data_source
stringclasses 9
values | prompt
listlengths 2
2
| ability
stringclasses 2
values | reward_model
dict | extra_info
dict |
|---|---|---|---|---|
olympiads
|
[
{
"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. If applicable, include the answer in \\boxed{} for closed-form results like multiple choices or mathematical solutions.",
"role": "system"
},
{
"content": "## Task B-1.3.\n\nA ship traveling along a river has covered $24 \\mathrm{~km}$ upstream and $28 \\mathrm{~km}$ downstream. For this journey, it took half an hour less than for traveling $30 \\mathrm{~km}$ upstream and $21 \\mathrm{~km}$ downstream, or half an hour more than for traveling $15 \\mathrm{~km}$ upstream and $42 \\mathrm{~km}$ downstream, assuming that both the ship and the river move uniformly.\n\nDetermine the speed of the ship in still water and the speed of the river.",
"role": "user"
}
] |
{
"ground_truth": "v_{R}=4\\mathrm{~}/\\mathrm{},v_{B}=10\\mathrm{~}/\\mathrm{}",
"style": "rule"
}
|
{
"index": -1,
"split": "default"
}
|
|
olympiads
|
[
{
"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. If applicable, include the answer in \\boxed{} for closed-form results like multiple choices or mathematical solutions.",
"role": "system"
},
{
"content": "3. (6 points) A construction company was building a tunnel. When $\\frac{1}{3}$ of the tunnel was completed at the original speed, they started using new equipment, which increased the construction speed by $20 \\%$ and reduced the working hours to $80 \\%$ of the original. As a result, it took a total of 185 days to complete the tunnel. If they had not used the new equipment and continued at the original speed, it would have taken $\\qquad$ days to complete the tunnel.",
"role": "user"
}
] |
{
"ground_truth": "180",
"style": "rule"
}
|
{
"index": -1,
"split": "default"
}
|
|
cn_contest
|
[
{
"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. If applicable, include the answer in \\boxed{} for closed-form results like multiple choices or mathematical solutions.",
"role": "system"
},
{
"content": "4. Given the three sides of an obtuse triangle are 3, $4, x$, then the range of values for $x$ is ( ).\n(A) $1<x<7$.\n(B) $5 \\ll x<7$.\n(C) $1<x<\\sqrt{7}$.\n(D) $5<x<7$ or $1<x<\\sqrt{7}$.",
"role": "user"
}
] |
{
"ground_truth": "D",
"style": "rule"
}
|
{
"index": -1,
"split": "default"
}
|
|
olympiads
|
[
{
"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. If applicable, include the answer in \\boxed{} for closed-form results like multiple choices or mathematical solutions.",
"role": "system"
},
{
"content": "1. Solve the equation: $\\frac{8 x+13}{3}=\\frac{19-12 x}{2}-\\left(16 x-\\frac{7-4 x}{6}\\right)$.",
"role": "user"
}
] |
{
"ground_truth": "\\frac{1}{4}",
"style": "rule"
}
|
{
"index": -1,
"split": "default"
}
|
|
aops_forum
|
[
{
"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. If applicable, include the answer in \\boxed{} for closed-form results like multiple choices or mathematical solutions.",
"role": "system"
},
{
"content": "Let $a_n\\ (n\\geq 1)$ be the value for which $\\int_x^{2x} e^{-t^n}dt\\ (x\\geq 0)$ is maximal. Find $\\lim_{n\\to\\infty} \\ln a_n.$",
"role": "user"
}
] |
{
"ground_truth": "-\\ln 2",
"style": "rule"
}
|
{
"index": -1,
"split": "default"
}
|
|
cn_contest
|
[
{
"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. If applicable, include the answer in \\boxed{} for closed-form results like multiple choices or mathematical solutions.",
"role": "system"
},
{
"content": "6. As shown in Figure 2, let $P$ be a point inside the equilateral $\\triangle ABC$ with side length 12. Draw perpendiculars from $P$ to the sides $BC$, $CA$, and $AB$, with the feet of the perpendiculars being $D$, $E$, and $F$ respectively. Given that $PD: PE: PF = 1: 2: 3$. Then, the area of quadrilateral $BDPF$ is",
"role": "user"
}
] |
{
"ground_truth": "11 \\sqrt{3}",
"style": "rule"
}
|
{
"index": -1,
"split": "default"
}
|
|
inequalities
|
[
{
"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. If applicable, include the answer in \\boxed{} for closed-form results like multiple choices or mathematical solutions.",
"role": "system"
},
{
"content": "Given $0 \\leqslant x, y, z \\leqslant 1$, solve the equation:\n$$\\frac{x}{1+y+z x}+\\frac{y}{1+z+x y}+\\frac{z}{1+x+y z}=\\frac{3}{x+y+z} .$$",
"role": "user"
}
] |
{
"ground_truth": "x=y=z=1",
"style": "rule"
}
|
{
"index": -1,
"split": "default"
}
|
|
olympiads
|
[
{
"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. If applicable, include the answer in \\boxed{} for closed-form results like multiple choices or mathematical solutions.",
"role": "system"
},
{
"content": "Example 6 The rules of a \"level-up game\" stipulate: On the $n$-th level, a die must be rolled $n$ times. If the sum of the points obtained from these $n$ rolls is greater than $2^{n}$, the level is considered passed. Questions:\n(1) What is the maximum number of levels a person can pass in this game?\n(2) What is the probability that he can pass the first three levels consecutively?\n(Note: A die is a uniform cube with points numbered $1,2,3,4,5,6$ on its faces. The number of points on the face that lands up after rolling the die is the result of the roll.)",
"role": "user"
}
] |
{
"ground_truth": "\\frac{100}{243}",
"style": "rule"
}
|
{
"index": -1,
"split": "default"
}
|
|
olympiads
|
[
{
"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. If applicable, include the answer in \\boxed{} for closed-form results like multiple choices or mathematical solutions.",
"role": "system"
},
{
"content": "2. (9th Canadian Mathematical Competition) $N$ is an integer, its representation in base $b$ is 777. Find the smallest positive integer $b$ such that $N$ is a fourth power of an integer in decimal notation.",
"role": "user"
}
] |
{
"ground_truth": "18",
"style": "rule"
}
|
{
"index": -1,
"split": "default"
}
|
|
olympiads
|
[
{
"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. If applicable, include the answer in \\boxed{} for closed-form results like multiple choices or mathematical solutions.",
"role": "system"
},
{
"content": "Problem 6. (8 points) In the plane, there is a non-closed, non-self-intersecting broken line consisting of 31 segments (adjacent segments do not lie on the same straight line). For each segment, the line defined by it is constructed. It is possible for some of the 31 constructed lines to coincide. What is the minimum number of different lines that can be obtained?\n\nAnswer. 9.",
"role": "user"
}
] |
{
"ground_truth": "9",
"style": "rule"
}
|
{
"index": -1,
"split": "default"
}
|
|
olympiads
|
[
{
"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. If applicable, include the answer in \\boxed{} for closed-form results like multiple choices or mathematical solutions.",
"role": "system"
},
{
"content": "7.1. Solve the equation $\\frac{n!}{2}=k!+l!$ in natural numbers, where $n!=1 \\cdot 2 \\cdot \\ldots n$. If there are no solutions, write 0; if there is one solution, write $n$; if there are multiple solutions, write the sum of the values of $n$ for all solutions. Recall that a solution is a triplet $(n, k, l)$; if solutions differ in at least one component, they are considered different.",
