": "14"
} | {
"index": -1,
"repeat": 0,
"raw_problem": "",
"split": "",
"source": ""
} |
math_dapo | [
{
"role": "user",
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nJoe has $1729$ randomly oriented and randomly arranged unit cubes, which are initially unpainted. ... | MATH | {
"style": "rule-lighteval/MATH_v2",
"ground_truth": "7"
} | {
"index": -1,
"repeat": 0,
"raw_problem": "",
"split": "",
"source": ""
} |
math_dapo | [
{
"role": "user",
"content": "Solve the following math problem step by step. 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 circle $C_1$ is tangent to the circle $C_2$ internally at the point $A$. Let $O$ be the center... | MATH | {
"style": "rule-lighteval/MATH_v2",
"ground_truth": "3"
} | {
"index": -1,
"repeat": 0,
"raw_problem": "",
"split": "",
"source": ""
} |
math_dapo | [
{
"role": "user",
"content": "Solve the following math problem step by step. 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 two distinct positive integers $a$ and $b$ that have integer arithmetic, geometric, and h... | MATH | {
"style": "rule-lighteval/MATH_v2",
"ground_truth": "30"
} | {
"index": -1,
"repeat": 0,
"raw_problem": "",
"split": "",
"source": ""
} |
math_dapo | [
{
"role": "user",
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nDexter and Raquel are playing a game with $N$ stones. Dexter goes first and takes one stone from t... | MATH | {
"style": "rule-lighteval/MATH_v2",
"ground_truth": "1010"
} | {
"index": -1,
"repeat": 0,
"raw_problem": "",
"split": "",
"source": ""
} |
math_dapo | [
{
"role": "user",
"content": "Solve the following math problem step by step. 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}$ is isosceles with $AB = AC$. Let the incircle of $\\triangle{ABC}$ inte... | MATH | {
"style": "rule-lighteval/MATH_v2",
"ground_truth": "40"
} | {
"index": -1,
"repeat": 0,
"raw_problem": "",
"split": "",
"source": ""
} |
math_dapo | [
{
"role": "user",
"content": "Solve the following math problem step by step. 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 possible values of $a + b$ where $a$ and $b$ are nonnegative integers such tha... | MATH | {
"style": "rule-lighteval/MATH_v2",
"ground_truth": "9"
} | {
"index": -1,
"repeat": 0,
"raw_problem": "",
"split": "",
"source": ""
} |
math_dapo | [
{
"role": "user",
"content": "Solve the following math problem step by step. 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 those positive integers which are not divisible by $3$. The sum of $2n$ cons... | MATH | {
"style": "rule-lighteval/MATH_v2",
"ground_truth": "10"
} | {
"index": -1,
"repeat": 0,
"raw_problem": "",
"split": "",
"source": ""
} |
math_dapo | [
{
"role": "user",
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nPetya and Vasya play the following game. Petya conceives a polynomial $P(x)$ with integer coeffici... | MATH | {
"style": "rule-lighteval/MATH_v2",
"ground_truth": "4"
} | {
"index": -1,
"repeat": 0,
"raw_problem": "",
"split": "",
"source": ""
} |
math_dapo | [
{
"role": "user",
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nDetermine the greatest power of $2$ that is a factor of $3^{15} + 3^{11} + 3^{6} + 1$.\n\nRemember... | MATH | {
"style": "rule-lighteval/MATH_v2",
"ground_truth": "64"
} | {
"index": -1,
"repeat": 0,
"raw_problem": "",
"split": "",
"source": ""
} |
math_dapo | [
{
"role": "user",
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nOn a board, the numbers from 1 to 2009 are written. A couple of them are erased and instead of the... | MATH | {
"style": "rule-lighteval/MATH_v2",
"ground_truth": "8"
} | {
"index": -1,
"repeat": 0,
"raw_problem": "",
"split": "",
"source": ""
} |
math_dapo | [
{
"role": "user",
"content": "Solve the following math problem step by step. 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 positive integers $n$, let $s(n)$ be the sum of the digits of $n$. Over all four-digit positiv... | MATH | {
