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\n现有 20 盘红灯和 10 盘绿灯.初始时，所有灯都是亮着的.我们每次从所有亮着的灯中等可能地随机熄灭一角，直到某一种颜色的灯全部被熄灭为止.用 $a$ 表示停止后仍旧亮着的灯的数目的期望值，则 $[10 a]=$ $\\qquad$ ... | 22 | {
"ability": "MATH",
"data_source": "math_dapo",
"extra_info": {
"index": "0a358b2a-d1a0-4ad5-b273-d2907e6ac7f8"
}
} | math_dapo |
[
{
"content": "Solve the following math problem step by step. 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 given constant $b > 10,$ there are two possible triangles $ABC$ satisfying $AB = 10,$ $AC = b,$ and $\\sin B = \... | 16 | {
"ability": "MATH",
"data_source": "math_dapo",
"extra_info": {
"index": "5d1cd258-c060-487a-b88a-ed7dbd87e5f3"
}
} | math_dapo |
[
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nTravis has to babysit the terrible Thompson triplets. Knowing that they love big numbers, Travis devises a counting ga... | 5979 | {
"ability": "MATH",
"data_source": "math_dapo",
"extra_info": {
"index": "cfce1a23-e08b-4d7d-a8c5-8bdfea5544ee"
}
} | math_dapo |
[
{
"content": "Solve the following math problem step by step. 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 $A=\\{1,2,3\\}, B=\\{2 x+y \\mid x, y \\in A, x<y\\}, C=\\{2 x+y \\mid x, y \\in A, x>y\\}$ ，则 $B \\cap C$ 的所有元素之和为 ... | 12 | {
"ability": "MATH",
"data_source": "math_dapo",
"extra_info": {
"index": "9af3b479-f8c9-48fd-9aae-02282891d5f4"
}
} | math_dapo |
[
{
"content": "Solve the following math problem step by step. 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 last three digits of the product of the positive roots of $\\sqrt{1995}x^{\\log_{1995}x}=x^2$ .\n\nRemember t... | 25 | {
"ability": "MATH",
"data_source": "math_dapo",
"extra_info": {
"index": "2f9d954b-27bc-4de0-9410-9af87074d88f"
}
} | math_dapo |
[
{
"content": "Solve the following math problem step by step. 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 real number $x$ , let $\\lfloor x \\rfloor$ denote the greatest integer that does not exceed $x$. For how man... | 340 | {
"ability": "MATH",
"data_source": "math_dapo",
"extra_info": {
"index": "49ad6599-4a94-4f46-8ce1-9366e02324c9"
}
} | math_dapo |
[
{
"content": "Solve the following math problem step by step. 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 positive integers such that\n\\[\\begin{pmatrix} 3 & 0 \\\\ 0 & 2 \\end{pmatrix} \\begin{pma... | 16 | {
"ability": "MATH",
"data_source": "math_dapo",
"extra_info": {
"index": "49369bdf-f72e-47e3-9872-76847d842520"
}
} | math_dapo |
[
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nIf \\(a+b=b-c=c-a=3\\), find the value of \\(a+b+c\\) in the form of \\(\\frac{k}{m}\\), where \\(\\frac{k}{m}\\) is a... | 11 | {
"ability": "MATH",
"data_source": "math_dapo",
"extra_info": {
"index": "12e40cd9-03b4-4792-a5e7-2a6d2352df77"
}
} | math_dapo |
[
{
"content": "Solve the following math problem step by step. 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 infinite sheet of paper is divided into equal squares, some of which are colored red. In each $2 \\times 3$ rectang... | 33 | {
"ability": "MATH",
"data_source": "math_dapo",
"extra_info": {
"index": "56de5fac-ee77-4db3-90e2-9f471df29ffe"
}
} | math_dapo |
[
{
"content": "Solve the following math problem step by step. 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 for the real numbers $x, y, z, k$ the following conditions are valid: $x \\ne y \\ne z \\ne x$ and \\[ x^3 + y^3 + ... | 1004 | {
"ability": "MATH",
"data_source": "math_dapo",
"extra_info": {
"index": "a0828051-808d-461e-acf0-7e4a1636419d"
}
} | math_dapo |
[
{
"content": "Solve the following math problem step by step. 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 such that $AB \\parallel CD$ and let $P = AC \\cap BD$, with $AB = 21$, $CD = 7$, $AD = 13$,... | 17 | {
"ability": "MATH",
"data_source": "math_dapo",
"extra_info": {
"index": "dad6fbd6-0ef0-4127-9d93-549e59dfff56"
}
} | math_dapo |
[
{
"content": "Solve the following math problem step by step. 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 the sequence $a_1, a_2, a_3, \\cdots$ by $a_n = \\sum\\limits_{k=1}^n \\sin{k}$, where $k$ represents radian me... | 628 | {
"ability": "MATH",
"data_source": "math_dapo",
"extra_info": {
"index": "c40108e9-2928-4ab7-b4d1-25fb6f5a0f93"
}
} | math_dapo |
[
{
"content": "Solve the following math problem step by step. 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 number $x$ satisfies\n\\[3x + \\frac{1}{2x} = 3.\\]Find\n\\[64x^6 + \\frac{1}{729x^6}.\\]The answer is in the... | 443 | {
