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": "Andrew and Beatrice practice their free throws in basketball. One day, they attempted a total of $105$ free throws between them, with each person taking at least one free throw. If Andrew made exactly $\\frac{1}{3}$ of his free throw attempts and Beatrice made exactly $\\frac{3}{5}$ of her free throw attempts, what is the highest number of successful free throws they could have made between them?\n\nPresent the answer in LaTeX format: \\boxed{Your answer}.",
"role": "user"
}
] |
MATH
|
{
"ground_truth": "59",
"style": "rule-lighteval/MATH_v2"
}
|
{
"index": "5d3e6a57-0458-446b-a236-5aa5819bee28"
}
|
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 $ABC$ has $\\overline{AB} = 5$, $\\overline{BC} = 4$, $\\overline{CA} = 6$. Points $D$ and $E$ are on sides $AB$ and $AC$, respectively, such that $\\overline{AD} = \\overline{AE} = \\overline{BC}$. Let $CD$ and $BE$ intersect at $F$, and let $AF$ and $DE$ intersect at $G$. The length of $FG$ can be expressed in the form $\\frac{a\\sqrt{b}}{c}$ in simplified form. What is $a + b + c$?\n\nPresent the answer in LaTeX format: \\boxed{Your answer}.",
"role": "user"
}
] |
MATH
|
{
"ground_truth": "255",
"style": "rule-lighteval/MATH_v2"
}
|
{
"index": "aad31baa-7596-4450-8fff-c473cb2b97fe"
}
|
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 $x$ be the largest root of $x^4 - 2009x + 1$. Find the nearest integer to $\\frac{1}{x^3-2009}$ .\n\nPresent the answer in LaTeX format: \\boxed{Your answer}.",
"role": "user"
}
] |
MATH
|
{
"ground_truth": "-13",
"style": "rule-lighteval/MATH_v2"
}
|
{
"index": "007c391f-5314-4c76-a45d-61d5005270a1"
}
|
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$100\\times100$方格表的左上角小方格中有一只老鼠，右下角小方格中有一块奶酪。老鼠希望移动到右下角小方格中吃奶酪，每次可以从一个小方格移动到相邻的小方格（两个小方格相邻指它们有公共边）。现在在一些小方格的边上放置隔板，老鼠在移动时不能越过隔板。称一种放置隔板的方式是“仁慈的”，如果放置隔板后老鼠仍能吃到奶酪。求最小的正整数$n$，使得对任意一种“仁慈的”放置2023个隔板的方式，老鼠都能通过不超过$n$次移动吃到奶酪。\n\nPresent the answer in LaTeX format: \\boxed{Your answer}.",
"role": "user"
}
] |
MATH
|
{
"ground_truth": "2220",
"style": "rule-lighteval/MATH_v2"
}
|
{
"index": "7436a70f-e2b2-4e92-8b23-736da608573d"
}
|
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": "Mike draws five cards from a standard 52-card deck. What is the probability that he draws a card from at least three of the four suits? Express your answer as a simplified 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": "1102",
"style": "rule-lighteval/MATH_v2"
}
|
{
"index": "49307d1a-b6ff-4017-99e2-2228dceef36d"
}
|
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 prime factor of 8091?\n\nPresent the answer in LaTeX format: \\boxed{Your answer}.",
"role": "user"
}
] |
MATH
|
{
"ground_truth": "31",
"style": "rule-lighteval/MATH_v2"
}
|
{
"index": "395e35a3-1e60-4398-a753-a06e1cc134fa"
}
|
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 $m$ and $n$ be positive integers such that $m = 24n + 51$. What is the largest possible value of the greatest common divisor of $2m$ and $3n$?\n\nPresent the answer in LaTeX format: \\boxed{Your answer}.",
"role": "user"
}
] |
MATH
|
{
"ground_truth": "102",
"style": "rule-lighteval/MATH_v2"
}
|
{
"index": "ba781724-1b20-4eb0-b9f0-7fe1f986e441"
}
|
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 sum of real roots of the equation \\(x^4 - 7x^3 + 14x^2 - 14x + 4 = 0\\)?\n\nPresent the answer in LaTeX format: \\boxed{Your answer}.",
"role": "user"
}
] |
MATH
|
{
"ground_truth": "5",
"style": "rule-lighteval/MATH_v2"
}
|
{
"index": "1b025316-baea-4910-b0d5-1a63bce8309f"
}
|
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 $ABCD$, $\\overline{AB}=20$ and $\\overline{BC}=10$. Let $E$ be a point on $\\overline{CD}$ such that $\\angle CBE=15^\\circ$. Find the length of $\\overline{AE}$.\n\nPresent the answer in LaTeX format: \\boxed{Your answer}.",
"role": "user"
}
] |
MATH
|
{
"ground_truth": "20",
"style": "rule-lighteval/MATH_v2"
}
|
{
"index": "c830b09a-a35d-46f0-89ff-6e83ac3b5d1e"
}
|
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": "Markov plays a game for three turns. On each turn, he either rolls a fair, six sided die or flips a fair coin. If he rolls a 1 or 2 on the die, he will switch to the coin on the next turn, and if he flips a tails on the coin, he will switch to the die on the next turn. If Markov starts by rolling the die, what is the probability that he will flip the coin on the third turn?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": "25",
"style": "rule-lighteval/MATH_v2"
}
|
{
"index": "fbdc0367-0ac7-4f95-bda5-78addeee1d94"
}
|
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 $ABCDEF$ be an equiangular hexagon such that $AB=6, BC=8, CD=10$, and $DE=12$. Denote by $d$ the diameter of the largest circle that fits inside the hexagon. Find $d^2$.\n\nPresent the answer in LaTeX format: \\boxed{Your answer}.",
"role": "user"
}
] |
MATH
|
{
"ground_truth": "147",
"style": "rule-lighteval/MATH_v2"
}
|
{
"index": "95db2704-5a78-413e-8609-d0393b0d19d1"
}
|
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 three-element subsets of $\\{1, 2, 3,...,13\\}$ that contain at least one element that is a multiple of $2$, at least one element that is a multiple of $3$, and at least one element that is a multiple of $5$ such as $\\{2,3, 5\\}$ or $\\{6, 10,13\\}$.\n\nPresent the answer in LaTeX format: \\boxed{Your answer}.",
"role": "user"
}
] |
MATH
|
{
"ground_truth": "63",
"style": "rule-lighteval/MATH_v2"
}
|
{
"index": "eb3566bc-e96a-43dc-af47-8ecd80c8e848"
}
|
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 $\\lfloor \\sqrt{n^2 - 10n + 29} \\rfloor$ when $n = 19941994.$\n\nPresent the answer in LaTeX format: \\boxed{Your answer}.",
"role": "user"
}
] |
MATH
|
{
"ground_truth": "19941989",
"style": "rule-lighteval/MATH_v2"
}
|
{
"index": "c437444f-18c6-4fd9-8a1a-6786a9635959"
}
|
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": "在平面直角坐标系 $x O y$ 中, 抛物线 $\\Gamma: y^{2}=2 p x(p>0)$ 的焦点为 $F$, 过 $\\Gamma$上一点 $P$ (异于 $O$ ) 作 $\\Gamma$ 的切线，与 $y$ 轴交于点 $Q$ 。若 $|F P|=2,|F Q|=1$ ，则向量 $\\overrightarrow{O P}$ 与 $\\overrightarrow{O Q}$ 的数量积为 $\\qquad$.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": "5",
"style": "rule-lighteval/MATH_v2"
}
|
{
"index": "fbe3ae49-0c56-4b15-9bf2-90efdc379ac3"
}
|
