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\nQuadrilateral $ABCD$ is neither a kite nor a rectangle. It is known that its side lengths are integers, $AB = 6$, $BC ... | MATH | {
"ground_truth": "30",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "7a713d73-87f2-40b9-9139-68d550092d1d"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 volume of a certain rectangular solid is $216\\text{ cm}^3$, its total surface area is $288\\text{ cm}^2$, and its... | MATH | {
"ground_truth": "96",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "58b6351f-abba-4c58-9dbb-6e58578471ee"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 $n$, define a function $f_n(x)$ on the interval $[0, n+1]$ as follows:\n\\[ f_n(x) = \\left( \\... | MATH | {
"ground_truth": "450",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "2af23121-8d46-4591-8bbd-dc9a55a4ba85"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 trapezoid with $AB \\parallel CD$, $AB = 5$, $BC = 9$, $CD = 10$, and $DA = 7$. Lines $BC$ and $DA$ in... | MATH | {
"ground_truth": "90011",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "b0b703af-fd85-4b67-937b-d94a956bc287"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 value of $(a+5)^2 + (b-2)^2 + (c-9)^2$ for all real numbers $a, b, c$ satisfying $a^2 + b^2 + c... | MATH | {
"ground_truth": "72",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "0b83273f-4417-4df9-86e6-20ee49dfe2bc"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 $u_n$ be the $n^{\\text{th}}$ term of the sequence:\n\\[\n1, \\quad 2, \\quad 5, \\quad 6, \\quad 9, \\quad 12, \\... | MATH | {
"ground_truth": "5898",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "3c4e9f27-193c-4fbc-977e-e2ed097f8677"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 \\((a, b)\\) of positive integers that are solutions of the following equation: \n\\[... | MATH | {
"ground_truth": "1",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "d0da039e-1006-4394-ba1b-80b2765d18cf"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 $f : \\mathbb{R} \\to \\mathbb{R}$ satisfy $f(x + f(y)) = 2x + 4y + 2547$ for all reals $x, y$. Compute $f(0)$.\n\... | MATH | {
"ground_truth": "849",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "e3d81341-adab-4ca5-aaf9-081aedc698ff"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nJim has two fair 6-sided dice: one die has faces labelled from 1 to 6, and the second die has faces labelled from 3 to... | MATH | {
"ground_truth": "7",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "a9790f96-8ee3-4aaa-a1a1-64270996b02f"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 $N$ denote the number of all natural numbers $n$ such that $n$ is divisible by a prime $p > \\sqrt{n}$ and $p < 20... | MATH | {
"ground_truth": "69",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "d4b510d6-9806-4e17-9d15-df8148db3518"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 real numbers $x$, $y$, $z$, and $t$ satisfy the following equation:\n\\[ 2x^2 + 4xy + 3y^2 - 2xz - 2yz + z^2 + 1 =... | MATH | {
"ground_truth": "125",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "486bc237-1793-424c-93c7-acffe02f1454"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nHow many functions $f : \\{1, 2, \\ldots, 16\\} \\to \\{1, 2, \\ldots, 16\\}$ have the property that $f(f(x)) - 4x$ is... | MATH | {
"ground_truth": "16",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "1278bc73-d0f3-475a-9d48-bba6a9951a7c"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nDaniel had a string that formed the perimeter of a square with area $98$. Daniel cut the string into two pieces. With ... | MATH | {
"ground_truth": "67",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "1cc7dbf9-ddbf-4645-a695-5856be769e50"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 following diagram, $AB = 1$. The radius of the circle with center $C$ can be expressed as $\\frac{p}{q}$. Deter... | MATH | {
"ground_truth": "3",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "fb4c5728-2eb3-40d4-8999-8acfa915029c"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 $26!^{26} + 27!^{27}$ is divided by $29$.\n\nRemember to put your answer on its own line after... | MATH | {
"ground_truth": "5",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "0afdae4e-2e85-4b13-8e37-537ac5e4e135"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 integer \\( a \\) greater than 14 such that a triangle with side lengths \\( a - 1 \\), \\( a \\)... | MATH | {
"ground_truth": "52",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "ae87d509-b0a5-4124-bda7-7432c234f53b"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 rhombus with sidelength $1$ has an inscribed circle with radius $\\frac{1}{3}$. If the area of the rhombus can be ex... | MATH | {
