messages listlengths 1 1 | label stringlengths 1 23 | metadata dict | data_source stringclasses 1
value |
|---|---|---|---|
[
{
"content": "Solve the following math problem step by step. 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 = \\sum_{a_1 = 0}^2 \\sum_{a_2 = 0}^{a_1} \\sum_{a_3 = 0}^{a_2} \\dots \\sum_{a_{2011} = 0}^{a_{2010}} \\lef... | 95 | {
"ability": "MATH",
"data_source": "math_dapo",
"extra_info": {
"index": "c7f8213f-5ba1-460b-b871-b02469ef5ad3"
}
} | math_dapo |
[
{
"content": "Solve the following math problem step by step. 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 $100$th digit after the decimal point when $\\frac{3}{26}$ is expressed as a decimal?\n\nRemember to put y... | 3 | {
"ability": "MATH",
"data_source": "math_dapo",
"extra_info": {
"index": "0ae65275-475e-406e-b286-9fd32ef3c8e7"
}
} | math_dapo |
[
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nAn integer between $1000$ and $9999$, inclusive, is chosen at random. Find the probability that it is an odd integer w... | 281 | {
"ability": "MATH",
"data_source": "math_dapo",
"extra_info": {
"index": "5b404910-748d-47b7-a683-eb44589835ca"
}
} | math_dapo |
[
{
"content": "Solve the following math problem step by step. 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若 $A, B, C \\subseteq\\{1,2,3, \\cdots, 2020\\}, A \\subseteq C, B \\subseteq C$ ，求有序集合组 $(A, B, C)$ 的组数。原始答案的形式为 $k^m... | 2025 | {
"ability": "MATH",
"data_source": "math_dapo",
"extra_info": {
"index": "280a99c0-bfce-4772-b0bd-3a223c538bcd"
}
} | math_dapo |
[
{
"content": "Solve the following math problem step by step. 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 $(a_n)$ is defined recursively by $a_0=1$, $a_1=\\sqrt[19]{2}$, and $a_n=a_{n-1}a_{n-2}^2$ for $n \\ge 2$... | 17 | {
"ability": "MATH",
"data_source": "math_dapo",
"extra_info": {
"index": "0840f30b-ff40-4dca-8450-f350e343db2c"
}
} | math_dapo |
[
{
"content": "Solve the following math problem step by step. 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在平面直角坐标系 $x O y$ 中, 两圆均经过点 $(1,1)$, 且与直线 $y=\\frac{4}{3} x$ 及 $x$ 轴均相切.则该两圆的半径之和为 _____.原始的答案是\\frac{m}{n}的形式，其中m、n是互质... | 5 | {
"ability": "MATH",
"data_source": "math_dapo",
"extra_info": {
"index": "78b20366-3b34-4120-b4dd-6f47a1a9fc4c"
}
} | math_dapo |
[
{
"content": "Solve the following math problem step by step. 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 adjoining figure shows two intersecting chords in a circle, with $B$ on minor arc $AD$. Suppose that the radius of... | 175 | {
"ability": "MATH",
"data_source": "math_dapo",
"extra_info": {
"index": "496b2a3b-a57d-41a1-829c-5c3544996213"
}
} | math_dapo |
[
{
"content": "Solve the following math problem step by step. 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 collection of 8 cubes consists of one cube with edge-length $k$ for each integer $k, 1 \\le k \\le 8.$ A tower is to... | 458 | {
"ability": "MATH",
"data_source": "math_dapo",
"extra_info": {
"index": "95c6cef5-719b-48d9-a324-ac191d53ec9f"
}
} | math_dapo |
[
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nAn integer-valued function $f$ is called tenuous if $f(x) + f(y) > y^2$ for all positive integers $x$ and $y.$ Let $g... | 136 | {
"ability": "MATH",
"data_source": "math_dapo",
"extra_info": {
"index": "c8d40ede-9e08-42e7-96ed-7d31101fb813"
}
} | math_dapo |
[
{
"content": "Solve the following math problem step by step. 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设正四棱柱 $A B C D-A_{1} B_{1} C_{1} D_{1}$ 的底面 $A B C D$ 是单位正方形, 如果二面角 $A_{1}-B D-C_{1}$ 的大小是 $\\frac{\\pi}{3}$, 则 $A A_{... | 8 | {
"ability": "MATH",
"data_source": "math_dapo",
"extra_info": {
"index": "3ecb142e-7113-46f0-8cca-64e53091ae4b"
}
} | math_dapo |
[
{
"content": "Solve the following math problem step by step. 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 $C$ denote the curve $y^2 = \\frac{x(x+1)(2x+1)}{6}$. The points $(\\frac{1}{2}, a)$, $(b, c)$, and $(24, d)$ lie ... | 101 | {
"ability": "MATH",
"data_source": "math_dapo",
"extra_info": {
"index": "2daa464a-dd55-43d4-bffd-4d53ac8bd78f"
}
} | math_dapo |
[
{
"content": "Solve the following math problem step by step. 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 5-digit numbers that each contains the block '15' and is divisible by 15.\n\nRemember to put your a... | 479 | {
"ability": "MATH",
"data_source": "math_dapo",
"extra_info": {