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": "已知复数 $|z|=1, z^{n}=z+\\sqrt{2}$, 则 $n$ 的最小值为\n\nPresent the answer in LaTeX format: \\boxed{Your answer}.",
"role": "user"
}
] |
MATH
|
{
"ground_truth": "3",
"style": "rule-lighteval/MATH_v2"
}
|
{
"index": "52acbcfd-d02d-4948-b2e5-10ddcc5dfaf4"
}
|
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 rectangular box has sides of length 2003, 2004, and $2003 \\cdot 2004.$ Compute the length of the space diagonal of the box.\n\nPresent the answer in LaTeX format: \\boxed{Your answer}.",
"role": "user"
}
] |
MATH
|
{
"ground_truth": "4014013",
"style": "rule-lighteval/MATH_v2"
}
|
{
"index": "adf8146c-7865-4099-8011-5bee92c4e1e4"
}
|
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": "Paul starts at $1$ and counts by threes: $1, 4, 7, 10, ... $. At the same time and at the same speed, Penny counts backwards from $2017$ by fi\fves: $2017, 2012, 2007, 2002,...$ . Find the one number that both Paul and Penny count at the same time.\n\nPresent the answer in LaTeX format: \\boxed{Your answer}.",
"role": "user"
}
] |
MATH
|
{
"ground_truth": "757",
"style": "rule-lighteval/MATH_v2"
}
|
{
"index": "6abe39f6-5244-462d-8627-592a9f31593c"
}
|
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 \\( |x - \\log y| = x + \\log y \\) where \\( x \\) and \\( \\log y \\) are real, find the expression that represents the relationship between \\( x \\) and \\( y \\). The original answer is in the form \\( mx(y-n)=p \\). Please provide the value of \\( m+n+p \\).\n\nPresent the answer in LaTeX format: \\boxed{Your answer}.",
"role": "user"
}
] |
MATH
|
{
"ground_truth": "2",
"style": "rule-lighteval/MATH_v2"
}
|
{
"index": "29d971f4-2bfa-47d2-b04b-3936c288458a"
}
|
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 are $2022$ grids in a row. Two people, A and B, play a game with these grids. Initially, each odd-numbered grid from the left is marked with A's name, and each even-numbered grid from the left is marked with B's name. The players take turns performing the following action, starting with player A:\n\n- One should select two grids marked with their own name, such that these two grids are not adjacent, and all grids between them are marked with the opponent's name. Then, change the name in all the grids between those two grids to one's own name.\n\nThe game continues until one player can no longer make a move. Find the largest positive integer $m$ such that:\n\n- No matter how player B acts, player A can always ensure that there are at least $m$ grids marked with A's name.\n\nPresent the answer in LaTeX format: \\boxed{Your answer}.",
"role": "user"
}
] |
MATH
|
{
"ground_truth": "1011",
"style": "rule-lighteval/MATH_v2"
}
|
{
"index": "d8ad1943-d93f-4d64-b717-57f63b554304"
}
|
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": "将函数 $y=\\sqrt{4+6 x-x^{2}}-2(x \\in[0,6])$ 的图象逆时针方向旋转 $\\theta(0 \\leqslant \\theta \\leqslant \\alpha)$, 得到曲线 C。若对于每一个旋转角 $\\theta$，曲线 C 都是一个函数的图象，则 $\\alpha$ 的最大值为多少？原始答案的形式为\\arctan \\frac{k}{m}，请给出k+m的值。\n\nPresent the answer in LaTeX format: \\boxed{Your answer}.",
"role": "user"
}
] |
MATH
|
{
"ground_truth": "5",
"style": "rule-lighteval/MATH_v2"
}
|
{
"index": "63d11d7c-f1d2-42a9-b303-3fd5e29c0f6a"
}
|
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 $h_1$ and $h_2$ be the altitudes of a triangle drawn to the sides with lengths $5$ and $2\\sqrt{6}$, respectively. If $5 + h_1 \\leq 2\\sqrt{6} + h_2$, find the length of the third side of the triangle.\n\nPresent the answer in LaTeX format: \\boxed{Your answer}.",
"role": "user"
}
] |
MATH
|
{
"ground_truth": "7",
"style": "rule-lighteval/MATH_v2"
}
|
{
"index": "fe928764-a14c-452a-8f77-d0443fa9901c"
}
|
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 $S=\\{1,2,3,\\ldots,12\\}$. How many subsets of $S$, excluding the empty set, have an even sum but not an even product?\n\nPresent the answer in LaTeX format: \\boxed{Your answer}.",
"role": "user"
}
] |
MATH
|
{
"ground_truth": "31",
"style": "rule-lighteval/MATH_v2"
}
|
{
"index": "4c4d10e2-d3f7-454d-836f-e81a2ed391a5"
}
|
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 fraction $\\tfrac1{2015}$ has a unique \"(restricted) partial fraction decomposition'' of the form \\[\\dfrac1{2015}=\\dfrac a5+\\dfrac b{13}+\\dfrac c{31},\\] where $a$, $b$, and $c$ are integers with $0\\leq a<5$ and $0\\leq b<13$. Find $a+b$.\n\nPresent the answer in LaTeX format: \\boxed{Your answer}.",
"role": "user"
}
] |
MATH
|
{
"ground_truth": "14",
"style": "rule-lighteval/MATH_v2"
}
|
{
"index": "a6f38b6e-d05a-4139-bab6-9ef9e68830ed"
}
|
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 $\\triangle ABC$ be an acute triangle with circumcircle $\\omega,$ and let $H$ be the intersection of the altitudes of $\\triangle ABC.$ Suppose the tangent to the circumcircle of $\\triangle HBC$ at $H$ intersects $\\omega$ at points $X$ and $Y$ with $HA=3,HX=2,$ and $HY=6.$ The area of $\\triangle ABC$ can be written in the form $m\\sqrt{n},$ where $m$ and $n$ are positive integers, and $n$ is not divisible by the square of any prime. Find $m+n.$\n\nPresent the answer in LaTeX format: \\boxed{Your answer}.",
"role": "user"
}
] |
MATH
|
{
"ground_truth": "58",
"style": "rule-lighteval/MATH_v2"
}
|
{
"index": "b805c469-43fe-499a-aaf0-fcf30688992b"
}
|
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 $R$ be a set of nine distinct integers. Six of the elements are $2$, $3$, $4$, $6$, $9$, and $14$. What is the number of possible values of the median of $R$?\n\nPresent the answer in LaTeX format: \\boxed{Your answer}.",
"role": "user"
}
] |
MATH
|
{
"ground_truth": "7",
"style": "rule-lighteval/MATH_v2"
}
|
{
"index": "9cb5cec5-385c-414d-a43c-9a5eab384569"
}
|
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": "David has a collection of 40 rocks, 30 stones, 20 minerals, and 10 gemstones. An operation consists of removing three objects, no two of the same type. What is the maximum number of operations he can possibly perform?\n\nPresent the answer in LaTeX format: \\boxed{Your answer}.",
"role": "user"
}
] |
MATH
|
{
"ground_truth": "30",
"style": "rule-lighteval/MATH_v2"
}
|
{
"index": "4159200d-a843-48c8-8f98-cefae8c71713"
}
|