"ability": "MATH",
"data_source": "math_dapo",
"extra_info": {
"index": "aeca3dc0-371e-44e2-9046-4bb6bc4b9f23"
}
} | math_dapo |
[
{
"content": "Solve the following math problem step by step. 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 adjacent sides of the decagon shown meet at right angles. What is its perimeter?\n\n[asy]\nunitsize(1 cm);\n\npai... | 44 | {
"ability": "MATH",
"data_source": "math_dapo",
"extra_info": {
"index": "4b5e3aeb-88a8-46e6-a453-af558d257c1a"
}
} | math_dapo |
[
{
"content": "Solve the following math problem step by step. 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 set of all solutions of the system \\[ \\begin{cases}& 2x+y \\le 4 \\\\& x+y \\ge 1 \\\\& x \\ge 0 \\\\& y \\ge 0... | 7 | {
"ability": "MATH",
"data_source": "math_dapo",
"extra_info": {
"index": "d61d705a-d43e-47f0-9612-e3c0de58b551"
}
} | math_dapo |
[
{
"content": "Solve the following math problem step by step. 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 $T$ be the triangle in the coordinate plane with vertices $(0,0), (4,0),$ and $(0,3).$ Consider the following five... | 12 | {
"ability": "MATH",
"data_source": "math_dapo",
"extra_info": {
"index": "f1a08743-07bb-4150-b218-4429b450ab6d"
}
} | math_dapo |
[
{
"content": "Solve the following math problem step by step. 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 integers $0 \\leq x < 25$ such that $x^3 + 3x^2 - 2x + 4 \\equiv 0 \\pmod{25}$. What is this sum congr... | 17 | {
"ability": "MATH",
"data_source": "math_dapo",
"extra_info": {
"index": "ed613d18-c8bd-4bc6-82f1-188b78681da3"
}
} | math_dapo |
[
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\n5. Let $S$ denote the set of all positive integers whose prime factors are elements of $\\{2,3,5,7,11\\}$. (We include... | 1537 | {
"ability": "MATH",
"data_source": "math_dapo",
"extra_info": {
"index": "72cdec67-0a2a-4cc6-90db-f063dbcd8abb"
}
} | math_dapo |
[
{
"content": "Solve the following math problem step by step. 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 xOy 中，A 为椭圆 \\df{x^2}{4}+y^2=1 上一点，M 为线段 OA 上的动点. 过 M 作直线与椭圆交于 P, Q 两点，若 \\overrightarrow{PM}=2\\overrightarr... | 5 | {
"ability": "MATH",
"data_source": "math_dapo",
"extra_info": {
"index": "db96da68-896d-4506-bfa7-38573270c7e5"
}
} | math_dapo |
[
{
"content": "Solve the following math problem step by step. 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设正六边形 $A B C D E F$ 的边长为 1, 则 $(\\overrightarrow{A B}+\\overrightarrow{D C}) \\cdot(\\overrightarrow{A D}+\\overrighta... | -3 | {
"ability": "MATH",
"data_source": "math_dapo",
"extra_info": {
"index": "910cf2a5-aed1-4697-a8c2-bd830afe1276"
}
} | math_dapo |
[
{
"content": "Solve the following math problem step by step. 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... | 90 | {
"ability": "MATH",
"data_source": "math_dapo",
"extra_info": {
"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\n数列 $\\left\\{a_{n}\\right\\}$ 满足 $a_{n+1}=(-1)^{n} n-a_{n}, n=1,2,3, \\cdots$, 且 $a_{10}=a_{1}$, 则 $a_{n} a_{n+1}$ 的最大... | 37 | {
"ability": "MATH",
"data_source": "math_dapo",
"extra_info": {
"index": "9242d285-67a7-4230-accd-266fd7cecc6e"
}
} | math_dapo |
[
{
"content": "Solve the following math problem step by step. 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一个正数，若其小数部分、整数部分和其自身成等比数列，则该数为 $\\qquad$. 原始答案为\\frac{m+\\sqrt{n}}{k}的格式，请给出m + n + k的值。\n\nRemember to put your answe... | 8 | {
"ability": "MATH",
"data_source": "math_dapo",
"extra_info": {
"index": "30c46b7a-bda8-4649-854d-52fbf3edbbed"
}
} | math_dapo |
[
{
"content": "Solve the following math problem step by step. 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 points are chosen uniformly at random on a circle. What is the probability that no two of these points form an o... | 19 | {
"ability": "MATH",
"data_source": "math_dapo",
"extra_info": {
"index": "7e36dcd0-16a8-4600-9b4d-1ee0b56645c7"
}
} | math_dapo |
[
{
"content": "Solve the following math problem step by step. 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 $n$, the $n^{th}$ triangular number is $T(n)=\\dfrac{n(n+1)}{2}.$\n\nFor example, $T(3) = \\fra... | 2015 | {
"ability": "MATH",
"data_source": "math_dapo",
"extra_info": {
"index": "1d1739f2-ae1b-4388-8ac4-02656e9dbc06"
}
} | math_dapo |
[
{
"content": "Solve the following math problem step by step. 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 circles with radii 1, 2, 3, and $r$ are externally tangent to one another, where $r$ is the smallest radius. Com... | 29 | {