"ground_truth": "5",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "ac122479-3749-4fc7-8b9d-1ba976d9eb51"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nWhat is the largest integer $n$ with no repeated digits that is relatively prime to $6$? Note that two numbers are con... | MATH | {
"ground_truth": "987654301",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "8ac321a0-666a-4c46-a563-fb204ff2339c"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 $ABC$, we have $AB=36$, $BC=48$, and $CA=60$. The incircle of $\\triangle ABC$ is centered at $I$ and touc... | MATH | {
"ground_truth": "720",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "c60cede7-80b8-4aab-9afd-84c17fce6709"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 parallelogram. Let $E$ be the midpoint of $AB$ and $F$ be the midpoint of $CD$. Points $P$ and $Q$ are... | MATH | {
"ground_truth": "8",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "7a6bfa23-5a34-4fc1-b2c8-71c01653db0c"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 a hexagon with vertices labeled $M$, $M$, $A$, $T$, $H$, $S$ in that order. Clayton starts at the $M$ adjacen... | MATH | {
"ground_truth": "16",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "deb64353-8818-479a-b8b4-918ad957d979"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 $O$, $A$, $B$, and $C$ be points in space such that $\\angle AOB = 60^{\\circ}$, $\\angle BOC = 90^{\\circ}$, and ... | MATH | {
"ground_truth": "109",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "84716a12-fea6-4397-a311-eb2f624581a8"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 numbers of the form $1a1$, where $a$ is a digit. How many pairs of such numbers are there such that their sum... | MATH | {
"ground_truth": "30",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "d2466dc6-ec77-4e1f-a3f2-a9d3b82c3ae8"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 the smallest integer such that the sum of digits of $n$ is divisible by $5$, and the sum of digits of $(n+1... | MATH | {
"ground_truth": "49",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "f8493e11-0df9-468e-9b68-7e682b95dc0d"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nFind the largest two-digit number $N$ which is divisible by 4, such that all integral powers of $N$ end with $N$.\n\nR... | MATH | {
"ground_truth": "76",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "55e8d43e-4911-4aba-a70d-933eaf6af081"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nAidan rolls a pair of fair, six-sided dice. Let $n$ be the probability that the product of the two numbers on top is p... | MATH | {
"ground_truth": "7",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "51eeb376-40ac-4851-80a3-5f08dbf34d41"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 constant such that exactly three real values of $x$ satisfy $$x - |x^2 - 4x + 3| = k.$$ The sum of all po... | MATH | {
"ground_truth": "11",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "e68bee68-ebb8-45cf-b884-001ad0a12fd7"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 $x, y \\in \\mathbb{R}$ such that $x > 2, y > 3$. Find the minimum value of \\( \\frac{(x+y)^2}{\\sqrt{x^2-4} + \\... | MATH | {
"ground_truth": "10",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "8433a606-198a-467e-9b14-fd786b6dc761"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\n$p, q, r$ are real numbers satisfying the following equations: \n\\[ \\frac{(p+q)(q+r)(r+p)}{pqr} = 24 \\] \n\\[ \\f... | MATH | {
"ground_truth": "67",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "b14d7f0b-beca-4f94-9a25-9ae85e887f35"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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. When the leftmost digit of the standard base 10 representation of $n$ is shifted to the... | MATH | {
"ground_truth": "126",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "4768bf74-99f2-4e99-a9cd-0c0ac0eb33fe"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 real numbers $a$ and $b$ that satisfy the equations:\n\\[\na^4 + a^2b^2 + b^4 = 900,\n\\]\n\\[\na^2 + ab + b... | MATH | {
"ground_truth": "25",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "cc18ad6a-3203-437f-9c91-5e7822c4ee55"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 integer solutions exist that satisfy the equation?\n\n$$x + 4y - 343\\sqrt{x} - 686\\sqrt{y} + 4\\sqrt{xy} + ... | MATH | {
"ground_truth": "173",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "2187a1e2-4d8f-44bc-a54b-5c7676f426ce"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 non-negative integers $m > n$, let's say that $m$ ends in $n$ if we can obtain $n$ by erasing some digits (f... | MATH | {
"ground_truth": "103",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "a525e413-f13b-4832-8719-7a805bef7f31"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 sets of positive integers \\((a, b, c)\\) satisfy \\(a > b > c > 0\\) and \\(a + b + c = 103\\)?\n\nRemember ... | MATH | {