"index": "b9a6c30d-694e-4135-b823-7c8d97710010"
}
} | math_dapo |
[
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nVernonia High School has 85 seniors, each of whom plays on at least one of the school’s three varsity sports teams: fo... | 11 | {
"ability": "MATH",
"data_source": "math_dapo",
"extra_info": {
"index": "8f264a19-7e74-4b7b-9786-a0721b37d569"
}
} | math_dapo |
[
{
"content": "Solve the following math problem step by step. 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 four-digit integers $abcd$, with $a \\neq 0$, have the property that the three two-digit integers $ab<bc<cd$ ... | 17 | {
"ability": "MATH",
"data_source": "math_dapo",
"extra_info": {
"index": "03114c0c-b326-42a8-9c79-4e0e9facea3d"
}
} | math_dapo |
[
{
"content": "Solve the following math problem step by step. 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 $\\star (x)$ be the sum of the digits of a positive integer $x$. $\\mathcal{S}$ is the set of positive integers su... | 26 | {
"ability": "MATH",
"data_source": "math_dapo",
"extra_info": {
"index": "c6f50096-f437-450b-813c-4838bf16326b"
}
} | math_dapo |
[
{
"content": "Solve the following math problem step by step. 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给定整数 $n \\geqslant 3$ 。求最小的正整数 $k$, 使得存在一个 $k$ 元集合 $A$ 和 $n$ 个两两不同的实数 $x_{1}, x_{2}, \\cdots, x_{n}$, 满足 $x_{1}+x_{2},... | 3 | {
"ability": "MATH",
"data_source": "math_dapo",
"extra_info": {
"index": "b6eb4a0f-9da4-47bb-85b8-fe9ba5056f5a"
}
} | math_dapo |
[
{
"content": "Solve the following math problem step by step. 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 $n$, consider the highest common factor $h_n$ of the two numbers $n! + 1$ and $(n+1)!$. For ... | 97 | {
"ability": "MATH",
"data_source": "math_dapo",
"extra_info": {
"index": "2365020b-e688-45fd-8fa7-17793a699183"
}
} | math_dapo |
[
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nFind the smallest positive integer $n$ such that for every integer $m$,\nwith $0<m<1993$, there exists an integer $k$ ... | 3987 | {
"ability": "MATH",
"data_source": "math_dapo",
"extra_info": {
"index": "aae87b1f-d91b-40be-b94f-657c8bf77d08"
}
} | math_dapo |
[
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nEmma's calculator has ten buttons: one for each digit $1, 2, \\ldots, 9$, and one marked \"clear\". When Emma presses ... | 6642902 | {
"ability": "MATH",
"data_source": "math_dapo",
"extra_info": {
"index": "5863aff8-d08e-4e14-bf4e-4531fc996482"
}
} | math_dapo |
[
{
"content": "Solve the following math problem step by step. 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 product \\(8 \\times 0.25 \\times 2 \\times 0.125\\). Provide your answer in the form of \\(\\frac{k}{m}... | 3 | {
"ability": "MATH",
"data_source": "math_dapo",
"extra_info": {
"index": "73af046a-81c5-429a-829c-38625150641f"
}
} | math_dapo |
[
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nKelvin and $15$ other frogs are in a meeting, for a total of $16$ frogs. During the meeting, each pair of distinct fro... | 1167 | {
"ability": "MATH",
"data_source": "math_dapo",
"extra_info": {
"index": "e98866f7-0de1-49c9-ada3-3765ee8b4757"
}
} | math_dapo |
[
{
"content": "Solve the following math problem step by step. 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 graph of \\( (x^2 + y^2 - 1)^3 = x^2 y^3 \\) is a heart-shaped curve. \n\nFor how many ordered pairs of integers \... | 7 | {
"ability": "MATH",
"data_source": "math_dapo",
"extra_info": {
"index": "d569de2c-f26a-4e1b-8b31-71495d35a576"
}
} | math_dapo |
[
{
"content": "Solve the following math problem step by step. 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\\[ a^2... | 1 | {
"ability": "MATH",
"data_source": "math_dapo",
"extra_info": {
"index": "a7844f84-46d1-4b16-bdc8-22c35457cd8d"
}
} | math_dapo |
[
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nLet $x, y, z$ be real numbers such that $x+y+z=-2$ and\n\\[\n(x^2+xy+y^2)(y^2+yz+z^2) + (y^2+yz+z^2)(z^2+zx+x^2) + (z^... | 14 | {
"ability": "MATH",
"data_source": "math_dapo",
"extra_info": {
"index": "0a3a7cc1-21b8-43d2-98a2-4058e934c814"
}
} | math_dapo |
[
{
"content": "Solve the following math problem step by step. 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设集合 T=\\{1,2,\\cdots,8\\}. 对 T 的非空子集 A，用 S(A) 表示 A 中所有元素的和. 问：T 有多少个非空子集 A，使得 S(A) 是 3 的倍数，但不是 5 的倍数？\n\nRemember to p... | 70 | {
"ability": "MATH",
"data_source": "math_dapo",
"extra_info": {