"ability": "MATH",
"data_source": "math_dapo",
"extra_info": {
"index": "44f40147-4a88-42af-88d9-b4430f6f33c5"
}
} | math_dapo |
[
{
"content": "Solve the following math problem step by step. 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 has eight vertices (corners) and twelve edges. A segment, such as $x$, which joins two vertices not joined by a... | 16 | {
"ability": "MATH",
"data_source": "math_dapo",
"extra_info": {
"index": "c23af060-7188-4d59-98e2-861a0c69be0e"
}
} | math_dapo |
[
{
"content": "Solve the following math problem step by step. 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 set $S$, let $|S|$ denote the number of elements in $S$, and let $n(S)$ be the number of subsets of $S$, inclu... | 97 | {
"ability": "MATH",
"data_source": "math_dapo",
"extra_info": {
"index": "25376ea6-88c7-48a7-875e-2b24da554863"
}
} | math_dapo |
[
{
"content": "Solve the following math problem step by step. 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 convex quadrilateral with $AC \\perp BD$, and let $P$ be the intersection of $AC$ and $BD$. Suppose th... | 231 | {
"ability": "MATH",
"data_source": "math_dapo",
"extra_info": {
"index": "14247bce-f768-4618-8b97-0772d78e81b9"
}
} | math_dapo |
[
{
"content": "Solve the following math problem step by step. 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 first digit after the decimal point of the number $\\displaystyle \\frac{1}{1009} + \\frac{1}{1010} + \\cdots... | 6 | {
"ability": "MATH",
"data_source": "math_dapo",
"extra_info": {
"index": "0e498bbf-4991-40f8-bb75-9e5229d3ed34"
}
} | math_dapo |
[
{
"content": "Solve the following math problem step by step. 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 B$ 为过抛物线 $y^{2}=4 x$ 焦点 $F$ 的弦, $O$ 为坐标原点, 且 $\\angle O F A=135^{\\circ}, C$ 为抛物线准线与 $x$ 轴的交点，求 $\\angle A C B$ 的正切... | 4 | {
"ability": "MATH",
"data_source": "math_dapo",
"extra_info": {
"index": "1cfb31f6-ebc8-4fd4-8585-4b60c6579d25"
}
} | math_dapo |
[
{
"content": "Solve the following math problem step by step. 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 right circular cylinder with its diameter equal to its height is inscribed in a right circular cone. The cone has di... | 41 | {
"ability": "MATH",
"data_source": "math_dapo",
"extra_info": {
"index": "0df02d1d-1891-4c5e-88c9-ebeae362d6fa"
}
} | math_dapo |
[
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nEvaluate $\\lfloor -4 -.5 \\rfloor \\cdot \\lceil 4 +.5 \\rceil \\cdot \\lfloor -3 -.5 \\rfloor \\cdot \\lceil 3 +.5 \... | -14400 | {
"ability": "MATH",
"data_source": "math_dapo",
"extra_info": {
"index": "cb07ed9d-6388-4b12-a5a7-988b9def26f9"
}
} | math_dapo |
[
{
"content": "Solve the following math problem step by step. 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 triangle has side lengths of $x$, $75$, and $100$, where $x < 75$, and altitudes of lengths $y$, $28$, and $60$, whe... | 56 | {
"ability": "MATH",
"data_source": "math_dapo",
"extra_info": {
"index": "762fcce5-28bb-402e-9871-cf8154ea1fd8"
}
} | math_dapo |
[
{
"content": "Solve the following math problem step by step. 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 event occurs periodically over $x$ consecutive years, followed by a break of $y$ consecutive years. The event occur... | 2018 | {
"ability": "MATH",
"data_source": "math_dapo",
"extra_info": {
"index": "643e4d74-ca1e-4be9-b171-de54b80a71b6"
}
} | math_dapo |
[
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nThe sum $$\\sum_{m=1}^{2023} \\frac{2m}{m^4+m^2+1}$$ can be expressed as $\\tfrac{a}{b}$ for relatively prime positive... | 105 | {
"ability": "MATH",
"data_source": "math_dapo",
"extra_info": {
"index": "5a4db036-40e6-4a92-a5d6-dd2cf3cd46fc"
}
} | math_dapo |
[
{
"content": "Solve the following math problem step by step. 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 $a_0, a_1, \\ldots, a_{2018}$ are integers such that \\[ (x^2 - 3x + 1)^{1009} = \\sum_{k=0}^{2018} a_k x^k \\... | 9 | {
"ability": "MATH",
"data_source": "math_dapo",
"extra_info": {
"index": "3f845069-75a5-4154-bf16-97af2b8140a8"
}
} | math_dapo |
[
{
"content": "Solve the following math problem step by step. 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 triangle $ABC$ is given where $\\angle BAC = 40^\\circ$ and $\\angle ABC = 20^\\circ$. Find the length of the angle ... | 4 | {
