data_source
stringclasses 1
value | prompt
listlengths 2
2
| ability
stringclasses 1
value | reward_model
dict | extra_info
dict |
|---|---|---|---|---|
math_dapo
|
[
{
"content": "Your task is to follow a systematic, thorough reasoning process before providing the final solution. This involves analyzing, summarizing, exploring, reassessing, and refining your thought process through multiple iterations. Structure your response into two sections: Thought and Solution. In the Thought section, present your reasoning using the format: \"<think>\n {thoughts} </think>\n\". Each thought should include detailed analysis, brainstorming, verification, and refinement of ideas. After \"</think>\n,\" in the Solution section, provide the final, logical, and accurate answer, clearly derived from the exploration in the Thought section.",
"role": "system"
},
{
"content": "将有 2018 行 4 列的方格表的每个格染成红色或蓝色，使得方格表每行的红格数与蓝格数相等，每列的红格数与蓝格数也相等. 记 m 为满足上述要求的染色方法的总数，求 m 除以 2018 所得的余数.\n\nPresent the answer in LaTeX format: \\boxed{Your answer}.",
"role": "user"
}
] |
MATH
|
{
"ground_truth": "6",
"style": "rule-lighteval/MATH_v2"
}
|
{
"index": "ff404c1f-75a7-459a-96f1-8485a9f933e1"
}
|
math_dapo
|
[
{
"content": "Your task is to follow a systematic, thorough reasoning process before providing the final solution. This involves analyzing, summarizing, exploring, reassessing, and refining your thought process through multiple iterations. Structure your response into two sections: Thought and Solution. In the Thought section, present your reasoning using the format: \"<think>\n {thoughts} </think>\n\". Each thought should include detailed analysis, brainstorming, verification, and refinement of ideas. After \"</think>\n,\" in the Solution section, provide the final, logical, and accurate answer, clearly derived from the exploration in the Thought section.",
"role": "system"
},
{
"content": "In the triangle $ABC$, $\\angle ABC = \\angle ACB = 78^\\circ$. On the sides $AB$ and $AC$, respectively, the points $D$ and $E$ are chosen such that $\\angle BCD = 24^\\circ$, $\\angle CBE = 51^\\circ$. Find the measure of angle $\\angle BED$.\n\nPresent the answer in LaTeX format: \\boxed{Your answer}.",
"role": "user"
}
] |
MATH
|
{
"ground_truth": "12",
"style": "rule-lighteval/MATH_v2"
}
|
{
"index": "2ff0283c-62e9-4be9-967d-1e89b4d86c06"
}
|
math_dapo
|
[
{
"content": "Your task is to follow a systematic, thorough reasoning process before providing the final solution. This involves analyzing, summarizing, exploring, reassessing, and refining your thought process through multiple iterations. Structure your response into two sections: Thought and Solution. In the Thought section, present your reasoning using the format: \"<think>\n {thoughts} </think>\n\". Each thought should include detailed analysis, brainstorming, verification, and refinement of ideas. After \"</think>\n,\" in the Solution section, provide the final, logical, and accurate answer, clearly derived from the exploration in the Thought section.",
"role": "system"
},
{
"content": "Find the last three digits of the product of the positive roots of $\\sqrt{1995}x^{\\log_{1995}x}=x^2$ .\n\nPresent the answer in LaTeX format: \\boxed{Your answer}.",
"role": "user"
}
] |
MATH
|
{
"ground_truth": "25",
"style": "rule-lighteval/MATH_v2"
}
|
{
"index": "2f9d954b-27bc-4de0-9410-9af87074d88f"
}
|
math_dapo
|
[
{
"content": "Your task is to follow a systematic, thorough reasoning process before providing the final solution. This involves analyzing, summarizing, exploring, reassessing, and refining your thought process through multiple iterations. Structure your response into two sections: Thought and Solution. In the Thought section, present your reasoning using the format: \"<think>\n {thoughts} </think>\n\". Each thought should include detailed analysis, brainstorming, verification, and refinement of ideas. After \"</think>\n,\" in the Solution section, provide the final, logical, and accurate answer, clearly derived from the exploration in the Thought section.",
"role": "system"
},
{
"content": "The values of $a$, $b$, $c$ and $d$ are 1, 2, 3 and 4, but not necessarily in that order. What is the largest possible value of the sum of the four products $ab$, $bc$, $cd$ and $da$?\n\nPresent the answer in LaTeX format: \\boxed{Your answer}.",
"role": "user"
}
] |
MATH
|
{
"ground_truth": "25",
"style": "rule-lighteval/MATH_v2"
}
|
{
"index": "106d185f-627c-475f-84ca-0a4c4335587e"
}
|
math_dapo
|
[
{
"content": "Your task is to follow a systematic, thorough reasoning process before providing the final solution. This involves analyzing, summarizing, exploring, reassessing, and refining your thought process through multiple iterations. Structure your response into two sections: Thought and Solution. In the Thought section, present your reasoning using the format: \"<think>\n {thoughts} </think>\n\". Each thought should include detailed analysis, brainstorming, verification, and refinement of ideas. After \"</think>\n,\" in the Solution section, provide the final, logical, and accurate answer, clearly derived from the exploration in the Thought section.",
"role": "system"
},
{
"content": "Find the least positive integer such that the product of its digits is $8! = 8 \\cdot 7 \\cdot6 \\cdot 5 \\cdot 4 \\cdot 3 \\cdot 2 \\cdot 1$.\n\nPresent the answer in LaTeX format: \\boxed{Your answer}.",
"role": "user"
}
] |
MATH
|
{
"ground_truth": "257889",
"style": "rule-lighteval/MATH_v2"
}
|
{
"index": "b95f2717-7f00-41b0-91f4-8bc7ba4b65aa"
}
|
math_dapo
|
[
{
"content": "Your task is to follow a systematic, thorough reasoning process before providing the final solution. This involves analyzing, summarizing, exploring, reassessing, and refining your thought process through multiple iterations. Structure your response into two sections: Thought and Solution. In the Thought section, present your reasoning using the format: \"<think>\n {thoughts} </think>\n\". Each thought should include detailed analysis, brainstorming, verification, and refinement of ideas. After \"</think>\n,\" in the Solution section, provide the final, logical, and accurate answer, clearly derived from the exploration in the Thought section.",
"role": "system"
},
{
"content": "The energy stored by any pair of positive charges is inversely proportional to the distance between them, and directly proportional to their charges. Three identical point charges start at the vertices of an equilateral triangle, and this configuration stores 15 Joules of energy. How much more energy, in Joules, would be stored if one of these charges was moved to the midpoint of the opposite side?\n\nPresent the answer in LaTeX format: \\boxed{Your answer}.",
"role": "user"
}
] |
MATH
|
{
"ground_truth": "10",
"style": "rule-lighteval/MATH_v2"
}
|
{
"index": "646f9b4a-6cd3-4954-a80f-1d5dc0b3f89f"
}
|
math_dapo
|
[
{
"content": "Your task is to follow a systematic, thorough reasoning process before providing the final solution. This involves analyzing, summarizing, exploring, reassessing, and refining your thought process through multiple iterations. Structure your response into two sections: Thought and Solution. In the Thought section, present your reasoning using the format: \"<think>\n {thoughts} </think>\n\". Each thought should include detailed analysis, brainstorming, verification, and refinement of ideas. After \"</think>\n,\" in the Solution section, provide the final, logical, and accurate answer, clearly derived from the exploration in the Thought section.",
"role": "system"
},
{
"content": "Compute the number of triangles of different sizes which contain the gray triangle in the figure below.\n\n\\[ \\text{[asy]} \\]\n\n```asy\nsize(5cm);\nreal n = 4;\nfor (int i = 0; i < n; ++i) {\n draw((0.5*i,0.866*i)--(n-0.5*i,0.866*i));\n}\nfor (int i = 0; i < n; ++i) {\n draw((n-i,0)--((n-i)/2,(n-i)*0.866));\n}\nfor (int i = 0; i < n; ++i) {\n draw((i,0)--((n+i)/2,(n-i)*0.866));\n}\nfilldraw((1.5,0.866)--(2,2*0.866)--(2.5,0.866)--cycle, gray);\n```\n\nPresent the answer in LaTeX format: \\boxed{Your answer}.",
"role": "user"
}
] |
MATH
|
{
"ground_truth": "4",
"style": "rule-lighteval/MATH_v2"
}
|
{
"index": "f5fb58de-e35f-445b-bf30-b4092503ebdf"
}
|
math_dapo
|
[
{
"content": "Your task is to follow a systematic, thorough reasoning process before providing the final solution. This involves analyzing, summarizing, exploring, reassessing, and refining your thought process through multiple iterations. Structure your response into two sections: Thought and Solution. In the Thought section, present your reasoning using the format: \"<think>\n {thoughts} </think>\n\". Each thought should include detailed analysis, brainstorming, verification, and refinement of ideas. After \"</think>\n,\" in the Solution section, provide the final, logical, and accurate answer, clearly derived from the exploration in the Thought section.",
"role": "system"
},
{
"content": "在椭圆 $\\Gamma$ 中, $A$ 为长轴的一个端点, $B$ 为短轴的一个端点, $F_{1}, F_{2}$ 为两个焦点. 若 $\\overrightarrow{A F_{1}} \\cdot \\overrightarrow{A F_{2}}+\\overrightarrow{B F_{1}} \\cdot \\overrightarrow{B F_{2}}=0$, 则 $\\frac{|A B|}{\\left|F_{1} F_{2}\\right|}$ 的值为 $\\frac{\\sqrt{m}}{n}$ 的形式，请给出 $m + n$ 的值。\n\nPresent the answer in LaTeX format: \\boxed{Your answer}.",
"role": "user"
}
] |
MATH
|
{
"ground_truth": "4",
"style": "rule-lighteval/MATH_v2"
}
|
{
"index": "5b2a3f34-f2dc-4dd5-9302-e5341333a14f"
}
|
math_dapo
|
[
{
"content": "Your task is to follow a systematic, thorough reasoning process before providing the final solution. This involves analyzing, summarizing, exploring, reassessing, and refining your thought process through multiple iterations. Structure your response into two sections: Thought and Solution. In the Thought section, present your reasoning using the format: \"<think>\n {thoughts} </think>\n\". Each thought should include detailed analysis, brainstorming, verification, and refinement of ideas. After \"</think>\n,\" in the Solution section, provide the final, logical, and accurate answer, clearly derived from the exploration in the Thought section.",
"role": "system"
},
{
"content": "Suppose that $ABC$ is a triangle with $AB = 6$, $BC = 12$, and $\\angle B = 90^{\\circ}$. Point $D$ lies on side $BC$, and point $E$ is constructed on $AC$ such that $\\angle ADE = 90^{\\circ}$. Given that $DE = EC = \\frac{a\\sqrt{b}}{c}$ for positive integers $a$, $b$, and $c$ with $b$ squarefree and $\\gcd(a,c) = 1$, find $a + b + c$.\n\nPresent the answer in LaTeX format: \\boxed{Your answer}.",
"role": "user"
}
] |
MATH
|
{
"ground_truth": "18",
"style": "rule-lighteval/MATH_v2"
}
|
{
"index": "27e33e54-dcab-4fd4-a7f4-a9d64f89df93"
}
|
math_dapo
|
[
{
"content": "Your task is to follow a systematic, thorough reasoning process before providing the final solution. This involves analyzing, summarizing, exploring, reassessing, and refining your thought process through multiple iterations. Structure your response into two sections: Thought and Solution. In the Thought section, present your reasoning using the format: \"<think>\n {thoughts} </think>\n\". Each thought should include detailed analysis, brainstorming, verification, and refinement of ideas. After \"</think>\n,\" in the Solution section, provide the final, logical, and accurate answer, clearly derived from the exploration in the Thought section.",
"role": "system"
},
{
"content": "设函数 $f(x)$ 的定义域为 $\\mathbf{R}$, 且当 $x \\geq 0$ 时, $f(x)=|x-2|+a$ (其中 $a$ 为实数). 若 $f(x)$ 为奇函数, 则不等式 $f(x) \\geq 1$ 的解集为$[a,b] \\cup[c,+\\infty)$，求$a+b+c$的值。\n\nPresent the answer in LaTeX format: \\boxed{Your answer}.",
"role": "user"
}
] |
MATH
|
{
"ground_truth": "1",
"style": "rule-lighteval/MATH_v2"
}
|
{
"index": "2ba0284e-a389-47a1-a25d-85a9dd0f0a12"
}
|
math_dapo
|
[
{
"content": "Your task is to follow a systematic, thorough reasoning process before providing the final solution. This involves analyzing, summarizing, exploring, reassessing, and refining your thought process through multiple iterations. Structure your response into two sections: Thought and Solution. In the Thought section, present your reasoning using the format: \"<think>\n {thoughts} </think>\n\". Each thought should include detailed analysis, brainstorming, verification, and refinement of ideas. After \"</think>\n,\" in the Solution section, provide the final, logical, and accurate answer, clearly derived from the exploration in the Thought section.",
"role": "system"
},
{
"content": "Find the last digit of $7^1 \\times 7^2 \\times 7^3 \\times \\cdots \\times 7^{2009} \\times 7^{2010}$.\n\nPresent the answer in LaTeX format: \\boxed{Your answer}.",
"role": "user"
}
] |
MATH
|
{
"ground_truth": "3",
"style": "rule-lighteval/MATH_v2"
}
|
{
"index": "27b179b7-1741-481e-94d4-1405ccf598a9"
}
|
math_dapo
|
[
{
"content": "Your task is to follow a systematic, thorough reasoning process before providing the final solution. This involves analyzing, summarizing, exploring, reassessing, and refining your thought process through multiple iterations. Structure your response into two sections: Thought and Solution. In the Thought section, present your reasoning using the format: \"<think>\n {thoughts} </think>\n\". Each thought should include detailed analysis, brainstorming, verification, and refinement of ideas. After \"</think>\n,\" in the Solution section, provide the final, logical, and accurate answer, clearly derived from the exploration in the Thought section.",
"role": "system"
},
{
"content": "Let $m$ be the least positive integer divisible by $17$ whose digits sum to $17$. Find $m$.\n\nPresent the answer in LaTeX format: \\boxed{Your answer}.",
"role": "user"
}
] |
MATH
|
{
"ground_truth": "476",
"style": "rule-lighteval/MATH_v2"
}
|
{
"index": "5e76ea79-e169-43eb-9e50-cf29b13dd45c"
}
|
math_dapo
|
[
{
"content": "Your task is to follow a systematic, thorough reasoning process before providing the final solution. This involves analyzing, summarizing, exploring, reassessing, and refining your thought process through multiple iterations. Structure your response into two sections: Thought and Solution. In the Thought section, present your reasoning using the format: \"<think>\n {thoughts} </think>\n\". Each thought should include detailed analysis, brainstorming, verification, and refinement of ideas. After \"</think>\n,\" in the Solution section, provide the final, logical, and accurate answer, clearly derived from the exploration in the Thought section.",
"role": "system"
},
{