"style": "rule-lighteval/MATH_v2",
"ground_truth": "1099"
} | {
"index": -1,
"repeat": 0,
"raw_problem": "",
"split": "",
"source": ""
} |
math_dapo | [
{
"role": "user",
"content": "Solve the following math problem step by step. 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 $n$ persons meet in a meeting, and that each of the persons is acquainted with exactl... | MATH | {
"style": "rule-lighteval/MATH_v2",
"ground_truth": "21"
} | {
"index": -1,
"repeat": 0,
"raw_problem": "",
"split": "",
"source": ""
} |
math_dapo | [
{
"role": "user",
"content": "Solve the following math problem step by step. 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 $8$ mutually non-attacking rooks be placed on a $9 \\times 9$ chessboard so that... | MATH | {
"style": "rule-lighteval/MATH_v2",
"ground_truth": "40320"
} | {
"index": -1,
"repeat": 0,
"raw_problem": "",
"split": "",
"source": ""
} |
math_dapo | [
{
"role": "user",
"content": "Solve the following math problem step by step. 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 a necessary and sufficient condition on the positive integer $n$ such that the equation $x^n ... | MATH | {
"style": "rule-lighteval/MATH_v2",
"ground_truth": "1"
} | {
"index": -1,
"repeat": 0,
"raw_problem": "",
"split": "",
"source": ""
} |
math_dapo | [
{
"role": "user",
"content": "Solve the following math problem step by step. 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 $ABCDEFGHIJ$ be a regular 10-sided polygon inscribed in a circle with center $O$ and radius $5... | MATH | {
"style": "rule-lighteval/MATH_v2",
"ground_truth": "5"
} | {
"index": -1,
"repeat": 0,
"raw_problem": "",
"split": "",
"source": ""
} |
math_dapo | [
{
"role": "user",
"content": "Solve the following math problem step by step. 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 all integers $m$ for which all solutions of the equation $3x^3 - 3x^2 + m = 0$ are ratio... | MATH | {
"style": "rule-lighteval/MATH_v2",
"ground_truth": "0"
} | {
"index": -1,
"repeat": 0,
"raw_problem": "",
"split": "",
"source": ""
} |
math_dapo | [
{
"role": "user",
"content": "Solve the following math problem step by step. 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 boxes contain 600 balls each. The first box contains 600 identical red balls, the second box... | MATH | {
"style": "rule-lighteval/MATH_v2",
"ground_truth": "270901"
} | {
"index": -1,
"repeat": 0,
"raw_problem": "",
"split": "",
"source": ""
} |
math_dapo | [
{
"role": "user",
"content": "Solve the following math problem step by step. 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 three points on the edge of a circular chord such that $B$ is due west of... | MATH | {
"style": "rule-lighteval/MATH_v2",
"ground_truth": "12"
} | {
"index": -1,
"repeat": 0,
"raw_problem": "",
"split": "",
"source": ""
} |
math_dapo | [
{
"role": "user",
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nLet $A$, $B$, $C$, and $D$ be points on a circle such that $AB = 11$ and $CD = 19$. Point $P$ is o... | MATH | {
"style": "rule-lighteval/MATH_v2",
"ground_truth": "31"
} | {
"index": -1,
"repeat": 0,
"raw_problem": "",
"split": "",
"source": ""
} |
math_dapo | [
{
"role": "user",
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nFor any real numbers $x$ and $y$ that satisfy the equations:\n\\[\nx + y - xy = 155\n\\]\nand\n\\[... | MATH | {
"style": "rule-lighteval/MATH_v2",
"ground_truth": "4375"
} | {
"index": -1,
"repeat": 0,
"raw_problem": "",
"split": "",
"source": ""
} |
math_dapo | [
{
"role": "user",
"content": "Solve the following math problem step by step. 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 $2023$ distinct points on a plane, which are colored either white or red. For each white... | MATH | {
"style": "rule-lighteval/MATH_v2",
"ground_truth": "45"
} | {
"index": -1,
"repeat": 0,
"raw_problem": "",
"split": "",
"source": ""
} |
