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\nTriangle $ABC$ has side lengths $AB = 13$, $AC = 14$, and $BC = 15$ and centroid $G$. What is the area of the triangle... | MATH | {
"ground_truth": "28",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "1ed08373-1cba-4121-8224-b95e918507a6"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 integer was removed from the set $S=\\{1, 2, 3, \\ldots, n\\}$ of the integers from $1$ to $n$. The arithmetic mea... | MATH | {
"ground_truth": "61",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "f5bc70d9-c098-44ac-b41f-db05cff4c095"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 integer divisors of $12!$ that leave a remainder of $1$ when divided by $3$.\n\nRemember t... | MATH | {
"ground_truth": "66",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "5d993e2c-4653-49ba-8788-92c4ceef9919"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 solution to the equation $2^{2^k} \\equiv k \\pmod{29}$.\n\nRemember to put your an... | MATH | {
"ground_truth": "24",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "ef7c1698-7bed-42df-bd29-54db78eaebb8"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 three equilateral triangles $\\triangle HOW$, $\\triangle BOW$, and $\\triangle DAH$ in a plane:\n- $WO = 7$\n- ... | MATH | {
"ground_truth": "11",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "29201a6c-9ce5-496b-9a01-5765f287c662"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 $r$ be a real number such that $\\sqrt[3]{r} - \\frac{1}{\\sqrt[3]{r}} = 2$. Find $r^3 - \\frac{1}{r^3}$.\n\nRemem... | MATH | {
"ground_truth": "2786",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "b7b05dbe-9882-455e-bd70-b49312c3f0c7"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nA cyclic quadrilateral $ABCD$ has side lengths $AB = 3$, $BC = AD = 5$, and $CD = 8$. The radius of its circumcircle c... | MATH | {
"ground_truth": "13",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "31f55c2c-9c49-435d-a64c-82ac6d4dcb0a"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nLet $ABC$ be a triangle with vertices located at the centers of mass of Vincent Huang's house, Tristan Shin's house, a... | MATH | {
"ground_truth": "6049",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "f2edafc3-a1c1-44ac-b4d3-aed180fff80f"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nAmong the four-digit numbers greater than $2022$ that are divisible by $3$, find the smallest integer whose four digit... | MATH | {
"ground_truth": "2112",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "44160176-b712-45a4-9423-eb9afdf7ab3d"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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. What is the smallest sum of digits that $5^n + 6^n + 2022^n$ can take?\n\nRemember to p... | MATH | {
"ground_truth": "8",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "b86cb74a-fc7e-4f2c-acec-dc06afeb7126"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 greatest number of balls with a radius of $\\frac{1}{2}$ that can be placed within a rectangular box of si... | MATH | {
"ground_truth": "106",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "ea8fda8c-5835-40c4-b372-d0739d6dce7f"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nFor a positive integer $n$, let $d(n)$ be the number of positive divisors of $n$. What is the smallest positive intege... | MATH | {
"ground_truth": "864",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "eb5a1137-11bd-44ca-bcdf-a63675980d7e"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 polynomials $P(x) = a_nx^n + \\cdots + a_0$, let $f(P) = a_n \\cdots a_0$ be the product of the coefficients of $P... | MATH | {
"ground_truth": "32",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "f9324206-c9e0-420f-aeb5-8867c650c1f3"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nCompute the sum of the distinct prime factors of $10101$.\n\nRemember to put your answer on its own line after \"Answe... | MATH | {
"ground_truth": "60",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "c1525087-bfe3-4add-adc9-5cf55318f12b"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nSequences $a_n$ and $b_n$ are defined for all positive integers $n$ such that $a_1 = 5$, $b_1 = 7$, \n\n$$a_{n+1} = \... | MATH | {
"ground_truth": "24",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "e791025c-0c68-449d-9414-838f15783b5d"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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} = \\sum_{i=1}^{\\infty}\\left(\\prod_{j=1}^i \\dfrac{3j - 2}{12j}\\right).$ Then $(\\mathcal{S} + 1)... | MATH | {
"ground_truth": "43",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "17734d7d-6c0b-4dd6-812c-5ec4176b1d03"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 $\\alpha = \\cos^{-1} \\left( \\frac{3}{5} \\right)$ and $\\beta = \\sin^{-1} \\left( \\frac{3}{5} \\right)$. \n\... | MATH | {