"content": "The Miami Heat and the San Antonio Spurs are playing a best-of-five series basketball championship, in which the team that first wins three games wins the whole series. Assume that the probability that the Heat wins a given game is $x$ (there are no ties). The expected value for the total number of games played can be written as $f(x)$, with $f$ a polynomial. Find $f(-1)$.\n\nPresent the answer in LaTeX format: \\boxed{Your answer}.",
"role": "user"
}
] |
MATH
|
{
"ground_truth": "21",
"style": "rule-lighteval/MATH_v2"
}
|
{
"index": "7f250801-b1f0-4f6f-9dab-3c4150e08ef8"
}
|
math_dapo
|
[
{
"content": "Your task is to follow a systematic, thorough reasoning process before providing the final solution. This involves analyzing, summarizing, exploring, reassessing, and refining your thought process through multiple iterations. Structure your response into two sections: Thought and Solution. In the Thought section, present your reasoning using the format: \"<think>\n {thoughts} </think>\n\". Each thought should include detailed analysis, brainstorming, verification, and refinement of ideas. After \"</think>\n,\" in the Solution section, provide the final, logical, and accurate answer, clearly derived from the exploration in the Thought section.",
"role": "system"
},
{
"content": "What is the minimum possible perimeter of a right triangle with integer side lengths whose perimeter is equal to its area?\n\nPresent the answer in LaTeX format: \\boxed{Your answer}.",
"role": "user"
}
] |
MATH
|
{
"ground_truth": "24",
"style": "rule-lighteval/MATH_v2"
}
|
{
"index": "fdf8321c-7986-4a31-b382-412334e6bae8"
}
|
math_dapo
|
[
{
"content": "Your task is to follow a systematic, thorough reasoning process before providing the final solution. This involves analyzing, summarizing, exploring, reassessing, and refining your thought process through multiple iterations. Structure your response into two sections: Thought and Solution. In the Thought section, present your reasoning using the format: \"<think>\n {thoughts} </think>\n\". Each thought should include detailed analysis, brainstorming, verification, and refinement of ideas. After \"</think>\n,\" in the Solution section, provide the final, logical, and accurate answer, clearly derived from the exploration in the Thought section.",
"role": "system"
},
{
"content": "已知集合\n$T=\\left\\{n \\mid n=5^{a}+5^{b}, 0 \\leqslant a \\leqslant b \\leqslant 30, a 、 b \\in \\mathbf{Z}\\right\\}$ 。\n若从集合 $T$ 中随机取出一个数，则该数是 $9$ 的倍数的概率为 $\\qquad$.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 + n的值\n\nPresent the answer in LaTeX format: \\boxed{Your answer}.",
"role": "user"
}
] |
MATH
|
{
"ground_truth": "36",
"style": "rule-lighteval/MATH_v2"
}
|
{
"index": "cbc81144-ea81-4e2a-b764-23f7667d178c"
}
|
math_dapo
|
[
{
"content": "Your task is to follow a systematic, thorough reasoning process before providing the final solution. This involves analyzing, summarizing, exploring, reassessing, and refining your thought process through multiple iterations. Structure your response into two sections: Thought and Solution. In the Thought section, present your reasoning using the format: \"<think>\n {thoughts} </think>\n\". Each thought should include detailed analysis, brainstorming, verification, and refinement of ideas. After \"</think>\n,\" in the Solution section, provide the final, logical, and accurate answer, clearly derived from the exploration in the Thought section.",
"role": "system"
},
{
"content": "Find the number of four-element subsets of $\\{1,2,3,4,\\cdots, 20\\}$ with the property that two distinct elements of a subset have a sum of $16$, and two distinct elements of a subset have a sum of $24$. For example, $\\{3,5,13,19\\}$ and $\\{6,10,20,18\\}$ are two such subsets.\n\nPresent the answer in LaTeX format: \\boxed{Your answer}.",
"role": "user"
}
] |
MATH
|
{
"ground_truth": "210",
"style": "rule-lighteval/MATH_v2"
}
|
{
"index": "5b7135e8-48a3-4529-9929-7e7cb48d6822"
}
|
math_dapo
|
[
{
"content": "Your task is to follow a systematic, thorough reasoning process before providing the final solution. This involves analyzing, summarizing, exploring, reassessing, and refining your thought process through multiple iterations. Structure your response into two sections: Thought and Solution. In the Thought section, present your reasoning using the format: \"<think>\n {thoughts} </think>\n\". Each thought should include detailed analysis, brainstorming, verification, and refinement of ideas. After \"</think>\n,\" in the Solution section, provide the final, logical, and accurate answer, clearly derived from the exploration in the Thought section.",
"role": "system"
},
{
"content": "The five solutions to the equation\\[(z-1)(z^2+2z+4)(z^2+4z+6)=0\\] may be written in the form $x_k+y_ki$ for $1\\le k\\le 5,$ where $x_k$ and $y_k$ are real. Let $\\mathcal E$ be the unique ellipse that passes through the points $(x_1,y_1),(x_2,y_2),(x_3,y_3),(x_4,y_4),$ and $(x_5,y_5)$. The eccentricity of $\\mathcal E$ can be written in the form $\\sqrt{\\frac mn}$, where $m$ and $n$ are relatively prime positive integers. Find the value of $m+n$. (Recall that the eccentricity of an ellipse $\\mathcal E$ is the ratio $\\frac ca$, where $2a$ is the length of the major axis of $\\mathcal E$ and $2c$ is the distance between its two foci.)\n\nPresent the answer in LaTeX format: \\boxed{Your answer}.",
"role": "user"
}
] |
MATH
|
{
"ground_truth": "7",
"style": "rule-lighteval/MATH_v2"
}
|
{
"index": "a4022163-9370-41c3-9d4a-df46c1293efe"
}
|
math_dapo
|
[
{
"content": "Your task is to follow a systematic, thorough reasoning process before providing the final solution. This involves analyzing, summarizing, exploring, reassessing, and refining your thought process through multiple iterations. Structure your response into two sections: Thought and Solution. In the Thought section, present your reasoning using the format: \"<think>\n {thoughts} </think>\n\". Each thought should include detailed analysis, brainstorming, verification, and refinement of ideas. After \"</think>\n,\" in the Solution section, provide the final, logical, and accurate answer, clearly derived from the exploration in the Thought section.",
"role": "system"
},
{
"content": "What is the largest integer $n$ that satisfies $(100^2-99^2)(99^2-98^2)\\cdots(3^2-2^2)(2^2-1^2)$ is divisible by $3^n$?\n\nPresent the answer in LaTeX format: \\boxed{Your answer}.",
"role": "user"
}
] |
MATH
|
{
"ground_truth": "49",
"style": "rule-lighteval/MATH_v2"
}
|
{
"index": "c35ba1b7-e65d-4ab2-bcd8-58c2248d9240"
}
|
math_dapo
|
[
{
"content": "Your task is to follow a systematic, thorough reasoning process before providing the final solution. This involves analyzing, summarizing, exploring, reassessing, and refining your thought process through multiple iterations. Structure your response into two sections: Thought and Solution. In the Thought section, present your reasoning using the format: \"<think>\n {thoughts} </think>\n\". Each thought should include detailed analysis, brainstorming, verification, and refinement of ideas. After \"</think>\n,\" in the Solution section, provide the final, logical, and accurate answer, clearly derived from the exploration in the Thought section.",
"role": "system"
},
{
"content": "Segments $\\overline{AB}, \\overline{AC},$ and $\\overline{AD}$ are edges of a cube and $\\overline{AG}$ is a diagonal through the center of the cube. Point $P$ satisfies $BP=60\\sqrt{10}$, $CP=60\\sqrt{5}$, $DP=120\\sqrt{2}$, and $GP=36\\sqrt{7}$. Find $AP.$\n\nPresent the answer in LaTeX format: \\boxed{Your answer}.",
"role": "user"
}
] |
MATH
|
{
"ground_truth": "192",
"style": "rule-lighteval/MATH_v2"
}
|
{
"index": "a5a317c3-1449-46eb-bd59-38bd41461d79"
}
|
math_dapo
|
[
{
"content": "Your task is to follow a systematic, thorough reasoning process before providing the final solution. This involves analyzing, summarizing, exploring, reassessing, and refining your thought process through multiple iterations. Structure your response into two sections: Thought and Solution. In the Thought section, present your reasoning using the format: \"<think>\n {thoughts} </think>\n\". Each thought should include detailed analysis, brainstorming, verification, and refinement of ideas. After \"</think>\n,\" in the Solution section, provide the final, logical, and accurate answer, clearly derived from the exploration in the Thought section.",
"role": "system"
},
{
"content": "At Stanford in 1988, human calculator Shakuntala Devi was asked to compute $m = \\sqrt[3]{61,629,875}$ and $n = \\sqrt[7]{170,859,375}$. Given that $m$ and $n$ are both integers, compute $100m+n$.\n\nPresent the answer in LaTeX format: \\boxed{Your answer}.",
"role": "user"
}
] |
MATH
|
{
"ground_truth": "39515",
"style": "rule-lighteval/MATH_v2"
}
|
{
"index": "c73e94de-9033-4ba8-b620-363abd51fbbc"
}
|
math_dapo
|
[
{
"content": "Your task is to follow a systematic, thorough reasoning process before providing the final solution. This involves analyzing, summarizing, exploring, reassessing, and refining your thought process through multiple iterations. Structure your response into two sections: Thought and Solution. In the Thought section, present your reasoning using the format: \"<think>\n {thoughts} </think>\n\". Each thought should include detailed analysis, brainstorming, verification, and refinement of ideas. After \"</think>\n,\" in the Solution section, provide the final, logical, and accurate answer, clearly derived from the exploration in the Thought section.",
"role": "system"
},
{
"content": "Initially, a natural number $n$ is written on the blackboard. Then, at each minute, Esmeralda chooses a divisor $d > 1$ of $n$, erases $n$, and writes $n + d$. If the initial number on the board is $2022$, what is the largest composite number that Esmeralda will never be able to write on the blackboard?\n\nPresent the answer in LaTeX format: \\boxed{Your answer}.",
"role": "user"
}
] |
MATH
|
{
"ground_truth": "2023",
"style": "rule-lighteval/MATH_v2"
}
|
{
"index": "57a9956b-3a96-435f-a599-fa15c08e7189"
}
|
math_dapo
|
[
{
"content": "Your task is to follow a systematic, thorough reasoning process before providing the final solution. This involves analyzing, summarizing, exploring, reassessing, and refining your thought process through multiple iterations. Structure your response into two sections: Thought and Solution. In the Thought section, present your reasoning using the format: \"<think>\n {thoughts} </think>\n\". Each thought should include detailed analysis, brainstorming, verification, and refinement of ideas. After \"</think>\n,\" in the Solution section, provide the final, logical, and accurate answer, clearly derived from the exploration in the Thought section.",
"role": "system"
},
{
"content": "Compute the smallest positive integer $a$ for which $$\\sqrt{a +\\sqrt{a +...}} - \\frac{1}{a +\\frac{1}{a+...}}> 7$$\n\nPresent the answer in LaTeX format: \\boxed{Your answer}.",
"role": "user"
}
] |
MATH
|
{
"ground_truth": "43",
"style": "rule-lighteval/MATH_v2"
}
|
{
"index": "4e254ea6-64dc-46d5-8690-7b8f0fd04982"
}
|
math_dapo
|
[
{
"content": "Your task is to follow a systematic, thorough reasoning process before providing the final solution. This involves analyzing, summarizing, exploring, reassessing, and refining your thought process through multiple iterations. Structure your response into two sections: Thought and Solution. In the Thought section, present your reasoning using the format: \"<think>\n {thoughts} </think>\n\". Each thought should include detailed analysis, brainstorming, verification, and refinement of ideas. After \"</think>\n,\" in the Solution section, provide the final, logical, and accurate answer, clearly derived from the exploration in the Thought section.",
"role": "system"
},
{
"content": "Find the number of ordered pairs of positive integers $(a,b)$ such that $a+b=1000$ and neither $a$ nor $b$ has a zero digit.\n\nPresent the answer in LaTeX format: \\boxed{Your answer}.",
"role": "user"
}
] |
MATH
|
{
"ground_truth": "738",
"style": "rule-lighteval/MATH_v2"
}
|
{
"index": "326febfc-72f4-4e3b-96fa-b52cfeda2700"
}
|
math_dapo
|
[
{
"content": "Your task is to follow a systematic, thorough reasoning process before providing the final solution. This involves analyzing, summarizing, exploring, reassessing, and refining your thought process through multiple iterations. Structure your response into two sections: Thought and Solution. In the Thought section, present your reasoning using the format: \"<think>\n {thoughts} </think>\n\". Each thought should include detailed analysis, brainstorming, verification, and refinement of ideas. After \"</think>\n,\" in the Solution section, provide the final, logical, and accurate answer, clearly derived from the exploration in the Thought section.",
"role": "system"
},
{
"content": "Let $q$ be a real number. Gugu has a napkin with ten distinct real numbers written on it, and he writes the following three lines of real numbers on the blackboard:\n- In the first line, Gugu writes down every number of the form $a-b$, where $a$ and $b$ are two (not necessarily distinct) numbers on his napkin.\n- In the second line, Gugu writes down every number of the form $qab$, where $a$ and $b$ are two (not necessarily distinct) numbers from the first line.\n- In the third line, Gugu writes down every number of the form $a^2+b^2-c^2-d^2$, where $a, b, c, d$ are four (not necessarily distinct) numbers from the first line.\n\nDetermine all values of $q$ such that, regardless of the numbers on Gugu's napkin, every number in the second line is also a number in the third line.\n\nPresent the answer in LaTeX format: \\boxed{Your answer}.",
"role": "user"
}
] |
MATH
|
{
"ground_truth": "0",
"style": "rule-lighteval/MATH_v2"
}
|
{
"index": "cf6640af-1d43-414e-a62c-593105292999"
}
|
math_dapo
|
[
{
"content": "Your task is to follow a systematic, thorough reasoning process before providing the final solution. This involves analyzing, summarizing, exploring, reassessing, and refining your thought process through multiple iterations. Structure your response into two sections: Thought and Solution. In the Thought section, present your reasoning using the format: \"<think>\n {thoughts} </think>\n\". Each thought should include detailed analysis, brainstorming, verification, and refinement of ideas. After \"</think>\n,\" in the Solution section, provide the final, logical, and accurate answer, clearly derived from the exploration in the Thought section.",
"role": "system"
},
{
"content": "Compute the smallest positive integer $n$ for which $\\sqrt{100+\\sqrt{n}} + \\sqrt{100-\\sqrt{n}}$ is an integer.\n\nPresent the answer in LaTeX format: \\boxed{Your answer}.",