"ability": "MATH",
"data_source": "math_dapo",
"extra_info": {
"index": "d0b33563-2ed4-4cd4-89e2-b54fe5c78bef"
}
} | math_dapo |
[
{
"content": "Solve the following math problem step by step. 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 $2 \\cdot 5^{-1} + 8 \\cdot 11^{-1} \\pmod{56}$.\n\nExpress your answer as an integer from $0$ to $55$, inclusive... | 50 | {
"ability": "MATH",
"data_source": "math_dapo",
"extra_info": {
"index": "09f3502d-8710-4d18-8210-d9dc67f99231"
}
} | math_dapo |
[
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nLet $\\mathcal{S}_{n}$ be the set of strings with only 0's or 1's with length $n$ such that any 3 adjacent place numbe... | 927 | {
"ability": "MATH",
"data_source": "math_dapo",
"extra_info": {
"index": "9085bcc8-dbec-4234-b328-f16a269815c6"
}
} | math_dapo |
[
{
"content": "Solve the following math problem step by step. 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若正实数 x,y 满足 x(x+2y)=9，则 x^5y 的最大值为__________.\n\nRemember to put your answer on its own line after \"Answer:\".",
... | 54 | {
"ability": "MATH",
"data_source": "math_dapo",
"extra_info": {
"index": "9e7dff14-b186-4495-bd59-feaac5e16d28"
}
} | math_dapo |
[
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nFor a positive integer $N$, let $f_N^{1}$ be the function defined by\n$$f_N(x)=\\sum_{n=0}^N\\frac{N+1/2-n}{(N+1)(2n+1... | 5 | {
"ability": "MATH",
"data_source": "math_dapo",
"extra_info": {
"index": "51f12f85-9bae-4d7e-91a9-05a25c40fafc"
}
} | math_dapo |
[
{
"content": "Solve the following math problem step by step. 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 triples $(x,y,z)$ of real numbers that satisfy\n\\begin{align*}\nx &= 2018 - 2019 \\operatorname{si... | 3 | {
"ability": "MATH",
"data_source": "math_dapo",
"extra_info": {
"index": "0456027d-1522-4ad2-8228-1133710ad628"
}
} | math_dapo |
[
{
"content": "Solve the following math problem step by step. 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 scalene triangles having all sides of integral lengths, and a perimeter less than $13$.\n\nRemember... | 3 | {
"ability": "MATH",
"data_source": "math_dapo",
"extra_info": {
"index": "752582b2-34b3-41c9-863b-6a5624b56aa7"
}
} | math_dapo |
[
{
"content": "Solve the following math problem step by step. 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 integer values of $x$ such that $P = x^4 + 6x^3 + 11x^2 + 3x + 31$ is the square of an intege... | 1 | {
"ability": "MATH",
"data_source": "math_dapo",
"extra_info": {
"index": "3676c8e3-4848-41eb-9876-08c9e79fa0ba"
}
} | math_dapo |
[
{
"content": "Solve the following math problem step by step. 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$ and $\\beta$ be angles such that\n\\[\\frac{\\cos \\alpha}{\\cos \\beta} + \\frac{\\sin \\alpha}{\\sin \... | 1 | {
"ability": "MATH",
"data_source": "math_dapo",
"extra_info": {
"index": "91cbb6b5-b52d-4f47-a50b-107fc29794dd"
}
} | math_dapo |
[
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nFind all values of $a$ for which the equation $x^3 - x + a = 0$ has three different integer solutions.\n\nRemember to ... | 0 | {
"ability": "MATH",
"data_source": "math_dapo",
"extra_info": {
"index": "0406a53b-4202-4b22-bb9e-e2c224220fd3"
}
} | math_dapo |
[
{
"content": "Solve the following math problem step by step. 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$ and $b$ be two positive integers satisfying the equation \n\\[ 20\\sqrt{12} = a\\sqrt{b}. \\] \nCompute the ... | 10800 | {
"ability": "MATH",
"data_source": "math_dapo",
"extra_info": {
"index": "6873eedb-5cfd-41f4-9508-be005a4a8685"
}
} | math_dapo |
[
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nLet $a,$ $b,$ and $c$ be positive real numbers such that $a + b^2 + c^3 = \\frac{325}{9}.$ Find the minimum value of\... | 2834 | {
"ability": "MATH",
"data_source": "math_dapo",
"extra_info": {
"index": "15e85cfe-473e-43e9-b396-9c995b65762a"
}
} | math_dapo |
[
{
"content": "Solve the following math problem step by step. 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\n$T=\\left\\{(a, b, c) \\mid a 、 b 、 c \\in \\mathbf{Z}_{+}\\right.$，且 $a 、 b 、 c$可构成某个三角形的三边长\\}。\n则 $\\sum_{(a, ... | 38 | {
"ability": "MATH",
"data_source": "math_dapo",
"extra_info": {
"index": "67f71d33-1619-4041-b92b-0fe87f1f080e"
}
} | math_dapo |
[
{
"content": "Solve the following math problem step by step. 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 $|\\boldsymbol{a}|=|\\boldsymbol{b}|=1, \\boldsymbol{a} \\cdot \\boldsymbol{b}=\\frac{1}{2},(\\boldsymbol{c}-\\bold... | 8 | {