"ground_truth": "833",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "b8def60b-cde3-4670-95b9-28110cdcc822"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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$ with $AB=23$, $AC=27$, and $BC=20$, let $D$ be the foot of the $A$ altitude. Let $\\mathcal{P}$ be t... | MATH | {
"ground_truth": "96",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "2670f803-b3f5-4795-8e87-f8258fb15630"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 parallelogram such that $AB = 35$ and $BC = 28$. Suppose that $BD \\perp BC$. Let $\\ell_1$ be the ref... | MATH | {
"ground_truth": "113",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "b933d603-7e2e-4a1b-b877-7174d80161c1"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nWhat is the largest two-digit integer for which the product of its digits is $17$ more than their sum?\n\nRemember to ... | MATH | {
"ground_truth": "74",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "1faa31ad-d6d2-44e7-a12b-ccc8b0b465a2"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 unit cube $ABCDEFGH$ (with faces $ABCD$, $EFGH$ and connecting vertices labeled so that $\\overline{AE}$, $\\ov... | MATH | {
"ground_truth": "7",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "96123bc1-0bfe-4251-b196-f175130d1a8e"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nEight red boxes and eight blue boxes are randomly placed in four stacks of four boxes each. The probability that exact... | MATH | {
"ground_truth": "843",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "726bc673-305d-4381-9da2-28ebed210b8a"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 distinct four-letter arrangements can be formed by rearranging the letters found in the word **FLUFFY**? For ... | MATH | {
"ground_truth": "72",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "55e15ac5-cdd1-46a4-b2ef-ff7e319e4344"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 mason has bricks with dimensions $2 \\times 5 \\times 8$ and other bricks with dimensions $2 \\times 3 \\times 7$. S... | MATH | {
"ground_truth": "24",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "47110c14-6853-4f51-b9ba-69a9968b2ea1"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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\\}$ be a sequence of integers such that $a_1=2016$ and \\[\\frac{a_{n-1}+a_n}{2}=n^2-n+1\\] for all $n\\ge... | MATH | {
"ground_truth": "7986",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "38fd23b8-e07b-4d9b-a074-29a9dec1275d"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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=1$, $a_2=2^{a_1}$, $a_3=3^{a_2}$, $a_4=4^{a_3}$, \\dots, $a_9 = 9^{a_8}$. Find the last two digits of $a_9$.\... | MATH | {
"ground_truth": "21",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "50343bf9-a202-4e53-8ff4-4aaf54403036"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nSquare trinomial $f(x)$ is such that the polynomial $f(x)^5 - f(x)$ has exactly three real roots. Find the ordinate of... | MATH | {
"ground_truth": "0",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "a36dc33d-ce63-4348-9fe5-7662282d5294"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 following number is the product of the divisors of $n$:\n$$46,656,000,000$$\nWhat is $n$?\n\nRemember to put your ... | MATH | {
"ground_truth": "60",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "dae27980-55df-476a-ad07-5611cb4bdf86"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nDefine $\\{p_n\\}_{n=0}^\\infty\\subset\\mathbb{N}$ and $\\{q_n\\}_{n=0}^\\infty\\subset\\mathbb{N}$ to be sequences o... | MATH | {
"ground_truth": "17",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "abb405f3-e4d4-4514-a215-764c5f3d28c7"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 the number of functions $f: \\{1,2,3,4,5,6,7,8,9,10\\} \\rightarrow \\{1,2,3,4,5\\}$ that have the property... | MATH | {
"ground_truth": "31",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "a517605d-d83b-4f3b-8dba-94a230818bd1"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 3-term geometric sequences $a$, $b$, $c$ are there where $a$, $b$, and $c$ are positive integers with $a < b ... | MATH | {
"ground_truth": "39",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "f377341f-38e9-40ed-872e-85deb004e135"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nWhat is the largest number of points that can be arranged on a given circle such that in all the triangles they form, ... | MATH | {
"ground_truth": "7",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "0b42eed2-bcd3-4a94-9dfe-f69c5f2f9314"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 the positive integer with 1998 decimal digits, all of them 1; that is, \\[ N = 1111\\cdots 11. \\] Find the... | MATH | {