"role": "user"
}
] |
MATH
|
{
"ground_truth": "6156",
"style": "rule-lighteval/MATH_v2"
}
|
{
"index": "db7fdc76-c57f-4512-8241-9303a5a74c98"
}
|
math_dapo
|
[
{
"content": "Your task is to follow a systematic, thorough reasoning process before providing the final solution. This involves analyzing, summarizing, exploring, reassessing, and refining your thought process through multiple iterations. Structure your response into two sections: Thought and Solution. In the Thought section, present your reasoning using the format: \"<think>\n {thoughts} </think>\n\". Each thought should include detailed analysis, brainstorming, verification, and refinement of ideas. After \"</think>\n,\" in the Solution section, provide the final, logical, and accurate answer, clearly derived from the exploration in the Thought section.",
"role": "system"
},
{
"content": "What is the smallest possible natural number $n$ for which the equation $x^2 - nx + 2014 = 0$ has integer roots?\n\nPresent the answer in LaTeX format: \\boxed{Your answer}.",
"role": "user"
}
] |
MATH
|
{
"ground_truth": "91",
"style": "rule-lighteval/MATH_v2"
}
|
{
"index": "93cdb2cb-d083-4cca-92b6-5e235bc91394"
}
|
math_dapo
|
[
{
"content": "Your task is to follow a systematic, thorough reasoning process before providing the final solution. This involves analyzing, summarizing, exploring, reassessing, and refining your thought process through multiple iterations. Structure your response into two sections: Thought and Solution. In the Thought section, present your reasoning using the format: \"<think>\n {thoughts} </think>\n\". Each thought should include detailed analysis, brainstorming, verification, and refinement of ideas. After \"</think>\n,\" in the Solution section, provide the final, logical, and accurate answer, clearly derived from the exploration in the Thought section.",
"role": "system"
},
{
"content": "若四棱雉 $P-A B C D$ 的棱 $A B, B C$ 的长均为 $\\sqrt{2}$, 其他各条棱长均为 1, 则该四棱雉的体积为$\\frac{\\sqrt{m}}{n}$的形式，请给出$m + n$的值。\n\nPresent the answer in LaTeX format: \\boxed{Your answer}.",
"role": "user"
}
] |
MATH
|
{
"ground_truth": "8",
"style": "rule-lighteval/MATH_v2"
}
|
{
"index": "2fdad358-c88f-449d-8ba3-3af0872ea878"
}
|
math_dapo
|
[
{
"content": "Your task is to follow a systematic, thorough reasoning process before providing the final solution. This involves analyzing, summarizing, exploring, reassessing, and refining your thought process through multiple iterations. Structure your response into two sections: Thought and Solution. In the Thought section, present your reasoning using the format: \"<think>\n {thoughts} </think>\n\". Each thought should include detailed analysis, brainstorming, verification, and refinement of ideas. After \"</think>\n,\" in the Solution section, provide the final, logical, and accurate answer, clearly derived from the exploration in the Thought section.",
"role": "system"
},
{
"content": "Find all three-digit numbers such that the square of the number is equal to the sum of their digits raised to the power of 5.\n\nPresent the answer in LaTeX format: \\boxed{Your answer}.",
"role": "user"
}
] |
MATH
|
{
"ground_truth": "243",
"style": "rule-lighteval/MATH_v2"
}
|
{
"index": "e2adf1a7-5875-47b4-89ae-b05815bfaec7"
}
|
math_dapo
|
[
{
"content": "Your task is to follow a systematic, thorough reasoning process before providing the final solution. This involves analyzing, summarizing, exploring, reassessing, and refining your thought process through multiple iterations. Structure your response into two sections: Thought and Solution. In the Thought section, present your reasoning using the format: \"<think>\n {thoughts} </think>\n\". Each thought should include detailed analysis, brainstorming, verification, and refinement of ideas. After \"</think>\n,\" in the Solution section, provide the final, logical, and accurate answer, clearly derived from the exploration in the Thought section.",
"role": "system"
},
{
"content": "Cutting equilateral triangle $BFC$ out of square $ABCD$ and translating it to the left of the square creates the shaded figure $ABFCDE$. The perimeter of square $ABCD$ was 48 inches. What is the perimeter, in inches, of $ABFCDE$?\n\n[asy]\nfilldraw((0,0)--(sqrt(3),1)--(sqrt(3)+2,1)--(2,0)--(sqrt(3)+2,-1)--(sqrt(3),-1)--(0,0)--cycle,gray,linewidth(1));\ndraw((sqrt(3),1)--(sqrt(3),-1),linewidth(1));\ndraw((sqrt(3)+2,-1)--(sqrt(3)+2,1)--(2,0)--(sqrt(3)+2,-1)--cycle,dashed);\n\nlabel(\"A\",(sqrt(3),1),N);\nlabel(\"B\",(sqrt(3)+2,1),N);\nlabel(\"C\",(sqrt(3)+2,-1),S);\nlabel(\"D\",(sqrt(3),-1),S);\nlabel(\"E\",(0,0),W);\nlabel(\"F\",(2,0),N);\n[/asy]\n\nPresent the answer in LaTeX format: \\boxed{Your answer}.",
"role": "user"
}
] |
MATH
|
{
"ground_truth": "72",
"style": "rule-lighteval/MATH_v2"
}
|
{
"index": "b550a8fb-2581-492c-a3bf-3ded553a42c0"
}
|
math_dapo
|
[
{
"content": "Your task is to follow a systematic, thorough reasoning process before providing the final solution. This involves analyzing, summarizing, exploring, reassessing, and refining your thought process through multiple iterations. Structure your response into two sections: Thought and Solution. In the Thought section, present your reasoning using the format: \"<think>\n {thoughts} </think>\n\". Each thought should include detailed analysis, brainstorming, verification, and refinement of ideas. After \"</think>\n,\" in the Solution section, provide the final, logical, and accurate answer, clearly derived from the exploration in the Thought section.",
"role": "system"
},
{
"content": "Determine the smallest natural number written in the decimal system such that the product of its digits equals $10! = 1 \\times 2 \\times 3 \\times \\ldots \\times 9 \\times 10$.\n\nPresent the answer in LaTeX format: \\boxed{Your answer}.",
"role": "user"
}
] |
MATH
|
{
"ground_truth": "45578899",
"style": "rule-lighteval/MATH_v2"
}
|
{
"index": "2b52d2f0-59a0-480b-b5e0-e3a5bbaf8d20"
}
|
math_dapo
|
[
{
"content": "Your task is to follow a systematic, thorough reasoning process before providing the final solution. This involves analyzing, summarizing, exploring, reassessing, and refining your thought process through multiple iterations. Structure your response into two sections: Thought and Solution. In the Thought section, present your reasoning using the format: \"<think>\n {thoughts} </think>\n\". Each thought should include detailed analysis, brainstorming, verification, and refinement of ideas. After \"</think>\n,\" in the Solution section, provide the final, logical, and accurate answer, clearly derived from the exploration in the Thought section.",
"role": "system"
},
{
"content": "Calculate the sum of the coordinates of all pairs of positive integers $(n, k)$ such that $k\\equiv 0, 3\\pmod 4$, $n > k$, and $\\displaystyle\\sum^n_{i = k + 1} i^3 = (96^2\\cdot3 - 1)\\displaystyle\\left(\\sum^k_{i = 1} i\\right)^2 + 48^2$\n\nPresent the answer in LaTeX format: \\boxed{Your answer}.",
"role": "user"
}
] |
MATH
|
{
"ground_truth": "103",
"style": "rule-lighteval/MATH_v2"
}
|
{
"index": "19b02f3f-fed8-49d8-b4a8-c25ddc9d836c"
}
|
math_dapo
|
[
{
"content": "Your task is to follow a systematic, thorough reasoning process before providing the final solution. This involves analyzing, summarizing, exploring, reassessing, and refining your thought process through multiple iterations. Structure your response into two sections: Thought and Solution. In the Thought section, present your reasoning using the format: \"<think>\n {thoughts} </think>\n\". Each thought should include detailed analysis, brainstorming, verification, and refinement of ideas. After \"</think>\n,\" in the Solution section, provide the final, logical, and accurate answer, clearly derived from the exploration in the Thought section.",
"role": "system"
},
{
"content": "Let $S$ be the set of points whose coordinates $x,$ $y,$ and $z$ are integers that satisfy $0\\le x\\le2,$ $0\\le y\\le3,$ and $0\\le z\\le4.$ Two distinct points are randomly chosen from $S.$ The probability that the midpoint of the segment they determine also belongs to $S$ is $m/n,$ where $m$ and $n$ are relatively prime positive integers. Find $m + n.$\n\nPresent the answer in LaTeX format: \\boxed{Your answer}.",
"role": "user"
}
] |
MATH
|
{
"ground_truth": "200",
"style": "rule-lighteval/MATH_v2"
}
|
{
"index": "17051c97-34b2-43e8-8f67-80ab35c16c74"
}
|
math_dapo
|
[
{
"content": "Your task is to follow a systematic, thorough reasoning process before providing the final solution. This involves analyzing, summarizing, exploring, reassessing, and refining your thought process through multiple iterations. Structure your response into two sections: Thought and Solution. In the Thought section, present your reasoning using the format: \"<think>\n {thoughts} </think>\n\". Each thought should include detailed analysis, brainstorming, verification, and refinement of ideas. After \"</think>\n,\" in the Solution section, provide the final, logical, and accurate answer, clearly derived from the exploration in the Thought section.",
"role": "system"
},
{
"content": "在正四面体 $A B C D$ 中, $E, F$ 分别在棱 $A B, A C$ 上, 满足 $B E=3, E F=4$, 且 $E F$与面 $B C D$ 平行，则 $\\triangle D E F$ 的面积为 $\\qquad$.\n原始的答案是k\\sqrt{m}+n的形式，请给出k + m + n的值。\n\nPresent the answer in LaTeX format: \\boxed{Your answer}.",
"role": "user"
}
] |
MATH
|
{
"ground_truth": "35",
"style": "rule-lighteval/MATH_v2"
}
|
{
"index": "06110a8b-a70a-4af6-8093-ac120db93a95"
}
|
math_dapo
|
[
{
"content": "Your task is to follow a systematic, thorough reasoning process before providing the final solution. This involves analyzing, summarizing, exploring, reassessing, and refining your thought process through multiple iterations. Structure your response into two sections: Thought and Solution. In the Thought section, present your reasoning using the format: \"<think>\n {thoughts} </think>\n\". Each thought should include detailed analysis, brainstorming, verification, and refinement of ideas. After \"</think>\n,\" in the Solution section, provide the final, logical, and accurate answer, clearly derived from the exploration in the Thought section.",
"role": "system"
},
{
"content": "How many four-digit numbers whose digits add up to $9$ are divisible by $11$?\n\nPresent the answer in LaTeX format: \\boxed{Your answer}.",
"role": "user"
}
] |
MATH
|
{
"ground_truth": "0",
"style": "rule-lighteval/MATH_v2"
}
|
{
"index": "10c5579e-2c55-4a66-999c-b9fa11ea2e11"
}
|
math_dapo
|
[
{
"content": "Your task is to follow a systematic, thorough reasoning process before providing the final solution. This involves analyzing, summarizing, exploring, reassessing, and refining your thought process through multiple iterations. Structure your response into two sections: Thought and Solution. In the Thought section, present your reasoning using the format: \"<think>\n {thoughts} </think>\n\". Each thought should include detailed analysis, brainstorming, verification, and refinement of ideas. After \"</think>\n,\" in the Solution section, provide the final, logical, and accurate answer, clearly derived from the exploration in the Thought section.",
"role": "system"
},
{
"content": "Players $A$ and $B$ play a game on a blackboard that initially contains 2020 copies of the number 1 . In every round, player $A$ erases two numbers $x$ and $y$ from the blackboard, and then player $B$ writes one of the numbers $x+y$ and $|x-y|$ on the blackboard. The game terminates as soon as, at the end of some round, one of the following holds:\n(1) one of the numbers on the blackboard is larger than the sum of all other numbers;\n(2) there are only zeros on the blackboard.\n\nPlayer $B$ must then give as many cookies to player $A$ as there are numbers on the blackboard. Player $A$ wants to get as many cookies as possible, whereas player $B$ wants to give as few as possible. Determine the number of cookies that $A$ receives if both players play optimally.\n\nPresent the answer in LaTeX format: \\boxed{Your answer}.",
"role": "user"
}
] |
MATH
|
{
"ground_truth": "7",
"style": "rule-lighteval/MATH_v2"
}
|
{
"index": "29267fa5-4acc-4983-80d3-7620d96135ee"
}
|
math_dapo
|
[
{
"content": "Your task is to follow a systematic, thorough reasoning process before providing the final solution. This involves analyzing, summarizing, exploring, reassessing, and refining your thought process through multiple iterations. Structure your response into two sections: Thought and Solution. In the Thought section, present your reasoning using the format: \"<think>\n {thoughts} </think>\n\". Each thought should include detailed analysis, brainstorming, verification, and refinement of ideas. After \"</think>\n,\" in the Solution section, provide the final, logical, and accurate answer, clearly derived from the exploration in the Thought section.",
"role": "system"
},
{
"content": "The diagonals of rectangle $PQRS$ intersect at point $X$. If $PS = 10$ and $RS=24$, then what is $\\cos \\angle PXS$?The answer is in the form \frac{m}{n}, where gcd(m, n) = 1. Please provide the value of m + n.\n\nPresent the answer in LaTeX format: \\boxed{Your answer}.",
"role": "user"
}
] |
MATH
|
{
"ground_truth": "288",
"style": "rule-lighteval/MATH_v2"
}
|
{
"index": "2c00a696-672d-42b4-aaa2-7ed1afcf176e"
}
|
math_dapo
|
[
{
"content": "Your task is to follow a systematic, thorough reasoning process before providing the final solution. This involves analyzing, summarizing, exploring, reassessing, and refining your thought process through multiple iterations. Structure your response into two sections: Thought and Solution. In the Thought section, present your reasoning using the format: \"<think>\n {thoughts} </think>\n\". Each thought should include detailed analysis, brainstorming, verification, and refinement of ideas. After \"</think>\n,\" in the Solution section, provide the final, logical, and accurate answer, clearly derived from the exploration in the Thought section.",
"role": "system"
},
{
"content": "如图3，在直角坐标系 $x O y$中， $\\\\odot O: x^{2}+y^{2}=4$ 与 $x$ 轴的正半轴交于点 $A, \\\\odot A:(x-2)^{2}+y^{2}=r^{2}(r>0)$ 与 $\\\\odot O$ 交于 $B 、 C$ 两点. (1) 求 $\\\\overrightarrow{A B} \\\\cdot \\\\overrightarrow{A C}$ 的最小值; (2) 设 $P$ 为 $\\\\odot O$ 上异于 $B 、 C$ 的任一点，直线 $P B 、 P C$ 与 $x$ 轴分别交于点 $M 、 N$, 求 $S_{\\\\triangle P O M} S_{\\\\triangle P O N}$ 的最大值。请给出这两个值的和。\n\nPresent the answer in LaTeX format: \\boxed{Your answer}.",
"role": "user"
}
] |
MATH
|
{
"ground_truth": "3",
"style": "rule-lighteval/MATH_v2"
}
|
{
"index": "92a4dff5-3c78-4c50-91dc-392cba07898a"
}