"ground_truth": "15013",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "76383e44-8990-4c2a-a7d9-9b31f526d88f"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 positive integer $n$ such that $20 \\equiv n^{15} \\pmod{29}$?\n\nRemember to put your answer on ... | MATH | {
"ground_truth": "20",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "8f8e9f04-b541-45f0-bf04-68e60326e412"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 two natural numbers $w$ and $n$, the tower of $n$ $w$'s is the natural number $T_n(w)$ defined by\n\n\\[ T_n(w) ... | MATH | {
"ground_truth": "1988",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "e7aeb936-5084-4a84-9f89-ba964da328fb"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 arrange the array of positive integers such that:\n- The number $2012$ is in the first posi... | MATH | {
"ground_truth": "201",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "dc6ee2be-1c67-4787-99b5-dc484c8eda2f"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 her daughter's $12^{\\text{th}}$ birthday, Ingrid decides to bake a dodecagon pie in celebration. Unfortunately, t... | MATH | {
"ground_truth": "64",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "b7de1c96-9bce-4c71-b3ee-fa1c22aa98e6"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nHow many of the numbers $1 \\cdot 2 \\cdot 3$, $2 \\cdot 3 \\cdot 4$, ..., $2020 \\cdot 2021 \\cdot 2022$ are divisibl... | MATH | {
"ground_truth": "27",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "e9c879f7-f465-4f6d-8548-b48fec7e80f4"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 circumradius of the triangle with side lengths $104$, $112$, and $120$.\n\nRemember to put your answer on its... | MATH | {
"ground_truth": "65",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "f63f3b3c-d51b-42c4-b32f-ee69d6d7892e"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nPositive integers $a < b < c$ are such that $b + a$ is a multiple of $b - a$ and $c + b$ is a multiple of $c - b$. If ... | MATH | {
"ground_truth": "2013",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "afc6f70f-ccc2-4f9d-95ea-25fac9e26d2a"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 coloring of all plane points with coordinates belonging to the set $S=\\{0,1,\\ldots,99\\}$ into red and white color... | MATH | {
"ground_truth": "5000",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "974c6892-4e0d-4f62-985b-6374995bf30d"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 $1000$ students in a school. Every student has exactly $4$ friends. A group of three students $\\{A,B,C\\}$ ... | MATH | {
"ground_truth": "2000",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "a086f604-ec58-414f-8d78-0bfbee3eccfd"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nHow many positive integers between 1 and 400 (inclusive) have exactly 15 positive integer factors?\n\nRemember to put ... | MATH | {
"ground_truth": "3",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "1015b85f-02cf-4036-9f81-4a8ee06a59eb"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 function such that $f(1) = 1234$, $f(2) = 1800$, and $f(x) = f(x-1) + 2f(x-2) - 1$ for all integers $x... | MATH | {
"ground_truth": "8092",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "fd5ed13b-ed0b-481d-97eb-e291d887fc5b"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nCalculate the value of $\\sqrt{\\frac{11^4+100^4+111^4}{2}}$ and provide your answer as an integer.\n\nRemember to put... | MATH | {
"ground_truth": "11221",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "963b1505-226c-4023-8ed1-0949bdbd8e20"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nFind the number of ordered pairs of integers \\((a, b)\\) that satisfy the inequality\n\n\\[\n1 < a < b+2 < 10.\n\\]\n... | MATH | {
"ground_truth": "28",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "6a9833c2-ea4d-4a5c-add1-3025b7201299"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nMr. DoBa likes to listen to music occasionally while he does his math homework. When he listens to classical music, he... | MATH | {
"ground_truth": "280",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "506f72bc-1b8f-4e58-bd18-f32b9cbbca21"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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$q$ is the smallest rational number having the following properties:\n\n1. $q > \\frac{31}{17}$\n\n2. When $q$ is writ... | MATH | {
"ground_truth": "17",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "62881210-68ab-4ee8-b0ab-345b144764c3"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 $4 \\times 4$ array of $16$ dots, shown below.\n\nCounting the number of squares whose vertices are among... | MATH | {
"ground_truth": "4",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "1a240ce5-3e6d-423b-8654-718ea8d0fbcd"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nJeffrey rolls three fair six-sided dice and records their results. The probability that the mean of these three number... | MATH | {
