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\nShrek throws $5$ balls into $5$ empty bins, where each ball’s target is chosen uniformly at random. After Shrek throws... | MATH | {
"ground_truth": "173",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "bc44ca43-4207-4970-b6a1-8f3465046484"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nLet $x$ be a real number such that $3 \\sin^4 x - 2 \\cos^6 x = -\\frac{17}{25}$. Then, $3 \\cos^4 x - 2 \\sin^6 x = \... | MATH | {
"ground_truth": "445",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "e92a511f-cff3-4e91-841b-8aa86b17b39b"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 answer to this question. What is the value of $2m - 5$?\n\nRemember to put your answer on its own line ... | MATH | {
"ground_truth": "5",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "632adb44-f0c5-48cc-9031-e344a5912de8"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 of two regular polygons $P$ and $Q$ was divided by a line into two parts. One part of $P$ was attached to one par... | MATH | {
"ground_truth": "12",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "07496eb4-77ce-42bc-835f-944494dec8d2"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 student walks down a hallway with a row of closed lockers numbered from $1$ to $1024$. He opens locker No. $1$, skip... | MATH | {
"ground_truth": "1024",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "d5e29cd7-03b1-432e-89a0-44ffda55e954"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 numbers $x$, $y$, and $z$ satisfy the following equality: \n\\[4(x+y+z) = x^2 + y^2 + z^2\\] \nLet $M$ be the max... | MATH | {
"ground_truth": "28",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "7783adb7-c6fd-490a-b4ca-667eb7599d6c"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 equation $ax^3 + bx^2 + cx + d = 0$ has three distinct solutions. How many distinct solutions does the following e... | MATH | {
"ground_truth": "2",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "14a383a2-3ea1-4509-984d-0e45e847599b"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nThere are $n$ players in a round-robin ping-pong tournament, meaning every two players will play exactly one game. Aft... | MATH | {
"ground_truth": "9",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "a6874e38-0c36-4399-ad09-f4eae26efcc9"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nHow many integers $n$ are there such that $0 \\le n \\le 720$ and $n^2 \\equiv 1 \\pmod{720}$?\n\nRemember to put your... | MATH | {
"ground_truth": "16",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "35f34bb2-936a-4967-b858-d85a727fc298"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\n12. In a rectangle $ABCD$ with $AB = 8$ and $BC = 20$, let $P$ be a point on $AD$ such that $\\angle BPC = 90^\\circ$.... | MATH | {
"ground_truth": "8",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "7f3ee2e1-9423-4988-8b94-73a5910a200a"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nJoey wrote a system of equations on a blackboard, where each of the equations was of the form $a + b = c$ or $a \\cdot... | MATH | {
"ground_truth": "2037",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "dbf42675-27f6-419c-ab95-0b018446c43f"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 quadrilateral $ABCD$ has a right angle at $\\angle ABC$ and satisfies $AB = 12$, $BC = 9$, $CD = 20$, and $DA = 25$.... | MATH | {
"ground_truth": "769",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "45670f80-fbb5-4487-a960-cf7c66b64b08"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 is called *purple* if it can be expressed in the form $\\frac{1}{2^a 5^b}$ for positive integers $a > b$. The... | MATH | {
"ground_truth": "109",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "d6b38688-a76d-4642-8168-38c7b788bab9"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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. Determine the smallest possible value of $1 - n + n^2 - n^3 + \\dots + n^{1000}$.\n\nRe... | MATH | {
"ground_truth": "1",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "6c449acc-54cc-423f-aa4c-6abbceba0091"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 $x_1, x_2, \\dots, x_n$ be a sequence of integers such that $-1 \\leq x_i \\leq 2$ for $i = 1, 2, \\dots, n$. It i... | MATH | {
"ground_truth": "511",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "56a6e6e2-a71e-426b-aa52-ed9d21fabfce"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nThere is a row of $100$ cells, each containing a token. For $1$ dollar, it is allowed to interchange two neighboring t... | MATH | {
"ground_truth": "50",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "6e43eded-e00a-4bfb-86af-3eb6feef4e48"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 sequence $1, 2, 1, 2, 2, 1, 2, 2, 2, 1, 2, 2, 2, 2, 1, \\ldots$ Find $n$ such that the first $n$ terms su... | MATH | {