"ability": "MATH",
"data_source": "math_dapo",
"extra_info": {
"index": "a94d302f-d578-4914-8029-6ef55aa4a499"
}
} | math_dapo |
[
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nSets $A, B$, and $C$ satisfy $|A| = 92$, $|B| = 35$, $|C| = 63$, $|A\\cap B| = 16$, $|A\\cap C| = 51$, $|B\\cap C| = 1... | 10 | {
"ability": "MATH",
"data_source": "math_dapo",
"extra_info": {
"index": "d3f2a75c-99bf-4899-98db-c8e2f669d6eb"
}
} | math_dapo |
[
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nFind all natural numbers $n$ such that the product of its decimal digits equals $n^2 - 10n - 22$.\n\nRemember to put y... | 12 | {
"ability": "MATH",
"data_source": "math_dapo",
"extra_info": {
"index": "25227437-6490-413b-bc75-e6bc7fcf798d"
}
} | math_dapo |
[
{
"content": "Solve the following math problem step by step. 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 perfect squares less than $10^6$ are multiples of $24$? \n\n\nRemember to put your answer on its own... | 83 | {
"ability": "MATH",
"data_source": "math_dapo",
"extra_info": {
"index": "7fbe62b6-6a14-4bbc-858d-a2564de5c006"
}
} | math_dapo |
[
{
"content": "Solve the following math problem step by step. 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 dollar is now worth $\\frac{1}{980}$ ounce of gold. After the $n^{th}$ 7001 billion dollars bailout package passed... | 506 | {
"ability": "MATH",
"data_source": "math_dapo",
"extra_info": {
"index": "462ac8d5-1467-4f10-8b42-25f4d28e20c6"
}
} | math_dapo |
[
{
"content": "Solve the following math problem step by step. 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 square grid $100 \\times 100$ is tiled in two ways: only with dominoes and only with $2 \\times 2$ squares. What is ... | 100 | {
"ability": "MATH",
"data_source": "math_dapo",
"extra_info": {
"index": "70212cb8-d092-4af9-90bb-a7f5e3c6c039"
}
} | math_dapo |
[
{
"content": "Solve the following math problem step by step. 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 positive integers $n$ satisfying the following conditions:\n\n1. $n < 10^6$\n2. $n$ is divisib... | 104 | {
"ability": "MATH",
"data_source": "math_dapo",
"extra_info": {
"index": "d9b23a4d-7bed-488f-98bd-8d9f6421f73e"
}
} | math_dapo |
[
{
"content": "Solve the following math problem step by step. 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$, let\n\\[ f(n) = \\sum_{k=1}^n \\varphi(k) \\left\\lfloor \\frac{n}{k} \\right\\rfloor^2... | 11431 | {
"ability": "MATH",
"data_source": "math_dapo",
"extra_info": {
"index": "16de7078-1812-414a-8076-849d2b271836"
}
} | math_dapo |
[
{
"content": "Solve the following math problem step by step. 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 certain function $f$ has the properties that $f(3x) = 3f(x)$ for all positive real values of $x$, and that $f(x) = 1... | 429 | {
"ability": "MATH",
"data_source": "math_dapo",
"extra_info": {
"index": "d38d81c7-3bfe-47a1-9e47-2a7bd8bf354d"
}
} | math_dapo |
[
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nLet $\\mathcal{S}$ be a regular 18-gon. For two vertices in $\\mathcal{S}$, define the \\textit{distance} between them... | 240 | {
"ability": "MATH",
"data_source": "math_dapo",
"extra_info": {
"index": "d2cbd2df-6ac1-4f0e-a2a5-64c5968fae44"
}
} | math_dapo |
[
{
"content": "Solve the following math problem step by step. 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 certain integer has $4$ digits when written in base $8$. The same integer has $d$ digits when written in base $2$. W... | 33 | {
"ability": "MATH",
"data_source": "math_dapo",
"extra_info": {
"index": "883c1a4a-e31b-40fe-b110-c4cb005ee944"
}
} | math_dapo |
[
{
"content": "Solve the following math problem step by step. 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 color some unit squares in a $99 \\times 99$ square grid with one of $5$ given distinct colors, such that each colo... | 1900 | {
"ability": "MATH",
"data_source": "math_dapo",
"extra_info": {
"index": "673450ce-e926-4ba5-a2cd-29aa98fe59d3"
}
} | math_dapo |
[
{
"content": "Solve the following math problem step by step. 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: $x_1=19,x_2=95,x_{n+2}=\\text{lcm} (x_{n+1},x_n)+x_n$, for $n>1$, where $\\text{lcm} (a,b)$ mea... | 19 | {
"ability": "MATH",
"data_source": "math_dapo",
"extra_info": {
"index": "02a6d4dc-77be-4721-8de2-928d538181da"
}
} | math_dapo |