|
math_dapo
|
[
{
"content": "Your task is to follow a systematic, thorough reasoning process before providing the final solution. This involves analyzing, summarizing, exploring, reassessing, and refining your thought process through multiple iterations. Structure your response into two sections: Thought and Solution. In the Thought section, present your reasoning using the format: \"<think>\n {thoughts} </think>\n\". Each thought should include detailed analysis, brainstorming, verification, and refinement of ideas. After \"</think>\n,\" in the Solution section, provide the final, logical, and accurate answer, clearly derived from the exploration in the Thought section.",
"role": "system"
},
{
"content": "For a positive integer $k$, let $f_1(k)$ be the square of the sum of the digits of $k$. Define $f_{n+1} = f_1 \\circ f_n$. Evaluate $f_{2007}(2^{2006})$.\n\nPresent the answer in LaTeX format: \\boxed{Your answer}.",
"role": "user"
}
] |
MATH
|
{
"ground_truth": "169",
"style": "rule-lighteval/MATH_v2"
}
|
{
"index": "a02830e7-032c-4d72-a861-0ca08776256a"
}
|
math_dapo
|
[
{
"content": "Your task is to follow a systematic, thorough reasoning process before providing the final solution. This involves analyzing, summarizing, exploring, reassessing, and refining your thought process through multiple iterations. Structure your response into two sections: Thought and Solution. In the Thought section, present your reasoning using the format: \"<think>\n {thoughts} </think>\n\". Each thought should include detailed analysis, brainstorming, verification, and refinement of ideas. After \"</think>\n,\" in the Solution section, provide the final, logical, and accurate answer, clearly derived from the exploration in the Thought section.",
"role": "system"
},
{
"content": "一种密码锁的密码设置是在正 $n$ 边形 $A_{1} A_{2} \\cdots A_{n}$ 的每个顶点处赋值 0 和 1 两个数中的一个，同时在每个顶点处涂染红、蓝两种颜色之一，使得任意相邻的两个顶点的数字或颜色中至少有一个相同。假设 $n = 2$，请给出该种密码锁共有多少种不同的密码设置的值减去 4 的结果。\n\nPresent the answer in LaTeX format: \\boxed{Your answer}.",
"role": "user"
}
] |
MATH
|
{
"ground_truth": "8",
"style": "rule-lighteval/MATH_v2"
}
|
{
"index": "d84bdc59-100e-452b-9811-f44fc8be3344"
}
|
math_dapo
|
[
{
"content": "Your task is to follow a systematic, thorough reasoning process before providing the final solution. This involves analyzing, summarizing, exploring, reassessing, and refining your thought process through multiple iterations. Structure your response into two sections: Thought and Solution. In the Thought section, present your reasoning using the format: \"<think>\n {thoughts} </think>\n\". Each thought should include detailed analysis, brainstorming, verification, and refinement of ideas. After \"</think>\n,\" in the Solution section, provide the final, logical, and accurate answer, clearly derived from the exploration in the Thought section.",
"role": "system"
},
{
"content": "Spot's doghouse has a regular hexagonal base that measures one yard on each side. He is tethered to a vertex with a two-yard rope. What is the area, in square yards, of the region outside of the doghouse that Spot can reach? If the area can be expressed as $x\\pi$, find the value of $x$.\n\nPresent the answer in LaTeX format: \\boxed{Your answer}.",
"role": "user"
}
] |
MATH
|
{
"ground_truth": "3",
"style": "rule-lighteval/MATH_v2"
}
|
{
"index": "d3ada10a-69aa-40d7-9786-d6d193a12943"
}
|
math_dapo
|
[
{
"content": "Your task is to follow a systematic, thorough reasoning process before providing the final solution. This involves analyzing, summarizing, exploring, reassessing, and refining your thought process through multiple iterations. Structure your response into two sections: Thought and Solution. In the Thought section, present your reasoning using the format: \"<think>\n {thoughts} </think>\n\". Each thought should include detailed analysis, brainstorming, verification, and refinement of ideas. After \"</think>\n,\" in the Solution section, provide the final, logical, and accurate answer, clearly derived from the exploration in the Thought section.",
"role": "system"
},
{
"content": "The diagram shows a circle with radius $24$ that contains two smaller circles, each with a radius of $12$. These two circles are tangent to each other and to the larger circle. There is also a smallest circle that is tangent to the three other circles. Determine the radius of this smallest circle.\n\nPresent the answer in LaTeX format: \\boxed{Your answer}.",
"role": "user"
}
] |
MATH
|
{
"ground_truth": "8",
"style": "rule-lighteval/MATH_v2"
}
|
{
"index": "fb88f09b-f337-45ca-8df8-7a3c48247309"
}
|
math_dapo
|
[
{
"content": "Your task is to follow a systematic, thorough reasoning process before providing the final solution. This involves analyzing, summarizing, exploring, reassessing, and refining your thought process through multiple iterations. Structure your response into two sections: Thought and Solution. In the Thought section, present your reasoning using the format: \"<think>\n {thoughts} </think>\n\". Each thought should include detailed analysis, brainstorming, verification, and refinement of ideas. After \"</think>\n,\" in the Solution section, provide the final, logical, and accurate answer, clearly derived from the exploration in the Thought section.",
"role": "system"
},
{
"content": "Let $a, b$ be positive real numbers with $a > b$. Compute the minimum possible value of the expression\n\n\\[\n\\frac{a^2b - ab^2 + 8}{ab - b^2}.\n\\]\n\nPresent the answer in LaTeX format: \\boxed{Your answer}.",
"role": "user"
}
] |
MATH
|
{
"ground_truth": "6",
"style": "rule-lighteval/MATH_v2"
}
|
{
"index": "a1ad4027-b4e3-4490-968b-7b4f3052197e"
}
|
math_dapo
|
[
{
"content": "Your task is to follow a systematic, thorough reasoning process before providing the final solution. This involves analyzing, summarizing, exploring, reassessing, and refining your thought process through multiple iterations. Structure your response into two sections: Thought and Solution. In the Thought section, present your reasoning using the format: \"<think>\n {thoughts} </think>\n\". Each thought should include detailed analysis, brainstorming, verification, and refinement of ideas. After \"</think>\n,\" in the Solution section, provide the final, logical, and accurate answer, clearly derived from the exploration in the Thought section.",
"role": "system"
},
{
"content": "Twenty tiles are numbered 1 through 20 and are placed into box $A$. Twenty other tiles numbered 11 through 30 are placed into box $B$. One tile is randomly drawn from each box. What is the probability that the tile from box $A$ is less than 15 and the tile from box $B$ is either even or greater than 25? Express your answer as a common fraction.The answer is in the form \frac{m}{n}, where gcd(m, n) = 1. Please provide the value of m + n.\n\nPresent the answer in LaTeX format: \\boxed{Your answer}.",
"role": "user"
}
] |
MATH
|
{
"ground_truth": "71",
"style": "rule-lighteval/MATH_v2"
}
|
{
"index": "6ec12487-f9a7-4006-9ca1-307a1499e9a3"
}
|
math_dapo
|
[
{
"content": "Your task is to follow a systematic, thorough reasoning process before providing the final solution. This involves analyzing, summarizing, exploring, reassessing, and refining your thought process through multiple iterations. Structure your response into two sections: Thought and Solution. In the Thought section, present your reasoning using the format: \"<think>\n {thoughts} </think>\n\". Each thought should include detailed analysis, brainstorming, verification, and refinement of ideas. After \"</think>\n,\" in the Solution section, provide the final, logical, and accurate answer, clearly derived from the exploration in the Thought section.",
"role": "system"
},
{
"content": "The graphs of $y = -|x - a| + b$ and $y = |x - c| + d$ intersect at points $(2,5)$ and $(8,3)$. Find the value of $a + c$.\n\nPresent the answer in LaTeX format: \\boxed{Your answer}.",
"role": "user"
}
] |
MATH
|
{
"ground_truth": "10",
"style": "rule-lighteval/MATH_v2"
}
|
{
"index": "55446c5f-f8b2-4bb1-b555-2efa438fad25"
}
|
math_dapo
|
[
{
"content": "Your task is to follow a systematic, thorough reasoning process before providing the final solution. This involves analyzing, summarizing, exploring, reassessing, and refining your thought process through multiple iterations. Structure your response into two sections: Thought and Solution. In the Thought section, present your reasoning using the format: \"<think>\n {thoughts} </think>\n\". Each thought should include detailed analysis, brainstorming, verification, and refinement of ideas. After \"</think>\n,\" in the Solution section, provide the final, logical, and accurate answer, clearly derived from the exploration in the Thought section.",
"role": "system"
},
{
"content": "Let \\( G, O, D, I, \\) and \\( T \\) be digits that satisfy the following equation:\n\n\\[\n\\begin{array}{cccc}\n & G & O & G & O \\\\\n+ & D & I & D & I \\\\\n\\hline\nG & O & D & O & T\n\\end{array}\n\\]\n\n(Note that \\( G \\) and \\( D \\) cannot be \\( 0 \\), and that the five variables are not necessarily different.)\n\nCompute the value of GODOT.\n\nPresent the answer in LaTeX format: \\boxed{Your answer}.",
"role": "user"
}
] |
MATH
|
{
"ground_truth": "10908",
"style": "rule-lighteval/MATH_v2"
}
|
{
"index": "8849b66d-e422-479a-8e95-b715fa24cc95"
}
|
math_dapo
|
[
{
"content": "Your task is to follow a systematic, thorough reasoning process before providing the final solution. This involves analyzing, summarizing, exploring, reassessing, and refining your thought process through multiple iterations. Structure your response into two sections: Thought and Solution. In the Thought section, present your reasoning using the format: \"<think>\n {thoughts} </think>\n\". Each thought should include detailed analysis, brainstorming, verification, and refinement of ideas. After \"</think>\n,\" in the Solution section, provide the final, logical, and accurate answer, clearly derived from the exploration in the Thought section.",
"role": "system"
},
{
"content": "设函数 $f(x)=2^{x}-2^{-x}$ 的反函数为 $y=f^{-1}(x)$, 则不等式 $\\left|f^{-1}(x-1)\\right|<1$ 的解集为一个区间$(a,b)$，求$a-b$。\n\nPresent the answer in LaTeX format: \\boxed{Your answer}.",
"role": "user"
}
] |
MATH
|
{
"ground_truth": "3",
"style": "rule-lighteval/MATH_v2"
}
|
{
"index": "6ac576af-55c4-4b22-8222-0a69c2f468ea"
}
|
math_dapo
|
[
{
"content": "Your task is to follow a systematic, thorough reasoning process before providing the final solution. This involves analyzing, summarizing, exploring, reassessing, and refining your thought process through multiple iterations. Structure your response into two sections: Thought and Solution. In the Thought section, present your reasoning using the format: \"<think>\n {thoughts} </think>\n\". Each thought should include detailed analysis, brainstorming, verification, and refinement of ideas. After \"</think>\n,\" in the Solution section, provide the final, logical, and accurate answer, clearly derived from the exploration in the Thought section.",
"role": "system"
},
{
"content": "在梯形 ABCD 中，BC\\parallel AD, AB=AD, \\angle ABC=\\df{2\\pi}{3}, \\angle BCD=\\df{\\pi}{2}. 将 \\triangle ABD 沿 BD 翻折，点 A 在面 BCD 上的投影为点 P. 已知 AB 与 CD 所成角的余弦值为 \\df{\\sqrt{3}}{6}，则 BP 与 CD 所成角的余弦值为__________.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\nPresent the answer in LaTeX format: \\boxed{Your answer}.",
"role": "user"
}
] |
MATH
|
{
"ground_truth": "3",
"style": "rule-lighteval/MATH_v2"
}
|
{
"index": "758a788a-3349-408e-8e23-f9ee041f2766"
}
|
math_dapo
|
[
{
"content": "Your task is to follow a systematic, thorough reasoning process before providing the final solution. This involves analyzing, summarizing, exploring, reassessing, and refining your thought process through multiple iterations. Structure your response into two sections: Thought and Solution. In the Thought section, present your reasoning using the format: \"<think>\n {thoughts} </think>\n\". Each thought should include detailed analysis, brainstorming, verification, and refinement of ideas. After \"</think>\n,\" in the Solution section, provide the final, logical, and accurate answer, clearly derived from the exploration in the Thought section.",
"role": "system"
},
{
"content": "Solve the equation:\n$$(1 + x + x^ 2 )(1 + x + . . . + x^{10}) = (1 + x + . . . + x^6 ) ^2.$$\nPlease write the sum of all solutions for $x$.\n\nPresent the answer in LaTeX format: \\boxed{Your answer}.",
"role": "user"
}
] |
MATH
|
{
"ground_truth": "-1",
"style": "rule-lighteval/MATH_v2"
}
|
{
"index": "afca8a14-e33a-4234-af50-9a422d7073d1"
}
|
math_dapo
|
[
{
"content": "Your task is to follow a systematic, thorough reasoning process before providing the final solution. This involves analyzing, summarizing, exploring, reassessing, and refining your thought process through multiple iterations. Structure your response into two sections: Thought and Solution. In the Thought section, present your reasoning using the format: \"<think>\n {thoughts} </think>\n\". Each thought should include detailed analysis, brainstorming, verification, and refinement of ideas. After \"</think>\n,\" in the Solution section, provide the final, logical, and accurate answer, clearly derived from the exploration in the Thought section.",
"role": "system"
},
{
"content": "Define a sequence $a_i$ as follows: $a_1 = 181$ and for $i \\ge 2$, \\( a_i = a_{i-1}^2 - 1 \\) if $a_{i-1}$ is odd and \\( a_i = \\frac{a_{i-1}}{2} \\) if $a_{i-1}$ is even. Find the least $i$ such that $a_i = 0$.\n\nPresent the answer in LaTeX format: \\boxed{Your answer}.",
"role": "user"
}
] |
MATH
|
{
"ground_truth": "105",
"style": "rule-lighteval/MATH_v2"
}
|
{
"index": "47205549-e489-4b9f-96de-a89a98dccce7"
}
|
math_dapo
|
[
{
"content": "Your task is to follow a systematic, thorough reasoning process before providing the final solution. This involves analyzing, summarizing, exploring, reassessing, and refining your thought process through multiple iterations. Structure your response into two sections: Thought and Solution. In the Thought section, present your reasoning using the format: \"<think>\n {thoughts} </think>\n\". Each thought should include detailed analysis, brainstorming, verification, and refinement of ideas. After \"</think>\n,\" in the Solution section, provide the final, logical, and accurate answer, clearly derived from the exploration in the Thought section.",
"role": "system"
},
{