"ground_truth": "1",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "776eff90-260c-4375-b2f0-d0ee6a1d5d05"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 $BCDE$ be a trapezoid with $BE \\parallel CD$, $BE = 20$, $BC = 2\\sqrt{34}$, $CD = 8$, $DE = 2\\sqrt{10}$. Draw a... | MATH | {
"ground_truth": "203",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "3369807c-2f29-4157-9d65-dbf121f23616"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 $\\sum_{n=1}^{\\infty}\\frac{n + 1}{n^2(n + 2)^2}$.\n\nExpress your answer in simplest form as $\\frac{a}{b}$,... | MATH | {
"ground_truth": "21",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "97cb86a5-9189-41ca-83f4-26b0a0782eaa"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nLet $M$ be the set of all polynomials $P(x)$ with pairwise distinct integer roots, integer coefficients, and all absol... | MATH | {
"ground_truth": "9",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "6fc17680-0ead-448c-bc9d-43e53b789991"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 largest integer \\( N \\leq 2012 \\) with four distinct digits.\n\nRemember to put your answer on its own ... | MATH | {
"ground_truth": "1987",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "f7495acc-4413-4c6e-99e6-e3feae1b176b"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 competition room of HOMC has $m \\times n$ students where $m, n$ are integers larger than $2$. Their seats are arran... | MATH | {
"ground_truth": "18",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "3fca0e45-977e-40f2-8ba3-97e1c3e3d54c"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nPoints $A$ and $B$ are the endpoints of a diameter of a circle with center $C$. Points $D$ and $E$ lie on the same dia... | MATH | {
"ground_truth": "47",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "3b0aa3f3-39f6-43c4-addf-5b997353a4cf"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 Occidentalia, there are $20$ different companies, each looking to hire $15$ new employees. A group of $300$ applica... | MATH | {
"ground_truth": "20",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "ff4e529c-e361-4774-a741-f8aa8b0071fe"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 number $x$, let $\\lfloor x \\rfloor$ denote the integer part of $x$; $\\{ x \\}$ be the fractional part ... | MATH | {
"ground_truth": "21",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "5be0dd35-1dff-48a4-93ae-a3ba9abb8819"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 area of the largest square that can be inscribed in a regular hexagon with side length $1$ can be expressed as $a ... | MATH | {
"ground_truth": "21",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "8d20efff-a225-41e3-b66a-d39fbb2a1bae"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 geometric sequences $16$, $a_1$, $a_2$, $\\ldots$ and $56$, $b_1$, $b_2$, $\\ldots$ with the same common ... | MATH | {
"ground_truth": "490",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "b6cd15df-506e-457a-b97a-ce3e915c5b7b"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 integer solutions does the equation have:\n\\[ \\left\\lfloor \\frac{x}{10} \\right\\rfloor = \\left... | MATH | {
"ground_truth": "110",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "47e15d8b-5c71-46a9-9dbe-f661681feba5"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nDoes there exist a four-digit positive integer with different non-zero digits, which has the following property: if we... | MATH | {
"ground_truth": "1234",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "2ff633c6-2149-47e5-a470-208772180184"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nLet $B = (20, 14)$ and $C = (18, 0)$ be two points in the plane. For every line $\\ell$ passing through $B$, we color ... | MATH | {
"ground_truth": "157",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "2c557f8d-1f97-4480-a4cc-8e37b371b849"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 $5$ dogs, $4$ cats, and $7$ bowls of milk at an animal gathering. Dogs and cats are distinguishable, but all... | MATH | {
"ground_truth": "20",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "02eabf53-1a7d-4884-ba5b-6acc59d00d2c"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 monic cubic polynomial with \\( f(0) = -64 \\), and all roots of \\( f(x) \\) are non-negative r... | MATH | {
"ground_truth": "-125",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "18f35d93-4990-4a49-ac44-76d6324f2b2e"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 number is nine more than four times the answer to this question?\n\nRemember to put your answer on its own line a... | MATH | {
"ground_truth": "-3",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "55316e74-f625-493d-bf47-89cf2088ad91"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 are racing an Artificially Intelligent Robot, called Al, that you built. You can run at a constant speed of $10$ m... | MATH | {