"index": "f164ec92-2ffe-4032-b58a-d25cede0b5ae"
}
} | math_dapo |
[
{
"content": "Solve the following math problem step by step. 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 real numbers such that\n\\[\\frac{\\sin x}{\\cos y} + \\frac{\\sin y}{\\cos x} = 1 \\quad \\text{an... | 137 | {
"ability": "MATH",
"data_source": "math_dapo",
"extra_info": {
"index": "b5a57d80-7870-47bc-9404-1b3a5bad12e9"
}
} | math_dapo |
[
{
"content": "Solve the following math problem step by step. 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设函数 $f(x)=\\frac{x^{2}+x+16}{x}(2 \\leq x \\leq a)$, 其中实数 $a>2$. 若 $f(x)$ 的值域为 $[9,11]$, 请给出 $a$ 的取值范围端点的和。\n\nRemembe... | 12 | {
"ability": "MATH",
"data_source": "math_dapo",
"extra_info": {
"index": "fdbd4b29-11c2-43a7-bd54-8925f24ca9c0"
}
} | math_dapo |
[
{
"content": "Solve the following math problem step by step. 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 such that angle $C$ is obtuse. Let $D \\in [AB]$ and $[DC] \\perp [BC]$. If $m(\\widehat{ABC})... | 20 | {
"ability": "MATH",
"data_source": "math_dapo",
"extra_info": {
"index": "cb59071e-dcd7-4004-a9c4-222cb221e534"
}
} | math_dapo |
[
{
"content": "Solve the following math problem step by step. 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已知数列 $\\left\\{a_{n}\\right\\}$ 满足: $a_{n}=\\left[(2+\\sqrt{5})^{n}+\\frac{1}{2^{n}}\\right]\\left(n \\in \\mathbf{N}^... | 289 | {
"ability": "MATH",
"data_source": "math_dapo",
"extra_info": {
"index": "e9e47046-885f-4c69-81af-c422701e6754"
}
} | math_dapo |
[
{
"content": "Solve the following math problem step by step. 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已知 $\\alpha, \\beta \\in(0, \\pi), \\tan \\alpha 、 \\tan \\beta$ 为方程 $x^{2}+3 x+1=0$ 的两个根。求 $\\cos (\\alpha-\\beta)$ 的... | 5 | {
"ability": "MATH",
"data_source": "math_dapo",
"extra_info": {
"index": "d8c886a8-914e-4d18-b6a7-6dc0d7f0081f"
}
} | math_dapo |
[
{
"content": "Solve the following math problem step by step. 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记 \\( S = \\frac{3^2+4}{3^2-4} + \\frac{4^2+4}{4^2-4} + \\frac{5^2+4}{5^2-4} + \\cdots + \\frac{13^2+4}{13^2-4} \\)，则与... | 15 | {
"ability": "MATH",
"data_source": "math_dapo",
"extra_info": {
"index": "a46c635e-3f6d-4401-873d-6e8cdbc132ab"
}
} | math_dapo |
[
{
"content": "Solve the following math problem step by step. 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 $n$ for which $n^2$ is divisible by 18 and $n^3$ is divisible by 640?\n\nRemembe... | 120 | {
"ability": "MATH",
"data_source": "math_dapo",
"extra_info": {
"index": "bb932a96-018c-4bb3-ad26-91f0152a444b"
}
} | math_dapo |
[
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nExcept for the first two terms, each term of the sequence $1000, x, 1000 - x,\\ldots$ is obtained by subtracting the p... | 618 | {
"ability": "MATH",
"data_source": "math_dapo",
"extra_info": {
"index": "47f1c0a9-1fb2-41ab-8a01-9f6f70f60720"
}
} | math_dapo |
[
{
"content": "Solve the following math problem step by step. 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 triangle, $\\angle A=\\angle B$. What is $x$? [asy]\n\ndraw((.5,0)--(3,2)--(0,1)--cycle);\n\nlabel(\"$A$\",(.5,... | 3 | {
"ability": "MATH",
"data_source": "math_dapo",
"extra_info": {
"index": "5793742b-a289-445d-8815-f51944f6c6c9"
}
} | math_dapo |
[
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nLet $S = \\{1, 2, \\ldots, 100\\}$. Consider a partition of $S$ into $S_1, S_2, \\ldots, S_n$ for some $n$, i.e., $S_i... | 10 | {
"ability": "MATH",
"data_source": "math_dapo",
"extra_info": {
"index": "bd226844-8757-4d4c-981b-83a646997a00"
}
} | math_dapo |
[
{
"content": "Solve the following math problem step by step. 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}... | 90 | {
"ability": "MATH",
"data_source": "math_dapo",
"extra_info": {
"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\n一项赛事共有 100 位选手参加. 对于任意两位选手 x,y，他们之间恰比赛一次且分出胜负，用 x\\rightarrow y 表示 x 战胜 y. 如果对任意两位选手 x,y，均能找到某个选手序列 u_1, u_2, \\cdots,... | 3 | {
"ability": "MATH",
"data_source": "math_dapo",
"extra_info": {
"index": "161e335a-a89b-4772-888a-f666d03e3a6b"
}
} | math_dapo |
[
{
"content": "Solve the following math problem step by step. 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现有 7 把钥匙和 7 把锁。用这些钥匙随机开锁，则 $D_{1}, D_{2}, D_{3}$ 这三把钥匙不能打开对应的锁的概率是 $\\qquad$.原始的答案是\\frac{m}{n}的形式，其中m、n是互质的。请给出最终m + ... | 172 | {
"ability": "MATH",
"data_source": "math_dapo",