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": "已知正方体 \\(A B C D-A_{1} B_{1} C_{1} D_{1}\\) 的棱长为 1, 棱 \\(A A_{1}\\) 的中点为 \\(E\\), \\(A C\\) 与 \\(B D\\) 交于点 \\(O\\)。若平面 \\(\\alpha\\) 过 \\(E\\) 且与 \\(O C_{1}\\) 垂直，则 \\(\\alpha\\) 截该正方体所得截面的面积的原始答案是\\(\\frac{\\sqrt{k}}{m}\\)的形式，请给出k + m的值。\n\nPresent the answer in LaTeX format: \\boxed{Your answer}.",
"role": "user"
}
] |
MATH
|
{
"ground_truth": "10",
"style": "rule-lighteval/MATH_v2"
}
|
{
"index": "b913f460-4f01-489e-9ad7-f2ca7333809b"
}
|
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,b,c\\in\\bC，且 a+b+c=a^2+b^2+c^2=3, a^3+b^3+c^3=6，则 (a-1)^{2023}+(b-1)^{2023}+(c-1)^{2023}=__________.\n\nPresent the answer in LaTeX format: \\boxed{Your answer}.",
"role": "user"
}
] |
MATH
|
{
"ground_truth": "0",
"style": "rule-lighteval/MATH_v2"
}
|
{
"index": "f706f056-bb52-4a83-bc5f-5dbe11352ccd"
}
|
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 exist two triples of real numbers \\((a,b,c)\\) such that \\(a-\\frac{1}{b}, b-\\frac{1}{c}, c-\\frac{1}{a}\\) are the roots to the cubic equation \\(x^3-5x^2-15x+3\\) listed in increasing order. Denote those \\((a_1, b_1, c_1)\\) and \\((a_2, b_2, c_2)\\). If \\(a_1, b_1,\\) and \\(c_1\\) are the roots to the monic cubic polynomial \\(f\\) and \\(a_2, b_2,\\) and \\(c_2\\) are the roots to the monic cubic polynomial \\(g\\), find \\(f(0)^3+g(0)^3\\).\n\nPresent the answer in LaTeX format: \\boxed{Your answer}.",
"role": "user"
}
] |
MATH
|
{
"ground_truth": "-14",
"style": "rule-lighteval/MATH_v2"
}
|
{
"index": "65a43bd3-c51d-477f-aa71-a0d0d0ce7bc8"
}
|
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 $\\overline{523abc}$ divisible by $7, 8$ and $9$.\n\nPresent the answer in LaTeX format: \\boxed{Your answer}.",
"role": "user"
}
] |
MATH
|
{
"ground_truth": "523152",
"style": "rule-lighteval/MATH_v2"
}
|
{
"index": "7d5747e1-d669-4e8f-be95-923b2a351a0b"
}
|
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": "Any five points are taken inside or on a square with side length \\(1\\). Let \\(a\\) be the smallest possible number with the property that it is always possible to select one pair of points from these five such that the distance between them is equal to or less than \\(a\\). The original answer is in the format \\(\\frac{\\sqrt{n}}{m}\\). Please calculate the value of \\(k + m + n\\).\n\nPresent the answer in LaTeX format: \\boxed{Your answer}.",
"role": "user"
}
] |
MATH
|
{
"ground_truth": "5",
"style": "rule-lighteval/MATH_v2"
}
|
{
"index": "cfb97b7b-835f-410e-a1d8-f6152a324a4a"
}
|
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": "Circles $\\omega_1$, $\\omega_2$, and $\\omega_3$ each have radius $4$ and are placed in the plane so that each circle is externally tangent to the other two. Points $P_1$, $P_2$, and $P_3$ lie on $\\omega_1$, $\\omega_2$, and $\\omega_3$ respectively such that $P_1P_2=P_2P_3=P_3P_1$ and line $P_iP_{i+1}$ is tangent to $\\omega_i$ for each $i=1,2,3$, where $P_4 = P_1$. See the figure below. The area of $\\triangle P_1P_2P_3$ can be written in the form $\\sqrt{a}+\\sqrt{b}$ for positive integers $a$ and $b$. Find the value of $a+b$.\n\nPresent the answer in LaTeX format: \\boxed{Your answer}.",
"role": "user"
}
] |
MATH
|
{
"ground_truth": "552",
"style": "rule-lighteval/MATH_v2"
}
|
{
"index": "cf2c184d-ed05-4657-8253-2106a14a4d9f"
}
|
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 entire graph of the function $f(x)$ is shown below ($f$ is only defined when $x$ is between $-4$ and $4$ inclusive). How many values of $x$ satisfy $f(f(x)) = 2$?\n\n[asy]\nimport graph; size(9cm);\n\nreal lsf=0.5;\n\npen dps=linewidth(0.7)+fontsize(10);\n\ndefaultpen(dps); pen ds=black;\n\nreal xmin=-4.5,xmax=4.5,ymin=-0.5,ymax=4.5;\n\nLabel laxis; laxis.p=fontsize(10);\n\nxaxis(\"$x$\",xmin,xmax,defaultpen+black,Ticks(laxis,Step=1.0,Size=2,OmitTick(0)),Arrows(6),above=true);\nyaxis(\"$y$\",ymin,ymax,defaultpen+black,Ticks(laxis,Step=1.0,Size=2,OmitTick(0)),Arrows(6),above=true);\n\n//draw((xmin,(-(0)-(-2)*xmin)/-2)--(-1,(-(0)-(-2)*-1)/-2),linewidth(1.2),BeginArrow(6)); //draw((-1,1)--(3,5),linewidth(1.2));\n\n//draw((3,(-(-16)-(2)*3)/2)--(xmax,(-(-16)-(2)*xmax)/2),linewidth(1.2),EndArrow(6));\n\nreal f(real x) { return -.5*x^2-1.5*x+2;}\ndraw(graph(f,-4,-2));\ndraw((-2,3)--(2,1));\nreal f(real x) { return .5*x^2-1.5x+2;}\ndraw(graph(f,2,4));\n\nlabel(\"$f(x)$\",(-3,5),E);\n\ndot(\"$(-4,0)$\", (-4,0), NW);\ndot(\"$(-3,2)$\", (-3,2), NW);\ndot(\"$(-2,3)$\", (-2,3), N);\ndot(\"$(0,2)$\", (0,2), NE);\ndot(\"$(2,1)$\", (2,1), S);\ndot(\"$(3,2)$\", (3,2), SE);\ndot(\"$(4,4)$\", (4,4), NE);\n\n//clip((xmin,ymin)--(xmin,ymax)--(xmax,ymax)--(xmax,ymin)--cycle);\n[/asy]\n\nPresent the answer in LaTeX format: \\boxed{Your answer}.",
"role": "user"
}
] |
MATH
|
{
"ground_truth": "3",
"style": "rule-lighteval/MATH_v2"
}
|
{
"index": "e57d4b56-7b22-4a2f-a619-485398cd72a4"
}
|
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 area of the figure on the coordinate plane bounded by the straight lines $x = 0$, $x = 2$, and the graphs of the functions $y = \\sqrt{x^3 + 1}$ and $y = -\\sqrt[3]{x^2 + 2x}$.\n\nPresent the answer in LaTeX format: \\boxed{Your answer}.",
"role": "user"
}
] |
MATH
|
{
"ground_truth": "6",
"style": "rule-lighteval/MATH_v2"
}
|
{
"index": "32e558b9-ba7e-4595-98a5-76018f74a54e"
}
|
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 any real number $x$, let $\\lfloor x \\rfloor$ denote the integer part of $x$; $\\{ x \\}$ be the fractional part of $x$ ($\\{x\\} = x - \\lfloor x \\rfloor$). Let $A$ denote the set of all real numbers $x$ satisfying: \n\\[\\{x\\} = \\frac{x + \\lfloor x \\rfloor + \\lfloor x + \\frac{1}{2} \\rfloor}{20}\\] \nIf $S$ is the sum of all numbers in $A$, find $\\lfloor S \\rfloor$.\n\nPresent the answer in LaTeX format: \\boxed{Your answer}.",
"role": "user"
}
] |
MATH
|
{
"ground_truth": "21",
"style": "rule-lighteval/MATH_v2"
}
|
{
"index": "5be0dd35-1dff-48a4-93ae-a3ba9abb8819"
}
|
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 $ABCDE$ be a pentagon inscribed in a circle such that $AB = CD = 3$, $BC = DE = 10$, and $AE= 14$. The sum of the lengths of all diagonals of $ABCDE$ is equal to $\\frac{m}{n}$, where $m$ and $n$ are relatively prime positive integers. Find the value of $m+n$.\n\nPresent the answer in LaTeX format: \\boxed{Your answer}.",
"role": "user"
}
] |
MATH
|
{
"ground_truth": "391",
"style": "rule-lighteval/MATH_v2"