"ground_truth": "1027",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "ccd690ef-5c10-4e42-afb2-78a3497630aa"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 $a, b$ be two real numbers such that \\(\\sqrt[3]{a} - \\sqrt[3]{b} = 10\\) and \\(ab = \\left( \\frac{8 - a - b}{... | MATH | {
"ground_truth": "280",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "7ca76152-5b41-40f0-b2c0-73fe9e80b38f"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 initial number of inhabitants in a city, which is greater than 150, is a perfect square. With an increase of 1000 ... | MATH | {
"ground_truth": "249001",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "547c9234-bb64-415f-9315-898bdb65ff52"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 $2018$ ones in a row: $$\\underbrace{1\\,\\,\\,1\\,\\,\\,1\\,\\,\\,1 \\,\\,\\, ... \\,\\,\\,1 \\,\\,\\,1 \\,\\,\... | MATH | {
"ground_truth": "1991",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "541d6bd3-338b-48b2-89ca-d9ec5829a185"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 multiples of $12$ divide $12!$ and have exactly $12$ divisors?\n\nRemember to put your answer on its own line... | MATH | {
"ground_truth": "6",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "dee9b4f2-d2a3-417d-894f-10cce6c5dd55"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nFreddy, the king of flavortext, has an infinite chest of coins. For each number \\( p \\) in the interval \\([0, 1]\\)... | MATH | {
"ground_truth": "23",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "6b3aaeeb-949a-4a05-8e5d-0d301b07711f"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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. Schwartz has been hired to paint a row of 7 houses. Each house must be painted red, blue, or green. However, to ma... | MATH | {
"ground_truth": "1344",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "6a2ed796-50e4-4ef2-b0c8-84640ba5291e"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 addition problems in which a two-digit number is added to a second two-digit number to give a two-d... | MATH | {
"ground_truth": "3240",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "2accfb0b-e1b5-406a-a15d-65035912f505"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 integer $n$ such that:\n\\[\nn + \\lfloor \\sqrt{n} \\rfloor + \\lfloor \\sqrt{\\sqrt{n}} \\rfloor = 2017.\\]... | MATH | {
"ground_truth": "1967",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "9f93c1d8-208d-4d28-9a0b-737ee5cb68c5"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nRight triangle $ABC$ has hypotenuse $AB = 26$, and the inscribed circle of $\\triangle ABC$ has radius $5$. The larges... | MATH | {
"ground_truth": "1814",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "86380144-70d1-40df-a20b-a8baf6561518"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 fair six-sided dice are labeled with the numbers $\\{1, 2, 3, 4, 5, 6\\},$ $\\{1, 2, 3, 4, 5, 6\\},$ and $\\{1, ... | MATH | {
"ground_truth": "1136",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "78cb00bf-3f21-4218-95a2-198e0cd52701"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nLet $a, b, c, d$ be natural numbers such that $a + b + c + d = 2018$. Find the minimum value of the expression:\n$$E =... | MATH | {
"ground_truth": "14",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "de54844a-5236-42a4-a79a-a73f0844a770"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 incenter $I$ and $AB = 1400$, $AC = 1800$, $BC = 2014$. The circle centered at $I$ passin... | MATH | {
"ground_truth": "1186",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "d6ee3a69-827e-4fce-b0d0-636b525bbb74"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 several teacups in the kitchen, some with handles and others without handles. The number of ways to select t... | MATH | {
"ground_truth": "29",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "72f6c4b9-7ebc-4dad-a06b-e7313f3542ca"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nFind the number of pairs of integer solutions \\((x,y)\\) that satisfy the equation:\n\\[\n(x-y+2)(x-y-2) = -(x-2)(y-2... | MATH | {
"ground_truth": "6",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "e65d7a10-534c-4002-8b2e-bffe0b310f82"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 smallest integer $n \\geq 4$ such that $\\binom{n}{4}$ ends in 4 or more zeroes (i.e., the rightmost four ... | MATH | {
"ground_truth": "8128",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "425754ab-c453-46c3-bcca-fe9857252263"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 $k$ such that there exist positive integers $a$ and $b$ satisfying the equation:\n\\[\na^2 ... | MATH | {
"ground_truth": "3",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "a8c414e5-c522-49d6-a1af-2afcb37e3ddc"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 prime. It is given that there exists a unique nonconstant function $\\chi:\\{1,2,\\ldots, p-1\\}\\to\\{-1... | MATH | {