"ground_truth": "101",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "b5681218-4dcd-4a97-97df-495f1e0de034"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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\\) and \\(y\\) be positive real numbers satisfying the following system of equations:\n\\[\n\\begin{cases}\n\... | MATH | {
"ground_truth": "5",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "e41003a3-91e4-4f08-8ce3-7e54619808d5"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 $3 \\times 3$ grid is to be painted with three colors: red, green, and blue, such that:\n1. No two squares that shar... | MATH | {
"ground_truth": "24",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "f1398a93-1fa5-4307-aa82-ead26ab08c4a"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nPortraits of famous scientists hang on a wall. The scientists lived between 1600 and 2008, and none of them lived long... | MATH | {
"ground_truth": "5",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "60561016-46ef-44b5-a00e-4525adc0be5d"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 \\) has \\( AB = 4 \\) and \\( AC = 6 \\). Let point \\( D \\) be on line \\( AB \\) so that \\( A ... | MATH | {
"ground_truth": "13",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "c83617d8-7d93-4b68-bc6f-f9b9c5183f48"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 = 4024$, $AC = 4024$, and $BC = 2012$. The reflection of line $AC$ over line $AB$ mee... | MATH | {
"ground_truth": "3521",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "cd3f3e4b-dd2a-49ed-83b1-9d27b15c4c0d"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 32 objects are placed along a circle at equal distances. In how many ways can 3 objects be chosen from among t... | MATH | {
"ground_truth": "3616",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "1bfbfe24-e338-48a8-87fe-6dfb977bbfbb"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 2020 piles of coins in front of you. The first pile contains 1 coin, the second pile contains 2 coins, the th... | MATH | {
"ground_truth": "11",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "2da6a628-1723-4d8a-aa17-8f2effa2b4c8"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nLet $M$ be a set of six distinct positive integers whose sum is $60$. These numbers are written on the faces of a cube... | MATH | {
"ground_truth": "84",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "ad9152cd-a606-4550-88a6-f5fc0abd85f6"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 the expected amount of $1$s in a randomly selected $2021$-digit number is $\\frac{m}{n}$, where $m$ and $n$... | MATH | {
"ground_truth": "1828",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "92aa03c0-f480-460f-bd02-85999420f9c2"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 pyramid $OABC$. Let the equilateral triangle $ABC$ with side length $6$ be the base. Also, $OA = OB = OC ... | MATH | {
"ground_truth": "23",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "34cbdafe-7316-4734-9d98-cf7e8fc7602f"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 that do not have a multiple ending in $2015$.\n\nRemember to put your answer on its own line af... | MATH | {
"ground_truth": "2",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "500daa08-be87-4b77-a4e9-f20ae3af7318"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 remainder obtained when the largest prime factor of $999999999999$ is divided by $2006$.\n\nRemember to ... | MATH | {
"ground_truth": "1877",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "625e517d-86ff-437b-8ba3-eaea84306fde"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nJanet played a song on her clarinet in \\(3\\) minutes and \\(20\\) seconds. Janet’s goal is to play the song at a \\(... | MATH | {
"ground_truth": "160",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "6ea0cc27-77c0-4c15-907a-b6369fdb5f1a"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nTsrutsuna starts in the bottom left cell of a $7 \\times 7$ square table, while Tsuna is in the upper right cell. The ... | MATH | {
"ground_truth": "400",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "c5ff01ff-1a85-48fd-8914-c9af0b08db66"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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$, points $D$, $E$, and $F$ lie on side $\\overline{BC}$ such that $\\overline{AD}$ is an angle bise... | MATH | {
"ground_truth": "94",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "c075bdad-4b1e-4725-864e-260b720a042f"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 four-digit numbers $\\overline{abcd}$ such that\n\n$$a(a+b+c+d)(a^{2}+b^{2}+c^{2}+d^{2})(a^{6}+2b^{6}+3c... | MATH | {