}
|
{
"index": "bdb21960-bfae-43fc-a64d-7679e2d8a405"
}
|
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": "On a blackboard lies $50$ magnets in a line numbered from $1$ to $50$, with different magnets containing different numbers. David walks up to the blackboard and rearranges the magnets into some arbitrary order. He then writes underneath each pair of consecutive magnets the positive difference between the numbers on the magnets. If the expected number of times he writes the number $1$ can be written in the form $\\frac{m}{n}$ for relatively prime positive integers $m$ and $n$, compute $100m+n$.\n\nPresent the answer in LaTeX format: \\boxed{Your answer}.",
"role": "user"
}
] |
MATH
|
{
"ground_truth": "4925",
"style": "rule-lighteval/MATH_v2"
}
|
{
"index": "f96bf278-f0c6-4945-99c7-65f259136055"
}
|
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": "Yan is somewhere between his home and the stadium. To get to the stadium, he can either walk directly to the stadium or walk home first and then ride his bicycle to the stadium. He rides 7 times as fast as he walks, and both choices require the same amount of time. What is the ratio of Yan's distance from his home to his distance from the stadium? Express your answer in the form \\(\\frac{k}{m}\\), where \\(\\frac{k}{m}\\) is in simplest form, and provide the value of k + m.\n\nPresent the answer in LaTeX format: \\boxed{Your answer}.",
"role": "user"
}
] |
MATH
|
{
"ground_truth": "7",
"style": "rule-lighteval/MATH_v2"
}
|
{
"index": "2104e67f-6528-4763-9730-19166ba40ada"
}
|
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 congruent circles of radius $2$ are drawn in the plane such that each circle passes through the centers of the other two circles. The region common to all three circles has a boundary consisting of three congruent circular arcs. Let $K$ be the area of the triangle whose vertices are the midpoints of those arcs. If $K = \\sqrt{a} - b$ for positive integers $a, b$, find $100a+b$.\n\nPresent the answer in LaTeX format: \\boxed{Your answer}.",
"role": "user"
}
] |
MATH
|
{
"ground_truth": "4806",
"style": "rule-lighteval/MATH_v2"
}
|
{
"index": "790225ad-f98f-4f96-a31a-247978a7192a"
}
|
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 $n$ for which there exists a set $\\{s_1,s_2,\\ldots,s_n\\}$ consisting of $n$ distinct positive integers such that\n$\\left(1-\\dfrac{1}{s_1}\\right)\\left(1-\\dfrac{1}{s_2}\\right)\\dots\\left(1-\\dfrac{1}{s_n}\\right)=\\dfrac{51}{2010}.$\nPlease provide the value of $n$.\n\nPresent the answer in LaTeX format: \\boxed{Your answer}.",
"role": "user"
}
] |
MATH
|
{
"ground_truth": "39",
"style": "rule-lighteval/MATH_v2"
}
|
{
"index": "4564df84-6808-4b62-9bd4-5f1b4786edad"
}
|
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 total number of different integers the function\n\n\\[ f(x) = \\left\\lfloor x \\right\\rfloor + \\left\\lfloor 2 \\cdot x \\right\\rfloor + \\left\\lfloor \\frac{5 \\cdot x}{3} \\right\\rfloor + \\left\\lfloor 3 \\cdot x \\right\\rfloor + \\left\\lfloor 4 \\cdot x \\right\\rfloor \\]\n\ntakes for $0 \\leq x \\leq 100.$\n\nPresent the answer in LaTeX format: \\boxed{Your answer}.",
"role": "user"
}
] |
MATH
|
{
"ground_truth": "734",
"style": "rule-lighteval/MATH_v2"
}
|
{
"index": "8c3728b0-b874-49db-8635-0e56b73eca33"
}
|
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 boxes in the expression below are filled with the numbers $3$, $4$, $5$, $6$, $7$, and $8$, so that each number is used exactly once. What is the least possible value of the expression?\n\n$$ \\square \\times \\square + \\square \\times \\square - \\square \\times \\square $$\n\nPresent the answer in LaTeX format: \\boxed{Your answer}.",
"role": "user"
}
] |
MATH
|
{
"ground_truth": "-18",
"style": "rule-lighteval/MATH_v2"
}
|
{
"index": "95c8b785-592b-4144-8555-35cfac347266"
}
|
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，设椭圆 $\\frac{x^{2}}{a^{2}}+\\frac{y^{2}}{b^{2}}=1(a>b>0)$ 的左、右焦点分别为 $F_{1} 、 F_{2}$ ，过点 $F_{2}$ 的直线交栯圆于 $A\\left(x_{1}, y_{1}\\right), B\\left(x_{2}, y_{2}\\right)$ 两点. 若 $\\triangle A F_{1} B$ 内切圆的面积为 $\\pi$ ，且 $\\left|y_{1}-y_{2}\\right|=4$ ，则椭圆的离心率为___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": "2edd9c28-3a56-4f74-bb2b-097a2dc8a30c"
}
|
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 sum of all integer values $n$ for which $\\binom{26}{13}+\\binom{26}{n}=\\binom{27}{14}$?\n\nPresent the answer in LaTeX format: \\boxed{Your answer}.",
"role": "user"
}
] |
MATH
|
{
"ground_truth": "26",
"style": "rule-lighteval/MATH_v2"
}
|
{
"index": "9cb8f262-6246-4e58-93e3-92668410eff2"
}
|
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": "求所有的整数 n\\geq 2，使得 \\df{\\sigma(n)}{p(n)-1}=n，其中 p(n) 是 n 的最大质因子.\n\nPresent the answer in LaTeX format: \\boxed{Your answer}.",
"role": "user"
}
] |
MATH
|
{
"ground_truth": "6",
"style": "rule-lighteval/MATH_v2"
}
|
{
"index": "a9c0ed22-2322-40d2-b870-0db3a8443916"
}
|
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 all even positive integers less than $233$ that are not divisible by $10$.\n\nPresent the answer in LaTeX format: \\boxed{Your answer}.",
"role": "user"
}
] |
MATH
|
{
"ground_truth": "10812",
"style": "rule-lighteval/MATH_v2"
}
|
{
"index": "3807d023-cf19-4bdc-809b-10f4d29f2306"
}
|
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 $LMT$ has $\\overline{MA}$ as an altitude. Given that $MA = 16$, $MT = 20$, and $LT = 25$, find the length of the altitude from $L$ to $\\overline{MT}$.\n\nPresent the answer in LaTeX format: \\boxed{Your answer}.",
"role": "user"
}
] |
MATH
|
{
"ground_truth": "20",
"style": "rule-lighteval/MATH_v2"
}
|
{
"index": "89798993-ead0-4985-95ff-3752302002b9"
}
|
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 triangle $ABC,$ $\\angle A = 90^\\circ,$ $AC = 1,$ and $AB = 5.$ Point $D$ lies on ray $\\overrightarrow{AC}$ such that $\\angle DBC = 2 \\angle CBA.$ Compute $AD.$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": "48",
"style": "rule-lighteval/MATH_v2"
}
|
{
"index": "33b51622-b5e7-4a2c-96f0-2bdd22ed329e"
}
|
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 positive integer $8833$ has the property that $8833 = 88^2 + 33^2$. Find the unique other four-digit positive integer $\\overline{abcd}$ such that $\\overline{abcd} = (\\overline{ab})^2 + (\\overline{cd})^2$.\n\nPresent the answer in LaTeX format: \\boxed{Your answer}.",