"content": "A large sphere is on a horizontal field on a sunny day. At a certain time, the shadow of the sphere reaches out a distance of $10$ m from the point where the sphere touches the ground. At the same instant, a meter stick (held vertically with one end on the ground) casts a shadow of length $2$ m. What is the radius of the sphere in meters? (Assume the sun's rays are parallel and the meter stick is a line segment.) The original answer is in the form \\( k\\sqrt{m} - n \\). Please give the value of \\( k + m + n \\).\n\nPresent the answer in LaTeX format: \\boxed{Your answer}.",
"role": "user"
}
] |
MATH
|
{
"ground_truth": "35",
"style": "rule-lighteval/MATH_v2"
}
|
{
"index": "6dbccc88-39d0-4436-baa1-3b27b49e74fd"
}
|
math_dapo
|
[
{
"content": "Your task is to follow a systematic, thorough reasoning process before providing the final solution. This involves analyzing, summarizing, exploring, reassessing, and refining your thought process through multiple iterations. Structure your response into two sections: Thought and Solution. In the Thought section, present your reasoning using the format: \"<think>\n {thoughts} </think>\n\". Each thought should include detailed analysis, brainstorming, verification, and refinement of ideas. After \"</think>\n,\" in the Solution section, provide the final, logical, and accurate answer, clearly derived from the exploration in the Thought section.",
"role": "system"
},
{
"content": "Three non-zero real numbers $a$, $b$, and $c$ satisfy the conditions $a + b + c = 0$ and $a^4 + b^4 + c^4 = 128$. Determine all possible values of $ab + bc + ca$.\n\nPresent the answer in LaTeX format: \\boxed{Your answer}.",
"role": "user"
}
] |
MATH
|
{
"ground_truth": "-8",
"style": "rule-lighteval/MATH_v2"
}
|
{
"index": "f1a74867-d4b7-4801-af44-7158a3fdea80"
}
|
math_dapo
|
[
{
"content": "Your task is to follow a systematic, thorough reasoning process before providing the final solution. This involves analyzing, summarizing, exploring, reassessing, and refining your thought process through multiple iterations. Structure your response into two sections: Thought and Solution. In the Thought section, present your reasoning using the format: \"<think>\n {thoughts} </think>\n\". Each thought should include detailed analysis, brainstorming, verification, and refinement of ideas. After \"</think>\n,\" in the Solution section, provide the final, logical, and accurate answer, clearly derived from the exploration in the Thought section.",
"role": "system"
},
{
"content": "In rhombus $ABCD$, point $P$ lies on segment $\\overline{AD}$ so that $\\overline{BP}$ $\\perp$ $\\overline{AD}$, $AP = 3$, and $PD = 2$. Find the area of $ABCD$. (Note: The figure is not drawn to scale.)\n\nPresent the answer in LaTeX format: \\boxed{Your answer}.",
"role": "user"
}
] |
MATH
|
{
"ground_truth": "20",
"style": "rule-lighteval/MATH_v2"
}
|
{
"index": "755e0e31-48db-4c9f-a95f-b9dfcccfcde4"
}
|
math_dapo
|
[
{
"content": "Your task is to follow a systematic, thorough reasoning process before providing the final solution. This involves analyzing, summarizing, exploring, reassessing, and refining your thought process through multiple iterations. Structure your response into two sections: Thought and Solution. In the Thought section, present your reasoning using the format: \"<think>\n {thoughts} </think>\n\". Each thought should include detailed analysis, brainstorming, verification, and refinement of ideas. After \"</think>\n,\" in the Solution section, provide the final, logical, and accurate answer, clearly derived from the exploration in the Thought section.",
"role": "system"
},
{
"content": "Triangle $ABC$ is right-angled at $A$. The circle with center $A$ and radius $AB$ intersects $BC$ and $AC$ internally at points $D$ and $E$ respectively. Given that $BD = 20$ and $DC = 16$, determine $AC^2$.\n\nPresent the answer in LaTeX format: \\boxed{Your answer}.",
"role": "user"
}
] |
MATH
|
{
"ground_truth": "936",
"style": "rule-lighteval/MATH_v2"
}
|
{
"index": "d613dfb1-9bf4-4824-90ab-dfc83bccb040"
}
|
math_dapo
|
[
{
"content": "Your task is to follow a systematic, thorough reasoning process before providing the final solution. This involves analyzing, summarizing, exploring, reassessing, and refining your thought process through multiple iterations. Structure your response into two sections: Thought and Solution. In the Thought section, present your reasoning using the format: \"<think>\n {thoughts} </think>\n\". Each thought should include detailed analysis, brainstorming, verification, and refinement of ideas. After \"</think>\n,\" in the Solution section, provide the final, logical, and accurate answer, clearly derived from the exploration in the Thought section.",
"role": "system"
},
{
"content": "有 8 块不同的积木，每块积木的形状为方形或者圆形，颜色为红色或者黄色，印有城市名为南昌或者北京. 从 8 块不同的积木中按顺序任取 n 块积木（2\\leq n\\leq 8），D_n 表示后一次与前一次取出的积木在形状、颜色、城市名三个方面恰好有两个相同的所有不同取法总数，则 \\displaystyle\\max_{2\\leq n\\leq 8}D_n=__________.\n\nPresent the answer in LaTeX format: \\boxed{Your answer}.",
"role": "user"
}
] |
MATH
|
{
"ground_truth": "240",
"style": "rule-lighteval/MATH_v2"
}
|
{
"index": "66e42505-542b-4ebc-a7ef-740a11ed1fdb"
}
|
math_dapo
|
[
{
"content": "Your task is to follow a systematic, thorough reasoning process before providing the final solution. This involves analyzing, summarizing, exploring, reassessing, and refining your thought process through multiple iterations. Structure your response into two sections: Thought and Solution. In the Thought section, present your reasoning using the format: \"<think>\n {thoughts} </think>\n\". Each thought should include detailed analysis, brainstorming, verification, and refinement of ideas. After \"</think>\n,\" in the Solution section, provide the final, logical, and accurate answer, clearly derived from the exploration in the Thought section.",
"role": "system"
},
{
"content": "设 $P(0, a)$ 是 $y$ 轴上异于原点的任意一点, 过点 $P$ 且平行于 $x$ 轴的直线与曲线 $y=$ $\\frac{1}{a} \\ln x$ 交于点 $Q$, 曲线 $y=\\frac{1}{a} \\ln x$ 在点 $Q$ 处的切线交 $y$ 轴于点 $R$. 则 $\\triangle P Q R$ 的面积的最小值是 $\\qquad$。原始答案为 \\(\\frac{\\sqrt{m\\mathbf{e}}}{n}\\) 格式，请给出 $m + n$ 的值。\n\nPresent the answer in LaTeX format: \\boxed{Your answer}.",
"role": "user"
}
] |
MATH
|
{
"ground_truth": "4",
"style": "rule-lighteval/MATH_v2"
}
|
{
"index": "a5aa5cc9-d7ce-4c4b-aae3-ad68b2912c37"
}
|
math_dapo
|
[
{
"content": "Your task is to follow a systematic, thorough reasoning process before providing the final solution. This involves analyzing, summarizing, exploring, reassessing, and refining your thought process through multiple iterations. Structure your response into two sections: Thought and Solution. In the Thought section, present your reasoning using the format: \"<think>\n {thoughts} </think>\n\". Each thought should include detailed analysis, brainstorming, verification, and refinement of ideas. After \"</think>\n,\" in the Solution section, provide the final, logical, and accurate answer, clearly derived from the exploration in the Thought section.",
"role": "system"
},
{
"content": "设实数 a,b,c,d 满足 a+b+c+d=8，求20(a^2+b^2+c^2+d^2)-\\ds{\\text{sym}}{}a^3b的最小值，其中求和有 12 项.\n\nPresent the answer in LaTeX format: \\boxed{Your answer}.",
"role": "user"
}
] |
MATH
|
{
"ground_truth": "112",
"style": "rule-lighteval/MATH_v2"
}
|
{
"index": "fbede98d-b65f-48e9-b51e-7c476274a563"
}
|
math_dapo
|
[
{
"content": "Your task is to follow a systematic, thorough reasoning process before providing the final solution. This involves analyzing, summarizing, exploring, reassessing, and refining your thought process through multiple iterations. Structure your response into two sections: Thought and Solution. In the Thought section, present your reasoning using the format: \"<think>\n {thoughts} </think>\n\". Each thought should include detailed analysis, brainstorming, verification, and refinement of ideas. After \"</think>\n,\" in the Solution section, provide the final, logical, and accurate answer, clearly derived from the exploration in the Thought section.",
"role": "system"
},
{
"content": "A zealous geologist is sponsoring a contest in which entrants have to guess the age of a shiny rock. He offers these clues: the age of the rock is formed from the six digits 2, 2, 2, 3, 7, and 9, and the rock's age begins with an odd digit.\n\nHow many possibilities are there for the rock's age?\n\nPresent the answer in LaTeX format: \\boxed{Your answer}.",
"role": "user"
}
] |
MATH
|
{
"ground_truth": "60",
"style": "rule-lighteval/MATH_v2"
}
|
{
"index": "89c3c6f0-d7f7-4381-b0e6-075c1c8f7906"
}
|
math_dapo
|
[
{
"content": "Your task is to follow a systematic, thorough reasoning process before providing the final solution. This involves analyzing, summarizing, exploring, reassessing, and refining your thought process through multiple iterations. Structure your response into two sections: Thought and Solution. In the Thought section, present your reasoning using the format: \"<think>\n {thoughts} </think>\n\". Each thought should include detailed analysis, brainstorming, verification, and refinement of ideas. After \"</think>\n,\" in the Solution section, provide the final, logical, and accurate answer, clearly derived from the exploration in the Thought section.",
"role": "system"
},
{
"content": "Let $ABCD$ be a square with $AB = 6$. A point $P$ inside the square is 2 units away from side $BC$ and 3 units away from side $CD$. What is the distance from $P$ to $A$?\n\nPresent the answer in LaTeX format: \\boxed{Your answer}.",
"role": "user"
}
] |
MATH
|
{
"ground_truth": "5",
"style": "rule-lighteval/MATH_v2"
}
|
{
"index": "d25a91c0-02c6-42cd-9cff-3fbce41ec3ba"
}
|
math_dapo
|
[
{
"content": "Your task is to follow a systematic, thorough reasoning process before providing the final solution. This involves analyzing, summarizing, exploring, reassessing, and refining your thought process through multiple iterations. Structure your response into two sections: Thought and Solution. In the Thought section, present your reasoning using the format: \"<think>\n {thoughts} </think>\n\". Each thought should include detailed analysis, brainstorming, verification, and refinement of ideas. After \"</think>\n,\" in the Solution section, provide the final, logical, and accurate answer, clearly derived from the exploration in the Thought section.",
"role": "system"
},
{
"content": "A hexagon inscribed in a circle has three consecutive sides, each of length 3, and three consecutive sides, each of length 5. The chord of the circle that divides the hexagon into two trapezoids, one with three sides, each of length 3, and the other with three sides, each of length 5, has length equal to $m/n$, where $m$ and $n$ are relatively prime positive integers. Find $m + n$.\n\nPresent the answer in LaTeX format: \\boxed{Your answer}.",
"role": "user"
}
] |
MATH
|
{
"ground_truth": "409",
"style": "rule-lighteval/MATH_v2"
}
|
{
"index": "c9c30a93-0f4f-46c6-b1de-1828e6f2e447"
}
|
math_dapo
|
[
{
"content": "Your task is to follow a systematic, thorough reasoning process before providing the final solution. This involves analyzing, summarizing, exploring, reassessing, and refining your thought process through multiple iterations. Structure your response into two sections: Thought and Solution. In the Thought section, present your reasoning using the format: \"<think>\n {thoughts} </think>\n\". Each thought should include detailed analysis, brainstorming, verification, and refinement of ideas. After \"</think>\n,\" in the Solution section, provide the final, logical, and accurate answer, clearly derived from the exploration in the Thought section.",
"role": "system"
},
{
"content": "求所有的正整数 k，使得对任意满足 k(ab+bc+ca)>5(a^2+b^2+c^2) 的正实数 a,b,c，都存在三边长分别为 a,b,c 的三角形.\n\nPresent the answer in LaTeX format: \\boxed{Your answer}.",
"role": "user"
}
] |
MATH
|
{
"ground_truth": "6",
"style": "rule-lighteval/MATH_v2"
}
|
{
"index": "80a825a8-6253-4875-8b54-c6e804f2182b"
}
|
math_dapo
|
[
{
"content": "Your task is to follow a systematic, thorough reasoning process before providing the final solution. This involves analyzing, summarizing, exploring, reassessing, and refining your thought process through multiple iterations. Structure your response into two sections: Thought and Solution. In the Thought section, present your reasoning using the format: \"<think>\n {thoughts} </think>\n\". Each thought should include detailed analysis, brainstorming, verification, and refinement of ideas. After \"</think>\n,\" in the Solution section, provide the final, logical, and accurate answer, clearly derived from the exploration in the Thought section.",
"role": "system"
},
{
"content": "Square $ABCD$ has side length $s$, a circle centered at $E$ has radius $r$, and $r$ and $s$ are both rational. The circle passes through $D$, and $D$ lies on $\\overline{BE}$. Point $F$ lies on the circle, on the same side of $\\overline{BE}$ as $A$. Segment $AF$ is tangent to the circle, and $AF=\\sqrt{9+5\\sqrt{2}}$. The original answer is in \\frac{k}{m} format, where $k$ and $m$ are integers. Please give the value of $k + m$.\n\nPresent the answer in LaTeX format: \\boxed{Your answer}.",
"role": "user"
}
] |
MATH
|
{
"ground_truth": "8",
"style": "rule-lighteval/MATH_v2"
}
|
{
"index": "23be0ede-05dd-4d70-9da4-626375fa23a8"
}
|
math_dapo
|
[
{
"content": "Your task is to follow a systematic, thorough reasoning process before providing the final solution. This involves analyzing, summarizing, exploring, reassessing, and refining your thought process through multiple iterations. Structure your response into two sections: Thought and Solution. In the Thought section, present your reasoning using the format: \"<think>\n {thoughts} </think>\n\". Each thought should include detailed analysis, brainstorming, verification, and refinement of ideas. After \"</think>\n,\" in the Solution section, provide the final, logical, and accurate answer, clearly derived from the exploration in the Thought section.",
"role": "system"
},
{
"content": "Points $A,$ $B,$ $C,$ and $D$ are equally spaced along a line such that $AB = BC = CD.$ A point $P$ is located so that $\\cos \\angle APC = \\frac{4}{5}$ and $\\cos \\angle BPD = \\frac{3}{5}.$ Determine $\\sin (2 \\angle BPC).$The answer is in the form \frac{m}{n}, where gcd(m, n) = 1. Please provide the value of m + n.\n\nPresent the answer in LaTeX format: \\boxed{Your answer}.",
"role": "user"
}
] |
MATH
|
{
"ground_truth": "43",
"style": "rule-lighteval/MATH_v2"
}
|
{
"index": "16a8f2b4-ae92-4d67-abb2-1ef2acdf5a6e"
}
|
math_dapo
|
[
{