"role": "user"
}
] |
{
"ground_truth": "10",
"style": "rule"
}
|
{
"index": -1,
"split": "default"
}
|
|
cn_contest
|
[
{
"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. If applicable, include the answer in \\boxed{} for closed-form results like multiple choices or mathematical solutions.",
"role": "system"
},
{
"content": "1. If the set\n$$\nA=\\{1,2, \\cdots, 10\\}, B=\\{1,2,3,4\\},\n$$\n$C$ is a subset of $A$, and $C \\cap B \\neq \\varnothing$, then the number of such subsets $C$ is $(\\quad)$.\n(A) 256\n(B) 959\n(C) 960\n(D) 961",
"role": "user"
}
] |
{
"ground_truth": "C",
"style": "rule"
}
|
{
"index": -1,
"split": "default"
}
|
|
olympiads
|
[
{
"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. If applicable, include the answer in \\boxed{} for closed-form results like multiple choices or mathematical solutions.",
"role": "system"
},
{
"content": "12.180. A side of the triangle is equal to 15, the sum of the other two sides is 27. Find the cosine of the angle opposite the given side, if the radius of the inscribed circle in the triangle is 4.",
"role": "user"
}
] |
{
"ground_truth": "\\frac{5}{13}",
"style": "rule"
}
|
{
"index": -1,
"split": "default"
}
|
|
aops_forum
|
[
{
"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. If applicable, include the answer in \\boxed{} for closed-form results like multiple choices or mathematical solutions.",
"role": "system"
},
{
"content": "On a board, the numbers from 1 to 2009 are written. A couple of them are erased and instead of them, on the board is written the remainder of the sum of the erased numbers divided by 13. After a couple of repetition of this erasing, only 3 numbers are left, of which two are 9 and 999. Find the third number.",
"role": "user"
}
] |
{
"ground_truth": "8",
"style": "rule"
}
|
{
"index": -1,
"split": "default"
}
|
|
cn_contest
|
[
{
"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. If applicable, include the answer in \\boxed{} for closed-form results like multiple choices or mathematical solutions.",
"role": "system"
},
{
"content": "4. The number of real solutions to the equation $\\left|x^{2}-3 x+2\\right|+\\left|x^{2}+2 x-3\\right|=11$ is ( ).\n(A) 0\n(B) 1\n(C) 2\n(D) 4",
"role": "user"
}
] |
{
"ground_truth": "C",
"style": "rule"
}
|
{
"index": -1,
"split": "default"
}
|
|
olympiads
|
[
{
"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. If applicable, include the answer in \\boxed{} for closed-form results like multiple choices or mathematical solutions.",
"role": "system"
},
{
"content": "## Problem Statement\n\nCalculate the limit of the numerical sequence:\n\n$\\lim _{n \\rightarrow \\infty} \\frac{(n+1)^{4}-(n-1)^{4}}{(n+1)^{3}+(n-1)^{3}}$",
"role": "user"
}
] |
{
"ground_truth": "4",
"style": "rule"
}
|
{
"index": -1,
"split": "default"
}
|
|
olympiads
|
[
{
"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. If applicable, include the answer in \\boxed{} for closed-form results like multiple choices or mathematical solutions.",
"role": "system"
},
{
"content": "Condition of the problem\n\nFind the derivative.\n\n$$\ny=\\frac{1}{24}\\left(x^{2}+8\\right) \\sqrt{x^{2}-4}+\\frac{x^{2}}{16} \\arcsin \\frac{2}{x}, x>0\n$$",
"role": "user"
}
] |
{
"ground_truth": "\\frac{x^{3}-x}{8\\sqrt{x^{2}-4}}+\\frac{x}{8}\\cdot\\arcsin\\frac{2}{x}",
"style": "rule"
}
|
{
"index": -1,
"split": "default"
}
|
|
cn_contest
|
[
{
"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. If applicable, include the answer in \\boxed{} for closed-form results like multiple choices or mathematical solutions.",
"role": "system"
},
{
"content": "6. Let $[x]$ denote the greatest integer not exceeding the real number $x$,\n$$\n\\begin{array}{c}\nS=\\left[\\frac{1}{1}\\right]+\\left[\\frac{2}{1}\\right]+\\left[\\frac{1}{2}\\right]+\\left[\\frac{2}{2}\\right]+\\left[\\frac{3}{2}\\right]+ \\\\\n{\\left[\\frac{4}{2}\\right]+\\left[\\frac{1}{3}\\right]+\\left[\\frac{2}{3}\\right]+\\left[\\frac{3}{3}\\right]+\\left[\\frac{4}{3}\\right]+} \\\\\n{\\left[\\frac{5}{3}\\right]+\\left[\\frac{6}{3}\\right]+\\cdots}\n\\end{array}\n$$\n\nup to 2016 terms, where, for a segment with denominator $k$, there are $2 k$ terms $\\left[\\frac{1}{k}\\right],\\left[\\frac{2}{k}\\right], \\cdots,\\left[\\frac{2 k}{k}\\right]$, and only the last segment may have fewer than $2 k$ terms. Then the value of $S$ is",
"role": "user"
}
] |
{
"ground_truth": "1078",
"style": "rule"
}
|
{
"index": -1,
"split": "default"
}
|
|
cn_contest
|
[
{
"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. If applicable, include the answer in \\boxed{} for closed-form results like multiple choices or mathematical solutions.",
"role": "system"
},
{
"content": "19. Given $m \\in\\{11,13,15,17,19\\}$, $n \\in\\{1999,2000, \\cdots, 2018\\}$.\nThen the probability that the unit digit of $m^{n}$ is 1 is ( ).\n(A) $\\frac{1}{5}$\n(B) $\\frac{1}{4}$\n(C) $\\frac{3}{10}$\n(D) $\\frac{7}{20}$\n(E) $\\frac{2}{5}$",
"role": "user"
}
] |
{
"ground_truth": "E",
"style": "rule"
}
|
{
"index": -1,
"split": "default"
}
|
|
olympiads
|
[
{
"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. If applicable, include the answer in \\boxed{} for closed-form results like multiple choices or mathematical solutions.",
"role": "system"
},
{
"content": "1. (6 points) Today is January 31, 2015, welcome to the 2015 \"Spring Cup\" Final. The calculation result of the expression $\\frac{\\frac{2015}{1}+\\frac{2015}{0.31}}{1+0.31}$ is",
"role": "user"
}
] |
{
"ground_truth": "6500",
"style": "rule"
}
|
{
"index": -1,
"split": "default"
}
|
|
aops_forum
|
[
{
"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. If applicable, include the answer in \\boxed{} for closed-form results like multiple choices or mathematical solutions.",
"role": "system"
},
{
"content": "Consider a regular hexagon with an incircle. What is the ratio of the area inside the incircle to the area of the hexagon?\n",
"role": "user"
}
] |
{
"ground_truth": "\\frac{\\pi \\sqrt{3}}{6}",
"style": "rule"
}
|
{
"index": -1,
"split": "default"
}
|
|
aops_forum
|
[
{
"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. If applicable, include the answer in \\boxed{} for closed-form results like multiple choices or mathematical solutions.",
"role": "system"
},
{
"content": "Let $ABC$ be a triangle with centroid $G$. Determine, with proof, the position of the point $P$ in the plane of $ABC$ such that $AP{\\cdot}AG + BP{\\cdot}BG + CP{\\cdot}CG$ is a minimum, and express this minimum value in terms of the side lengths of $ABC$.",
"role": "user"
}
] |
{
"ground_truth": "\\frac{a^2 + b^2 + c^2}{3}",
"style": "rule"
}
|
{
"index": -1,
"split": "default"
}
|
|
cn_contest
|
[
{
"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. If applicable, include the answer in \\boxed{} for closed-form results like multiple choices or mathematical solutions.",
"role": "system"
},
{
"content": "1. Four points $A, B, C, D$ in space are pairwise 1 unit apart, and points $P, Q$ move on line segments $AB, CD$ respectively. The minimum distance between point $P$ and $Q$ is",
"role": "user"
}
] |
{
"ground_truth": "\\frac{\\sqrt{2}}{2}",
"style": "rule"
}
|
{
"index": -1,
"split": "default"
}
|
|