"ground_truth": "2010",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "6ee9d62e-a565-4b05-8530-25cc7bcfc7ec"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 positive integers such that $77^a \\cdot 637^b = 143^c \\cdot 49^d$. Compute the minimal... | MATH | {
"ground_truth": "9",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "fbf77003-f8bf-4bd7-a499-ed4911f72468"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nPassing through the origin of the coordinate plane are $180$ lines, including the coordinate axes, which form $1^\\cir... | MATH | {
"ground_truth": "8950",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "7ed1ea85-46cd-4ff7-b87e-3c3e0bc46394"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 4-digit numbers using the digits \\(2, 3, 4, 5, 6\\) without repeating any digit.\n\nRemember to p... | MATH | {
"ground_truth": "533280",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "baa01db1-e091-49d3-99dd-3bec2c2f84c7"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 sides of a right triangle, regular nonagons are constructed outside. These nonagons are built on one of the cat... | MATH | {
"ground_truth": "417",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "b6f68b00-8824-41b1-80ea-7986f933a2ae"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 $\\left\\lfloor\\frac{1}{\\frac{1}{2022}+\\frac{1}{2023}+\\dots+\\frac{1}{2064}}\\right\\rfloor$.\n\nRemember ... | MATH | {
"ground_truth": "47",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "74a06cbd-06ce-4303-a9d3-85790c85ea7d"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 $AB=3$, $AC=5$, and $\\angle A=90^\\circ$. Point $D$ is the foot of the altitude from $A$ to... | MATH | {
"ground_truth": "22534",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "e0e5ae7c-2968-4c52-aea0-a44a5c1a0694"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 diagram below, how many rectangles can be drawn using the grid lines which contain none of the letters $N$, $I$... | MATH | {
"ground_truth": "73",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "b40eb02b-595a-4684-b369-2a19fdc33bc0"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nCompute the number of ordered quadruples $(a, b, c, d)$ of distinct positive integers such that $\\binom{\\binom{a}{b}... | MATH | {
"ground_truth": "13",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "2d6b819f-6728-4cc1-900b-388cf0cdeac2"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nEach cell of a $7 \\times 7$ table is painted with one of several colors. It is known that for any two distinct rows, ... | MATH | {
"ground_truth": "22",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "3ef238be-047c-4891-b078-2f4ed4bd56ce"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 two-digit numbers have exactly $4$ positive factors? (Here $1$ and the number $n$ are also considered as fact... | MATH | {
"ground_truth": "30",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "399e66fb-6541-4035-b849-0025077c3415"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 digits $A$, $B$, and $C$ (between $0$ and $9$ inclusive) satisfy:\n\\[\n\\begin{array}{c@{\\,}c@{\\,}c@{\\,}c}\n & ... | MATH | {
"ground_truth": "42",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "426ef5ac-6664-4faa-a778-ef2e25e2efdf"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nThe sum \\[\\sum_{i=0}^{1000} \\frac{\\binom{1000}{i}}{\\binom{2019}{i}}\\] can be expressed in the form $\\frac{p}{q}... | MATH | {
"ground_truth": "152",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "a9e2f066-efca-47f9-a46d-2b0125b52f96"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nLet $\\sigma(n)$ be the number of positive divisors of $n$, and let $\\operatorname{rad} n$ be the product of the dist... | MATH | {
"ground_truth": "164",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "357ed618-1aaa-4685-9105-8d8e44a4578d"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 a positive integer such that $1 + \\frac{1}{2} + \\frac{1}{3} + \\ldots + \\frac{1}{13} = \\frac{k}{13!}$. ... | MATH | {
"ground_truth": "1",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "11cb3593-1e94-41c9-9a70-5888ce622d86"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 $A=\\{1,2,3,\\ldots,40\\}$. Find the least positive integer $k$ for which it is possible to partition $A$ into $k$... | MATH | {
"ground_truth": "4",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "bf66f909-56fb-4cfe-a38c-595ead6350ae"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nIn $\\triangle ABC$, $AB = 30$, $BC = 40$, and $CA = 50$. Squares $A_1A_2BC$, $B_1B_2AC$, and $C_1C_2AB$ are erected o... | MATH | {
"ground_truth": "124",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "32b1a46f-1942-4f5c-ae28-54b726674e3d"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 $P(x)$ is the least degree polynomial with rational coefficients such that \n\\[P(\\sqrt{2} + \\sqrt{3}) = ... | MATH | {