"content": "Your task is to follow a systematic, thorough reasoning process before providing the final solution. This involves analyzing, summarizing, exploring, reassessing, and refining your thought process through multiple iterations. Structure your response into two sections: Thought and Solution. In the Thought section, present your reasoning using the format: \"<think>\n {thoughts} </think>\n\". Each thought should include detailed analysis, brainstorming, verification, and refinement of ideas. After \"</think>\n,\" in the Solution section, provide the final, logical, and accurate answer, clearly derived from the exploration in the Thought section.",
"role": "system"
},
{
"content": "Let $n$ be a positive integer. Find the number of pairs $P,Q$ of polynomials with real coefficients such that $$(P(X))^2+(Q(X))^2=X^{2n}+1$$ and $\\deg P>\\deg Q.$ Provide the value when $n=3$. The answer should be an integer.\n\nPresent the answer in LaTeX format: \\boxed{Your answer}.",
"role": "user"
}
] |
MATH
|
{
"ground_truth": "16",
"style": "rule-lighteval/MATH_v2"
}
|
{
"index": "d679162d-d425-4f13-a403-a9fb97b5ef52"
}
|
math_dapo
|
[
{
"content": "Your task is to follow a systematic, thorough reasoning process before providing the final solution. This involves analyzing, summarizing, exploring, reassessing, and refining your thought process through multiple iterations. Structure your response into two sections: Thought and Solution. In the Thought section, present your reasoning using the format: \"<think>\n {thoughts} </think>\n\". Each thought should include detailed analysis, brainstorming, verification, and refinement of ideas. After \"</think>\n,\" in the Solution section, provide the final, logical, and accurate answer, clearly derived from the exploration in the Thought section.",
"role": "system"
},
{
"content": "Find the sum of the non-repeated roots of the polynomial $P(x) = x^6 - 5x^5 - 4x^4 - 5x^3 + 8x^2 + 7x + 7$.\n\nPresent the answer in LaTeX format: \\boxed{Your answer}.",
"role": "user"
}
] |
MATH
|
{
"ground_truth": "7",
"style": "rule-lighteval/MATH_v2"
}
|
{
"index": "2b12d2db-63fd-4b59-be8c-aeffb098e5fa"
}
|
math_dapo
|
[
{
"content": "Your task is to follow a systematic, thorough reasoning process before providing the final solution. This involves analyzing, summarizing, exploring, reassessing, and refining your thought process through multiple iterations. Structure your response into two sections: Thought and Solution. In the Thought section, present your reasoning using the format: \"<think>\n {thoughts} </think>\n\". Each thought should include detailed analysis, brainstorming, verification, and refinement of ideas. After \"</think>\n,\" in the Solution section, provide the final, logical, and accurate answer, clearly derived from the exploration in the Thought section.",
"role": "system"
},
{
"content": "已知 $a_{1}=1, a_{n+1}=\\lambda a_{n}^{2}+2\\left(n \\in \\mathbf{Z}_{+}\\right)$.若数列 $\\left\\{a_{n}\\right\\}$ 有上界，即存在常数 $M>0$ ，使得 $a_{n} \\leqslant M$ 对 $n \\in \\mathbf{Z}_{+}$恒成立，则实数 $\\lambda$ 的最大值是 $\\qquad$。 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 + n的值\n\nPresent the answer in LaTeX format: \\boxed{Your answer}.",
"role": "user"
}
] |
MATH
|
{
"ground_truth": "9",
"style": "rule-lighteval/MATH_v2"
}
|
{
"index": "19cfd273-9370-4434-8d12-0bda2eecf3d7"
}
|
math_dapo
|
[
{
"content": "Your task is to follow a systematic, thorough reasoning process before providing the final solution. This involves analyzing, summarizing, exploring, reassessing, and refining your thought process through multiple iterations. Structure your response into two sections: Thought and Solution. In the Thought section, present your reasoning using the format: \"<think>\n {thoughts} </think>\n\". Each thought should include detailed analysis, brainstorming, verification, and refinement of ideas. After \"</think>\n,\" in the Solution section, provide the final, logical, and accurate answer, clearly derived from the exploration in the Thought section.",
"role": "system"
},
{
"content": "Let $a$ and $b$ satisfy the conditions \\( \\begin{cases} a^3 - 6a^2 + 15a = 9 \\\\ b^3 - 3b^2 + 6b = -1 \\end{cases} \\). Find the value of \\((a - b)^{2014}\\).\n\nPresent the answer in LaTeX format: \\boxed{Your answer}.",
"role": "user"
}
] |
MATH
|
{
"ground_truth": "1",
"style": "rule-lighteval/MATH_v2"
}
|
{
"index": "e1b81f3e-0445-4dd4-8e73-ee0aa5dada29"
}
|
math_dapo
|
[
{
"content": "Your task is to follow a systematic, thorough reasoning process before providing the final solution. This involves analyzing, summarizing, exploring, reassessing, and refining your thought process through multiple iterations. Structure your response into two sections: Thought and Solution. In the Thought section, present your reasoning using the format: \"<think>\n {thoughts} </think>\n\". Each thought should include detailed analysis, brainstorming, verification, and refinement of ideas. After \"</think>\n,\" in the Solution section, provide the final, logical, and accurate answer, clearly derived from the exploration in the Thought section.",
"role": "system"
},
{
"content": "In rectangle \\(ABCD\\), \\(AB=5\\) and \\(BC=3\\). Points \\(F\\) and \\(G\\) are on \\(\\overline{CD}\\) so that \\(DF=1\\) and \\(GC=2\\). Lines \\(AF\\) and \\(BG\\) intersect at \\(E\\). The area of \\(\\triangle AEB\\) is in the form \\(\\frac{k}{m}\\). Please find the value of \\(k + m\\).\n\nPresent the answer in LaTeX format: \\boxed{Your answer}.",
"role": "user"
}
] |
MATH
|
{
"ground_truth": "27",
"style": "rule-lighteval/MATH_v2"
}
|
{
"index": "fe13e738-fdec-4084-b61b-8060ec4113d2"
}
|
math_dapo
|
[
{
"content": "Your task is to follow a systematic, thorough reasoning process before providing the final solution. This involves analyzing, summarizing, exploring, reassessing, and refining your thought process through multiple iterations. Structure your response into two sections: Thought and Solution. In the Thought section, present your reasoning using the format: \"<think>\n {thoughts} </think>\n\". Each thought should include detailed analysis, brainstorming, verification, and refinement of ideas. After \"</think>\n,\" in the Solution section, provide the final, logical, and accurate answer, clearly derived from the exploration in the Thought section.",
"role": "system"
},
{
"content": "Let $S$ be the set of integers of the form $2^x + 2^y + 2^z$, where $x$, $y$, $z$ are pairwise distinct non-negative integers. Determine the 100th smallest element of $S$.\n\nPresent the answer in LaTeX format: \\boxed{Your answer}.",
"role": "user"
}
] |
MATH
|
{
"ground_truth": "577",
"style": "rule-lighteval/MATH_v2"
}
|
{
"index": "4cfc73b0-924d-4ecf-a8e7-e15cfec9bbae"
}
|
math_dapo
|
[
{
"content": "Your task is to follow a systematic, thorough reasoning process before providing the final solution. This involves analyzing, summarizing, exploring, reassessing, and refining your thought process through multiple iterations. Structure your response into two sections: Thought and Solution. In the Thought section, present your reasoning using the format: \"<think>\n {thoughts} </think>\n\". Each thought should include detailed analysis, brainstorming, verification, and refinement of ideas. After \"</think>\n,\" in the Solution section, provide the final, logical, and accurate answer, clearly derived from the exploration in the Thought section.",
"role": "system"
},
{
"content": "Let $\\mathcal{T}$ be the set of ordered triples $(x,y,z)$ of nonnegative real numbers that lie in the plane $x+y+z=1.$ Let us say that $(x,y,z)$ supports $(a,b,c)$ when exactly two of the following are true: $x\\ge a, y\\ge b, z\\ge c.$ Let $\\mathcal{S}$ consist of those triples in $\\mathcal{T}$ that support $\\left(\\frac 12,\\frac 13,\\frac 16\\right).$ The area of $\\mathcal{S}$ divided by the area of $\\mathcal{T}$ is $m/n,$ where $m_{}$ and $n_{}$ are relatively prime positive integers. Find $m+n.$\n\n\nPresent the answer in LaTeX format: \\boxed{Your answer}.",
"role": "user"
}
] |
MATH
|
{
"ground_truth": "25",
"style": "rule-lighteval/MATH_v2"
}
|
{
"index": "6fd64891-07f8-4b62-a811-47aabe8be82c"
}
|
math_dapo
|
[
{
"content": "Your task is to follow a systematic, thorough reasoning process before providing the final solution. This involves analyzing, summarizing, exploring, reassessing, and refining your thought process through multiple iterations. Structure your response into two sections: Thought and Solution. In the Thought section, present your reasoning using the format: \"<think>\n {thoughts} </think>\n\". Each thought should include detailed analysis, brainstorming, verification, and refinement of ideas. After \"</think>\n,\" in the Solution section, provide the final, logical, and accurate answer, clearly derived from the exploration in the Thought section.",
"role": "system"
},
{
"content": "In an increasing sequence of four positive integers, the first three terms form an arithmetic progression, the last three terms form a geometric progression, and the first and fourth terms differ by $30.$ Find the sum of the four terms.\n\nPresent the answer in LaTeX format: \\boxed{Your answer}.",
"role": "user"
}
] |
MATH
|
{
"ground_truth": "129",
"style": "rule-lighteval/MATH_v2"
}
|
{
"index": "d1e72bf7-64ed-4f12-ad2d-ef9bd79c87b2"
}
|
math_dapo
|
[
{
"content": "Your task is to follow a systematic, thorough reasoning process before providing the final solution. This involves analyzing, summarizing, exploring, reassessing, and refining your thought process through multiple iterations. Structure your response into two sections: Thought and Solution. In the Thought section, present your reasoning using the format: \"<think>\n {thoughts} </think>\n\". Each thought should include detailed analysis, brainstorming, verification, and refinement of ideas. After \"</think>\n,\" in the Solution section, provide the final, logical, and accurate answer, clearly derived from the exploration in the Thought section.",
"role": "system"
},
{
"content": "已知实数 $x, y$ 满足\n$3|x+1|+2|y-1| \\leqslant 6$.\n则 $2 x-3 y$ 的最大值是 $\\qquad$.\n\n\nPresent the answer in LaTeX format: \\boxed{Your answer}.",
"role": "user"
}
] |
MATH
|
{
"ground_truth": "4",
"style": "rule-lighteval/MATH_v2"
}
|
{
"index": "cfcc7c68-f847-4979-8ec3-8382d632cc6f"
}
|
math_dapo
|
[
{
"content": "Your task is to follow a systematic, thorough reasoning process before providing the final solution. This involves analyzing, summarizing, exploring, reassessing, and refining your thought process through multiple iterations. Structure your response into two sections: Thought and Solution. In the Thought section, present your reasoning using the format: \"<think>\n {thoughts} </think>\n\". Each thought should include detailed analysis, brainstorming, verification, and refinement of ideas. After \"</think>\n,\" in the Solution section, provide the final, logical, and accurate answer, clearly derived from the exploration in the Thought section.",
"role": "system"
},
{
"content": "Box is thinking of a number, whose digits are all \"1\". When he squares the number, the sum of its digits is $85$. How many digits does Box's number have?\n\nPresent the answer in LaTeX format: \\boxed{Your answer}.",
"role": "user"
}
] |
MATH
|
{
"ground_truth": "9",
"style": "rule-lighteval/MATH_v2"
}
|
{
"index": "1a3bb7ce-d59d-4a81-b140-aada0b305e03"
}
|
math_dapo
|
[
{
"content": "Your task is to follow a systematic, thorough reasoning process before providing the final solution. This involves analyzing, summarizing, exploring, reassessing, and refining your thought process through multiple iterations. Structure your response into two sections: Thought and Solution. In the Thought section, present your reasoning using the format: \"<think>\n {thoughts} </think>\n\". Each thought should include detailed analysis, brainstorming, verification, and refinement of ideas. After \"</think>\n,\" in the Solution section, provide the final, logical, and accurate answer, clearly derived from the exploration in the Thought section.",
"role": "system"
},
{
"content": "Let $ABCD$ be a parallelogram such that $AB = 35$ and $BC = 28$. Suppose that $BD \\perp BC$. Let $\\ell_1$ be the reflection of $AC$ across the angle bisector of $\\angle BAD$, and let $\\ell_2$ be the line through $B$ perpendicular to $CD$. $\\ell_1$ and $\\ell_2$ intersect at a point $P$. If $PD$ can be expressed in simplest form as $\\frac{m}{n}$, find $m + n$.\n\nPresent the answer in LaTeX format: \\boxed{Your answer}.",
"role": "user"
}
] |
MATH
|
{
"ground_truth": "113",
"style": "rule-lighteval/MATH_v2"
}
|
{
"index": "b933d603-7e2e-4a1b-b877-7174d80161c1"
}
|
math_dapo
|
[
{
"content": "Your task is to follow a systematic, thorough reasoning process before providing the final solution. This involves analyzing, summarizing, exploring, reassessing, and refining your thought process through multiple iterations. Structure your response into two sections: Thought and Solution. In the Thought section, present your reasoning using the format: \"<think>\n {thoughts} </think>\n\". Each thought should include detailed analysis, brainstorming, verification, and refinement of ideas. After \"</think>\n,\" in the Solution section, provide the final, logical, and accurate answer, clearly derived from the exploration in the Thought section.",
"role": "system"
},
{
"content": "一个 $10 \\times 10$ 的数表在初始状态下每个格内均填有数字1，现在对数表进行如下操作：选择某一行或某一列，并将该行（列）中所有格子内的数变为其相反数。对于非负整数 N ，如果可经过有限次操作，使得最终数表中 -1 的个数恰为 N ，则称 N 是 \"好的\"，则好的 N 的个数为 $\\qquad$.\n\nPresent the answer in LaTeX format: \\boxed{Your answer}.",
"role": "user"
}
] |
MATH
|
{
"ground_truth": "29",
"style": "rule-lighteval/MATH_v2"
}
|
{
"index": "2254d358-3a4d-4d5f-a2ba-00da6b2c481d"
}
|
math_dapo
|
[
{
"content": "Your task is to follow a systematic, thorough reasoning process before providing the final solution. This involves analyzing, summarizing, exploring, reassessing, and refining your thought process through multiple iterations. Structure your response into two sections: Thought and Solution. In the Thought section, present your reasoning using the format: \"<think>\n {thoughts} </think>\n\". Each thought should include detailed analysis, brainstorming, verification, and refinement of ideas. After \"</think>\n,\" in the Solution section, provide the final, logical, and accurate answer, clearly derived from the exploration in the Thought section.",
"role": "system"
},
{
"content": "If \\(V = gt + V_0\\) and \\(S = \\frac{1}{2}gt^2 + V_0t\\), find the expression for \\(t\\) in terms of \\(S\\), \\(V\\), and \\(V_0\\). The original answer is in the form \\(\\frac{kS}{m(V + V_0)}\\), please give the value of k + m.\n\nPresent the answer in LaTeX format: \\boxed{Your answer}.",
"role": "user"
}
] |
MATH
|
{
"ground_truth": "3",