"role": "user"
}
] |
MATH
|
{
"ground_truth": "1233",
"style": "rule-lighteval/MATH_v2"
}
|
{
"index": "fd97a4a0-b8ff-41f5-b5ce-2e1a36db85e4"
}
|
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 moth starts at vertex $A$ of a certain cube and is trying to get to vertex $B$, which is opposite $A$, in five or fewer “steps,” where a step consists in traveling along an edge from one vertex to another. The moth will stop as soon as it reaches $B$. How many ways can the moth achieve its objective?\n\nPresent the answer in LaTeX format: \\boxed{Your answer}.",
"role": "user"
}
] |
MATH
|
{
"ground_truth": "48",
"style": "rule-lighteval/MATH_v2"
}
|
{
"index": "0857ac46-f166-440c-9464-04dc4c1849b8"
}
|
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 convex and cyclic quadrilateral $ABCD$, we have $\\angle B = 110^{\\circ}$. The intersection of $AD$ and $BC$ is $E$, and the intersection of $AB$ and $CD$ is $F$. If the perpendicular from $E$ to $AB$ intersects the perpendicular from $F$ to $BC$ on the circumcircle of the quadrilateral at point $P$, what is $\\angle PDF$ in degrees?\n\nPresent the answer in LaTeX format: \\boxed{Your answer}.",
"role": "user"
}
] |
MATH
|
{
"ground_truth": "70",
"style": "rule-lighteval/MATH_v2"
}
|
{
"index": "044a50eb-272a-49d8-9396-e362aaf2bca1"
}
|
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 all ordered triple of integers $(a_1,a_2,a_3)$ with $1 \\le a_1,a_2,a_3 \\le 10$ . Each ordered triple in $S$ generates a sequence according to the rule $a_n=a_{n-1}\\cdot | a_{n-2}-a_{n-3} |$ for all $n\\ge 4$ . Find the number of such sequences for which $a_n=0$ for some $n$ .\n\nPresent the answer in LaTeX format: \\boxed{Your answer}.",
"role": "user"
}
] |
MATH
|
{
"ground_truth": "494",
"style": "rule-lighteval/MATH_v2"
}
|
{
"index": "d642f7ce-77a9-48aa-933f-74871ad631de"
}
|
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": "Kevin writes the multiples of three from $1$ to $100$ on the whiteboard. How many digits does he write?\n\nPresent the answer in LaTeX format: \\boxed{Your answer}.",
"role": "user"
}
] |
MATH
|
{
"ground_truth": "63",
"style": "rule-lighteval/MATH_v2"
}
|
{
"index": "c36bd46e-e92c-46cc-a0bc-c1f31eab2b19"
}
|
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 positive integer that cannot be written as the sum of two nonnegative palindromic integers? (An integer is palindromic if the sequence of decimal digits is the same when read backwards.)\n\nPresent the answer in LaTeX format: \\boxed{Your answer}.",
"role": "user"
}
] |
MATH
|
{
"ground_truth": "21",
"style": "rule-lighteval/MATH_v2"
}
|
{
"index": "0161be47-82d1-483e-82ab-96354d02ddb4"
}
|
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 $P(A)$ be the arithmetic mean of all elements of the set $A = \\{ a_1, a_2, \\ldots, a_n \\}$, defined as $P(A) = \\frac{1}{n} \\sum^{n}_{i=1} a_i$. A subset $B$ of $A$ is called a \"balanced subset\" if $B$ is non-empty and $P(B) = P(A)$. Given the set $M = \\{ 1, 2, 3, 4, 5, 6, 7, 8, 9 \\}$, find the number of all \"balanced subsets\" of $M$.\n\nPresent the answer in LaTeX format: \\boxed{Your answer}.",
"role": "user"
}
] |
MATH
|
{
"ground_truth": "51",
"style": "rule-lighteval/MATH_v2"
}
|
{
"index": "4966668f-c5d3-4feb-a8e6-5d1052767d2f"
}
|
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": "求方程\n$$\n\\frac{\\sqrt{3}+2 \\sin 2 x}{\\sqrt{3}+2 \\sin x}=\\sqrt{3} \\sin x+\\frac{\\cos 2 x}{2 \\cos x}\n$$\n在 $\\left(0, \\frac{\\pi}{2}\\right)$ 内的解.解得形式均为\\frac{m\\pi}{n}的形式，请给出所有解m+n的和\n\nPresent the answer in LaTeX format: \\boxed{Your answer}.",
"role": "user"
}
] |
MATH
|
{
"ground_truth": "15",
"style": "rule-lighteval/MATH_v2"
}
|
{
"index": "91a86162-3230-49f7-a820-1014e26206cd"
}
|
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": "Does there exist a polynomial of one variable that is irreducible over the field of integers, has degree $60$, and is a multiple of the form $X^n - 1$? If so, how many such polynomials exist?\n\nPresent the answer in LaTeX format: \\boxed{Your answer}.",
"role": "user"
}
] |
MATH
|
{
"ground_truth": "9",
"style": "rule-lighteval/MATH_v2"
}
|
{
"index": "9600d122-e83f-4372-b028-faa72d46faeb"
}
|
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 $p < q < r < s$ are prime numbers such that $pqrs + 1 = 4^{p+q}$. Find $r + s$.\n\nPresent the answer in LaTeX format: \\boxed{Your answer}.",
"role": "user"
}
] |
MATH
|
{
"ground_truth": "274",
"style": "rule-lighteval/MATH_v2"
}
|
{
"index": "cf018933-6321-4707-98e0-fb3eb828ef23"
}
|
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 $f(x)$ is a rational function such that $3f\\left(\\dfrac{1}{x}\\right)+\\dfrac{2f(x)}{x}=x^2$ for $x\\neq 0$. Find $f(-2)$.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": "87",
"style": "rule-lighteval/MATH_v2"
}
|
{
"index": "b8d47176-4683-489c-977e-c7dcef06e969"
}
|
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 smallest positive integer such that when the last digit is moved to the front, the new number is $\\frac{3}{2}$ times the original number.\n\nPresent the answer in LaTeX format: \\boxed{Your answer}.",
"role": "user"
}
] |
MATH
|
{
"ground_truth": "285714",
"style": "rule-lighteval/MATH_v2"
}
|
{
"index": "35751501-1ed5-4e93-86f2-aa93423597b5"
}
|
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": "An infinite geometric series has sum 2000. A new series, obtained by squaring each term of the original series, has sum 16 times the sum of the original series. The common ratio of the original series 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": "125",
"style": "rule-lighteval/MATH_v2"
}
|
{
"index": "e788fd59-ed9c-4aa7-9545-484d6f099f17"
}
|
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 region shown is bounded by the arcs of circles having radius 4 units, having a central angle measure of 60 degrees and intersecting at points of tangency. The area of the region can be expressed in the form $a\\sqrt{b}+c\\pi$ square units, where $\\sqrt{b}$ is a radical in simplest form. What is the value of $a + b + c$?\n[asy]\nsize(150);\ndraw(arc((-2,0),2,0,60));\ndraw(arc((0,3.464),2,-60,-120));\ndraw(arc((2,0),2,120,180));\n[/asy]\n\nPresent the answer in LaTeX format: \\boxed{Your answer}.",