"ground_truth": "210",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "4db14b96-b7f5-4c21-983c-17c2015de3e7"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 $a_n$ denote the remainder when $(n+1)^3$ is divided by $n^3$; in particular, $a_1=0$. Compute the remainder when ... | MATH | {
"ground_truth": "693",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "c37a0c3f-9467-4cfe-9896-28ae88ae991e"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 permute the letters $\\{S, C, R, A, M, B, L, E\\}$ without the permutation containing the s... | MATH | {
"ground_truth": "40200",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "9141ee19-67e6-4755-b8a0-90b737ceb2c5"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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\\( f \\) is a function whose domain is the set of nonnegative integers and whose range is contained in the set of non... | MATH | {
"ground_truth": "2015",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "aa8f3d32-6d91-4766-9925-82d2a5791598"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nFor all positive integers $n$, denote by $\\sigma(n)$ the sum of the positive divisors of $n$ and $\\nu_p(n)$ the larg... | MATH | {
"ground_truth": "8",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "7724a232-cc03-469c-b0a2-61556fba8b44"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nLet $x_n = 2^{2^n} + 1$ and let $m$ be the least common multiple of $x_2, x_3, \\ldots, x_{1971}$. Find the last digit... | MATH | {
"ground_truth": "9",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "938a0114-ebd7-4dd1-99f1-3056d4808d49"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nJuan makes a list of $2018$ numbers. The first number is $1$. Each subsequent number is obtained by adding one of the ... | MATH | {
"ground_truth": "17929",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "0a2bd050-c9cc-4296-893e-87a3c85b6b77"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 three-digit number that satisfies the following properties:\n- The hundreds digit and ones digit are the s... | MATH | {
"ground_truth": "171",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "66b42d2d-7f4f-40b0-8711-4f5027f9f284"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 grid below contains five rows with six points in each row. Points that are adjacent either horizontally or vertica... | MATH | {
"ground_truth": "14",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "6ea818cd-6301-4218-84a7-eadbf53b53e6"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 number of $8$-tuples $(\\epsilon_1, \\epsilon_2, \\ldots, \\epsilon_8)$ such that $\\epsilon_1, \\epsilo... | MATH | {
"ground_truth": "88",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "3f4aaa96-f027-45bb-af09-f1c75d19ca9c"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 regular hexagon $ABCDEF$, a point $X$ is marked on the diagonal $AD$ such that $\\angle AEX = 65^\\circ$. What ... | MATH | {
"ground_truth": "25",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "6502a46d-0521-4a79-91fe-c489d7fc88e8"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 cars travel along a circular track $n$ miles long, starting at the same point. One car travels $25$ miles along th... | MATH | {
"ground_truth": "89",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "33d1a4a2-c44f-4ff6-868e-4c3e81431229"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 positive integers $n$ such that the sum of all factors of $n$, including $1$ and $n$, is $12... | MATH | {
"ground_truth": "292",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "0b837b73-7a7d-4eb9-8962-35dde8db8cd4"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 Akbar and Birbal together have $n$ marbles, where $n > 0$. Akbar says to Birbal, \"If I give you some marbles then... | MATH | {
"ground_truth": "12",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "8b313ff9-0a61-4766-b733-9e0c19d2e5cc"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 $n \\ge 2$, define $k(n)$ to be the largest integer $m$ such that $(n!)^m$ divides $2016!$. ... | MATH | {
"ground_truth": "89",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "20b06d8d-8eb1-426d-8a34-8f82bd5a04d5"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 number consists of 3 different digits. The sum of the 5 other numbers formed with those digits is 2003. Find the num... | MATH | {
"ground_truth": "217",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "c1fd0bf3-3a7a-4878-9ed0-0b681acd8c5e"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nRthea, a distant planet, is home to creatures whose DNA consists of two distinguishable strands of bases with a fixed ... | MATH | {
"ground_truth": "28812",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "2517c249-d9de-47de-b421-8bb6c001635d"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nFind the largest positive integer $n$ such that the following equations have integer solutions in $x, y_1, y_2, \\ldot... | MATH | {