"ground_truth": "455",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "7a550875-d2ec-47d9-b4f0-e0b25a0b30de"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 function $f(n)$ is defined on the positive integers and takes non-negative integer values. Given the conditions:\n... | MATH | {
"ground_truth": "660",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "76c33b7b-63a5-4016-9881-ad5ff97c465c"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nCyclic pentagon $ABCDE$ has a right angle $\\angle ABC = 90^{\\circ}$ and side lengths $AB = 15$ and $BC = 20$. Suppos... | MATH | {
"ground_truth": "7",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "ab881982-f3df-4e57-a504-e9d82e5fa1c6"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nDima has written the numbers $\\frac{1}{80!}, \\frac{1}{81!}, \\ldots, \\frac{1}{99!}$ on 20 infinite pieces of paper ... | MATH | {
"ground_truth": "155",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "d9fd6374-db61-455f-9648-faa7fdc8383c"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 right triangle with a right angle at $C$. Two lines, one parallel to $AC$ and the other parallel to $BC... | MATH | {
"ground_truth": "256",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "71f8e4bf-711d-44f0-b218-00c8e55c0dfa"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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(x) = x^{2008} + x^{2007} + x^{2006} + \\cdots + x + 1, \\] and let $r(x)$ be the polynomial remainder when $... | MATH | {
"ground_truth": "64",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "35960cdc-ba90-4c1b-8443-5a3d0a573a7f"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\n2013 is the first year since the Middle Ages that consists of four consecutive digits. How many such years are there s... | MATH | {
"ground_truth": "149",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "1c1b28f1-3f95-4999-87a8-c8053814b690"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 rectangle in the figure has dimensions $16 \\times 20$ and is divided into $10$ smaller equal rectangles. What is ... | MATH | {
"ground_truth": "24",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "51e8e601-c8ad-45de-8765-709b6a317f23"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 call $\\overline{a_n\\ldots a_2}$ the Fibonacci representation of a positive integer $k$ if \n\\[k = \\sum_{i=2}^n ... | MATH | {
"ground_truth": "1596",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "4340a442-78f4-4ec3-aaf5-083f0a1aabd8"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 \\( \\text{Revolution}(x) = x^3 + Ux^2 + Sx + A \\), where \\( U \\), \\( S \\), and \\( A \\) are all integers an... | MATH | {
"ground_truth": "392",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "f97af8e4-9e7d-4c40-8ad1-fb1d73bbc4bf"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 polynomials $Q(x,y,z)$ with coefficients in \\{0,1\\} such that there exists a homogeneous p... | MATH | {
"ground_truth": "509545",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "04ccb950-8039-44df-8993-b89c04d6c999"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nJeff writes down the two-digit base-10 prime $\\overline{ab_{10}}$. He realizes that if he misinterprets the number as... | MATH | {
"ground_truth": "61",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "afbcbd2f-8952-4145-a920-3ffb0565adf0"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 will say that a list of positive integers is *admissible* if all its numbers are less than or equal to $100$ and th... | MATH | {
"ground_truth": "10",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "f48e4691-e4b8-4c90-80e9-9c1db204a978"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 $30$ cities in the empire of Euleria. Every week, Martingale City runs a very well-known lottery. $900$ visi... | MATH | {
"ground_truth": "405",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "96deafce-85b5-463d-ab96-b61cf104dd60"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 three solutions with different percentages of alcohol. If you mix them in a ratio of $1:2:3$, you get a $20\... | MATH | {
"ground_truth": "40",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "12a92709-8ac8-4bf8-94c6-24ca635875be"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 container is shaped like a square-based pyramid where the base has side length $23$ centimeters and the height is $1... | MATH | {
"ground_truth": "60",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "a470c9d1-e204-41f4-b6ff-2f5aa51645c3"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 $a_1 = 20$, $a_2 = 16$, and for $k \\ge 3$, let $a_k = \\sqrt[3]{k-a_{k-1}^3-a_{k-2}^3}$. Compute $a_1^3 + a_2^3 +... | MATH | {
"ground_truth": "8021",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "50d1de0f-1a7b-40d2-84c1-847cbc719d65"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 such that $\\lfloor\\sqrt{n}\\rfloor - 2$ divides $n - 4$ and $\\lfloor\\sqrt{n}\\rfloor... | MATH | {