math_dapo | [
{
"role": "user",
"content": "Solve the following math problem step by step. 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 $k$ for which the equation:\n$$ \\text{lcm}(m,n) - \\text{gcd}(m,n) = k... | MATH | {
"style": "rule-lighteval/MATH_v2",
"ground_truth": "2"
} | {
"index": -1,
"repeat": 0,
"raw_problem": "",
"split": "",
"source": ""
} |
math_dapo | [
{
"role": "user",
"content": "Solve the following math problem step by step. 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 $k$ such that for all competitive graphs with $2019$ vertices, if the differ... | MATH | {
"style": "rule-lighteval/MATH_v2",
"ground_truth": "1"
} | {
"index": -1,
"repeat": 0,
"raw_problem": "",
"split": "",
"source": ""
} |
math_dapo | [
{
"role": "user",
"content": "Solve the following math problem step by step. 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 regular tetrahedron with edge $a$, its edges are divided into $n$ equal segments, thus obt... | MATH | {
"style": "rule-lighteval/MATH_v2",
"ground_truth": "3"
} | {
"index": -1,
"repeat": 0,
"raw_problem": "",
"split": "",
"source": ""
} |
math_dapo | [
{
"role": "user",
"content": "Solve the following math problem step by step. 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 integer $n > m$, it turns out that $n$ can be represented as a sum of $2021$ non... | MATH | {
"style": "rule-lighteval/MATH_v2",
"ground_truth": "2021"
} | {
"index": -1,
"repeat": 0,
"raw_problem": "",
"split": "",
"source": ""
} |
math_dapo | [
{
"role": "user",
"content": "Solve the following math problem step by step. 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 integers $a < b < c$ satisfy the following conditions:\n\\[\n a + b + c = 95 \\\\\n a^2 + ... | MATH | {
"style": "rule-lighteval/MATH_v2",
"ground_truth": "37"
} | {
"index": -1,
"repeat": 0,
"raw_problem": "",
"split": "",
"source": ""
} |
math_dapo | [
{
"role": "user",
"content": "Solve the following math problem step by step. 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 real numbers such that $a^2 - 2 = 3b - c$, $b^2 + 4 = 3 + a$, and $c^2 + 4 = ... | MATH | {
"style": "rule-lighteval/MATH_v2",
"ground_truth": "18"
} | {
"index": -1,
"repeat": 0,
"raw_problem": "",
"split": "",
"source": ""
} |
math_dapo | [
{
"role": "user",
"content": "Solve the following math problem step by step. 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 $n$ such that the expression $n^2 - n + 11$ has exactly four prim... | MATH | {
"style": "rule-lighteval/MATH_v2",
"ground_truth": "132"
} | {
"index": -1,
"repeat": 0,
"raw_problem": "",
"split": "",
"source": ""
} |
math_dapo | [
{
"role": "user",
"content": "Solve the following math problem step by step. 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 regular $2006$-gon. A diagonal is called *good* if its endpoints divide the boundary ... | MATH | {
"style": "rule-lighteval/MATH_v2",
"ground_truth": "1003"
} | {
"index": -1,
"repeat": 0,
"raw_problem": "",
"split": "",
"source": ""
} |
math_dapo | [
{
"role": "user",
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nByan is playing a game called \"raven, raven, falcon\" with his three friends. His friends sit in ... | MATH | {
"style": "rule-lighteval/MATH_v2",
"ground_truth": "107"
} | {
"index": -1,
"repeat": 0,
"raw_problem": "",
"split": "",
"source": ""
} |
math_dapo | [
{
"role": "user",
"content": "Solve the following math problem step by step. 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 $n$ for which all positive divisors of $n$ can be placed into the cells... | MATH | {
"style": "rule-lighteval/MATH_v2",
"ground_truth": "1"
} | {
"index": -1,
"repeat": 0,
"raw_problem": "",
"split": "",
"source": ""
} |
math_dapo | [
{
"role": "user",
"content": "Solve the following math problem step by step. 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 day, students in school organized an exchange among themselves with the following rates:\n- $1... | MATH | {