olympiads
|
[
{
"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. If applicable, include the answer in \\boxed{} for closed-form results like multiple choices or mathematical solutions.",
"role": "system"
},
{
"content": "The function $f$ maps the set of positive integers into itself, and satisfies the equation\n\n$$\nf(f(n))+f(n)=2 n+6\n$$\n\nWhat could this function be?",
"role": "user"
}
] |
{
"ground_truth": "f(n)=n+2",
"style": "rule"
}
|
{
"index": -1,
"split": "default"
}
|
|
olympiads
|
[
{
"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. If applicable, include the answer in \\boxed{} for closed-form results like multiple choices or mathematical solutions.",
"role": "system"
},
{
"content": "30. Find the remainder when the 2018-digit number $\\underbrace{\\overline{55 \\cdots}}_{2018 \\text { 555 }}$ is divided by 13.",
"role": "user"
}
] |
{
"ground_truth": "3",
"style": "rule"
}
|
{
"index": -1,
"split": "default"
}
|
|
olympiads
|
[
{
"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. If applicable, include the answer in \\boxed{} for closed-form results like multiple choices or mathematical solutions.",
"role": "system"
},
{
"content": "1. A line $l$ intersects a hyperbola $c$, then the maximum number of intersection points is ( ).\nA. 1\nB. 2\nC. 3\nD. 4",
"role": "user"
}
] |
{
"ground_truth": "B",
"style": "rule"
}
|
{
"index": -1,
"split": "default"
}
|
|
olympiads
|
[
{
"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. If applicable, include the answer in \\boxed{} for closed-form results like multiple choices or mathematical solutions.",
"role": "system"
},
{
"content": "1. Let the universal set be the set of real numbers. If $A=\\{x \\mid \\sqrt{x-2} \\leqslant 0\\}, B=\\left\\{x \\mid 10^{x^{2}-2}=10^{x}\\right\\}$, then $A \\cap \\bar{B}$ is\nA. $\\{2\\}$\nB. $\\{-1\\}$\nC. $\\{x \\mid x \\leqslant 2\\}$\nD. $\\varnothing$",
"role": "user"
}
] |
{
"ground_truth": "D",
"style": "rule"
}
|
{
"index": -1,
"split": "default"
}
|
|
cn_contest
|
[
{
"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. If applicable, include the answer in \\boxed{} for closed-form results like multiple choices or mathematical solutions.",
"role": "system"
},
{
"content": "4. As shown in Figure 1, in the right triangular prism $A B C-A_{1} B_{1} C_{1}$, $A A_{1}=A B=A C$, and $M$ and $Q$ are the midpoints of $C C_{1}$ and $B C$ respectively. If for any point $P$ on the line segment $A_{1} B_{1}$, $P Q \\perp A M$, then $\\angle B A C$ equals ( ).\n(A) $30^{\\circ}$\n(B) $45^{\\circ}$\n(C) $60^{\\circ}$\n(D) $90^{\\circ}$",
"role": "user"
}
] |
{
"ground_truth": "D",
"style": "rule"
}
|
{
"index": -1,
"split": "default"
}
|
|
olympiads
|
[
{
"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. If applicable, include the answer in \\boxed{} for closed-form results like multiple choices or mathematical solutions.",
"role": "system"
},
{
"content": "7.242. $\\left(16 \\cdot 5^{2 x-1}-2 \\cdot 5^{x-1}-0.048\\right) \\lg \\left(x^{3}+2 x+1\\right)=0$.",
"role": "user"
}
] |
{
"ground_truth": "0",
"style": "rule"
}
|
{
"index": -1,
"split": "default"
}
|
|
olympiads
|
[
{
"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. If applicable, include the answer in \\boxed{} for closed-form results like multiple choices or mathematical solutions.",
"role": "system"
},
{
"content": "11.005. The plane angle at the vertex of a regular triangular pyramid is $90^{\\circ}$. Find the ratio of the lateral surface area of the pyramid to the area of its base.",
"role": "user"
}
] |
{
"ground_truth": "\\sqrt{3}",
"style": "rule"
}
|
{
"index": -1,
"split": "default"
}
|
|
olympiads
|
[
{
"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. If applicable, include the answer in \\boxed{} for closed-form results like multiple choices or mathematical solutions.",
"role": "system"
},
{
"content": "A father wants to divide his property among his children: first, he gives 1000 yuan and one-tenth of the remaining property to the eldest child, then 2000 yuan and one-tenth of the remaining property to the second child, then 3000 yuan and one-tenth of the remaining property to the third child, and so on. It turns out that each child receives the same amount of property. The father has $\\qquad$ children.",
"role": "user"
}
] |
{
"ground_truth": "9",
"style": "rule"
}
|
{
"index": -1,
"split": "default"
}
|
|
cn_contest
|
[
{
"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. If applicable, include the answer in \\boxed{} for closed-form results like multiple choices or mathematical solutions.",
"role": "system"
},
{
"content": "Example 11 Let $x>0, y>0, \\sqrt{x}(\\sqrt{x}+2 \\sqrt{y})$ $=\\sqrt{y}(6 \\sqrt{x}+5 \\sqrt{y})$. Find the value of $\\frac{x+\\sqrt{x y}-y}{2 x+\\sqrt{x y}+3 y}$.",
"role": "user"
}
] |
{
"ground_truth": "\\frac{1}{2}",
"style": "rule"
}
|
{
"index": -1,
"split": "default"
}
|
|
aops_forum
|
[
{
"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. If applicable, include the answer in \\boxed{} for closed-form results like multiple choices or mathematical solutions.",
"role": "system"
},
{
"content": "The equation of line $\\ell_1$ is $24x-7y = 319$ and the equation of line $\\ell_2$ is $12x-5y = 125$. Let $a$ be the number of positive integer values $n$ less than $2023$ such that for both $\\ell_1$ and $\\ell_2$ there exists a lattice point on that line that is a distance of $n$ from the point $(20,23)$. Determine $a$.\n\n[i]Proposed by Christopher Cheng[/i]\n\n[hide=Solution][i]Solution. [/i] $\\boxed{6}$\nNote that $(20,23)$ is the intersection of the lines $\\ell_1$ and $\\ell_2$. Thus, we only care about lattice points on the the two lines that are an integer distance away from $(20,23)$. Notice that $7$ and $24$ are part of the Pythagorean triple $(7,24,25)$ and $5$ and $12$ are part of the Pythagorean triple $(5,12,13)$. Thus, points on $\\ell_1$ only satisfy the conditions when $n$ is divisible by $25$ and points on $\\ell_2$ only satisfy the conditions when $n$ is divisible by $13$. Therefore, $a$ is just the number of positive integers less than $2023$ that are divisible by both $25$ and $13$. The LCM of $25$ and $13$ is $325$, so the answer is $\\boxed{6}$.[/hide]",
"role": "user"
}
] |
{
"ground_truth": "6",
"style": "rule"
}
|
{
"index": -1,
"split": "default"
}
|
|
olympiads
|
[
{
"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. If applicable, include the answer in \\boxed{} for closed-form results like multiple choices or mathematical solutions.",
"role": "system"
},
{
"content": "Example 1 The range of the function $y=-x^{2}-2 x+3(-5 \\leqslant x \\leqslant 0)$ is $(\\quad)$.\n(A) $(-\\infty, 4]$\n(B) $[3,12]$\n(C) $[-12,4]$\n(D) $[4,12]$",
"role": "user"
}
] |
{
"ground_truth": "C",
"style": "rule"
}
|
{
"index": -1,
"split": "default"
}
|
|
inequalities
|
[
{
"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. If applicable, include the answer in \\boxed{} for closed-form results like multiple choices or mathematical solutions.",
"role": "system"
},
{