"ground_truth": "24",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "70c381e5-fcd2-4c83-ad14-dfc5483a2377"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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’s the smallest integer $n>1$ such that $p \\mid \\left(n^{p-1}-1\\right)$ for all integers $2 \\leq p \\leq 10?$\... | MATH | {
"ground_truth": "361",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "17124f53-c3a8-4558-8b70-df4294b86ebd"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 real solutions for $x$ to the equation $(x^2 + 2x + 3)^{(x^2+2x+3)^{(x^2+2x+3)}} = 2012$.\n\nRemem... | MATH | {
"ground_truth": "-2",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "a66d12a0-6484-4c06-b5d6-ba3d0e7fd4ed"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 select a real number $\\alpha$ uniformly and at random from the interval $(0,500)$. Define \n\\[ S = \\frac{1}{\\al... | MATH | {
"ground_truth": "5",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "de42cd88-9524-402f-b378-83cf904efd97"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nFind the number of pairs of integers $x, y$ with different parities such that $\\frac{1}{x} + \\frac{1}{y} = \\frac{1}... | MATH | {
"ground_truth": "90",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "b35f3961-1b3d-46e6-99de-9e3360d4aacb"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nCircles $C_1$, $C_2$, $C_3$ have radius $1$ and centers $O$, $P$, $Q$ respectively. $C_1$ and $C_2$ intersect at $A$, ... | MATH | {
"ground_truth": "12",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "5348c051-c8a4-4a36-ad4a-97cb1c6c0b53"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 what positive integer $k$ is $\\binom{100}{k} \\binom{200}{k}$ maximal?\n\nRemember to put your answer on its own ... | MATH | {
"ground_truth": "67",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "a0044427-2691-4354-add8-d10e674acf3d"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 sequence of eleven squares with side lengths $3, 6, 9, 12, \\ldots, 33$. Eleven copies of a single square, ... | MATH | {
"ground_truth": "414",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "3935f7ba-e09c-4018-9183-b3938936ea09"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 vertices of a parallelogram are \\((2, -4), (-2, 8),\\) and \\((12, 7)\\). Determine the sum of the three possib... | MATH | {
"ground_truth": "12",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "29020bc3-07f0-4507-bc72-4ad37c1190c9"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 $\\odot$ be a binary operation on the natural numbers satisfying the properties that, for all $a, b,$ and $c$, $(a... | MATH | {
"ground_truth": "896",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "b350b871-9d23-43bc-b198-1315f17963b5"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 $v$ and $w$ be real numbers such that, for all real numbers $a$ and $b$, the inequality \\[(2^{a+b}+8)(3^a+3^b) \\... | MATH | {
"ground_truth": "62208",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "e7f2d5bd-cd8a-47da-b4d9-5bbe32bd9d85"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 $\\lfloor \\sqrt{19992000} \\rfloor$ where $\\lfloor x \\rfloor$ denotes the greatest integer less than or equal ... | MATH | {
"ground_truth": "4471",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "cc757dcb-3e0f-41e2-8cea-1a9c474307f2"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nPoint $A$ lies on the circumference of a circle $\\Omega$ with radius $78$. Point $B$ is placed such that $AB$ is tang... | MATH | {
"ground_truth": "60",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "a5f4eabc-c4de-42a0-b5a2-d4a3e6497c6d"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 all positive integers $N$ for which there exists a unique ordered triple of non-negative integers $... | MATH | {
"ground_truth": "280",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "6deb8132-69a9-4240-875b-2312ba2857d7"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 a *growing spiral* in the plane as a sequence of points with integer coordinates $P_0=(0,0), P_1, \\dots, P_n$ ... | MATH | {
"ground_truth": "10053",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "e374ad54-2f00-4cbe-86d4-cf754fd1b5ab"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 the answer as an integer.\n\nRemember to ... | MATH | {
"ground_truth": "11221",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "faed6b40-be89-4a38-b838-cd3cbbfab1ab"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 integer $n$ such that $n$ is divisible by all positive integers less than $\\sqrt[3]{n}$.\n\nRemember... | MATH | {
"ground_truth": "420",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "9ef48e83-e0ff-4d77-af65-b9ebba9299c8"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 $AB = AC$. Point $D$ is on side $\\overline{BC}$ so that $AD = CD$ and $\\angle BAD = 36^\\circ$. F... | MATH | {