"role": "user"
}
] |
MATH
|
{
"ground_truth": "11",
"style": "rule-lighteval/MATH_v2"
}
|
{
"index": "eaa07974-1a72-4321-919a-70459ca57080"
}
|
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": "Consider all ordered pairs \\((a, b)\\) of positive integers such that \\(\\frac{a^2 + b^2 + 2}{ab}\\) is an integer and \\(a \\leq b\\). We label all such pairs in increasing order by their distance from the origin. (It is guaranteed that no ties exist.) Thus \\(P_1 = (1, 1)\\), \\(P_2 = (1, 3)\\), and so on. If \\(P_{2020} = (x, y)\\), then compute the remainder when \\(x + y\\) is divided by \\(2017\\).\n\nPresent the answer in LaTeX format: \\boxed{Your answer}.",
"role": "user"
}
] |
MATH
|
{
"ground_truth": "52",
"style": "rule-lighteval/MATH_v2"
}
|
{
"index": "bf8eeabb-e074-4090-b6e9-a2d95b54b1bc"
}
|
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 there exist constants $A$, $B$, $C$, and $D$ such that \n\\[n^4 = A\\binom{n}{4} + B\\binom{n}{3} + C\\binom{n}{2} + D\\binom{n}{1}\\]\n holds true for all positive integers $n \\geq 4$. What is $A + B + C + D$?\n\nPresent the answer in LaTeX format: \\boxed{Your answer}.",
"role": "user"
}
] |
MATH
|
{
"ground_truth": "75",
"style": "rule-lighteval/MATH_v2"
}
|
{
"index": "2e215332-88db-47ac-9427-3052176340c8"
}
|
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 prime numbers $p$ between $100$ and $200$ for which the congruence equation $x^{11} + y^{16} \\equiv 2013 \\pmod{p}$ has a solution in integers $x$ and $y$.\n\nPresent the answer in LaTeX format: \\boxed{Your answer}.",
"role": "user"
}
] |
MATH
|
{
"ground_truth": "21",
"style": "rule-lighteval/MATH_v2"
}
|
{
"index": "ca505ca6-2d6b-47a1-add7-61093aa3c7f4"
}
|
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": "给定正整数 $n(n \\geqslant 2)$. 求最大的实数 $\\lambda$, 使得不等式 $a_{n}^{2} \\geqslant \\lambda\\left(a_{1}+a_{2}+\\cdots+a_{n-1}\\right)+2 a_{n}$ 对任何满足 $a_{1}<a_{2}<\\cdots<a_{n}$ 的正整数 $a_{1}, a_{2}, \\cdots, a_{n}$ 均成立。原始答案是 \\frac{2n - 4}{n - 1} 的形式，请给出 m + n 的值，当 n = 3 时。\n\nPresent the answer in LaTeX format: \\boxed{Your answer}.",
"role": "user"
}
] |
MATH
|
{
"ground_truth": "1",
"style": "rule-lighteval/MATH_v2"
}
|
{
"index": "4f9d0a0a-f36b-4d01-8683-cd382d20cb27"
}
|
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 are 16 cities participating in a football match. Each city has two teams: Team A and Team B. According to the rules, each team can compete with any other team from different cities at most once. After a few days, it is observed that the number of matches played by each team, except for Team A from City 1, is unique. Determine the number of matches that Team A from City 1 has played.\n\nPresent the answer in LaTeX format: \\boxed{Your answer}.",
"role": "user"
}
] |
MATH
|
{
"ground_truth": "15",
"style": "rule-lighteval/MATH_v2"
}
|
{
"index": "ca4fc224-3ac9-439b-b5ac-fbfd10bf8875"
}
|
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 $\\triangle A B C$ 中, $\\cos A, \\sin A, \\tan B$ 依次构成以 $\\frac{3}{4}$ 为公比的等比数列,则 $\\cot C$ 的原始答案是以$-\\frac{m}{n}$的形式给出，请给出$m + n$的值。\n\nPresent the answer in LaTeX format: \\boxed{Your answer}.",
"role": "user"
}
] |
MATH
|
{
"ground_truth": "149",
"style": "rule-lighteval/MATH_v2"
}
|
{
"index": "ebf23d37-e748-4e07-84b9-6172e41f29ac"
}
|
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 remainder when $333^{333}$ is divided by $33$.\n\nPresent the answer in LaTeX format: \\boxed{Your answer}.",
"role": "user"
}
] |
MATH
|
{
"ground_truth": "27",
"style": "rule-lighteval/MATH_v2"
}
|
{
"index": "bcd1fc05-c30d-444c-9a83-df89fc737f80"
}
|
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 tram ticket costs $1$ Tug, which is equivalent to $100$ tugriks. There are $20$ passengers, each having only coins in denominations of $2$ and $5$ tugriks. The conductor starts with no money at all. Despite this, all passengers manage to pay the fare and receive the necessary change. What is the smallest total number of passengers that the tram could have?\n\nPresent the answer in LaTeX format: \\boxed{Your answer}.",
"role": "user"
}
] |
MATH
|
{
"ground_truth": "20",
"style": "rule-lighteval/MATH_v2"
}
|
{
"index": "807c6510-7136-441a-8b15-6f966fd03d72"
}
|
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 $P$ be a point on the circle circumscribing square $ABCD$ that satisfies $PA \\cdot PC = 56$ and $PB \\cdot PD = 90.$ Find the area of $ABCD.$\n\n\nPresent the answer in LaTeX format: \\boxed{Your answer}.",
"role": "user"
}
] |
MATH
|
{
"ground_truth": "106",
"style": "rule-lighteval/MATH_v2"
}
|
{
"index": "f6f88a04-034b-45c2-a8b5-7ed8d63db34b"
}
|
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": "试求最小的正整数 $n$ ，使得对于满足条件 $\\sum\\limits_{i=1}^{n} a_{i}=2007$ 的任一具有 $n$ 项的正整数数列 $a_{1}, a_{2}, \\cdots, a_{n}$, 其中必有连续的若干项之和等于 $30$ . \n\nPresent the answer in LaTeX format: \\boxed{Your answer}.",
"role": "user"
}
] |
MATH
|
{
"ground_truth": "1018",
"style": "rule-lighteval/MATH_v2"
}
|
{
"index": "4ab25755-da9b-4cfa-85e1-3962fa4286de"
}
|
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 \\(\\triangle ABC\\), \\(\\angle C = 90^\\circ\\), \\(AC = 6\\), and \\(BC = 8\\). Points \\(D\\) and \\(E\\) are on \\(\\overline{AB}\\) and \\(\\overline{BC}\\), respectively, and \\(\\angle BED = 90^\\circ\\). If \\(DE = 4\\), find the value of \\(BD\\). The original answer is in \\(\\frac{k}{m}\\) format, please give the value of k + m.\n\nPresent the answer in LaTeX format: \\boxed{Your answer}.",
"role": "user"
}
] |
MATH
|
{
"ground_truth": "23",
"style": "rule-lighteval/MATH_v2"
}
|
{
"index": "779ada7a-8efa-406d-8bbe-7fe15055505b"
}
|
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 cyclic quadrilateral with $AB = 5$, $BC = 10$, $CD = 11$, and $DA = 14$. The value of $AC + BD$ can be written as $\\tfrac{n}{\\sqrt{pq}}$, where $n$ is a positive integer and $p$ and $q$ are distinct primes. Find $n + p + q$.\n\nPresent the answer in LaTeX format: \\boxed{Your answer}.",
"role": "user"
}
] |
MATH
|
{
"ground_truth": "446",
"style": "rule-lighteval/MATH_v2"
}
|
{
"index": "d210e806-21fd-4666-b1f1-02a89c8f698a"
}
|