"content": "4.206 There are two forces $f_{1}$ and $f_{2}$ acting on the origin $O$ of the coordinate axis,\n$$\\begin{array}{l}\n\\vec{f}_{1}=\\overrightarrow{O A}=\\sqrt{2}\\left(\\cos 45^{\\circ}+i \\sin 45^{\\circ}\\right) \\\\\n\\vec{f}_{2}=\\overrightarrow{O B}=2\\left[\\cos \\left(-30^{\\circ}\\right)+i \\sin \\left(-30^{\\circ}\\right)\\right]\n\\end{array}$$\n(1) Find the magnitude and direction of their resultant force;\n(2) Find the distance between points $A$ and $B$ (accurate to 0.1).",
"role": "user"
}
] |
{
"ground_truth": "2.1",
"style": "rule"
}
|
{
"index": -1,
"split": "default"
}
|
|
cn_contest
|
[
{
"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. If applicable, include the answer in \\boxed{} for closed-form results like multiple choices or mathematical solutions.",
"role": "system"
},
{
"content": "2. As shown in Figure 1, the side length of rhombus $A B C D$ is $a$, and $O$ is a point on the diagonal $A C$, with $O A=a, O B=$ $O C=O D=1$. Then $a$ equals ( ).\n(A) $\\frac{\\sqrt{5}+1}{2}$\n(B) $\\frac{\\sqrt{5}-1}{2}$\n(C) 1\n(D) 2",
"role": "user"
}
] |
{
"ground_truth": "A",
"style": "rule"
}
|
{
"index": -1,
"split": "default"
}
|
|
olympiads
|
[
{
"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. If applicable, include the answer in \\boxed{} for closed-form results like multiple choices or mathematical solutions.",
"role": "system"
},
{
"content": "1. Given $a, b>0, a \\neq 1$, and $a^{b}=\\log _{a} b$, then the value of $a^{a^{b}}-\\log _{a} \\log _{a} b^{a}$ is",
"role": "user"
}
] |
{
"ground_truth": "-1",
"style": "rule"
}
|
{
"index": -1,
"split": "default"
}
|
|
cn_contest
|
[
{
"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. If applicable, include the answer in \\boxed{} for closed-form results like multiple choices or mathematical solutions.",
"role": "system"
},
{
"content": "4. Let the sequence $\\left\\{a_{n}\\right\\}$ satisfy $a_{1}=0, a_{2}=1$, and for all $n \\geqslant 3, a_{n}$ is the smallest positive integer greater than $a_{n-1}$ such that there is no subsequence of $a_{1}, a_{2}, \\cdots, a_{n}$ that forms an arithmetic sequence. Find $a_{2014}$.",
"role": "user"
}
] |
{
"ground_truth": "88327",
"style": "rule"
}
|
{
"index": -1,
"split": "default"
}
|
|
olympiads
|
[
{
"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. If applicable, include the answer in \\boxed{} for closed-form results like multiple choices or mathematical solutions.",
"role": "system"
},
{
"content": "In a stairwell, there are 10 mailboxes. One distributor drops a flyer into 5 mailboxes. Later, another distributor also drops a flyer into 5 mailboxes. What is the probability that this way, at least 8 mailboxes will contain a flyer?",
"role": "user"
}
] |
{
"ground_truth": "\\frac{1}{2}",
"style": "rule"
}
|
{
"index": -1,
"split": "default"
}
|
|
olympiads
|
[
{
"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. If applicable, include the answer in \\boxed{} for closed-form results like multiple choices or mathematical solutions.",
"role": "system"
},
{
"content": "18. (3 points) Li Shuang rides a bike at a speed of 320 meters per minute from location $A$ to location $B$. On the way, due to a bicycle malfunction, he pushes the bike and walks for 5 minutes to a place 1800 meters from $B$ to repair the bike. After 15 minutes, he continues towards $B$ at 1.5 times his original riding speed, and arrives at $B$ 17 minutes later than the expected time. What is Li Shuang's walking speed in meters per minute?",
"role": "user"
}
] |
{
"ground_truth": "72",
"style": "rule"
}
|
{
"index": -1,
"split": "default"
}
|
|
olympiads
|
[
{
"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. If applicable, include the answer in \\boxed{} for closed-form results like multiple choices or mathematical solutions.",
"role": "system"
},
{
"content": "53. How many four-digit numbers contain at least one even digit?",
"role": "user"
}
] |
{
"ground_truth": "8375",
"style": "rule"
}
|
{
"index": -1,
"split": "default"
}
|
|
olympiads
|
[
{
"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. If applicable, include the answer in \\boxed{} for closed-form results like multiple choices or mathematical solutions.",
"role": "system"
},
{
"content": "10.319. The diagonals of an isosceles trapezoid are perpendicular to each other, and its area is $a^{2}$. Determine the height of the trapezoid.",
"role": "user"
}
] |
{
"ground_truth": "a",
"style": "rule"
}
|
{
"index": -1,
"split": "default"
}
|
|
olympiads
|
[
{
"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. If applicable, include the answer in \\boxed{} for closed-form results like multiple choices or mathematical solutions.",
"role": "system"
},
{
"content": "9.27 In the metro train at the initial stop, 100 passengers entered. How many ways are there to distribute the exit of all these passengers at the next 16 stops of the train?",
"role": "user"
}
] |
{
"ground_truth": "16^{100}",
"style": "rule"
}
|
{
"index": -1,
"split": "default"
}
|
|
cn_contest
|
[
{
"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. If applicable, include the answer in \\boxed{} for closed-form results like multiple choices or mathematical solutions.",
"role": "system"
},
{
"content": "2. In the complex plane, there are 7 points corresponding to the 7 roots of the equation $x^{7}=$ $-1+\\sqrt{3} i$. Among the four quadrants where these 7 points are located, only 1 point is in ( ).\n(A) the I quadrant\n(B) the II quadrant\n(C) the III quadrant\n(D) the IV quadrant",
"role": "user"
}
] |
{
"ground_truth": "C",
"style": "rule"
}
|
{
"index": -1,
"split": "default"
}
|
|
olympiads
|
[
{
"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. If applicable, include the answer in \\boxed{} for closed-form results like multiple choices or mathematical solutions.",
"role": "system"
},
{
"content": "Father played chess with uncle. For a won game, the winner received 8 crowns from the opponent, and for a draw, nobody got anything. Uncle won four times, there were five draws, and in the end, father earned 24 crowns.\n\nHow many games did father play with uncle?\n\n(M. Volfová)",
"role": "user"
}
] |
{
"ground_truth": "16",
"style": "rule"
}
|
{
"index": -1,
"split": "default"
}
|
|
olympiads
|
[
{
"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. If applicable, include the answer in \\boxed{} for closed-form results like multiple choices or mathematical solutions.",
"role": "system"
},
{
"content": "## Problem 4\n\nGiven the numbers $1,2,3, \\ldots, 1000$. Find the largest number $m$ with the property that by removing any $m$ numbers from these 1000 numbers, among the $1000-m$ remaining numbers, there exist two such that one divides the other.\n\nSelected problems by Prof. Cicortas Marius\n\nNote: a) The actual working time is 3 hours.\n\nb) All problems are mandatory.\n\nc) Each problem is graded from 0 to 7.\n\n## NATIONAL MATHEMATICS OLYMPIAD\n\nLocal stage - 15.02.2014\n\n## Grade IX\n\n## Grading Rubric",
"role": "user"
}
] |
{
"ground_truth": "499",
"style": "rule"
}
|
{
"index": -1,
"split": "default"
}
|
|
aops_forum
|
[
{
"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. If applicable, include the answer in \\boxed{} for closed-form results like multiple choices or mathematical solutions.",
"role": "system"
},
{