"style": "rule-lighteval/MATH_v2"
}
|
{
"index": "de42286e-a633-4ae6-b708-33d83b97fc71"
}
|
math_dapo
|
[
{
"content": "Your task is to follow a systematic, thorough reasoning process before providing the final solution. This involves analyzing, summarizing, exploring, reassessing, and refining your thought process through multiple iterations. Structure your response into two sections: Thought and Solution. In the Thought section, present your reasoning using the format: \"<think>\n {thoughts} </think>\n\". Each thought should include detailed analysis, brainstorming, verification, and refinement of ideas. After \"</think>\n,\" in the Solution section, provide the final, logical, and accurate answer, clearly derived from the exploration in the Thought section.",
"role": "system"
},
{
"content": "The alphabet in its natural order $\\text{ABCDEFGHIJKLMNOPQRSTUVWXYZ}$ is $T_0$. We apply a permutation to $T_0$ to get $T_1$, which is $\\text{JQOWIPANTZRCVMYEGSHUFDKBLX}$. If we apply the same permutation to $T_1$, we get $T_2$, which is $\\text{ZGYKTEJMUXSODVLIAHNFPWRQCB}$. We continually apply this permutation to each $T_m$ to get $T_{m+1}$. Find the smallest positive integer $n$ such that $T_n = T_0$.\n\nPresent the answer in LaTeX format: \\boxed{Your answer}.",
"role": "user"
}
] |
MATH
|
{
"ground_truth": "252",
"style": "rule-lighteval/MATH_v2"
}
|
{
"index": "801723a0-cbc8-419f-adb2-5838f464ce3a"
}
|
math_dapo
|
[
{
"content": "Your task is to follow a systematic, thorough reasoning process before providing the final solution. This involves analyzing, summarizing, exploring, reassessing, and refining your thought process through multiple iterations. Structure your response into two sections: Thought and Solution. In the Thought section, present your reasoning using the format: \"<think>\n {thoughts} </think>\n\". Each thought should include detailed analysis, brainstorming, verification, and refinement of ideas. After \"</think>\n,\" in the Solution section, provide the final, logical, and accurate answer, clearly derived from the exploration in the Thought section.",
"role": "system"
},
{
"content": "What is the average of all positive integers that have four digits when written in base $3$, but two digits when written in base $6$? Write your answer in base $10$.\n\nPresent the answer in LaTeX format: \\boxed{Your answer}.",
"role": "user"
}
] |
MATH
|
{
"ground_truth": "31",
"style": "rule-lighteval/MATH_v2"
}
|
{
"index": "7f415c2a-7740-492d-90f7-42ea8206439a"
}
|
math_dapo
|
[
{
"content": "Your task is to follow a systematic, thorough reasoning process before providing the final solution. This involves analyzing, summarizing, exploring, reassessing, and refining your thought process through multiple iterations. Structure your response into two sections: Thought and Solution. In the Thought section, present your reasoning using the format: \"<think>\n {thoughts} </think>\n\". Each thought should include detailed analysis, brainstorming, verification, and refinement of ideas. After \"</think>\n,\" in the Solution section, provide the final, logical, and accurate answer, clearly derived from the exploration in the Thought section.",
"role": "system"
},
{
"content": "In the figure, $ABCD$ is a $2 \\times 2$ square, $E$ is the midpoint of $\\overline{AD}$, and $F$ is on $\\overline{BE}$. If $\\overline{CF}$ is perpendicular to $\\overline{BE}$, find the area of quadrilateral $CDEF$. The original answer is in \\frac{k}{m} format, where k and m are coprime integers. Please give the value of k + m.\n\nPresent the answer in LaTeX format: \\boxed{Your answer}.",
"role": "user"
}
] |
MATH
|
{
"ground_truth": "16",
"style": "rule-lighteval/MATH_v2"
}
|
{
"index": "ce5457d2-4c14-4bf3-b823-2ae39997bea6"
}
|
math_dapo
|
[
{
"content": "Your task is to follow a systematic, thorough reasoning process before providing the final solution. This involves analyzing, summarizing, exploring, reassessing, and refining your thought process through multiple iterations. Structure your response into two sections: Thought and Solution. In the Thought section, present your reasoning using the format: \"<think>\n {thoughts} </think>\n\". Each thought should include detailed analysis, brainstorming, verification, and refinement of ideas. After \"</think>\n,\" in the Solution section, provide the final, logical, and accurate answer, clearly derived from the exploration in the Thought section.",
"role": "system"
},
{
"content": "Butch and Sundance need to get out of Dodge. To travel as quickly as possible, each alternates walking and riding their only horse, Sparky, as follows. Butch begins by walking while Sundance rides. When Sundance reaches the first of the hitching posts that are conveniently located at one-mile intervals along their route, he ties Sparky to the post and begins walking. When Butch reaches Sparky, he rides until he passes Sundance, then leaves Sparky at the next hitching post and resumes walking, and they continue in this manner. Sparky, Butch, and Sundance walk at $6,$ $4,$ and $2.5$ miles per hour, respectively. The first time Butch and Sundance meet at a milepost, they are $n$ miles from Dodge, and they have been traveling for $t$ minutes. Find $n + t$ .\n\nPresent the answer in LaTeX format: \\boxed{Your answer}.",
"role": "user"
}
] |
MATH
|
{
"ground_truth": "279",
"style": "rule-lighteval/MATH_v2"
}
|
{
"index": "2e9e8f01-ff95-44bd-aec4-081825d59f32"
}
|
math_dapo
|
[
{
"content": "Your task is to follow a systematic, thorough reasoning process before providing the final solution. This involves analyzing, summarizing, exploring, reassessing, and refining your thought process through multiple iterations. Structure your response into two sections: Thought and Solution. In the Thought section, present your reasoning using the format: \"<think>\n {thoughts} </think>\n\". Each thought should include detailed analysis, brainstorming, verification, and refinement of ideas. After \"</think>\n,\" in the Solution section, provide the final, logical, and accurate answer, clearly derived from the exploration in the Thought section.",
"role": "system"
},
{
"content": "Let \\[A=111111\\]and \\[B=142857\\]Find a positive integer $N$ with six or fewer digits such that $N$ is the multiplicative inverse of $AB$ modulo 1,000,000.\n\nPresent the answer in LaTeX format: \\boxed{Your answer}.",
"role": "user"
}
] |
MATH
|
{
"ground_truth": "63",
"style": "rule-lighteval/MATH_v2"
}
|
{
"index": "0337fdf5-5ec4-4810-bf53-4d1e88ac9d9b"
}
|
math_dapo
|
[
{
"content": "Your task is to follow a systematic, thorough reasoning process before providing the final solution. This involves analyzing, summarizing, exploring, reassessing, and refining your thought process through multiple iterations. Structure your response into two sections: Thought and Solution. In the Thought section, present your reasoning using the format: \"<think>\n {thoughts} </think>\n\". Each thought should include detailed analysis, brainstorming, verification, and refinement of ideas. After \"</think>\n,\" in the Solution section, provide the final, logical, and accurate answer, clearly derived from the exploration in the Thought section.",
"role": "system"
},
{
"content": "已知存在正整数 $a, b, c$ 满足 $a+b+c=407,10^{n} \\mid a b c$ ，则 $n$ 的最大值是多少？\n\nPresent the answer in LaTeX format: \\boxed{Your answer}.",
"role": "user"
}
] |
MATH
|
{
"ground_truth": "6",
"style": "rule-lighteval/MATH_v2"
}
|
{
"index": "09b20e4b-49ce-4261-b1c8-85a2d1a7beef"
}
|
math_dapo
|
[
{
"content": "Your task is to follow a systematic, thorough reasoning process before providing the final solution. This involves analyzing, summarizing, exploring, reassessing, and refining your thought process through multiple iterations. Structure your response into two sections: Thought and Solution. In the Thought section, present your reasoning using the format: \"<think>\n {thoughts} </think>\n\". Each thought should include detailed analysis, brainstorming, verification, and refinement of ideas. After \"</think>\n,\" in the Solution section, provide the final, logical, and accurate answer, clearly derived from the exploration in the Thought section.",
"role": "system"
},
{
"content": "In this Number Wall, you add the numbers next to each other and write the sum in the block directly above the two numbers. Which number will be the block labeled '$n$'? [asy]\ndraw((0,0)--(8,0)--(8,2)--(0,2)--cycle);\ndraw((2,0)--(2,2));\ndraw((4,0)--(4,2));\ndraw((6,0)--(6,2));\ndraw((1,2)--(7,2)--(7,4)--(1,4)--cycle);\ndraw((3,2)--(3,4));\ndraw((5,2)--(5,4));\ndraw((2,4)--(2,6)--(6,6)--(6,4)--cycle);\ndraw((4,4)--(4,6));\ndraw((3,6)--(3,8)--(5,8)--(5,6));\nlabel(\"$n$\",(1,1));\nlabel(\"4\",(3,1));\nlabel(\"8\",(5,1));\nlabel(\"7\",(7,1));\nlabel(\"15\",(6,3));\nlabel(\"46\",(4,7));\n[/asy]\n\nPresent the answer in LaTeX format: \\boxed{Your answer}.",
"role": "user"
}
] |
MATH
|
{
"ground_truth": "3",
"style": "rule-lighteval/MATH_v2"
}
|
{
"index": "b8538302-a3f8-4468-8f3b-903de1d2b44c"
}
|
math_dapo
|
[
{
"content": "Your task is to follow a systematic, thorough reasoning process before providing the final solution. This involves analyzing, summarizing, exploring, reassessing, and refining your thought process through multiple iterations. Structure your response into two sections: Thought and Solution. In the Thought section, present your reasoning using the format: \"<think>\n {thoughts} </think>\n\". Each thought should include detailed analysis, brainstorming, verification, and refinement of ideas. After \"</think>\n,\" in the Solution section, provide the final, logical, and accurate answer, clearly derived from the exploration in the Thought section.",
"role": "system"
},
{
"content": "Let $A$ be the area of the largest semicircle that can be inscribed in a quarter-circle of radius $1$. Compute $\\frac{120A}{\\pi}$.\n\nPresent the answer in LaTeX format: \\boxed{Your answer}.",
"role": "user"
}
] |
MATH
|
{
"ground_truth": "15",
"style": "rule-lighteval/MATH_v2"
}
|
{
"index": "132d51dd-cf9f-4698-a367-f2f17f7b299c"
}
|
math_dapo
|
[
{
"content": "Your task is to follow a systematic, thorough reasoning process before providing the final solution. This involves analyzing, summarizing, exploring, reassessing, and refining your thought process through multiple iterations. Structure your response into two sections: Thought and Solution. In the Thought section, present your reasoning using the format: \"<think>\n {thoughts} </think>\n\". Each thought should include detailed analysis, brainstorming, verification, and refinement of ideas. After \"</think>\n,\" in the Solution section, provide the final, logical, and accurate answer, clearly derived from the exploration in the Thought section.",
"role": "system"
},
{
"content": "设函数 f(x)=\\begin{cases}1,& x=0\\\\ \\frac{x}{e^x-1},& x\\neq0\\end{cases}. 记 f(x) 在 x=0 处的泰勒展开式为 \\ds{k=0}{\\infty}a_kx^k，则 \\left[\\df{10}{|a_4|}\\right]=__________.\n\nPresent the answer in LaTeX format: \\boxed{Your answer}.",
"role": "user"
}
] |
MATH
|
{
"ground_truth": "7200",
"style": "rule-lighteval/MATH_v2"
}
|
{
"index": "23ee813d-315d-47f0-ac89-10b932991557"
}
|
math_dapo
|
[
{
"content": "Your task is to follow a systematic, thorough reasoning process before providing the final solution. This involves analyzing, summarizing, exploring, reassessing, and refining your thought process through multiple iterations. Structure your response into two sections: Thought and Solution. In the Thought section, present your reasoning using the format: \"<think>\n {thoughts} </think>\n\". Each thought should include detailed analysis, brainstorming, verification, and refinement of ideas. After \"</think>\n,\" in the Solution section, provide the final, logical, and accurate answer, clearly derived from the exploration in the Thought section.",
"role": "system"
},
{
"content": "When we say that Ray is climbing up the stairs $m$ at a time, we mean that he starts on the floor (step $0$) then jumps to step $m$ and then to $2m$ and so on until the number of steps to the top is less than $m$. Ray climbs up a flight of stairs of $n$ steps in two ways. When he does it $4$ steps at a time, there are $3$ steps left at the top. When he does it $5$ steps at a time, there are $2$ steps left at the top. What is the smallest possible value of $n$ that is greater than $10$?\n\nPresent the answer in LaTeX format: \\boxed{Your answer}.",
"role": "user"
}
] |
MATH
|
{
"ground_truth": "27",
"style": "rule-lighteval/MATH_v2"
}
|
{
"index": "b207a3aa-b145-46e1-a041-96c84238e970"
}
|
math_dapo
|
[
{
"content": "Your task is to follow a systematic, thorough reasoning process before providing the final solution. This involves analyzing, summarizing, exploring, reassessing, and refining your thought process through multiple iterations. Structure your response into two sections: Thought and Solution. In the Thought section, present your reasoning using the format: \"<think>\n {thoughts} </think>\n\". Each thought should include detailed analysis, brainstorming, verification, and refinement of ideas. After \"</think>\n,\" in the Solution section, provide the final, logical, and accurate answer, clearly derived from the exploration in the Thought section.",
"role": "system"
},
{
"content": "Compute the integer $$\\frac{2^{\\left(2^5-2\\right)/5-1}-2}{5}.$$\n\nPresent the answer in LaTeX format: \\boxed{Your answer}.",
"role": "user"
}
] |
MATH
|
{
"ground_truth": "6",
"style": "rule-lighteval/MATH_v2"
}
|
{
"index": "40e70c73-4554-49b6-a736-8985cdb9373e"
}
|
math_dapo
|
[
{
"content": "Your task is to follow a systematic, thorough reasoning process before providing the final solution. This involves analyzing, summarizing, exploring, reassessing, and refining your thought process through multiple iterations. Structure your response into two sections: Thought and Solution. In the Thought section, present your reasoning using the format: \"<think>\n {thoughts} </think>\n\". Each thought should include detailed analysis, brainstorming, verification, and refinement of ideas. After \"</think>\n,\" in the Solution section, provide the final, logical, and accurate answer, clearly derived from the exploration in the Thought section.",
"role": "system"
},
{
"content": "Call a positive integer $n$ [i]tubular [/i] if for any two distinct primes $p$ and $q$ dividing $n, (p + q) | n$. Find the number of tubular numbers less than $100,000$. (Integer powers of primes, including $1, 3$, and $16$, are not considered [i]tubular[/i].)\n\nPresent the answer in LaTeX format: \\boxed{Your answer}.",