"style": "rule-lighteval/MATH_v2",
"ground_truth": "7"
} | {
"index": -1,
"repeat": 0,
"raw_problem": "",
"split": "",
"source": ""
} |
math_dapo | [
{
"role": "user",
"content": "Solve the following math problem step by step. 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 $ABC$, let $D$ be the foot of the altitude from $A$. Suppose that $AD = 4$, $BD = 3$, ... | MATH | {
"style": "rule-lighteval/MATH_v2",
"ground_truth": "80"
} | {
"index": -1,
"repeat": 0,
"raw_problem": "",
"split": "",
"source": ""
} |
math_dapo | [
{
"role": "user",
"content": "Solve the following math problem step by step. 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 integers $n$ such that $\\frac{5^n - 1}{3}$ is a prime or a perfect square of an integer.... | MATH | {
"style": "rule-lighteval/MATH_v2",
"ground_truth": "0"
} | {
"index": -1,
"repeat": 0,
"raw_problem": "",
"split": "",
"source": ""
} |
math_dapo | [
{
"role": "user",
"content": "Solve the following math problem step by step. 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 $x$ such that $|x^2-x-6|$ has exactly 4 positive integer div... | MATH | {
"style": "rule-lighteval/MATH_v2",
"ground_truth": "10"
} | {
"index": -1,
"repeat": 0,
"raw_problem": "",
"split": "",
"source": ""
} |
math_dapo | [
{
"role": "user",
"content": "Solve the following math problem step by step. 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 $1, 2, \\ldots, 10000$ are placed in the cells of a $100 \\times 100$ square grid, eac... | MATH | {
"style": "rule-lighteval/MATH_v2",
"ground_truth": "50"
} | {
"index": -1,
"repeat": 0,
"raw_problem": "",
"split": "",
"source": ""
} |
math_dapo | [
{
"role": "user",
"content": "Solve the following math problem step by step. 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 triangle $ABC$ has sides $AB = 137$, $AC = 241$, and $BC = 200$. There is a point $D$ on $BC$ ... | MATH | {
"style": "rule-lighteval/MATH_v2",
"ground_truth": "152"
} | {
"index": -1,
"repeat": 0,
"raw_problem": "",
"split": "",
"source": ""
} |
math_dapo | [
{
"role": "user",
"content": "Solve the following math problem step by step. 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 arrangement of 12 real numbers in a row is called *good* if for any four consecutive numbers, t... | MATH | {
"style": "rule-lighteval/MATH_v2",
"ground_truth": "45"
} | {
"index": -1,
"repeat": 0,
"raw_problem": "",
"split": "",
"source": ""
} |
math_dapo | [
{
"role": "user",
"content": "Solve the following math problem step by step. 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 odd natural numbers $n$ such that $d(n)$ is the largest divisor of the number $n$ differe... | MATH | {
"style": "rule-lighteval/MATH_v2",
"ground_truth": "9"
} | {
"index": -1,
"repeat": 0,
"raw_problem": "",
"split": "",
"source": ""
} |
math_dapo | [
{
"role": "user",
"content": "Solve the following math problem step by step. 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 all natural numbers $n$ for which the number $A = n^4 + 4n^3 + 5n^2 + 6n$ is a perfect s... | MATH | {
"style": "rule-lighteval/MATH_v2",
"ground_truth": "1"
} | {
"index": -1,
"repeat": 0,
"raw_problem": "",
"split": "",
"source": ""
} |
math_dapo | [
{
"role": "user",
"content": "Solve the following math problem step by step. 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 consider a set of distinct positive integers with a sum equal to 2023. Among these integers,... | MATH | {
"style": "rule-lighteval/MATH_v2",
"ground_truth": "200"
} | {
"index": -1,
"repeat": 0,
"raw_problem": "",
"split": "",
"source": ""
} |
math_dapo | [
{
"role": "user",
"content": "Solve the following math problem step by step. 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 $x = -2272$, $y = 10^3 + 10^2c + 10b + a$, and $z = 1$ satisfy the equation $ax +... | MATH | {