[
{
"content": "Solve the following math problem step by step. 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 points $(1, 7), (13, 16)$ and $(5, k)$, where $k$ is an integer, are vertices of a triangle. What is the sum of th... | 20 | {
"ability": "MATH",
"data_source": "math_dapo",
"extra_info": {
"index": "d865706c-55a1-4199-a05e-4d0bd8fa9974"
}
} | math_dapo |
[
{
"content": "Solve the following math problem step by step. 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 certain real numbers \\(a\\), \\(b\\), and \\(c\\), the polynomial \\[g(x) = x^3 + ax^2 + x + 10\\] has three dist... | 7007 | {
"ability": "MATH",
"data_source": "math_dapo",
"extra_info": {
"index": "3c650bec-5446-4432-90ce-63b23f5a944b"
}
} | math_dapo |
[
{
"content": "Solve the following math problem step by step. 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_n$ be the number of permutations $\\pi$ of $\\{1,2,\\ldots,n\\}$\nsuch that\n$|i-j|=1$ implies $|\\pi(i)-\\pi... | 4 | {
"ability": "MATH",
"data_source": "math_dapo",
"extra_info": {
"index": "cd5db260-7d56-41a4-a39a-89f0c6bb9929"
}
} | math_dapo |
[
{
"content": "Solve the following math problem step by step. 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 solutions does the equation:\n$$\\left\\lfloor \\frac{x}{20} \\right\\rfloor = \\left\\lfloor \\frac{x}{17} \... | 56 | {
"ability": "MATH",
"data_source": "math_dapo",
"extra_info": {
"index": "b2426955-1457-4e7e-8e25-553846ef5a7c"
}
} | math_dapo |
[
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nBilly and Bobby are located at points $A$ and $B$, respectively. They each walk directly toward the other point at a c... | 15 | {
"ability": "MATH",
"data_source": "math_dapo",
"extra_info": {
"index": "56aab51f-aa0e-4bfd-ac38-ed014c22f5fc"
}
} | math_dapo |
[
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nOn a circular board, there are $19$ squares numbered in order from $1$ to $19$. To the right of $1$ is $2$, to the rig... | 18 | {
"ability": "MATH",
"data_source": "math_dapo",
"extra_info": {
"index": "dbf4076d-0926-4241-a72c-ce15d300bf08"
}
} | math_dapo |
[
{
"content": "Solve the following math problem step by step. 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, the area of square $WXYZ$ is $25 \\text{ cm}^2$. The four smaller squares have sides 1 cm long, either... | 31 | {
"ability": "MATH",
"data_source": "math_dapo",
"extra_info": {
"index": "cc86db0e-55f8-4fc5-99c6-ba156eee9294"
}
} | math_dapo |
[
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nTerry decides to practice his arithmetic by adding the numbers between $10$ and $99$ inclusive. However, he accidental... | 59 | {
"ability": "MATH",
"data_source": "math_dapo",
"extra_info": {
"index": "908f57b2-c39e-48ec-a8e0-6830f8c38bb7"
}
} | math_dapo |
[
{
"content": "Solve the following math problem step by step. 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给定以正方形内的 2022 个点，且这 2022 个点以及正方形的顶点中任三点不共线。在这 2022 以及正方形的顶点之间连一些线段，将正方形划分为一些三角形，并要求这些线段之间只可以在端点处有公共点，则所连线段（不包含原正方形的边）的... | 6067 | {
"ability": "MATH",
"data_source": "math_dapo",
"extra_info": {
"index": "6cff56cb-b706-4948-9624-3173d1002012"
}
} | math_dapo |
[
{
"content": "Solve the following math problem step by step. 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 $2$ smallest prime factors of $2^{1024} - 1$.\n\nRemember to put your answer on its own line after... | 8 | {
"ability": "MATH",
"data_source": "math_dapo",
"extra_info": {
"index": "2042fe36-1ca4-4ced-b746-559821594bdb"
}
} | math_dapo |
[
{
"content": "Solve the following math problem step by step. 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 round table has radius \\(4\\). Six rectangular place mats are placed on the table. Each place mat has width \\(1\\)... | 15 | {
"ability": "MATH",
"data_source": "math_dapo",
"extra_info": {
"index": "c47fb232-2671-4d72-96ad-fc4375628c8c"
}
} | math_dapo |
[
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nCyclic pentagon $ ABCDE$ has a right angle $ \\angle{ABC} \\equal{} 90^{\\circ}$ and side lengths $ AB \\equal{} 15$ a... | 7 | {
"ability": "MATH",
"data_source": "math_dapo",
"extra_info": {
"index": "55c4ac2e-98b4-4075-a5cc-4271cad027ba"
}
} | math_dapo |
[
{
"content": "Solve the following math problem step by step. 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集合 $A=\\{1,2,3\\}, X=\\{4 x+y \\mid x, y \\in A\\}, Y=\\{4 x-y \\mid x, y \\in A\\}$, 则 $X \\cap Y$的元素之和为 $\\qquad$.\n... | 48 | {