"ground_truth": "84",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "312dd1da-8a6b-461c-8edc-3f47127532f8"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 $m$ and $n$ are relatively prime positive integers with $A = \\frac{m}{n}$, where\n\\[ A = \\frac{2+4+6+\... | MATH | {
"ground_truth": "2015",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "b1b9da69-5ef8-4cc8-b8de-36dc3bbd22c4"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 $U, S, M, C, A$ are distinct (not necessarily positive) integers such that $U \\cdot S \\cdot M \\cdot C \\cdot A =... | MATH | {
"ground_truth": "505",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "428449d3-6072-43da-9dcd-85ab2cde8858"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 maximal number of crosses that can fit in a $10 \\times 11$ board without overlapping?\n\nRemember to put ... | MATH | {
"ground_truth": "14",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "c8798ad8-e3cb-4763-8606-236a6714a3d1"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nLet $a$ be a real number greater than $1$ such that $\\frac{20a}{a^2+1} = \\sqrt{2}$. Find $\\frac{14a}{a^2 - 1}$.\n\n... | MATH | {
"ground_truth": "1",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "81480b4b-9805-4a7f-be1e-c000c941d9f7"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 given that \\(17! = 355687ab8096000\\) for some digits \\(a\\) and \\(b\\). Find the two-digit number \\(\\ove... | MATH | {
"ground_truth": "42",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "f314bcff-7829-4820-aac6-b2bf78576e75"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nFind the least positive integer such that the product of its digits is $8! = 8 \\times 7 \\times 6 \\times 5 \\times 4... | MATH | {
"ground_truth": "257889",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "e4ac552f-36b9-4dd3-87f3-e90ba85c99c5"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 equilateral triangle. Denote by $D$ the midpoint of $\\overline{BC}$, and denote the circle with diame... | MATH | {
"ground_truth": "80",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "9448511b-92b5-46dd-ad1f-dae79be354cb"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 $f(x) = x^4 - 4x^3 - 3x^2 - 4x + 1$. Compute the sum of the real roots of $f(x)$.\n\nRemember to put your answer o... | MATH | {
"ground_truth": "5",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "c70c7776-3a6c-4b70-9bc2-9707ea04f440"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nDarwin takes an $11 \\times 11$ grid of lattice points and connects every pair of points that are 1 unit apart, creati... | MATH | {
"ground_truth": "220",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "bc2c01c7-f272-4b9e-93d3-2f6d1a5a7589"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 $A$ denote the perimeter and area respectively of a right triangle with relatively prime integer side-leng... | MATH | {
"ground_truth": "45",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "273c3c42-8d1c-4138-a586-2a0dcee683e0"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 given a rectangular playing field of size $13 \\times 2$ and any number of dominoes of sizes $2 \\times 1$ and... | MATH | {
"ground_truth": "257",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "eef42db7-9954-4599-92ef-15eb020e0ac7"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 real numbers $x$ and $y$, define \\[ \\nabla(x,y)=x-\\frac{1}{y}. \\] If \\[ \\underbrace{\\nabla(2, \\nabla(2, \\... | MATH | {
"ground_truth": "203817",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "d0a7534c-57a5-4caf-a727-aa8c53d36b5b"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 real number $a$, define two parabolas on the coordinate plane with equations $x = y^2 + a$ and $y = x^2 + a$.... | MATH | {
"ground_truth": "91",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "eb833f5b-d1c1-45f3-84d5-c1d86c0d7504"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 mathletes and two coaches sit at a circular table. How many distinct arrangements are there of these six people i... | MATH | {
"ground_truth": "24",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "14188476-40d4-40e7-b278-3d0badf0bc59"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nAlice and Bob play a game together as a team on a $100 \\times 100$ board with all unit squares initially white. Alice... | MATH | {
"ground_truth": "100",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "b0805706-6161-4537-b545-61ca4b3b76ba"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nTwo points $A$ and $B$ are randomly chosen on a circle with a radius of $100$. For a positive integer $x$, denote $P(x... | MATH | {