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": "Consider an isosceles triangle $ABC$ with sides $BC = 30$, $CA = AB = 20$. Let $D$ be the foot of the perpendicular from $A$ to $BC$, and let $M$ be the midpoint of $AD$. Let $PQ$ be a chord of the circumcircle of triangle $ABC$, such that $M$ lies on $PQ$ and $PQ$ is parallel to $BC$. Determine the length of $PQ$.\n\nPresent the answer in LaTeX format: \\boxed{Your answer}.",
"role": "user"
}
] |
MATH
|
{
"ground_truth": "25",
"style": "rule-lighteval/MATH_v2"
}
|
{
"index": "78e90029-73a6-4f3e-b4fe-261d439cbf35"
}
|
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 rectangular pool table has vertices at $(0, 0)$, $(12, 0)$, $(0, 10)$, and $(12, 10)$. There are pockets only in the four corners. A ball is hit from $(0, 0)$ along the line $y = x$ and bounces off several walls before eventually entering a pocket. Find the number of walls that the ball bounces off of before entering a pocket.\n\nPresent the answer in LaTeX format: \\boxed{Your answer}.",
"role": "user"
}
] |
MATH
|
{
"ground_truth": "9",
"style": "rule-lighteval/MATH_v2"
}
|
{
"index": "acd44f12-19fa-4bde-9d1b-904b598438ae"
}
|
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": "设正四面体 $A B C D$ 的棱长为 2. 则与此正四面体的四个顶点距离相等的所有平面截这个四面体的外接球所得截面面积的总和为一个分数形式$\\frac{m\\pi}{n}$，请给出m + n的值。\n\nPresent the answer in LaTeX format: \\boxed{Your answer}.",
"role": "user"
}
] |
MATH
|
{
"ground_truth": "65",
"style": "rule-lighteval/MATH_v2"
}
|
{
"index": "24c5a58f-b896-4619-b68b-9ffc876f47c8"
}
|
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 $(a_n)$ and $(b_n)$ be the sequences of real numbers such that\n\\[ (2 + i)^n = a_n + b_ni \\] for all integers $n\\geq 0$, where $i = \\sqrt{-1}$. Find the value of \\[\\sum_{n=0}^\\infty\\frac{a_nb_n}{7^n}\\,.\\] The original answer is in the form \\(\\frac{k}{m}\\). Please give the value of \\(k + m\\).\n\nPresent the answer in LaTeX format: \\boxed{Your answer}.",
"role": "user"
}
] |
MATH
|
{
"ground_truth": "23",
"style": "rule-lighteval/MATH_v2"
}
|
{
"index": "4fe04a70-39e5-42cd-b629-d99a52b6426f"
}
|
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 each step, we change the positions of exactly two numbers from the sequence $1, 2, 3, 4, 5, 6, 7$. How many different arrangements can be formed after two steps?\n\nPresent the answer in LaTeX format: \\boxed{Your answer}.",
"role": "user"
}
] |
MATH
|
{
"ground_truth": "176",
"style": "rule-lighteval/MATH_v2"
}
|
{
"index": "fa2a4ea4-d1cd-4344-9a91-6c2ac953f965"
}
|
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 nonnegative integer $n$ and a strictly increasing sequence of real numbers $t_0,t_1,\\ldots,t_n$, let $f(t)$ be the corresponding real-valued function defined for $t\\geq t_0$ by the\nfollowing properties:\n(a) $f(t)$ is continuous for $t\\geq t_0$,and is twice differentiable for all $t>t_0$ other than $t_1,\\ldots,t_n;$\n(b)$f( t_0) = 1/ 2;$\n(c) $\\lim _{r\\to t_{k}^{+ }}f^{\\prime }( t) = 0$ for $0\\leq k\\leq n;$\n(d) For $0\\leq k\\leq n-1$, we have $f^{\\prime\\prime}(t)=k+1$ when\n$t_k<t<t_{k+1}$, and $f^{\\prime\\prime}(t)=n+1$ when $t>t_n.$\n\nConsidering all choices of $n$ and $t_0,t_1,\\ldots,t_n$ such that $t_k\\geq t_{k-1}+1$ for l$\\leq k\\leq n$,what is the least possible value of $T$ for which $f(t_0+T)=2023?$\n\nPresent the answer in LaTeX format: \\boxed{Your answer}.",
"role": "user"
}
] |
MATH
|
{
"ground_truth": "29",
"style": "rule-lighteval/MATH_v2"
}
|
{
"index": "d0861ad6-caf4-48cb-8868-90e74b83e30b"
}
|
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 positive integers $n < 2549$ are there such that $x^2 + x - n$ has an integer root?\n\nPresent the answer in LaTeX format: \\boxed{Your answer}.",
"role": "user"
}
] |
MATH
|
{
"ground_truth": "49",
"style": "rule-lighteval/MATH_v2"
}
|
{
"index": "6bcd50ab-9150-4bd7-85f9-78e08aeeb9ec"
}
|
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": "对正整数 n，记 g(n) 为 n 与 2015 的最大公约数. 求满足下列条件的有序三元数组 (a,b,c) 的个数：(1) a,b,c\\in\\{1,2,\\cdots,2015\\}；(2) g(a), g(b), g(c), g(a+b), g(b+c), g(c+a), g(a+b+c) 两两不同.\n\nPresent the answer in LaTeX format: \\boxed{Your answer}.",
"role": "user"
}
] |
MATH
|
{
"ground_truth": "138240",
"style": "rule-lighteval/MATH_v2"
}
|
{
"index": "9832cb04-0f16-4a1f-b6f0-cced0f4e5204"
}
|
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 Cartesian coordinates, two areas \\(M\\) and \\(N\\) are defined as follows: \n- \\(M: y \\geq 0, y \\leq x, y \\leq 2-x\\); \n- \\(N: t \\leq x \\leq t+1\\). \nHere, \\(t\\) is a real number such that \\(t \\in [0,1]\\). \n\nDetermine the area of \\(M \\cap N\\). The original answer is in the form \\(-at^2 + bt + \\frac{c}{d}\\), where \\(\\frac{c}{d}\\) is a simplified fraction. Please give the value of \\(a + b + c + d\\).\n\nPresent the answer in LaTeX format: \\boxed{Your answer}.",
"role": "user"
}
] |
MATH
|
{
"ground_truth": "5",
"style": "rule-lighteval/MATH_v2"
}
|
{
"index": "48980bb1-64f3-4e06-87e9-7b0350b5b119"
}
|
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 circle in the first quadrant with center on the curve $y=2x^2-27$ is tangent to the $y$-axis and the line $4x=3y$. The radius of the circle is $\\frac{m}{n}$ 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": "11",
"style": "rule-lighteval/MATH_v2"
}
|
{
"index": "fe17c0e7-4790-4394-a033-b1251a9e3010"
}
|
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 square in the $xy$-plane has area $A$, and three of its vertices have $x$-coordinates $2$, $0$, and $18$ in some order. Find the sum of all possible values of $A$.\n\nPresent the answer in LaTeX format: \\boxed{Your answer}.",
"role": "user"
}
] |
MATH
|
{
"ground_truth": "1168",
"style": "rule-lighteval/MATH_v2"
}
|
{
"index": "99f9109b-ed38-4ceb-bb0a-4b9eec36447e"
}
|
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 $\\Omega$ and $\\omega$ be circles with radii $123$ and $61$, respectively, such that the center of $\\Omega$ lies on $\\omega$. A chord of $\\Omega$ is cut by $\\omega$ into three segments, whose lengths are in the ratio $1 : 2 : 3$ in that order. Given that this chord is not a diameter of $\\Omega$, compute the length of this chord.\n\nPresent the answer in LaTeX format: \\boxed{Your answer}.",
"role": "user"
}
] |
MATH
|
{
"ground_truth": "42",
"style": "rule-lighteval/MATH_v2"
}
|
{
"index": "7f512713-1a5b-4f99-a93b-285324905510"
}
|