"content": "The function $f: \\mathbb{R}\\rightarrow \\mathbb{R}$ is such that $f(x+1)=2f(x)$ for $\\forall$ $x\\in \\mathbb{R}$ and $f(x)=x(x-1)$ for $\\forall$ $x\\in (0,1]$. Find the greatest real number $m$, for which the inequality $f(x)\\geq -\\frac{8}{9}$ is true for \n$\\forall$ $x\\in (-\\infty , m]$.\n",
"role": "user"
}
] |
{
"ground_truth": "\\frac{7}{3}",
"style": "rule"
}
|
{
"index": -1,
"split": "default"
}
|
|
olympiads
|
[
{
"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. If applicable, include the answer in \\boxed{} for closed-form results like multiple choices or mathematical solutions.",
"role": "system"
},
{
"content": "4. Let $A$ and $B$ be $n$-digit numbers, where $n$ is odd, which give the same remainder $r \\neq 0$ when divided by $k$. Find at least one number $k$, which does not depend on $n$, such that the number $C$, obtained by appending the digits of $A$ and $B$, is divisible by $k$.",
"role": "user"
}
] |
{
"ground_truth": "11",
"style": "rule"
}
|
{
"index": -1,
"split": "default"
}
|
|
olympiads
|
[
{
"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. If applicable, include the answer in \\boxed{} for closed-form results like multiple choices or mathematical solutions.",
"role": "system"
},
{
"content": "5. Given positive real numbers $a$ and $b$ satisfy $a+b=1$, then $M=$ $\\sqrt{1+a^{2}}+\\sqrt{1+2 b}$ the integer part is",
"role": "user"
}
] |
{
"ground_truth": "2",
"style": "rule"
}
|
{
"index": -1,
"split": "default"
}
|
|
olympiads
|
[
{
"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. If applicable, include the answer in \\boxed{} for closed-form results like multiple choices or mathematical solutions.",
"role": "system"
},
{
"content": "8. If $n$ is a natural number less than 50, find all values of $n$ such that the values of the algebraic expressions $4n+5$ and $7n+6$ have a common divisor greater than 1.",
"role": "user"
}
] |
{
"ground_truth": "7,18,29,40",
"style": "rule"
}
|
{
"index": -1,
"split": "default"
}
|
|
cn_contest
|
[
{
"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. If applicable, include the answer in \\boxed{} for closed-form results like multiple choices or mathematical solutions.",
"role": "system"
},
{
"content": "6. Let set $A=\\{1,2,3,4,5,6\\}$, and a one-to-one mapping $f: A \\rightarrow A$ satisfies that for any $x \\in A$, $f(f(f(x)))$ $=x$. Then the number of mappings $f$ that satisfy the above condition is ( ).\n(A) 40\n(B) 41\n(C) 80\n(D) 81",
"role": "user"
}
] |
{
"ground_truth": "D",
"style": "rule"
}
|
{
"index": -1,
"split": "default"
}
|
|
olympiads
|
[
{
"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. If applicable, include the answer in \\boxed{} for closed-form results like multiple choices or mathematical solutions.",
"role": "system"
},
{
"content": "5. 5.1. Find the largest natural number in which all digits are different and any two adjacent digits differ by 6 or 7.",
"role": "user"
}
] |
{
"ground_truth": "60718293",
"style": "rule"
}
|
{
"index": -1,
"split": "default"
}
|
|
olympiads
|
[
{
"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. If applicable, include the answer in \\boxed{} for closed-form results like multiple choices or mathematical solutions.",
"role": "system"
},
{
"content": "Example 5. Expand the function\n\n$$\nf(z)=\\frac{z}{z^{2}-2 z-3}\n$$\n\ninto a Taylor series in the neighborhood of the point $z_{0}=0$ using expansion (12), and find the radius of convergence of the series.",
"role": "user"
}
] |
{
"ground_truth": "1",
"style": "rule"
}
|
{
"index": -1,
"split": "default"
}
|
|
cn_contest
|
[
{
"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. If applicable, include the answer in \\boxed{} for closed-form results like multiple choices or mathematical solutions.",
"role": "system"
},
{
"content": "2. Given $0<x<1$. Simplify\n$$\n=\\quad \\sqrt{\\left(x-\\frac{1}{x}\\right)^{2}+4}-\\sqrt{\\left(x+\\frac{1}{x}\\right)^{2}-4}\n$$",
"role": "user"
}
] |
{
"ground_truth": "2x",
"style": "rule"
}
|
{
"index": -1,
"split": "default"
}
|
|
aops_forum
|
[
{
"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. If applicable, include the answer in \\boxed{} for closed-form results like multiple choices or mathematical solutions.",
"role": "system"
},
{
"content": "Let $a_1,a_2,a_3,a_4,a_5$ be distinct real numbers. Consider all sums of the form $a_i + a_j$ where $i,j \\in \\{1,2,3,4,5\\}$ and $i \\neq j$. Let $m$ be the number of distinct numbers among these sums. What is the smallest possible value of $m$?",
"role": "user"
}
] |
{
"ground_truth": "7",
"style": "rule"
}
|
{
"index": -1,
"split": "default"
}
|
|
cn_contest
|
[
{
"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. If applicable, include the answer in \\boxed{} for closed-form results like multiple choices or mathematical solutions.",
"role": "system"
},
{
"content": "3. There are ten small balls of the same size, five of which are red and five are white. Now, these ten balls are arranged in a row arbitrarily, and numbered from left to right as $1,2, \\cdots, 10$. Then the number of arrangements where the sum of the numbers of the red balls is greater than the sum of the numbers of the white balls is. $\\qquad$",
"role": "user"
}
] |
{
"ground_truth": "126",
"style": "rule"
}
|
{
"index": -1,
"split": "default"
}
|
|
olympiads
|
[
{
"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. If applicable, include the answer in \\boxed{} for closed-form results like multiple choices or mathematical solutions.",
"role": "system"
},
{
"content": "149. Two equally matched opponents are playing chess. Find the most probable number of wins for any chess player if $2 N$ decisive (without draws) games will be played.",
"role": "user"
}
] |
{
"ground_truth": "N",
"style": "rule"
}
|
{
"index": -1,
"split": "default"
}
|
|
olympiads
|
[
{
"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. If applicable, include the answer in \\boxed{} for closed-form results like multiple choices or mathematical solutions.",
"role": "system"
},
{
"content": "|\n\nThere are 85 balloons in the room - red and blue. It is known that: 1) at least one of the balloons is red; 2) in every arbitrarily chosen pair of balloons, at least one is blue. How many red balloons are in the room?\n\n#",
"role": "user"
}
] |
{
"ground_truth": "1",
"style": "rule"
}
|
{
"index": -1,
"split": "default"
}
|
|
olympiads
|
[
{
"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. If applicable, include the answer in \\boxed{} for closed-form results like multiple choices or mathematical solutions.",
"role": "system"
},
{
"content": "3. Given positive numbers $a, b, c$ satisfying $a+b+c=1$,\nthen $\\sqrt{\\frac{(a+b c)(b+c a)}{c+a b}}+\\sqrt{\\frac{(b+c a)(c+a b)}{a+b c}}+\\sqrt{\\frac{(c+a b)(a+b c)}{b+c a}}=$ $\\qquad$",
"role": "user"
}
] |
{
"ground_truth": "2",
"style": "rule"
}
|
{
"index": -1,
"split": "default"
}
|
|
cn_contest
|
[
{
"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. If applicable, include the answer in \\boxed{} for closed-form results like multiple choices or mathematical solutions.",
"role": "system"
},
{