"style": "rule-lighteval/MATH_v2",
"ground_truth": "1987"
} | {
"index": -1,
"repeat": 0,
"raw_problem": "",
"split": "",
"source": ""
} |
math_dapo | [
{
"role": "user",
"content": "Solve the following math problem step by step. 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 $f(x)$ be a quadratic polynomial such that $f(f(1)) = f(-f(-1)) = 0$ and $f(1) \\neq -f(-1)$. ... | MATH | {
"style": "rule-lighteval/MATH_v2",
"ground_truth": "3"
} | {
"index": -1,
"repeat": 0,
"raw_problem": "",
"split": "",
"source": ""
} |
math_dapo | [
{
"role": "user",
"content": "Solve the following math problem step by step. 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 natural numbers $a > 1$ with the property that every prime divisor of $a^6 - 1$ also divi... | MATH | {
"style": "rule-lighteval/MATH_v2",
"ground_truth": "2"
} | {
"index": -1,
"repeat": 0,
"raw_problem": "",
"split": "",
"source": ""
} |
math_dapo | [
{
"role": "user",
"content": "Solve the following math problem step by step. 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 nonzero real numbers $x$ and $y$ satisfy the equations $x + \\frac{1}{y} = 3$ and $y + ... | MATH | {
"style": "rule-lighteval/MATH_v2",
"ground_truth": "10"
} | {
"index": -1,
"repeat": 0,
"raw_problem": "",
"split": "",
"source": ""
} |
math_dapo | [
{
"role": "user",
"content": "Solve the following math problem step by step. 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 $k$ such that $k + 25973$ is a palindrome, a number that reads ... | MATH | {
"style": "rule-lighteval/MATH_v2",
"ground_truth": "89"
} | {
"index": -1,
"repeat": 0,
"raw_problem": "",
"split": "",
"source": ""
} |
math_dapo | [
{
"role": "user",
"content": "Solve the following math problem step by step. 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 values of the positive integer $m$ such that there exist polynomials $P(x)$, $Q(x)$, and ... | MATH | {
"style": "rule-lighteval/MATH_v2",
"ground_truth": "1"
} | {
"index": -1,
"repeat": 0,
"raw_problem": "",
"split": "",
"source": ""
} |
math_dapo | [
{
"role": "user",
"content": "Solve the following math problem step by step. 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 $n$ such that the decimal representation of $n!(n+1)!(2n+1)! - ... | MATH | {
"style": "rule-lighteval/MATH_v2",
"ground_truth": "34"
} | {
"index": -1,
"repeat": 0,
"raw_problem": "",
"split": "",
"source": ""
} |
math_dapo | [
{
"role": "user",
"content": "Solve the following math problem step by step. 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 the number of ways for a rook to return to its original square on a $4 \\times 4$ chessboard i... | MATH | {
"style": "rule-lighteval/MATH_v2",
"ground_truth": "4"
} | {
"index": -1,
"repeat": 0,
"raw_problem": "",
"split": "",
"source": ""
} |
math_dapo | [
{
"role": "user",
"content": "Solve the following math problem step by step. 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\\( \\triangle ABC \\) is an isosceles triangle with \\( AB = AC \\). Point \\( P \\) is located i... | MATH | {
"style": "rule-lighteval/MATH_v2",
"ground_truth": "13"
} | {
"index": -1,
"repeat": 0,
"raw_problem": "",
"split": "",
"source": ""
} |
math_dapo | [
{
"role": "user",
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nFive congruent circles have centers at the vertices of a regular pentagon so that each of the circ... | MATH | {
"style": "rule-lighteval/MATH_v2",
"ground_truth": "720"
} | {
"index": -1,
"repeat": 0,
"raw_problem": "",
"split": "",
"source": ""
} |
math_dapo | [
{
"role": "user",
"content": "Solve the following math problem step by step. 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 thousands digit of a five-digit number which is divisible by $37$ and $173$ is $3$. What is th... | MATH | {
"style": "rule-lighteval/MATH_v2",
"ground_truth": "2"
} | {
"index": -1,
"repeat": 0,
"raw_problem": "",
"split": "",
"source": ""
} |