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 July $1861, 366$ inches of rain fell in Cherrapunji, India. What was the average rainfall in inches per hour during that month? Provide your answer as a simplified fraction of the form \\(\\frac{m}{n}\\), and calculate the value of \\(m + n\\).\n\nPresent the answer in LaTeX format: \\boxed{Your answer}.",
"role": "user"
}
] |
MATH
|
{
"ground_truth": "185",
"style": "rule-lighteval/MATH_v2"
}
|
{
"index": "f95627e2-9ec8-42f5-9c4c-794a3f7eeb6a"
}
|
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 maximum possible value of $k$ for which $2013$ can be expressed as a sum of $k$ consecutive positive integers?\n\nPresent the answer in LaTeX format: \\boxed{Your answer}.",
"role": "user"
}
] |
MATH
|
{
"ground_truth": "61",
"style": "rule-lighteval/MATH_v2"
}
|
{
"index": "3a113d81-6198-4eb1-9b2d-c2b6e33e295b"
}
|
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 integers are less than 8000 and greater than 2000?\n\nPresent the answer in LaTeX format: \\boxed{Your answer}.",
"role": "user"
}
] |
MATH
|
{
"ground_truth": "5999",
"style": "rule-lighteval/MATH_v2"
}
|
{
"index": "fdc3f949-c6e4-421a-97c3-ea311ddbfa52"
}
|
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 arithmetic sequences $a_1, a_2, a_3$ of three nonzero integers such that the sum of the terms in the sequence is equal to the product of the terms in the sequence.\n\nPresent the answer in LaTeX format: \\boxed{Your answer}.",
"role": "user"
}
] |
MATH
|
{
"ground_truth": "4",
"style": "rule-lighteval/MATH_v2"
}
|
{
"index": "455bd69c-c54d-4a8f-a760-84d4df234aae"
}
|
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": "边长为 1 的正四面体在水平面上的正投影面积的最大值为__________.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": "43c55866-b9cc-4d07-b938-612f45deaec0"
}
|
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 a positive integer which is a multiple of 3 but not a multiple of 9. If adding the product of each digit of $A$ to $A$ results in a multiple of 9, find the possible minimum value of $A$.\n\nPresent the answer in LaTeX format: \\boxed{Your answer}.",
"role": "user"
}
] |
MATH
|
{
"ground_truth": "138",
"style": "rule-lighteval/MATH_v2"
}
|
{
"index": "bc3358bc-e160-4544-b49e-5cc05811a4ef"
}
|
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": "Chord $[AD]$ is perpendicular to the diameter $[BC]$ of a circle. Let $E$ and $F$ be the midpoints of the arcs $AC$ and $CD$, respectively. If $AD \\cap BE = \\{G\\}$, $AF \\cap BC = \\{H\\}$ and $m(AC) = \\alpha$, find the measure of angle $BHC$ in terms of $\\alpha$. The answer is in the form $x^\\circ$, where $x = k - \\frac{m\\alpha}{2}$. Please find the value of $k + m$.\n\nPresent the answer in LaTeX format: \\boxed{Your answer}.",
"role": "user"
}
] |
MATH
|
{
"ground_truth": "91",
"style": "rule-lighteval/MATH_v2"
}
|
{
"index": "92298c16-5151-46d5-87b3-ffa5ac4024a8"
}
|
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 $a_1, a_2, a_3, \\dots$ be a sequence of positive real numbers such that $a_k a_{k+2} = a_{k+1} + 1$ for all positive integers $k$. If $a_1$ and $a_2$ are positive integers, find the maximum possible value of $a_{2014}$.\n\nPresent the answer in LaTeX format: \\boxed{Your answer}.",
"role": "user"
}
] |
MATH
|
{
"ground_truth": "3",
"style": "rule-lighteval/MATH_v2"
}
|
{
"index": "ec8d6cc6-c8b2-4453-9d95-98d09831f2f4"
}
|
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 positive integers divide at least two of the numbers $120$, $144$, and $180$?\n\nPresent the answer in LaTeX format: \\boxed{Your answer}.",
"role": "user"
}
] |
MATH
|
{
"ground_truth": "17",
"style": "rule-lighteval/MATH_v2"
}
|
{
"index": "833b68a8-d586-4e67-97c4-f2b26b829382"
}
|
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 are integers \\( a \\), \\( b \\), and \\( c \\), each greater than 1, such that \\( \\sqrt[a]{N \\sqrt[b]{N \\sqrt[c]{N}}} = \\sqrt[36]{N^{25}} \\) for all \\( N > 1 \\). Find the value of \\( b \\).\n\nPresent the answer in LaTeX format: \\boxed{Your answer}.",
"role": "user"
}
] |
MATH
|
{
"ground_truth": "3",
"style": "rule-lighteval/MATH_v2"
}
|
{
"index": "2c79f2aa-8eb8-43bc-976a-9120bfd822da"
}
|
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 $x,$ $y,$ and $z$ be positive real numbers that satisfy \n$$2\\log_{x}(2y) = 2\\log_{2x}(4z) = \\log_{2x^4}(8yz) \\ne 0.$$\nThe value of $xy^5z$ can be expressed in the form $\\frac{1}{2^{p/q}},$ where $p$ and $q$ are relatively prime positive integers. Find $p+q.$\n\nPresent the answer in LaTeX format: \\boxed{Your answer}.",
"role": "user"
}
] |
MATH
|
{
"ground_truth": "49",
"style": "rule-lighteval/MATH_v2"
}
|
{
"index": "8a5f7b70-e9f5-499e-bae4-de54f5227422"
}
|
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 $\\alpha = \\cos^{-1} \\left( \\frac{3}{5} \\right)$ and $\\beta = \\sin^{-1} \\left( \\frac{3}{5} \\right)$. \n\n\\[\\sum_{n=0}^{\\infty}\\sum_{m=0}^{\\infty} \\frac{\\cos(\\alpha n +\\beta m)}{2^n3^m}\\]\n\ncan be written as $\\frac{A}{B}$ for relatively prime positive integers $A$ and $B$. Find $1000A +B$.\n\nPresent the answer in LaTeX format: \\boxed{Your answer}.",
"role": "user"
}
] |
MATH
|
{
"ground_truth": "15013",
"style": "rule-lighteval/MATH_v2"
}
|
{
"index": "6627fb14-480d-4341-887e-c811d6c0b3f6"
}
|
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": "Marko chose two prime numbers $a$ and $b$ with the same number of digits and wrote them down one after another, thus obtaining a number $c$. When he decreased $c$ by the product of $a$ and $b$, he got the result $154$. Determine the number $c$.\n\nPresent the answer in LaTeX format: \\boxed{Your answer}.",
"role": "user"
}
] |
MATH
|
{
"ground_truth": "1997",
"style": "rule-lighteval/MATH_v2"
}
|
{
"index": "db546b68-cadb-489a-b0d6-97f299256d93"
}
|
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 $a_0$ such that, for every positive integer $n$, there exists a sequence of positive integers $a_0, a_1, ..., a_{n-1}, a_n$ such that the first $n-1$ are all distinct, $a_0 = a_n$, and for $0 \\le i \\le n -1$, $a_i^{a_{i+1}}$ ends in the digits $\\overline{0a_i}$ when expressed without leading zeros in base $10$.\n\nPresent the answer in LaTeX format: \\boxed{Your answer}.",
"role": "user"
}
] |
MATH
|
{
"ground_truth": "7",
"style": "rule-lighteval/MATH_v2"
}
|
{
"index": "6ad9d809-c8f4-4c99-b030-289354c493f7"
}
|
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.