"content": "7. A circle with a radius of 1 has six points, these six points divide the circle into six equal parts. Take three of these points as vertices to form a triangle. If the triangle is neither equilateral nor isosceles, then the area of this triangle is ( ).\n(A) $\\frac{\\sqrt{3}}{3}$\n(B) $\\frac{\\sqrt{3}}{2}$\n(C) 1\n(D) $\\sqrt{2}$\n(E) 2",
"role": "user"
}
] |
{
"ground_truth": "B",
"style": "rule"
}
|
{
"index": -1,
"split": "default"
}
|
|
olympiads
|
[
{
"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. If applicable, include the answer in \\boxed{} for closed-form results like multiple choices or mathematical solutions.",
"role": "system"
},
{
"content": "# Problem 3.\n\nA polynomial $P(x)$ with integer coefficients has the properties\n\n$$\nP(1)=2019, \\quad P(2019)=1, \\quad P(k)=k,\n$$\n\nwhere the number $k$ is an integer. Find this number $k$.\n\n#",
"role": "user"
}
] |
{
"ground_truth": "1010",
"style": "rule"
}
|
{
"index": -1,
"split": "default"
}
|
|
olympiads
|
[
{
"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. If applicable, include the answer in \\boxed{} for closed-form results like multiple choices or mathematical solutions.",
"role": "system"
},
{
"content": "$7 \\cdot 74$ There are several locks, and now six people each hold a part of the keys. It is known that any two people trying to open the locks together will have exactly one lock that they cannot open, while any three people can open all the locks. How many locks are there at least?\n\n---\n\nNote: The translation keeps the original format and structure of the text, including the mathematical notation and the problem statement, to ensure the context and meaning are accurately conveyed.",
"role": "user"
}
] |
{
"ground_truth": "15",
"style": "rule"
}
|
{
"index": -1,
"split": "default"
}
|
|
olympiads
|
[
{
"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. If applicable, include the answer in \\boxed{} for closed-form results like multiple choices or mathematical solutions.",
"role": "system"
},
{
"content": "5. Let the complex numbers $z_{1}, z_{2}$ satisfy $\\left|z_{1}\\right|=\\left|z_{1}+z_{2}\\right|=3,\\left|z_{1}-z_{2}\\right|=3 \\sqrt{3}$, then $\\log _{3}\\left|\\left(z_{1} \\overline{z_{2}}\\right)^{2000}+\\left(\\overline{z_{1}} z_{2}\\right)^{2000}\\right|=$ $\\qquad$ .",
"role": "user"
}
] |
{
"ground_truth": "4000",
"style": "rule"
}
|
{
"index": -1,
"split": "default"
}
|
|
cn_contest
|
[
{
"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. If applicable, include the answer in \\boxed{} for closed-form results like multiple choices or mathematical solutions.",
"role": "system"
},
{
"content": "1. A three-digit number is 29 times the sum of its digits. Then this three-digit number is $\\qquad$",
"role": "user"
}
] |
{
"ground_truth": "261",
"style": "rule"
}
|
{
"index": -1,
"split": "default"
}
|
|
olympiads
|
[
{
"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. If applicable, include the answer in \\boxed{} for closed-form results like multiple choices or mathematical solutions.",
"role": "system"
},
{
"content": "22. A year is called a leap year if it is either divisible by 4 but not divisible by 100 , or divisible by 400 . Hence, the years 2000, 2004 and 2400 are leap years while the years 2006, 2100 and 2200 are not. Find the number of leap years between 2000 and 4000 inclusive.",
"role": "user"
}
] |
{
"ground_truth": "486",
"style": "rule"
}
|
{
"index": -1,
"split": "default"
}
|
|
number_theory
|
[
{
"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. If applicable, include the answer in \\boxed{} for closed-form results like multiple choices or mathematical solutions.",
"role": "system"
},
{
"content": "Example 7 How many positive integer factors does 20! have?",
"role": "user"
}
] |
{
"ground_truth": "41040",
"style": "rule"
}
|
{
"index": -1,
"split": "default"
}
|
|
aops_forum
|
[
{
"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. If applicable, include the answer in \\boxed{} for closed-form results like multiple choices or mathematical solutions.",
"role": "system"
},
{
"content": "The area of the region in the $xy$-plane satisfying the inequality \\[\\min_{1 \\le n \\le 10} \\max\\left(\\frac{x^2+y^2}{4n^2}, \\, 2 - \\frac{x^2+y^2}{4n^2-4n+1}\\right) \\le 1\\] is $k\\pi$, for some integer $k$. Find $k$.\n\n[i]Proposed by Michael Tang[/i]",
"role": "user"
}
] |
{
"ground_truth": "210",
"style": "rule"
}
|
{
"index": -1,
"split": "default"
}
|
|
olympiads
|
[
{
"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. If applicable, include the answer in \\boxed{} for closed-form results like multiple choices or mathematical solutions.",
"role": "system"
},
{
"content": "2. On a line, several points were marked, including points $A$ and $B$. All possible segments with endpoints at the marked points are considered. Vasya calculated that point $A$ is inside 50 of these segments, and point $B$ is inside 56 segments. How many points were marked? (The endpoints of a segment are not considered its internal points.)",
"role": "user"
}
] |
{
"ground_truth": "16",
"style": "rule"
}
|
{
"index": -1,
"split": "default"
}
|
|
olympiads
|
[
{
"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. If applicable, include the answer in \\boxed{} for closed-form results like multiple choices or mathematical solutions.",
"role": "system"
},
{
"content": "4.9 On a $10 \\times 10$ grid paper, there are 11 horizontal grid lines and 11 vertical grid lines. A line segment connecting two adjacent nodes on the same straight line is called a \"link segment\". How many link segments need to be erased at least, so that at most 3 link segments remain at each node?",
"role": "user"
}
] |
{
"ground_truth": "41",
"style": "rule"
}
|
{
"index": -1,
"split": "default"
}
|
|
olympiads
|
[
{
"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. If applicable, include the answer in \\boxed{} for closed-form results like multiple choices or mathematical solutions.",
"role": "system"
},
{
"content": "3. When $\\frac{\\pi}{4} \\leqslant x \\leqslant \\frac{\\pi}{2}$, the range of $y=\\sin ^{2} x+\\sqrt{3} \\sin x \\cos x$ is $\\qquad$",
"role": "user"
}
] |
{
"ground_truth": "y\\in[1,\\frac{3}{2}]",
"style": "rule"
}
|
{
"index": -1,
"split": "default"
}
|
|
olympiads
|
[
{
"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. If applicable, include the answer in \\boxed{} for closed-form results like multiple choices or mathematical solutions.",
"role": "system"
},
{
"content": "6.7. $f(x)=4 x^{3}-\\frac{5}{x^{7}}-8 \\sqrt[6]{x^{5}}+10$.\n\n6.7. $f(x)=4 x^{3}-\\frac{5}{x^{7}}-8 \\sqrt[6]{x^{5}}+10$.",
"role": "user"
}
] |
{
"ground_truth": "12x^{2}+\\frac{35}{x^{8}}-\\frac{20}{3\\sqrt[6]{x}}",
"style": "rule"
}
|
{
"index": -1,
"split": "default"
}
|
|
olympiads
|
[
{
"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. If applicable, include the answer in \\boxed{} for closed-form results like multiple choices or mathematical solutions.",
"role": "system"
},
{
"content": "Example 1. Find the general solution of the linear differential equation\n\n$$\ny^{\\prime}+y-k x=0\n$$",
"role": "user"
}
] |
{
"ground_truth": "k(x-1)+Ce^{-x}",
"style": "rule"
}
|
{
"index": -1,
"split": "default"
}
|
|
olympiads
|
[
{
"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. If applicable, include the answer in \\boxed{} for closed-form results like multiple choices or mathematical solutions.",