"extra_info": {
"index": "62709ae5-4340-414f-9fc6-007b64ca570d"
}
} | math_dapo |
[
{
"content": "Solve the following math problem step by step. 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 average number of pairs of consecutive integers in a randomly selected subset of $5$ distinct integers cho... | 5 | {
"ability": "MATH",
"data_source": "math_dapo",
"extra_info": {
"index": "8175ec94-20e1-46b1-a54f-42d537838f0b"
}
} | math_dapo |
[
{
"content": "Solve the following math problem step by step. 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已知下列不等式 $\\frac{e^{22 x}+e^{-22 x}}{2} \\leq e^{c x^{2}}$ 对所有实数 x 均成立, 则 $[c]$ 的最小值为 $\\qquad$.\n\nRemember to put you... | 242 | {
"ability": "MATH",
"data_source": "math_dapo",
"extra_info": {
"index": "89a3a36c-1403-4edc-b930-feda9100f4c9"
}
} | math_dapo |
[
{
"content": "Solve the following math problem step by step. 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对于任意闭区间 $I$ ，用 $M_{I}$ 表示函数 $y=\\sin x$ 在 $I$ 上的最大值。若正数 $a$ 满足 $M_{[0, a]}=2 M_{[a, 2 a]}$ ，则 $a$ 的值为\\frac{m\\pi}{n}。... | 36 | {
"ability": "MATH",
"data_source": "math_dapo",
"extra_info": {
"index": "15cd6314-190b-4d15-88f7-2ad6c555dc6f"
}
} | math_dapo |
[
{
"content": "Solve the following math problem step by step. 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有 $n(n>12)$ 个人参加某次数学邀请赛，试卷由十五道填空题组成，每答对一题得 1 分，不答或答错得 0 分。分析每一种可能的得分情况发现：只要其中任意 12 个人得分之和不少于 36 分，则这 $n$ 个人中至少有 3 个人答对... | 911 | {
"ability": "MATH",
"data_source": "math_dapo",
"extra_info": {
"index": "57879963-3930-413a-8737-c73a53827b4f"
}
} | math_dapo |
[
{
"content": "Solve the following math problem step by step. 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 internal angles of quadrilateral $ABCD$ form an arithmetic progression. Triangles $ABD$ and $DCB$ are similar with... | 240 | {
"ability": "MATH",
"data_source": "math_dapo",
"extra_info": {
"index": "b5abb768-a631-40bc-9a05-a8cfa8b8769c"
}
} | math_dapo |
[
{
"content": "Solve the following math problem step by step. 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 summary of a survey of 100 students listed the following totals:\n\n59 students did math homework\n\n49 students d... | 18 | {
"ability": "MATH",
"data_source": "math_dapo",
"extra_info": {
"index": "7978d310-109e-4ed3-9380-241d5bc4fc73"
}
} | math_dapo |
[
{
"content": "Solve the following math problem step by step. 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 set of five integers $S= \\{a_1, a_2, a_3, a_4, a_5\\}$, let $P_S$ be the product of all differences between ... | 288 | {
"ability": "MATH",
"data_source": "math_dapo",
"extra_info": {
"index": "7e0d2e7d-0d02-4d76-a9cd-76e8558df1c8"
}
} | math_dapo |
[
{
"content": "Solve the following math problem step by step. 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 diagram below shows a $4\\times4$ rectangular array of points, each of which is $1$ unit away from its nearest nei... | 240 | {
"ability": "MATH",
"data_source": "math_dapo",
"extra_info": {
"index": "65df6671-67ca-4359-a48d-3c85a9c584df"
}
} | math_dapo |
[
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nFor each positive integer $n$, let $k(n)$ be the number of ones in the binary representation of 2023·n. What is the mi... | 3 | {
"ability": "MATH",
"data_source": "math_dapo",
"extra_info": {
"index": "03f9d87e-a7a4-4a6c-9bdc-2de3d08fca56"
}
} | math_dapo |
[
{
"content": "Solve the following math problem step by step. 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若 3 个整数 a,b,c 满足 a^2+b^2+c^2+3<ab+3b+3c，则这样的有序整数组 (a,b,c) 共有__________组.\n\nRemember to put your answer on its own lin... | 14 | {
"ability": "MATH",
"data_source": "math_dapo",
"extra_info": {
"index": "34a59667-f70a-428e-9ee4-3bbcd3379b23"
}
} | math_dapo |
[
{
"content": "Solve the following math problem step by step. 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设平面上有 $n(n \\geqslant 4)$ 个点 $V_{1}, V_{2}, \\cdots$, $V_{n}$ ，任意三点不共线，某些点之间连有线段。把标号分别为 $1,2, \\cdots, n$ 的 $n$ 枚棋子放置在... | 4 | {
"ability": "MATH",
"data_source": "math_dapo",
"extra_info": {
"index": "4d7318b3-72bf-4827-bcc0-149671c130ad"
}
} | math_dapo |
[
{
"content": "Solve the following math problem step by step. 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 answer to the $n$th problem on this contest ($n=1, \\dots, 30$); in particular, the answer to thi... | 0 | {
"ability": "MATH",
"data_source": "math_dapo",
"extra_info": {