"ability": "MATH",
"data_source": "math_dapo",
"extra_info": {
"index": "c91e4693-4d57-4892-935a-ba69137c8171"
}
} | math_dapo |
[
{
"content": "Solve the following math problem step by step. 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 following three lines in the Cartesian plane:\n\n\\[\n\\begin{cases}\n\\ell_1: & 2x - y = 7\\\\\n\\ell_2:... | 260 | {
"ability": "MATH",
"data_source": "math_dapo",
"extra_info": {
"index": "48f8bc8b-02cd-4cf8-9831-5e5b45fd8a45"
}
} | math_dapo |
[
{
"content": "Solve the following math problem step by step. 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 tamer wants to line up five lions and four tigers. We know that a tiger cannot be placed after another tiger. How ma... | 15 | {
"ability": "MATH",
"data_source": "math_dapo",
"extra_info": {
"index": "37f273a8-7671-4a7d-8a37-4ea27850f05e"
}
} | math_dapo |
[
{
"content": "Solve the following math problem step by step. 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\\) 满足 \\(\\frac{\\angle A}{3}=\\frac{\\angle B}{4}=\\frac{\\angle C}{5}\\), 则 \\(\\frac{\\overri... | 10 | {
"ability": "MATH",
"data_source": "math_dapo",
"extra_info": {
"index": "34a5cdfd-95cc-4800-bae5-9246388b6456"
}
} | math_dapo |
[
{
"content": "Solve the following math problem step by step. 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 $N = 2^{\\left(2^2\\right)}$ and $x$ be a real number such that $N^{\\left(N^N\\right)} = 2^{(2^x)}$. Find $x$.\n\... | 66 | {
"ability": "MATH",
"data_source": "math_dapo",
"extra_info": {
"index": "4cd88028-cfd5-447e-ab5e-052080cd5d14"
}
} | math_dapo |
[
{
"content": "Solve the following math problem step by step. 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 0<x,y<1，求 \\df{xy(1-x-y)}{(x+y)(1-x)(1-y)} 的最大值.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 + n的值\n\nRemember to put your... | 9 | {
"ability": "MATH",
"data_source": "math_dapo",
"extra_info": {
"index": "baaa3159-f794-4da4-9170-c995545439e0"
}
} | math_dapo |
[
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nLet the *taxicab distance* between points $(x_1, y_1)$ and $(x_2, y_2)$ in the coordinate plane be given by $|x_1 - x_... | 841 | {
"ability": "MATH",
"data_source": "math_dapo",
"extra_info": {
"index": "d657a69a-bd32-47fd-8527-9fe1982e9104"
}
} | math_dapo |
[
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nLet $x, y, z$ be positive real numbers whose sum is 2012. Find the maximum value of:\n\\[ \\frac{(x^2 + y^2 + z^2)(x^3... | 2012 | {
"ability": "MATH",
"data_source": "math_dapo",
"extra_info": {
"index": "89458b70-79c6-4d4d-9da2-0e6d6d2c4193"
}
} | math_dapo |
[
{
"content": "Solve the following math problem step by step. 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 $f(x), g(x)$ 均为定义在 $\\mathbf{R}$ 上的函数, $f(x)$ 的图像关于直线 $x=1$ 对称, $g(x)$ 的图像关于点 $(1,-2)$ 中心对称, 且 $f(x)+g(x)=9^{x}+x^{... | 2016 | {
"ability": "MATH",
"data_source": "math_dapo",
"extra_info": {
"index": "9d024112-813a-4ef4-a79b-db916d93b23f"
}
} | math_dapo |
[
{
"content": "Solve the following math problem step by step. 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若复数 z 满足 \\left|\\df{z^2+1}{z+i}\\right|+\\left|\\df{z^2+4i-3}{z-i+2}\\right|=4，则 |z-1| 的最小值为__________.原始的答案是k\\sqrt{... | 3 | {
"ability": "MATH",
"data_source": "math_dapo",
"extra_info": {
"index": "bd6e224e-c92d-4d75-8d76-ad54561a9657"
}
} | math_dapo |
[
{
"content": "Solve the following math problem step by step. 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 roots of $z^{12}=64$ that have a positive real part? Express your answer in the form $a\\sqrt{b... | 11 | {
"ability": "MATH",
"data_source": "math_dapo",
"extra_info": {
"index": "9c0fb094-4de8-40b4-8d28-4f610cfb9a63"
}
} | math_dapo |
[
{
"content": "Solve the following math problem step by step. 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一个\"位置\"是指直角坐标平面上的一个点 (x,y)，其中 x,y 都是不超过 20 的正整数.最初时，所有 400 个位置都是空的. 甲乙两人轮流摆放石子，由甲先进行. 每次轮到甲时，他在一个空的位置上摆上一个新的红色石子，要求任意... | 100 | {
"ability": "MATH",
"data_source": "math_dapo",
"extra_info": {
"index": "e516e41a-80fe-43e2-a4a0-71e3db71ff84"
}
} | math_dapo |
[
{
"content": "Solve the following math problem step by step. 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在侧棱长和底面边长都是 4 的正四棱锥 $P-A B C D$ 的表面上与顶点 $P$ 的距离为 3的动点所形成的所有曲线段的长度之和为，请给出\\pi系数的值。\n\nRemember to put your answer on it... | 6 | {
"ability": "MATH",
"data_source": "math_dapo",
"extra_info": {
"index": "c907eb8e-291f-4430-8107-7a7e9be061ff"