"role": "system"
},
{
"content": "What is the $21^{\\varrho}$ term of the sequence\n\n$$\n1 ; 2+3 ; 4+5+6 ; 7+8+9+10 ; 11+12+13+14+15 ; \\ldots ?\n$$",
"role": "user"
}
] |
{
"ground_truth": "4641",
"style": "rule"
}
|
{
"index": -1,
"split": "default"
}
|
|
olympiads
|
[
{
"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. If applicable, include the answer in \\boxed{} for closed-form results like multiple choices or mathematical solutions.",
"role": "system"
},
{
"content": "2. Let the function $f(x)=x^{2}+a x+b$, for any $a, b \\in \\mathbf{R}$, there always exists $t \\in[0,4]$, such that $|f(t)| \\geqslant m$ holds, then the maximum value of the real number $m$ is $\\qquad$.",
"role": "user"
}
] |
{
"ground_truth": "2",
"style": "rule"
}
|
{
"index": -1,
"split": "default"
}
|
|
olympiads
|
[
{
"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. If applicable, include the answer in \\boxed{} for closed-form results like multiple choices or mathematical solutions.",
"role": "system"
},
{
"content": "A right truncated pyramid is inscribed around a sphere of radius $r$, with its base being a square. What is the volume of this truncated pyramid, if the diagonal of its base is $4 r$?",
"role": "user"
}
] |
{
"ground_truth": "\\frac{28r^{3}}{3}",
"style": "rule"
}
|
{
"index": -1,
"split": "default"
}
|
|
olympiads
|
[
{
"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. If applicable, include the answer in \\boxed{} for closed-form results like multiple choices or mathematical solutions.",
"role": "system"
},
{
"content": "$9 \\cdot 6$ For $a>b>c>0, \\quad m>n>0(m, n$ are integers), which of the following relations is correct?\n(A) $a^{m} b^{n}>b^{m} c^{n}>c^{n} a^{m}$.\n(B) $a^{m} b^{n}>c^{n} a^{m}>b^{n} c^{m}$.\n(C) $a^{m} c^{n}>a^{m} b^{n}>b^{n} c^{m}$.\n(D) $b^{n} c^{m}>c^{n} a^{m}>a^{m} b^{n}$.\n(E) $a^{m} c^{n}>b^{n} c^{m}>a^{m} b^{n}$.\n(China Beijing Junior High School Mathematics Competition, 1983)",
"role": "user"
}
] |
{
"ground_truth": "B",
"style": "rule"
}
|
{
"index": -1,
"split": "default"
}
|
|
amc_aime
|
[
{
"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. If applicable, include the answer in \\boxed{} for closed-form results like multiple choices or mathematical solutions.",
"role": "system"
},
{
"content": "Lines $l_1^{}$ and $l_2^{}$ both pass through the origin and make first-quadrant angles of $\\frac{\\pi}{70}$ and $\\frac{\\pi}{54}$ radians, respectively, with the positive x-axis. For any line $l^{}_{}$, the transformation $R(l)^{}_{}$ produces another line as follows: $l^{}_{}$ is reflected in $l_1^{}$, and the resulting line is reflected in $l_2^{}$. Let $R^{(1)}(l)=R(l)^{}_{}$ and $R^{(n)}(l)^{}_{}=R\\left(R^{(n-1)}(l)\\right)$. Given that $l^{}_{}$ is the line $y=\\frac{19}{92}x^{}_{}$, find the smallest positive integer $m^{}_{}$ for which $R^{(m)}(l)=l^{}_{}$.",
"role": "user"
}
] |
{
"ground_truth": "945",
"style": "rule"
}
|
{
"index": -1,
"split": "default"
}
|
|
cn_contest
|
[
{
"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. If applicable, include the answer in \\boxed{} for closed-form results like multiple choices or mathematical solutions.",
"role": "system"
},
{
"content": "2. Given the function $y=\\frac{a-x}{x-a-1}$, the graph of its inverse function is symmetric about the point $(-1,4)$. Then the value of the real number $a$ is $\\qquad$ .",
"role": "user"
}
] |
{
"ground_truth": "3",
"style": "rule"
}
|
{
"index": -1,
"split": "default"
}
|
|
olympiads
|
[
{
"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. If applicable, include the answer in \\boxed{} for closed-form results like multiple choices or mathematical solutions.",
"role": "system"
},
{
"content": "669. For which numbers $x$ does the equation $x+|x|=0$ hold?",
"role": "user"
}
] |
{
"ground_truth": "x\\leqslant0",
"style": "rule"
}
|
{
"index": -1,
"split": "default"
}
|
|
olympiads
|
[
{
"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. If applicable, include the answer in \\boxed{} for closed-form results like multiple choices or mathematical solutions.",
"role": "system"
},
{
"content": "Example 12 Given $a, b, c, d \\in \\mathbf{R}^{+}$, try to find\n$f(a, b, c, d)=\\frac{a}{b+c+d}+\\frac{b}{c+d+a}+\\frac{c}{a+b+d}+\\frac{d}{a+b+c}$ the minimum value.",
"role": "user"
}
] |
{
"ground_truth": "\\frac{4}{3}",
"style": "rule"
}
|
{
"index": -1,
"split": "default"
}
|
|
olympiads
|
[
{
"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. If applicable, include the answer in \\boxed{} for closed-form results like multiple choices or mathematical solutions.",
"role": "system"
},
{
"content": "Example 4 Find the integer solution of the equation $\\left[\\frac{x}{1!}\\right]+\\left[\\frac{x}{2!}\\right]+\\left[\\frac{x}{3!}\\right]+\\cdots+$ $\\left[\\frac{x}{10!}\\right]=1001$.",
"role": "user"
}
] |
{
"ground_truth": "584",
"style": "rule"
}
|
{
"index": -1,
"split": "default"
}
|
|
olympiads
|
[
{
"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. If applicable, include the answer in \\boxed{} for closed-form results like multiple choices or mathematical solutions.",
"role": "system"
},
{
"content": "321. $\\sqrt{2 x+5}+\\sqrt{x-1}=8$.\n\nTranslate the text above into English, keeping the original text's line breaks and format, and output the translation result directly.\n\n321. $\\sqrt{2 x+5}+\\sqrt{x-1}=8$.",
"role": "user"
}
] |
{
"ground_truth": "10",
"style": "rule"
}
|
{
"index": -1,
"split": "default"
}
|
|
olympiads
|
[
{
"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. If applicable, include the answer in \\boxed{} for closed-form results like multiple choices or mathematical solutions.",
"role": "system"
},
{
"content": "Problem 2. Find the number of the subsets $B$ of the set $\\{1,2, \\ldots, 2005\\}$ having the following property: the sum of the elements of $B$ is congruent to 2006 modulo 2048 .\n\nEmil Kolev",
"role": "user"
}
] |
{
"ground_truth": "2^{1994}",
"style": "rule"
}
|
{
"index": -1,
"split": "default"
}
|
|
olympiads
|
[
{
"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. If applicable, include the answer in \\boxed{} for closed-form results like multiple choices or mathematical solutions.",
"role": "system"
},
{
"content": "2、D Teacher has five vases, these five vases are arranged in a row from shortest to tallest, the height difference between adjacent vases is 2 centimeters, and the tallest vase is exactly equal to the sum of the heights of the two shortest vases, then the total height of the five vases is _ centimeters",
"role": "user"
}
] |
{
"ground_truth": "50",
"style": "rule"
}
|
{
"index": -1,
"split": "default"
}
|
|
olympiads
|
[
{
"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. If applicable, include the answer in \\boxed{} for closed-form results like multiple choices or mathematical solutions.",
"role": "system"
},
{
"content": "11. Choose three different digits from $0,1, \\cdots, 9$ to form a four-digit number (one of the digits can appear twice), such as 5 224. Then the total number of such four-digit numbers is $\\qquad$.",
"role": "user"
}
] |
{
"ground_truth": "3888",
"style": "rule"
}
|
{
"index": -1,