math_dapo | [
{
"role": "user",
"content": "Solve the following math problem step by step. 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 $f(n)$ be a function satisfying the following three conditions for all positive integers $n$:\... | MATH | {
"style": "rule-lighteval/MATH_v2",
"ground_truth": "3816"
} | {
"index": -1,
"repeat": 0,
"raw_problem": "",
"split": "",
"source": ""
} |
math_dapo | [
{
"role": "user",
"content": "Solve the following math problem step by step. 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 in the $xy$ plane, where $B$ is at the origin $(0,0)$. Extend $BC$ to $D$ ... | MATH | {
"style": "rule-lighteval/MATH_v2",
"ground_truth": "40"
} | {
"index": -1,
"repeat": 0,
"raw_problem": "",
"split": "",
"source": ""
} |
math_dapo | [
{
"role": "user",
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nReal nonzero numbers $x, y, z$ satisfy $x + y + z = 0$. Furthermore, it is given that:\n\\[\nA = \... | MATH | {
"style": "rule-lighteval/MATH_v2",
"ground_truth": "-1"
} | {
"index": -1,
"repeat": 0,
"raw_problem": "",
"split": "",
"source": ""
} |
math_dapo | [
{
"role": "user",
"content": "Solve the following math problem step by step. 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 prime numbers $p$ such that $4p^2 + 1$ and $6p^2 + 1$ are also prime numbers.\n\nRemember... | MATH | {
"style": "rule-lighteval/MATH_v2",
"ground_truth": "5"
} | {
"index": -1,
"repeat": 0,
"raw_problem": "",
"split": "",
"source": ""
} |
math_dapo | [
{
"role": "user",
"content": "Solve the following math problem step by step. 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 $x$ such that $3 \\times 2^x = n^2 - 1$ for some positive in... | MATH | {
"style": "rule-lighteval/MATH_v2",
"ground_truth": "7"
} | {
"index": -1,
"repeat": 0,
"raw_problem": "",
"split": "",
"source": ""
} |
math_dapo | [
{
"role": "user",
"content": "Solve the following math problem step by step. 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 $x$, $y$, $z$ be positive real numbers satisfying the simultaneous equations:\n\\[\n\\begin{al... | MATH | {
"style": "rule-lighteval/MATH_v2",
"ground_truth": "31"
} | {
"index": -1,
"repeat": 0,
"raw_problem": "",
"split": "",
"source": ""
} |
math_dapo | [
{
"role": "user",
"content": "Solve the following math problem step by step. 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 pentagon $ABCDE$ with the following properties:\n\n1. Angles $\\angle A$ and $\\angle C$ a... | MATH | {
"style": "rule-lighteval/MATH_v2",
"ground_truth": "90"
} | {
"index": -1,
"repeat": 0,
"raw_problem": "",
"split": "",
"source": ""
} |
math_dapo | [
{
"role": "user",
"content": "Solve the following math problem step by step. 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 $f(x) = x^3 + ax^2 + bx + c$ have solutions that are distinct negative integers. If $a+b+c = 2... | MATH | {
"style": "rule-lighteval/MATH_v2",
"ground_truth": "1440"
} | {
"index": -1,
"repeat": 0,
"raw_problem": "",
"split": "",
"source": ""
} |
math_dapo | [
{
"role": "user",
"content": "Solve the following math problem step by step. 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 $AB=9$ and $AC=10$. A semicircle is inscribed in $\\triangle ABC$ with i... | MATH | {
"style": "rule-lighteval/MATH_v2",
"ground_truth": "415"
} | {
"index": -1,
"repeat": 0,
"raw_problem": "",
"split": "",
"source": ""
} |
math_dapo | [
{
"role": "user",
"content": "Solve the following math problem step by step. 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 right-angled at $A$. The circle with center $A$ and radius $AB$ intersects $BC$ ... | MATH | {
"style": "rule-lighteval/MATH_v2",
"ground_truth": "936"
} | {
"index": -1,
"repeat": 0,
"raw_problem": "",
"split": "",
"source": ""
} |
math_dapo | [
{
"role": "user",
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nPetya gave Vasya a number puzzle. Petya chose a digit $X$ and said, \"I am thinking of a three-dig... | MATH | {