"role": "user"
}
] |
MATH
|
{
"ground_truth": "26",
"style": "rule-lighteval/MATH_v2"
}
|
{
"index": "312b892f-5ad0-430c-bb0f-446542671755"
}
|
math_dapo
|
[
{
"content": "Your task is to follow a systematic, thorough reasoning process before providing the final solution. This involves analyzing, summarizing, exploring, reassessing, and refining your thought process through multiple iterations. Structure your response into two sections: Thought and Solution. In the Thought section, present your reasoning using the format: \"<think>\n {thoughts} </think>\n\". Each thought should include detailed analysis, brainstorming, verification, and refinement of ideas. After \"</think>\n,\" in the Solution section, provide the final, logical, and accurate answer, clearly derived from the exploration in the Thought section.",
"role": "system"
},
{
"content": "如图所示，在平面直角坐标系中，椭圆 $\\Gamma: \\frac{x^{2}}{2}+y^{2}=1$的左、右焦点分别为 $F_{1}, F_{2}$, 设 $P$ 是第一象限内 $\\Gamma$ 上一点, $P F_{1}, P F_{2}$ 的延长线分别交 $\\Gamma$ 于点 $Q_{1}, Q_{2}$ 。设 $r_{1}, r_{2}$ 分别为 $\\triangle P F_{1} Q_{2}, \\Delta P F_{2} Q_{1}$ 的内切圆半径。求 $r_{1}-r_{2}$ 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\nPresent the answer in LaTeX format: \\boxed{Your answer}.",
"role": "user"
}
] |
MATH
|
{
"ground_truth": "4",
"style": "rule-lighteval/MATH_v2"
}
|
{
"index": "355b1eea-faaa-40e6-80f8-e855e8fc5751"
}
|
math_dapo
|
[
{
"content": "Your task is to follow a systematic, thorough reasoning process before providing the final solution. This involves analyzing, summarizing, exploring, reassessing, and refining your thought process through multiple iterations. Structure your response into two sections: Thought and Solution. In the Thought section, present your reasoning using the format: \"<think>\n {thoughts} </think>\n\". Each thought should include detailed analysis, brainstorming, verification, and refinement of ideas. After \"</think>\n,\" in the Solution section, provide the final, logical, and accurate answer, clearly derived from the exploration in the Thought section.",
"role": "system"
},
{
"content": "What is the smallest integer $n$, greater than $1$, such that $n^{-1}\\pmod{130}$ and $n^{-1}\\pmod{231}$ are both defined?\n\nPresent the answer in LaTeX format: \\boxed{Your answer}.",
"role": "user"
}
] |
MATH
|
{
"ground_truth": "17",
"style": "rule-lighteval/MATH_v2"
}
|
{
"index": "c23db54b-a829-449f-a3a4-5995910fb662"
}
|
math_dapo
|
[
{
"content": "Your task is to follow a systematic, thorough reasoning process before providing the final solution. This involves analyzing, summarizing, exploring, reassessing, and refining your thought process through multiple iterations. Structure your response into two sections: Thought and Solution. In the Thought section, present your reasoning using the format: \"<think>\n {thoughts} </think>\n\". Each thought should include detailed analysis, brainstorming, verification, and refinement of ideas. After \"</think>\n,\" in the Solution section, provide the final, logical, and accurate answer, clearly derived from the exploration in the Thought section.",
"role": "system"
},
{
"content": "Let $z_1,$ $z_2,$ $z_3,$ and $z_4$ be the four distinct complex solutions of the equation\n\\[\n z^4 - 6z^2 + 8z + 1 = -4(z^3 - z + 2)i.\n\\]Find the sum of the six pairwise distances between $z_1,$ $z_2,$ $z_3,$ and $z_4$ in the complex plane.The answer is in the form k\\sqrt{m}+n,. Please provide the value of k + m + n.\n\nPresent the answer in LaTeX format: \\boxed{Your answer}.",
"role": "user"
}
] |
MATH
|
{
"ground_truth": "15",
"style": "rule-lighteval/MATH_v2"
}
|
{
"index": "c9a4f466-5824-4ba7-989a-1509d0f9f987"
}
|
math_dapo
|
[
{
"content": "Your task is to follow a systematic, thorough reasoning process before providing the final solution. This involves analyzing, summarizing, exploring, reassessing, and refining your thought process through multiple iterations. Structure your response into two sections: Thought and Solution. In the Thought section, present your reasoning using the format: \"<think>\n {thoughts} </think>\n\". Each thought should include detailed analysis, brainstorming, verification, and refinement of ideas. After \"</think>\n,\" in the Solution section, provide the final, logical, and accurate answer, clearly derived from the exploration in the Thought section.",
"role": "system"
},
{
"content": "What is the largest positive integer that is not the sum of a positive integral multiple of $42$ and a positive composite integer?\n\nPresent the answer in LaTeX format: \\boxed{Your answer}.",
"role": "user"
}
] |
MATH
|
{
"ground_truth": "215",
"style": "rule-lighteval/MATH_v2"
}
|
{
"index": "07dd2b9a-7cb0-4a98-9878-d7d18159746f"
}
|
math_dapo
|
[
{
"content": "Your task is to follow a systematic, thorough reasoning process before providing the final solution. This involves analyzing, summarizing, exploring, reassessing, and refining your thought process through multiple iterations. Structure your response into two sections: Thought and Solution. In the Thought section, present your reasoning using the format: \"<think>\n {thoughts} </think>\n\". Each thought should include detailed analysis, brainstorming, verification, and refinement of ideas. After \"</think>\n,\" in the Solution section, provide the final, logical, and accurate answer, clearly derived from the exploration in the Thought section.",
"role": "system"
},
{
"content": "试求满足下列条件的大于 5 的最小奇数 $a$ : 存在正整数 $m_{1} 、 n_{1} 、 m_{2} 、 n_{2}$, 使得\n$$\n\\begin{array}{ll} \n& a=m_{1}^{2}+n_{1}^{2}, a^{2}=m_{2}^{2}+n_{2}^{2}, \\\\\n\\text { 且 } \\quad & m_{1}-n_{1}=m_{2}-n_{2}.\n\\end{array}\n$$\n\nPresent the answer in LaTeX format: \\boxed{Your answer}.",
"role": "user"
}
] |
MATH
|
{
"ground_truth": "261",
"style": "rule-lighteval/MATH_v2"
}
|
{
"index": "f75d0aa5-d8de-430c-b759-affcb83c5184"
}
|
math_dapo
|
[
{
"content": "Your task is to follow a systematic, thorough reasoning process before providing the final solution. This involves analyzing, summarizing, exploring, reassessing, and refining your thought process through multiple iterations. Structure your response into two sections: Thought and Solution. In the Thought section, present your reasoning using the format: \"<think>\n {thoughts} </think>\n\". Each thought should include detailed analysis, brainstorming, verification, and refinement of ideas. After \"</think>\n,\" in the Solution section, provide the final, logical, and accurate answer, clearly derived from the exploration in the Thought section.",
"role": "system"
},
{
"content": "设 $A=\\{a \\mid-1 \\leqslant a \\leqslant 2\\}$, 则平面点集 $B=\\{(x, y) \\mid x, y \\in A, x+y \\geqslant 0\\}$ 的面积为 $\\qquad$.\n\nPresent the answer in LaTeX format: \\boxed{Your answer}.",
"role": "user"
}
] |
MATH
|
{
"ground_truth": "7",
"style": "rule-lighteval/MATH_v2"
}
|
{
"index": "cbfc05e0-c64c-4da4-b67a-8811353f7f6b"
}
|
math_dapo
|
[
{
"content": "Your task is to follow a systematic, thorough reasoning process before providing the final solution. This involves analyzing, summarizing, exploring, reassessing, and refining your thought process through multiple iterations. Structure your response into two sections: Thought and Solution. In the Thought section, present your reasoning using the format: \"<think>\n {thoughts} </think>\n\". Each thought should include detailed analysis, brainstorming, verification, and refinement of ideas. After \"</think>\n,\" in the Solution section, provide the final, logical, and accurate answer, clearly derived from the exploration in the Thought section.",
"role": "system"
},
{
"content": "函数 $f(x)=\\frac{\\sqrt{2}}{2}(\\cos x-\\sin x) \\sin \\left(x+\\frac{\\pi}{4}\\right)-2 a \\sin x+b(a>0)$ 的最大值为 1, 最小值为 -4, 求 $b$ 的值. \n\nPresent the answer in LaTeX format: \\boxed{Your answer}.",
"role": "user"
}
] |
MATH
|
{
"ground_truth": "-1",
"style": "rule-lighteval/MATH_v2"
}
|
{
"index": "6a6a5e55-61c7-45a0-bd5e-eda8490cac0f"
}
|
math_dapo
|
[
{
"content": "Your task is to follow a systematic, thorough reasoning process before providing the final solution. This involves analyzing, summarizing, exploring, reassessing, and refining your thought process through multiple iterations. Structure your response into two sections: Thought and Solution. In the Thought section, present your reasoning using the format: \"<think>\n {thoughts} </think>\n\". Each thought should include detailed analysis, brainstorming, verification, and refinement of ideas. After \"</think>\n,\" in the Solution section, provide the final, logical, and accurate answer, clearly derived from the exploration in the Thought section.",
"role": "system"
},
{
"content": "Find the coefficient of $x^{70}$ in the expansion of\n\\[(x - 1)(x^2 - 2)(x^3 - 3) \\dotsm (x^{11} - 11)(x^{12} - 12).\\]\n\nPresent the answer in LaTeX format: \\boxed{Your answer}.",
"role": "user"
}
] |
MATH
|
{
"ground_truth": "4",
"style": "rule-lighteval/MATH_v2"
}
|
{
"index": "dcd7229e-8f9e-41c2-a4bc-e7c7e1701bbf"
}
|
math_dapo
|
[
{
"content": "Your task is to follow a systematic, thorough reasoning process before providing the final solution. This involves analyzing, summarizing, exploring, reassessing, and refining your thought process through multiple iterations. Structure your response into two sections: Thought and Solution. In the Thought section, present your reasoning using the format: \"<think>\n {thoughts} </think>\n\". Each thought should include detailed analysis, brainstorming, verification, and refinement of ideas. After \"</think>\n,\" in the Solution section, provide the final, logical, and accurate answer, clearly derived from the exploration in the Thought section.",
"role": "system"
},
{
"content": "Let $a$ and $b$ positive real numbers such that $(65a^2 + 2ab + b^2)(a^2 + 8ab + 65b^2) = (8a^2 + 39ab + 7b^2)^2$. Then one possible value of $\\frac{a}{b}$ satis\fes $2 \\left(\\frac{a}{b}\\right) = m +\\sqrt{n}$, where $m$ and $n$ are positive integers. Find $m + n$.\n\nPresent the answer in LaTeX format: \\boxed{Your answer}.",
"role": "user"
}
] |
MATH
|
{
"ground_truth": "2636",
"style": "rule-lighteval/MATH_v2"
}
|
{
"index": "12d55a77-6e23-4a4d-87e8-7b0d3b1bf338"
}
|
math_dapo
|
[
{
"content": "Your task is to follow a systematic, thorough reasoning process before providing the final solution. This involves analyzing, summarizing, exploring, reassessing, and refining your thought process through multiple iterations. Structure your response into two sections: Thought and Solution. In the Thought section, present your reasoning using the format: \"<think>\n {thoughts} </think>\n\". Each thought should include detailed analysis, brainstorming, verification, and refinement of ideas. After \"</think>\n,\" in the Solution section, provide the final, logical, and accurate answer, clearly derived from the exploration in the Thought section.",
"role": "system"
},
{
"content": "在三棱雉 $P-A B C$ 中, 若 $P A \\perp$ 底面 $A B C$, 且棱 $A B, B P, B C, C P$ 的长分别为 $1,2,3,4$ ，则该三棱雉的体积为 $\\qquad$. 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 + n的值\n\nPresent the answer in LaTeX format: \\boxed{Your answer}.",
"role": "user"
}
] |
MATH
|
{
"ground_truth": "7",
"style": "rule-lighteval/MATH_v2"
}
|
{
"index": "38e8b83e-f80a-4a08-b192-fb9c5387c603"
}
|
math_dapo
|
[
{
"content": "Your task is to follow a systematic, thorough reasoning process before providing the final solution. This involves analyzing, summarizing, exploring, reassessing, and refining your thought process through multiple iterations. Structure your response into two sections: Thought and Solution. In the Thought section, present your reasoning using the format: \"<think>\n {thoughts} </think>\n\". Each thought should include detailed analysis, brainstorming, verification, and refinement of ideas. After \"</think>\n,\" in the Solution section, provide the final, logical, and accurate answer, clearly derived from the exploration in the Thought section.",
"role": "system"
},
{
"content": "There exists a constant $k$ so that the minimum value of\n\\[4x^2 - 6kxy + (3k^2 + 2) y^2 - 4x - 4y + 6\\]over all real numbers $x$ and $y$ is 0. Find $k.$\n\nPresent the answer in LaTeX format: \\boxed{Your answer}.",
"role": "user"
}
] |
MATH
|
{
"ground_truth": "2",
"style": "rule-lighteval/MATH_v2"
}
|
{
"index": "864dd6cd-fdea-46d4-8d1c-90cc455a648a"
}
|
math_dapo
|
[
{
"content": "Your task is to follow a systematic, thorough reasoning process before providing the final solution. This involves analyzing, summarizing, exploring, reassessing, and refining your thought process through multiple iterations. Structure your response into two sections: Thought and Solution. In the Thought section, present your reasoning using the format: \"<think>\n {thoughts} </think>\n\". Each thought should include detailed analysis, brainstorming, verification, and refinement of ideas. After \"</think>\n,\" in the Solution section, provide the final, logical, and accurate answer, clearly derived from the exploration in the Thought section.",
"role": "system"
},
{
"content": "已知 $\\omega=\\cos \\frac{\\pi}{5}+\\mathrm{i} \\sin \\frac{\\pi}{5}$, 写出下列等式成立的完整表达式： \n$x^{4}-x^{3}+x^{2}-x+1=(x-\\omega^{a})(x-\\omega^{b})(x-\\omega^{c})(x-\\omega^{d})$ \n请计算 a+b+c+d 的值。\n\nPresent the answer in LaTeX format: \\boxed{Your answer}.",
"role": "user"
}
] |
MATH
|
{
"ground_truth": "20",
"style": "rule-lighteval/MATH_v2"
}
|
{
"index": "01486f62-3fe7-40af-9ed4-6660ab71d12c"
}
|
math_dapo
|
[
{
"content": "Your task is to follow a systematic, thorough reasoning process before providing the final solution. This involves analyzing, summarizing, exploring, reassessing, and refining your thought process through multiple iterations. Structure your response into two sections: Thought and Solution. In the Thought section, present your reasoning using the format: \"<think>\n {thoughts} </think>\n\". Each thought should include detailed analysis, brainstorming, verification, and refinement of ideas. After \"</think>\n,\" in the Solution section, provide the final, logical, and accurate answer, clearly derived from the exploration in the Thought section.",
"role": "system"
},
{
"content": "You roll three fair six-sided dice. Given that the highest number you rolled is $5$, the expected value of the sum of the three dice can be written as $\\frac{a}{b}$ in simplest form. Find $a+b$.\n\nPresent the answer in LaTeX format: \\boxed{Your answer}.",
"role": "user"
}
] |
MATH
|
{
"ground_truth": "706",
"style": "rule-lighteval/MATH_v2"
}
|
{
"index": "cc7bcbba-8f48-4973-845e-cf514dd94c40"
}
|
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