"index": "64ac797d-c85a-4e62-9f7a-6164c369d9b5"
}
} | math_dapo |
[
{
"content": "Solve the following math problem step by step. 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 figure, \\(ABCD\\) is a square of side length \\(1\\). The rectangles \\(JKHG\\) and \\(EBCF\\) are congruent. ... | 5 | {
"ability": "MATH",
"data_source": "math_dapo",
"extra_info": {
"index": "2804aff0-d56f-46e3-8c5a-aa7e6b981790"
}
} | math_dapo |
[
{
"content": "Solve the following math problem step by step. 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 for each prime $p$ with $2 < p < n$, the difference $n - p$ is also a ... | 10 | {
"ability": "MATH",
"data_source": "math_dapo",
"extra_info": {
"index": "d7ab5d49-bb9e-4ef4-921c-d544ef429f33"
}
} | math_dapo |
[
{
"content": "Solve the following math problem step by step. 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 nonzero coefficients can a polynomial $P(z)$ have if its coefficients are integers and $|P(z)| \\leq 2$ for a... | 3 | {
"ability": "MATH",
"data_source": "math_dapo",
"extra_info": {
"index": "2b07f357-2917-4c34-9cae-6e3504906238"
}
} | math_dapo |
[
{
"content": "Solve the following math problem step by step. 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 triples of positive integers $(x,y,z)$ that satisfy the equation \n\n$$\\begin{align*} 2(x+y+z+2xyz)^2=(2xy+... | 6 | {
"ability": "MATH",
"data_source": "math_dapo",
"extra_info": {
"index": "9cf96ce4-106e-4ba5-9f48-e9d6d89b2396"
}
} | math_dapo |
[
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nLet $ABCD$ be a quadrilateral such that $m(\\widehat{A}) = m(\\widehat{D}) = 90^\\circ$. Let $M$ be the midpoint of $[... | 6 | {
"ability": "MATH",
"data_source": "math_dapo",
"extra_info": {
"index": "5f704bf0-c39a-4b42-bf8c-e130bfda9cc8"
}
} | math_dapo |
[
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nFind the greatest $a$ such that $\\frac{7\\sqrt{(2a)^2+(1)^2}-4a^2-1}{\\sqrt{1+4a^2}+3}=2$.The answer is in the form k... | 3 | {
"ability": "MATH",
"data_source": "math_dapo",
"extra_info": {
"index": "dbd1cec5-87b8-438a-8658-b426e824bb53"
}
} | math_dapo |
[
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nBekah has exactly three brass house number digits: 2, 3 and 5. How many distinct numbers can she form using one or mor... | 15 | {
"ability": "MATH",
"data_source": "math_dapo",
"extra_info": {
"index": "cab8df8f-dae3-4f11-8f01-c1338b6d3ea1"
}
} | math_dapo |
[
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nCompute the smallest positive integer $a$ for which \n$$\\sqrt{a + \\sqrt{a + \\ldots}} - \\frac{1}{a + \\frac{1}{a+\\... | 43 | {
"ability": "MATH",
"data_source": "math_dapo",
"extra_info": {
"index": "8326d608-9960-4461-88ef-319dd12fe97b"
}
} | math_dapo |
[
{
"content": "Solve the following math problem step by step. 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 cube is cut into 99 smaller cubes, exactly 98 of which are unit cubes. Find the volume of the original cube.\n\nReme... | 125 | {
"ability": "MATH",
"data_source": "math_dapo",
"extra_info": {
"index": "ce46a338-b676-4477-a79f-cffb16348884"
}
} | math_dapo |
[
{
"content": "Solve the following math problem step by step. 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, and let $M$ be the midpoint of side $AB$. If $AB$ is $17$ units long and $CM$ is $8$ units lo... | 68 | {
"ability": "MATH",
"data_source": "math_dapo",
"extra_info": {
"index": "488130bf-e9f5-4484-a90a-7f3611d8530b"
}
} | math_dapo |
[
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nHalf the volume of a 12 foot high cone-shaped pile is grade A ore while the other half is grade B ore. The pile is wor... | 608 | {
"ability": "MATH",
"data_source": "math_dapo",
"extra_info": {
"index": "fb5ca027-8c89-45d8-b0f5-72686ca1e4be"
}
} | math_dapo |
[
{
"content": "Solve the following math problem step by step. 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 base-17 integer $\\overline{8323a02421_{17}}$ (where $a$ is a base-17 digit) is divisible by $16_{10}$,... | 7 | {
"ability": "MATH",
"data_source": "math_dapo",
"extra_info": {
"index": "91593343-0b11-4db1-941a-d564f99857bc"
}
} | math_dapo |
[
{
"content": "Solve the following math problem step by step. 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 area of rhombus $ABCD$ given that the radii of the circles circumscribed around triangles $ABD$ and $ACD$ are... | 400 | {
"ability": "MATH",