"ground_truth": "174",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "8153d39f-7925-40c3-be8d-3a7a62d210ca"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 have a calculator with two buttons that displays an integer $x$. Pressing the first button replaces $x$ by $\\lfloo... | MATH | {
"ground_truth": "233",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "6e21235e-2269-4542-9a8a-9bfed02140fe"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nFind the sum of the two smallest possible values of $x^\\circ$ (in degrees) that satisfy the following equation if $x$... | MATH | {
"ground_truth": "4064",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "c372612f-3948-4803-af00-90a855ee4fa3"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 the smallest positive integer such that the binomial coefficient $\\binom{10^9}{k}$ is less than the binomi... | MATH | {
"ground_truth": "38",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "e94a1ddb-a2e8-4632-be51-cdf049d2fed1"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 $f(n) = \\frac{n}{3}$ if $n$ is divisible by $3$, and $f(n) = 4n - 10$ otherwise. Find the sum of all positive int... | MATH | {
"ground_truth": "748",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "16e8cd82-b7ed-4384-aa25-58973a11a729"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 and B are friends at a summer school. When B asks A for his address, he answers: \"My house is on XYZ street, and my... | MATH | {
"ground_truth": "425",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "e6f96fad-87ce-4b96-b113-f0a423e394c7"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nFreddy the Frog is situated at 1 on an infinitely long number line. On day $n$, where $n \\ge 1$, Freddy can choose to... | MATH | {
"ground_truth": "6423",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "16e91a7f-d3f3-4a74-bcea-5b0421c058f9"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 $ABC$, angle $B$ is obtuse and equal to $a$. The bisectors of angles $A$ and $C$ intersect the opposite si... | MATH | {
"ground_truth": "90",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "7e793d09-5656-4fff-a2f0-5ff68f1ca6f4"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 tetrahedron has four congruent faces, each of which is a triangle with side lengths $6$, $5$, and $5$. If the volume... | MATH | {
"ground_truth": "252",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "6ce072d3-dff4-4fe8-a121-5a8df3362f38"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 rational numbers $x < y < z$ sum to $1$ and satisfy the equation:\n\\[ (x^2 + y^2 + z^2 - 1)^3 + 8xyz = 0. \\... | MATH | {
"ground_truth": "999",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "901dfc27-5cd8-495a-8938-e714261ffc0e"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 disk with radius $10$ and a disk with radius $8$ are drawn such that the distance between their centers is $3$. Two ... | MATH | {
"ground_truth": "19",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "6a55e03b-beb9-426b-83e6-7450581f6945"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 $n$ that has at least $7$ positive divisors $1 = d_1 < d_2 < \\ldots < d_k = n$, $k... | MATH | {
"ground_truth": "2024",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "140e38b8-0ce5-4cb3-a51d-15d7e3a1273d"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 a search algorithm called $\\texttt{powSearch}$. Assume $A$ is a 1-indexed sorted array of distinct integers. T... | MATH | {
"ground_truth": "808",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "f9ea83ad-231e-4fac-8b47-1aef6ff629f6"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 sequence of digits \\(1 2 3 4 5 6 7 8 9 1 0 1 1 1 2 1 3 1 4 1 5 1 6 1 7 1 8 1 9 2 0 2 1 \\dots\\) is obtained by w... | MATH | {
"ground_truth": "1984",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "74689d07-29e8-4990-9c34-a021aaa2b151"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nBill draws two circles which intersect at $X,Y$. Let $P$ be the intersection of the common tangents to the two circles... | MATH | {
"ground_truth": "4807",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "8f360b61-a462-4a85-9b66-25208c95ce0d"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 $m$ and $n$, let $r(m, n)$ be the remainder when $m$ is divided by $n$. Find the smallest positi... | MATH | {
"ground_truth": "120",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "a2091e81-4f8e-4632-8c8e-1f5f0d1b59e8"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 $ABCD$ satisfies the following conditions: \n- $AB = 8$, \n- $BC = 5$, \n- $CD = 17$, \n- $DA = 10$. \n\... | MATH | {
"ground_truth": "60",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "a19c02a6-5c65-4f50-9373-478fd81fbefc"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nA polynomial $p(x)$ of degree $1000$ is such that $p(n) = (n+1)2^n$ for all nonnegative integers $n$ such that $n \\le... | MATH | {