"style": "rule-lighteval/MATH_v2",
"ground_truth": "4"
} | {
"index": -1,
"repeat": 0,
"raw_problem": "",
"split": "",
"source": ""
} |
math_dapo | [
{
"role": "user",
"content": "Solve the following math problem step by step. 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 Haiku is a Japanese poem of seventeen syllables, in three lines of five, seven, and five.\n\nAda... | MATH | {
"style": "rule-lighteval/MATH_v2",
"ground_truth": "4"
} | {
"index": -1,
"repeat": 0,
"raw_problem": "",
"split": "",
"source": ""
} |
math_dapo | [
{
"role": "user",
"content": "Solve the following math problem step by step. 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 $ABCD$ satisfies the following conditions: \\( \\angle ABC = \\angle BCD = 150^{... | MATH | {
"style": "rule-lighteval/MATH_v2",
"ground_truth": "10"
} | {
"index": -1,
"repeat": 0,
"raw_problem": "",
"split": "",
"source": ""
} |
math_dapo | [
{
"role": "user",
"content": "Solve the following math problem step by step. 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 are given a coin of diameter $\\frac{1}{2}$ and a checkerboard of $1 \\times 1$ squares with an... | MATH | {
"style": "rule-lighteval/MATH_v2",
"ground_truth": "6029"
} | {
"index": -1,
"repeat": 0,
"raw_problem": "",
"split": "",
"source": ""
} |
math_dapo | [
{
"role": "user",
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nGraph $G_1$ of a quadratic trinomial $y = px^2 + qx + r$ with real coefficients intersects the gra... | MATH | {
"style": "rule-lighteval/MATH_v2",
"ground_truth": "2"
} | {
"index": -1,
"repeat": 0,
"raw_problem": "",
"split": "",
"source": ""
} |
math_dapo | [
{
"role": "user",
"content": "Solve the following math problem step by step. 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 an acute-angled triangle. Construct points $A'$, $B'$, $C'$ on its sides $BC$, $CA$, ... | MATH | {
"style": "rule-lighteval/MATH_v2",
"ground_truth": "1"
} | {
"index": -1,
"repeat": 0,
"raw_problem": "",
"split": "",
"source": ""
} |
math_dapo | [
{
"role": "user",
"content": "Solve the following math problem step by step. 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 radius $r$ of a circle with center at the origin is an odd integer. There is a point $(p^m, q^... | MATH | {
"style": "rule-lighteval/MATH_v2",
"ground_truth": "5"
} | {
"index": -1,
"repeat": 0,
"raw_problem": "",
"split": "",
"source": ""
} |
math_dapo | [
{
"role": "user",
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nUsing each of the digits $1, 2, 3, \\ldots, 8, 9$ exactly once, we form nine, not necessarily dist... | MATH | {
"style": "rule-lighteval/MATH_v2",
"ground_truth": "8"
} | {
"index": -1,
"repeat": 0,
"raw_problem": "",
"split": "",
"source": ""
} |
math_dapo | [
{
"role": "user",
"content": "Solve the following math problem step by step. 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 $n$ such that the following statement holds:\n\nIf $a_1, a_... | MATH | {
"style": "rule-lighteval/MATH_v2",
"ground_truth": "107"
} | {
"index": -1,
"repeat": 0,
"raw_problem": "",
"split": "",
"source": ""
} |
math_dapo | [
{
"role": "user",
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nSolve for $x$:\n\\[\nv - w + x - y + z = 79 \\\\\nv + w + x + y + z = -1 \\\\\nv + 2w + 4x + 8y + ... | MATH | {
"style": "rule-lighteval/MATH_v2",
"ground_truth": "24"
} | {
"index": -1,
"repeat": 0,
"raw_problem": "",
"split": "",
"source": ""
} |
math_dapo | [
{
"role": "user",
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nYou have a 4-digit whole number that is a perfect square. Another number is constructed by making ... | MATH | {
"style": "rule-lighteval/MATH_v2",
"ground_truth": "3025"
} | {
"index": -1,
"repeat": 0,
"raw_problem": "",
"split": "",
"source": ""
} |
End of preview. Expand in Data Studio
No dataset card yet
- Downloads last month
- 58