"ground_truth": "956",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "1161fdfd-846b-45cf-9915-4ab1a82dd98f"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 $f_0(x) = x$, and for each $n \\geq 0$, let $f_{n+1}(x) = f_n(x^2(3-2x))$. Find the smallest real number that is a... | MATH | {
"ground_truth": "2018",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "93e74047-27a3-4cf1-bb36-6460dd4f6a0d"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 permutation $a_1, a_2, \\ldots, a_{13}$ of the numbers from $1$ to $13$ is given such that $a_i > 5$ for $i=1,2,3,4,... | MATH | {
"ground_truth": "45",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "944027a8-f176-40a3-9ddd-6a0fadac4e53"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 point $P$ is chosen uniformly at random in the interior of triangle $ABC$ with side lengths $AB = 5$, $BC = 12$, $CA... | MATH | {
"ground_truth": "61",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "e2a6cf9c-d5fa-4364-a6f2-8f45be53dc69"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 digits $a$ and $b$ such that the 15-digit number $7a7ba7ab7ba7b77$ is divisible by 99. Find $10a + b$.\n\nRe... | MATH | {
"ground_truth": "53",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "71fbce85-35a9-498f-be9c-9aeb38be5580"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 $ABC$ and $DEF$ be two triangles, such that $AB = DE = 20$, $BC = EF = 13$, and $\\angle A = \\angle D$. If $AC - ... | MATH | {
"ground_truth": "126",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "92cc2b05-a092-49bd-8ce6-17f7c1ab9096"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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] = \\{1, 2, 3, \\ldots, n\\}\\) and for any set \\(S\\), let \\(P(S)\\) be the set of non-empty subsets of \... | MATH | {
"ground_truth": "7",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "30a1d949-5284-4b27-9d52-b7c9cef5b61d"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 $\\{a_n\\}_{n=1}^{\\infty}$ and $\\{b_n\\}_{n=1}^{\\infty}$ be sequences of integers such that $a_1 = 20$, $b_1 = ... | MATH | {
"ground_truth": "525825",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "e0561a6c-da2f-436a-b25e-aa476487ac4c"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 prime number $p$ for which the number $p^3 + 2p^2 + p$ has exactly 42 divisors.\n\nRemember to put y... | MATH | {
"ground_truth": "23",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "bba28c55-85ba-44db-95f1-eb369052f0e6"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 and let $E$ and $F$ be points inside $ABCD$ such that the line containing $\\overline{EF}$... | MATH | {
"ground_truth": "4",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "a8c73930-b242-4531-9e2a-a5fe283ca515"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 $A = 3^3 \\cdot 33^{33} \\cdot 333^{333} \\cdot 3333^{3333}$ is divided by $100$.\n\nRemember ... | MATH | {
"ground_truth": "19",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "4c610699-f7d4-48bd-9425-731d29a1ef0c"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nLet $P$ and $Q$ be the midpoints of sides $AB$ and $BC,$ respectively, of $\\triangle ABC.$ Suppose $\\angle A = 30^{\... | MATH | {
"ground_truth": "80",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "bee7e820-01d9-4c45-902f-bc9186dd1a1c"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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. Let $f(n)$ be the probability that, if divisors $a, b, c$ of $n$ are selected uniformly... | MATH | {
"ground_truth": "58",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "f33e97fe-c339-440f-b2eb-4db12ac387dc"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 two prime numbers $p$ such that $5p$ can be expressed in the form $\\left\\lfloor \\dfrac{n^2}{5} \\right\\r... | MATH | {
"ground_truth": "52",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "def729e9-b8ec-4c72-bc9e-612e326a0dff"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 incircle of triangle $\\triangle ABC$ is the unique inscribed circle that is internally tangent to the sides $\\ov... | MATH | {
"ground_truth": "8",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "d1679eec-0ade-4db6-b9e1-1caf741feed9"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nScrews are sold in packs of $10$ and $12$. Harry and Sam independently go to the hardware store, and by coincidence, e... | MATH | {
"ground_truth": "60",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "4da3e7ad-e6b7-4f1e-aa50-f14406bf1f87"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 million bucks (i.e., one million male deer) are in different cells of a $1000 \\times 1000$ grid. The left and rig... | MATH | {
"ground_truth": "1200000",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "11a8c85f-b656-44f0-9a42-ffe41c14b28a"
} |
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