"ground_truth": "3",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "2e494bb2-b8a9-47ce-9f64-994c4f779b00"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 non-negative integers $k$ such that there exists a function $f : \\mathbb{N} \\to \\mathbb{N}$ satisfyin... | MATH | {
"ground_truth": "0",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "a5c6ec38-b653-4f04-be28-afbbd006b978"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 integers $x$, where $x \\ge 3$, such that $201020112012_x$ (interpreted as a base $x$ number) is d... | MATH | {
"ground_truth": "32",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "094afc70-7e81-49fe-8d2d-e8437f151cd0"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nFor how many triples of positive integers $(a, b, c)$ with $1 \\leq a, b, c \\leq 5$ is the quantity $(a+b)(a+c)(b+c)$... | MATH | {
"ground_truth": "48",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "6e27ecd7-7427-4db6-9309-2c3cb7dd03b3"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 $m$, $n$, $a$, and $k$ be positive integers with $k > 1$ such that the equation \\(5^m + 63n + 49 = a^k\\) holds. ... | MATH | {
"ground_truth": "5",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "d262fdb5-fe62-4672-8c41-0911442a9937"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 $f(x) = ax^2 + bx + c$ satisfies the following conditions:\n1. $f(\\sqrt{2}) = 3$\n2. $|f(x)| \\le 1$ for... | MATH | {
"ground_truth": "4025",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "5de2d909-9009-410d-8112-48474f238d72"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 $1, 2, \\ldots, n$ are written in order on a long slip of paper. The slip is then cut into five pieces, s... | MATH | {
"ground_truth": "2014",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "8ec5b0fa-b743-4cac-89f2-b77655e3b9d9"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 number of integral points on the circle with center $ (199, 0) $ and radius $ 199 $ is ________.\n\nRemember to pu... | MATH | {
"ground_truth": "4",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "d6e67622-980f-4b68-993e-f36a9da1a309"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 $x, y,$ and $z$ be nonnegative real numbers with $x+y+z=120$. Compute the largest possible value of the median of ... | MATH | {
"ground_truth": "160",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "d574a26c-e531-49b7-b834-63799c31b4e9"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nHow many ordered pairs $(a, b)$ of positive integers with $1 \\le a, b \\le 10$ are there such that in the geometric s... | MATH | {
"ground_truth": "33",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "771bf093-ae91-400a-82b0-9461e525133a"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 $\\triangle AEF$ be a triangle with $EF = 20$ and $AE = AF = 21$. Let $B$ and $D$ be points chosen on segments $AE... | MATH | {
"ground_truth": "5300",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "5faa79a9-9c9e-4279-aad9-5e86e1353d31"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nNumber $125$ is written as the sum of several pairwise distinct and relatively prime numbers, greater than $1$. What i... | MATH | {
"ground_truth": "8",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "7414c69c-a554-417e-adb9-f74169c3410e"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nInitially, a natural number $n$ is written on the blackboard. Then, at each minute, Neymar chooses a divisor $d > 1$ o... | MATH | {
"ground_truth": "2033",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "d5072f82-c725-4b26-82b0-1b3fb1a51cc5"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 positive integer $k$ is $2014$-ambiguous if the quadratics $x^2 + kx + 2014$ and $x^2 + kx - 2014$ both have two int... | MATH | {
"ground_truth": "0",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "507e162f-fe52-4adf-a93b-fa6a76af4ceb"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nJay is given $99$ stacks of blocks, such that the $i$th stack has $i^2$ blocks. Jay must choose a positive integer $N$... | MATH | {
"ground_truth": "4489",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "068d5aa3-0ddb-451d-9eff-a9dc491acc85"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nCompute the remainder when $10^{2021}$ is divided by $10101$.\n\nRemember to put your answer on its own line after \"A... | MATH | {
"ground_truth": "9091",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "aa5adf25-8b6d-4b93-8a63-ad1da9edffcd"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 ways to erase 24 letters from the string ``OMOMO\\cdots OMO'' (with length 27), such that the th... | MATH | {
"ground_truth": "455",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "085231ce-6743-4450-bdd0-38f5f364c4c9"
} |
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