"data_source": "math_dapo",
"extra_info": {
"index": "5cd32910-cfe1-4908-aee5-d488b8a2edc9"
}
} | math_dapo |
[
{
"content": "Solve the following math problem step by step. 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 sum of the least and the greatest positive four-digit multiples of 4 that can be written each using the di... | 5636 | {
"ability": "MATH",
"data_source": "math_dapo",
"extra_info": {
"index": "4ff95ae7-5f6f-4507-9676-1dbdd4cc3c30"
}
} | math_dapo |
[
{
"content": "Solve the following math problem step by step. 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 two-digit numbers $\\overline{ab}$ with nonzero digits $a$ and $b$ such that $a$ and $b$ are bot... | 14 | {
"ability": "MATH",
"data_source": "math_dapo",
"extra_info": {
"index": "39fd0404-f3df-4adb-9cba-006f00cc3420"
}
} | math_dapo |
[
{
"content": "Solve the following math problem step by step. 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 zeroth project at Magic School, Emilia needs to grow six perfectly-shaped apple trees. First, she plants six t... | 789953 | {
"ability": "MATH",
"data_source": "math_dapo",
"extra_info": {
"index": "c313ae87-7556-479a-9fec-889db4f8828c"
}
} | math_dapo |
[
{
"content": "Solve the following math problem step by step. 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 $k$ such that:\n\\[\nk \\leq \\sqrt{2} + \\sqrt[3]{\\frac{3}{2}} + \\sqrt[4]{\\frac{4}{3}} + ... | 2014 | {
"ability": "MATH",
"data_source": "math_dapo",
"extra_info": {
"index": "dc203d15-e2eb-4783-83fb-f1f3eba30575"
}
} | math_dapo |
[
{
"content": "Solve the following math problem step by step. 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 hundred concentric circles with radii $1, 2, 3, \\dots, 100$ are drawn in a plane. The interior of the circle of ... | 301 | {
"ability": "MATH",
"data_source": "math_dapo",
"extra_info": {
"index": "79565a4e-d86b-4067-9e39-fbe8229f8947"
}
} | math_dapo |
[
{
"content": "Solve the following math problem step by step. 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 call a prime number a $\\textit{reversible prime}$ if the number formed by reversing its digits is also prime. W... | 31 | {
"ability": "MATH",
"data_source": "math_dapo",
"extra_info": {
"index": "7bda27b9-5b0d-442a-8a1d-68b5a3847d6d"
}
} | math_dapo |
[
{
"content": "Solve the following math problem step by step. 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... | 13500 | {
"ability": "MATH",
"data_source": "math_dapo",
"extra_info": {
"index": "87b03edb-d22a-4a88-8ae0-330e2c0f8414"
}
} | math_dapo |
[
{
"content": "Solve the following math problem step by step. 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 the boxes in the figure below is a square. How many different squares can be traced using the lines in the fig... | 38 | {
"ability": "MATH",
"data_source": "math_dapo",
"extra_info": {
"index": "ce13665d-cce1-4ca9-a284-e202784ac8c2"
}
} | math_dapo |
[
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nZou and Chou are practicing their $100$-meter sprints by running $6$ races against each other. Zou wins the first race... | 97 | {
"ability": "MATH",
"data_source": "math_dapo",
"extra_info": {
"index": "0d24b69a-1e51-40d9-84e6-b911b05840c2"
}
} | math_dapo |
[
{
"content": "Solve the following math problem step by step. 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若 $\\triangle A B C$ 的角 $A, C$ 满足 $5(\\cos A+\\cos C)+4(\\cos A \\cos C+1)=0$, 则 $\\tan \\frac{A}{2} \\cdot \\tan \\fr... | 3 | {
"ability": "MATH",
"data_source": "math_dapo",
"extra_info": {
"index": "a61a463f-a199-46f5-9e30-c06cb467a84d"
}
} | math_dapo |
[
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nTriangle $ABC$ is a right isosceles triangle. Points $D$, $E$ and $F$ are the midpoints of the sides of the triangle. ... | 16 | {
"ability": "MATH",
"data_source": "math_dapo",
"extra_info": {
"index": "1887ac79-7bba-4666-b72b-835081e0fbe2"
}
} | math_dapo |
[
{
"content": "Solve the following math problem step by step. 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 $\\overline{MN}$ be a diameter of a circle with diameter 1. Let $A$ and $B$ be points on one of the semicircular a... | 14 | {
"ability": "MATH",
"data_source": "math_dapo",
"extra_info": {
"index": "065a820c-1487-45ea-82a4-f118c9a9aa8d"
}
} | math_dapo |
[
{