"ground_truth": "500",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "a6691c42-3e14-48bc-ac62-e7ec5ac450d2"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 $f_1(x) = x^2 - 1$, and for each positive integer $n \\geq 2$, define $f_n(x) = f_{n-1}(f_1(x))$. How many distinc... | MATH | {
"ground_truth": "2005",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "1ce29bc5-0b4a-4e4e-b36b-425e553ebe1f"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\n30 segments of lengths $1, \\sqrt{3}, \\sqrt{5}, \\sqrt{7}, \\sqrt{9}, \\ldots, \\sqrt{59}$ have been drawn on a black... | MATH | {
"ground_truth": "30",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "4712705f-341d-4cad-a675-7644adcad7dd"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 large number of rocks are placed on a table. On each turn, one may remove some rocks from the table following these ... | MATH | {
"ground_truth": "18",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "ee436e60-dc6d-499d-a0ce-a22cf4711a5a"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nAt a movie theater, tickets for adults cost $4 more than tickets for children. One afternoon, the theater sold $100 mo... | MATH | {
"ground_truth": "1875",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "0e2d5997-4fa4-43d1-acd3-218b6099959d"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nAt a party, every guest is a friend of exactly fourteen other guests (not including themselves). Every two friends hav... | MATH | {
"ground_truth": "64",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "35aea490-8082-4ab7-bad7-a4a6806699e3"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nIn a right trapezoid $ABCD$ where $AB \\parallel CD$, the angle at vertex $B$ measures $75^\\circ$. Point $H$ is the f... | MATH | {
"ground_truth": "8",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "0d77c77b-437c-4fc2-8045-6fa27144265a"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 the digits in the decimal representations of all the positive integers less than $1000$.\n\nRememb... | MATH | {
"ground_truth": "13500",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "6e01398b-c78b-4091-9759-90caeaa440b1"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 $f(x) = (x^4 + 2x^3 + 4x^2 + 2x + 1)^5$. Compute the prime $p$ satisfying $f(p) = 418,195,493$.\n\nRemember to put... | MATH | {
"ground_truth": "2",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "980cb875-0e90-4471-8781-bc27e7760ebf"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 the parabola in the plane determined by the equation $y = x^2$. Suppose a circle $C$ in the plane intersect... | MATH | {
"ground_truth": "1247",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "6caa45cc-6db8-4051-ad5d-43044d1937c0"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 $5$-digit numbers $N$ (in base $10$) contain no digits greater than $3$ and satisfy the equality $\\gcd(N,15)... | MATH | {
"ground_truth": "256",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "a854c341-0ac3-41e6-bbc8-c5d87226b71b"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 $a = \\sqrt[401]{4} - 1$ and for each $n \\ge 2$, let $b_n = \\binom{n}{1} + \\binom{n}{2} a + \\ldots + \\binom{n... | MATH | {
"ground_truth": "1024",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "258ab714-2b85-460f-8aae-8a625fdb3feb"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nDilhan has objects of 3 types: $A$, $B$, and $C$. He also has 6 functions: $f_{A,B}$, $f_{A,C}$, $f_{B,A}$, $f_{B,C}$,... | MATH | {
"ground_truth": "18",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "c45c978d-2bb8-41a0-a624-10cb0ca9eb7a"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 $x$ is a random real number between $1$ and $4$, and $y$ is a random real number between $1$ and $9$. If the e... | MATH | {
"ground_truth": "1112",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "de8bd559-0c03-48e7-bb1a-c6bde6f1883a"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 $\\alpha, \\beta$ be the distinct positive roots of the equation $2x = \\tan x$. Evaluate the integral:\n\n$$\\int... | MATH | {
"ground_truth": "0",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "6a400259-7217-42f9-8840-ec7e73148897"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 5040 balls in \\(k\\) different colors, where the number of balls of each color is the same. The balls ar... | MATH | {
"ground_truth": "6",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "801c48c5-bc16-4fef-8166-7d97c4ff4023"
} |
math_dapo | [
{
"content": "Solve the following math problem step by step. 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 $2008 \\times 2009$ rectangle is divided into unit squares. In how many ways can you remove a pair of squares such t... | MATH | {
"ground_truth": "4068434225296",
"style": "rule-lighteval/MATH_v2"
} | {
"index": "6af8f3f6-16c8-4c2a-b247-95724102f1c2"
} |
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