}
} | math_dapo |
[
{
"content": "Solve the following math problem step by step. 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 $3 \\times 3$ 整数元矩阵 \n$$ \nM=\\left(\\begin{array}{ccc} \n11 & 11 & 20 \\\\ \n10 & 10 & -8 \\\\ \n-10 & 2 & 8 ... | 288 | {
"ability": "MATH",
"data_source": "math_dapo",
"extra_info": {
"index": "45fedb1a-93ca-42dd-ab13-752e94e99b85"
}
} | math_dapo |
[
{
"content": "Solve the following math problem step by step. 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 architect is building a structure that will place vertical pillars at the vertices of regular hexagon $ABCDEF$, whi... | 17 | {
"ability": "MATH",
"data_source": "math_dapo",
"extra_info": {
"index": "d74c327a-9cdb-4da8-af36-94605b34ca24"
}
} | math_dapo |
[
{
"content": "Solve the following math problem step by step. 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 tens digit of the sum \\[ \\left(1!\\right)^2 + \\left(2!\\right)^2 + \\left(3!\\right)^2 + \\ldots + \\le... | 1 | {
"ability": "MATH",
"data_source": "math_dapo",
"extra_info": {
"index": "7621bf7c-7a15-492c-a625-f7cc4ac42393"
}
} | math_dapo |
[
{
"content": "Solve the following math problem step by step. 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 last eight digits of the binary representation of $27^{1986}$.\n\nRemember to put your answer on its own line... | 11011001 | {
"ability": "MATH",
"data_source": "math_dapo",
"extra_info": {
"index": "e726e0dc-0d9d-4b9b-864e-6be5b832b05c"
}
} | math_dapo |
[
{
"content": "Solve the following math problem step by step. 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已知在三棱锥 $D-A B C$ 中, $\\angle A C B=\\angle A B D=90^{\\circ}, C A=C B, \\angle B A D=30^{\\circ}$.若点 $C$ 在平面 $A B D$ 上... | 9 | {
"ability": "MATH",
"data_source": "math_dapo",
"extra_info": {
"index": "62853b37-c7d4-4b69-8b90-5ae38c25d4b7"
}
} | math_dapo |
[
{
"content": "Solve the following math problem step by step. 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 how many ways can $7$ red and $7$ white balls be distributed into $7$ boxes such that every box contains exactly $2... | 393 | {
"ability": "MATH",
"data_source": "math_dapo",
"extra_info": {
"index": "36999dfa-b3a9-447b-9d67-848b54a48716"
}
} | math_dapo |
[
{
"content": "Solve the following math problem step by step. 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 $M=\\{1,2,3, \\cdots, 1995\\}, A$ 是 $M$ 的子集且满足条件：当 $x \\in A$ 时， $15 x \\notin A$ ，则 $A$ 中元素的个\n数最多是 $\\qquad$.\n\nR... | 1870 | {
"ability": "MATH",
"data_source": "math_dapo",
"extra_info": {
"index": "c16d58de-7449-4da0-b096-1a729e441374"
}
} | math_dapo |
[
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nLet $ABC$ be a triangle with $AB=7$, $BC=9$, and $CA=4$. Let $D$ be the point such that $AB\\parallel CD$ and $CA\\pa... | 180 | {
"ability": "MATH",
"data_source": "math_dapo",
"extra_info": {
"index": "3cee50e7-f055-4259-a662-728dd6f66772"
}
} | math_dapo |
[
{
"content": "Solve the following math problem step by step. 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 quarry wants to sell a large pile of gravel. At full price, the gravel would sell for $3200$ dollars. During the fir... | 3000 | {
"ability": "MATH",
"data_source": "math_dapo",
"extra_info": {
"index": "1c5da1ee-e1dd-40bf-b776-f04d49910c99"
}
} | math_dapo |
[
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nThe sum of the areas of all triangles whose vertices are also vertices of a $1$ by $1$ by $1$ cube is $m + \\sqrt{n} +... | 348 | {
"ability": "MATH",
"data_source": "math_dapo",
"extra_info": {
"index": "0d567fa5-80ec-4ae6-bffa-b6b92bab6894"
}
} | math_dapo |
[
{
"content": "Solve the following math problem step by step. 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 semi-circle of radius 8 cm, rocks back and forth along a line. The distance between the line on which the semi-circ... | 55 | {
"ability": "MATH",
"data_source": "math_dapo",
"extra_info": {
"index": "e162751f-a3a4-4030-aa76-da6c04f63adb"
}
} | math_dapo |
[
{
"content": "Solve the following math problem step by step. 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设复数 $z$ 满足 $|z|=1$ ，使得关于 $x$ 的方程 $z x^{2}+2 \\bar{z} x+2=0$ 有实根，则这样的复数 $z$ 的和为以分数形式表示，请给出分子与分母的和。\n\nRemember to put y... | -1 | {
"ability": "MATH",
"data_source": "math_dapo",
"extra_info": {
"index": "70f6e1a4-af0a-46b9-8c96-8c1a6db4a513"
}
} | math_dapo |
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