"content": "Solve the following math problem step by step. 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 the three diagrams in the image show a balance of weights using different objects. How many squares will balan... | 6 | {
"ability": "MATH",
"data_source": "math_dapo",
"extra_info": {
"index": "4b578eb4-1eb5-4e4e-9c89-68c2cffa64e0"
}
} | math_dapo |
[
{
"content": "Solve the following math problem step by step. 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 ways to arrange the letters of the word ELEVEN.\n\nRemember to put your answer on its own line... | 120 | {
"ability": "MATH",
"data_source": "math_dapo",
"extra_info": {
"index": "19d294ab-a5be-4dae-9436-b90eaa3e6db8"
}
} | math_dapo |
[
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nPhoenix hiked the Rocky Path Trail last week. It took four days to complete the trip. The first two days she hiked a t... | 54 | {
"ability": "MATH",
"data_source": "math_dapo",
"extra_info": {
"index": "3627ff9e-c96d-498f-a21c-91e3f0698f81"
}
} | math_dapo |
[
{
"content": "Solve the following math problem step by step. 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设数列 $\\left\\{a_{n}\\right\\}$ 满足\n$a_{0}=\\frac{1}{2}, a_{n+1}=a_{n}+\\frac{a_{n}^{2}}{2012}(n=0,1, \\cdots)$.\n求整数 $... | 2012 | {
"ability": "MATH",
"data_source": "math_dapo",
"extra_info": {
"index": "a12709ec-68b8-4edc-8416-375c23374aa2"
}
} | math_dapo |
[
{
"content": "Solve the following math problem step by step. 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 pile of eggs. Joan counted the eggs, but her count was off by $1$ in the $1$'s place. Tom counted the eggs,... | 439 | {
"ability": "MATH",
"data_source": "math_dapo",
"extra_info": {
"index": "1203b437-bb39-4cda-a91b-0a79c80aa72d"
}
} | math_dapo |
[
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nMichel starts with the string HMMT. An operation consists of either replacing an occurrence of H with HM, replacing an... | 144 | {
"ability": "MATH",
"data_source": "math_dapo",
"extra_info": {
"index": "08971c55-b4d4-45b0-a9b8-6ad51e526d36"
}
} | math_dapo |
[
{
"content": "Solve the following math problem step by step. 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已知 $M=\\{1,2, \\cdots, 8\\}, A 、 B$ 是集合 $M$的两个不同子集，满足： \n（1） $A$ 的元素个数比 $B$ 的元素个数少； \n（2） $A$ 中的最小元素比 $B$ 中的最大元素大。 ... | 321 | {
"ability": "MATH",
"data_source": "math_dapo",
"extra_info": {
"index": "fe833d25-7ea4-47db-91c9-d6e412f18d34"
}
} | math_dapo |
[
{
"content": "Solve the following math problem step by step. 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四面体 $A B C D$ 中, $A B \\perp B C, B C \\perp C D$, 且 $A B, B C, C D, D A$ 的长分别为 $1,2,3,4$,则四面体 $A B C D$ 的体积为。原始答案为\\f... | 7 | {
"ability": "MATH",
"data_source": "math_dapo",
"extra_info": {
"index": "e297922d-9bf0-47c0-ba98-3b2058ed7e44"
}
} | math_dapo |
[
{
"content": "Solve the following math problem step by step. 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 $n$ is considered \\textit{magical} if the following condition holds: \n\\[ \\lfloor \\sqrt{\\lceil... | 1330 | {
"ability": "MATH",
"data_source": "math_dapo",
"extra_info": {
"index": "1a6ad0d6-ac4f-41da-99ec-7b81b971a817"
}
} | math_dapo |
[
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nCall a positive integer monotonous if it is a one-digit number or its digits, when read from left to right, form eithe... | 1524 | {
"ability": "MATH",
"data_source": "math_dapo",
"extra_info": {
"index": "030de026-9293-4a5c-a2a0-743aa8d0e786"
}
} | math_dapo |
[
{
"content": "Solve the following math problem step by step. 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 rectangles are there with integer side lengths such that the numerical value of area of the rectangl... | 5 | {
"ability": "MATH",
"data_source": "math_dapo",
"extra_info": {
"index": "f4b6437d-4f58-49af-858e-5d67e77f980c"
}
} | math_dapo |
[
{
"content": "Solve the following math problem step by step. 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已知函数 \\(f(x)=3 \\lg (x+2)-\\log _{2} x\\),集合 \\(M=\\left\\{n \\in \\mathbf{Z} \\mid f\\left(n^{3}-3 n^{2}-10 n+32\\ri... | 6 | {
"ability": "MATH",
"data_source": "math_dapo",
"extra_info": {
"index": "d5ec579f-3fde-4c69-aa5e-630c1556b328"
}
} | math_dapo |
[
{
"content": "Solve the following math problem step by step. 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 number of square centimeters in the shaded area? (The 10 represents the hypotenuse of the white triangle o... | 30 | {
"ability": "MATH",
"data_source": "math_dapo",
"extra_info": {
"index": "07b5afd4-f445-4a1c-b683-f9fa33a4fe3c"
}
} | math_dapo |
[
{
"content": "Solve the following math problem step by step. 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 $2022$ grids in a row. Two people, A and B, play a game with these grids. Initially, each odd-numbered grid ... | 1011 | {
"ability": "MATH",
"data_source": "math_dapo",
"extra_info": {
"index": "d8ad1943-d93f-4d64-b717-57f63b554304"
}
} | math_dapo |
[
{
"content": "Solve the following math problem step by step. 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 complex number $u = a+bi$ and $v = c+di$ (where $i=\\sqrt{-1}$), define the binary operation $u \\otimes v = ac + ... | 7 | {
"ability": "MATH",
"data_source": "math_dapo",
"extra_info": {
"index": "15a38198-d5e7-4a3d-88e1-6d045c831da8"
}
} | math_dapo |
[
{
"content": "Solve the following math problem step by step. 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 adjoining figure, $AB$ and $BC$ are adjacent sides of square $ABCD$. Let $M$ be the midpoint of $AB$ and $N$ be... | 5 | {
"ability": "MATH",
"data_source": "math_dapo",
"extra_info": {
"index": "2e6f4f03-51b6-4a66-917c-336d023f682b"
}
} | math_dapo |
[
{
"content": "Solve the following math problem step by step. 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 two or more consecutive positive integers have a sum of $15$? Provide your answer as an integer.\n\nR... | 3 | {
"ability": "MATH",
"data_source": "math_dapo",
"extra_info": {
"index": "271069be-e62e-4923-a60f-cf070c0fb139"
}
} | math_dapo |
[
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\n$(a_n)_{n = 0}^\\infty$ is a sequence of integers. For every $n \\ge 0$, $a_{n + 1} = a_n^3 + a_n^2$. Find the maximum... | 3 | {
"ability": "MATH",
"data_source": "math_dapo",
"extra_info": {
"index": "9bd18788-e399-43b8-acac-14d28cf2a62d"
}
} | math_dapo |
[
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\n$A(-1,1)$, $B$, and $C$ are points on the hyperbola $x^2 - y^2 = 1$. If $\\triangle ABC$ is a regular triangle, find t... | 6 | {
"ability": "MATH",
"data_source": "math_dapo",
"extra_info": {
"index": "073bc705-0e14-4d51-b6d5-6a383b453c02"
}
} | math_dapo |
[
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nThe thousands digit of a five-digit number which is divisible by $37$ and $173$ is $3$. What is the hundreds digit of ... | 2 | {
"ability": "MATH",
"data_source": "math_dapo",
"extra_info": {
"index": "3fa5dd7f-22e1-4e9b-a158-ad08686cf480"
}
} | math_dapo |
[
{
"content": "Solve the following math problem step by step. 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已知函数 $f(x)=a x^{3}+b x^{2}+c x+d(a \\neq 0)$, 当 $0 \\leqslant x \\leqslant 1$ 时, $\\left|f^{\\prime}(x)\\right| \\leqs... | 11 | {
"ability": "MATH",
"data_source": "math_dapo",
"extra_info": {
"index": "5bd5c8cd-d618-4730-8e37-0d5a9e55f50c"
}
} | math_dapo |
[
{
"content": "Solve the following math problem step by step. 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 less than or equal to 100 have a prime factor that is greater than 4?\n\nRemember to put yo... | 80 | {
"ability": "MATH",
"data_source": "math_dapo",
"extra_info": {
"index": "ff35c0bf-3498-48eb-a048-8ecf99ee22f2"
}
} | math_dapo |
[
{
"content": "Solve the following math problem step by step. 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 concentric circles have radii $1$ and $4$. Six congruent circles form a ring where each of the six circles is tang... | 126 | {
"ability": "MATH",
"data_source": "math_dapo",
"extra_info": {
"index": "30d6fee2-e613-408e-b18e-06c523a3196e"
}
} | math_dapo |
[
{
"content": "Solve the following math problem step by step. 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 right triangle \\(ABC\\), \\(BC = 5\\), \\(AC = 12\\), and \\(AM = x\\); \\(\\overline{MN} \\perp \\overline{AC}\\)... | 163 | {
"ability": "MATH",
"data_source": "math_dapo",
"extra_info": {
"index": "938dfff4-1fa7-4d65-9bfb-3bcc18a90570"
}
} | math_dapo |
[
{
"content": "Solve the following math problem step by step. 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 knows that $3$ red cards and $3$ black cards will be revealed to her one at a time in random order. Before each ... | 51 | {
"ability": "MATH",
"data_source": "math_dapo",
"extra_info": {
"index": "5ea1274f-9e94-4647-9b5f-068a16384b1a"
}
} | math_dapo |
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