"split": "default"
}
|
|
olympiads
|
[
{
"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. If applicable, include the answer in \\boxed{} for closed-form results like multiple choices or mathematical solutions.",
"role": "system"
},
{
"content": "2. Function $f$ is defined on the set of integers, satisfying\n$$\nf(n)=\\left\\{\\begin{array}{ll}\nn-3 & n \\geqslant 1000 \\\\\nf[f(n+5)] & n<1000\n\\end{array},\\right.\n$$\n\nFind $f(84)$.",
"role": "user"
}
] |
{
"ground_truth": "997",
"style": "rule"
}
|
{
"index": -1,
"split": "default"
}
|
|
olympiads
|
[
{
"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. If applicable, include the answer in \\boxed{} for closed-form results like multiple choices or mathematical solutions.",
"role": "system"
},
{
"content": "## Problem Statement\n\nCalculate the definite integral:\n\n$$\n\\int_{0}^{\\frac{\\pi}{2}} \\frac{\\cos x \\, dx}{2+\\cos x}\n$$",
"role": "user"
}
] |
{
"ground_truth": "\\frac{(9-4\\sqrt{3})\\pi}{18}",
"style": "rule"
}
|
{
"index": -1,
"split": "default"
}
|
|
olympiads
|
[
{
"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. If applicable, include the answer in \\boxed{} for closed-form results like multiple choices or mathematical solutions.",
"role": "system"
},
{
"content": "Problem 10.7. The graph of the function $f(x)=\\frac{1}{12} x^{2}+a x+b$ intersects the $O x$ axis at points $A$ and $C$, and the $O y$ axis at point $B$, as shown in the figure. It turned out that for the point $T$ with coordinates $(3 ; 3)$, the condition $T A=T B=T C$ is satisfied. Find $b$.\n\n",
"role": "user"
}
] |
{
"ground_truth": "-6",
"style": "rule"
}
|
{
"index": -1,
"split": "default"
}
|
|
olympiads
|
[
{
"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. If applicable, include the answer in \\boxed{} for closed-form results like multiple choices or mathematical solutions.",
"role": "system"
},
{
"content": "3. The monotonic increasing interval of the function $f(x)$ $=\\frac{(x+1)^{2}}{x^{2}+1}$ is $\\qquad$",
"role": "user"
}
] |
{
"ground_truth": "(-1,1)",
"style": "rule"
}
|
{
"index": -1,
"split": "default"
}
|
|
olympiads
|
[
{
"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. If applicable, include the answer in \\boxed{} for closed-form results like multiple choices or mathematical solutions.",
"role": "system"
},
{
"content": "10.024. The lengths of the parallel sides of the trapezoid are 25 and 4 cm, and the lengths of the non-parallel sides are 20 and 13 cm. Find the height of the trapezoid.",
"role": "user"
}
] |
{
"ground_truth": "12",
"style": "rule"
}
|
{
"index": -1,
"split": "default"
}
|
|
olympiads
|
[
{
"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. If applicable, include the answer in \\boxed{} for closed-form results like multiple choices or mathematical solutions.",
"role": "system"
},
{
"content": "1. Without using calculators or other computational tools, determine which of the two numbers is greater:\n\n$$\n\\frac{1+\\sqrt{5}}{2} \\text { or } \\sqrt[6]{18} ?\n$$",
"role": "user"
}
] |
{
"ground_truth": "\\sqrt[6]{18}",
"style": "rule"
}
|
{
"index": -1,
"split": "default"
}
|
|
olympiads
|
[
{
"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. If applicable, include the answer in \\boxed{} for closed-form results like multiple choices or mathematical solutions.",
"role": "system"
},
{
"content": "6. (10 points) As shown in the figure, the area of square $A B C D$ is 840 square centimeters, $A E=E B, B F=2 F C, D F$ intersects $E C$ at $G$. Then the area of quadrilateral $A E G D$ is square centimeters.",
"role": "user"
}
] |
{
"ground_truth": "510",
"style": "rule"
}
|
{
"index": -1,
"split": "default"
}
|
|
olympiads
|
[
{
"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. If applicable, include the answer in \\boxed{} for closed-form results like multiple choices or mathematical solutions.",
"role": "system"
},
{
"content": "For example, in the sequence $x_{1}, x_{2}, \\cdots, x_{n}, \\cdots$, the sum of any three consecutive terms is 20, and $x_{1}=9, x_{12}=7$. Find the value of $x_{2000}$.",
"role": "user"
}
] |
{
"ground_truth": "4",
"style": "rule"
}
|
{
"index": -1,
"split": "default"
}
|
|
olympiads
|
[
{
"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. If applicable, include the answer in \\boxed{} for closed-form results like multiple choices or mathematical solutions.",
"role": "system"
},
{
"content": "13.223. Point $C$ is located 12 km downstream from point $B$. A fisherman set out from point $A$, located upstream from point $B$, to point $C$. After 4 hours, he arrived at $C$, and the return trip took 6 hours. On another occasion, the fisherman used a motorboat, thereby tripling his own speed relative to the water, and reached from $A$ to $B$ in 45 minutes. It is required to determine the speed of the current, assuming it is constant.",
"role": "user"
}
] |
{
"ground_truth": "1",
"style": "rule"
}
|
{
"index": -1,
"split": "default"
}
|
|
olympiads
|
[
{
"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. If applicable, include the answer in \\boxed{} for closed-form results like multiple choices or mathematical solutions.",
"role": "system"
},
{
"content": "Example 11 Find the minimum value of the bivariate function $f(x, y)=(x-y)^{2}+\\left(x+\\frac{1}{y}+1\\right)^{2}$.",
"role": "user"
}
] |
{
"ground_truth": "\\frac{1}{2}",
"style": "rule"
}
|
{
"index": -1,
"split": "default"
}
|
|
olympiads
|
[
{
"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. If applicable, include the answer in \\boxed{} for closed-form results like multiple choices or mathematical solutions.",
"role": "system"
},
{
"content": "4. Zhao, Qian, Sun, and Li each prepared a gift to give to one of the other three classmates when the new semester started. It is known that Zhao's gift was not given to Qian, Sun did not receive Li's gift, Sun does not know who Zhao gave the gift to, and Li does not know who Qian received the gift from. So, Qian gave the gift to ( ).\n(A) Zhao\n(B) Sun\n(C) Li\n(D) None of the above",
"role": "user"
}
] |
{
"ground_truth": "B",
"style": "rule"
}
|
{
"index": -1,
"split": "default"
}
|
|
cn_contest
|
[
{
"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. If applicable, include the answer in \\boxed{} for closed-form results like multiple choices or mathematical solutions.",
"role": "system"
},
{
"content": "II. (25 points) If $2 x+y \\geqslant 1$. Try to find the minimum value of the function $u=y^{2}-2 y$ $+x^{2}+4 x$.\n\n",
"role": "user"
}
] |
{
"ground_truth": "-\\frac{9}{5}",
"style": "rule"
}
|
{
"index": -1,
"split": "default"
}
|
|
cn_contest
|
[
{
"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. If applicable, include the answer in \\boxed{} for closed-form results like multiple choices or mathematical solutions.",
"role": "system"
},
{
"content": "II. Find the last four digits of $2^{1999}$.\n\nTranslate the text above into English, please keep the original text's line breaks and format, and output the translation result directly.",
"role": "user"
}
] |
{
"ground_truth": "4688",
"style": "rule"
}
|
{
"index": -1,
"split": "default"
}
|
|
olympiads
|
[
{
"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. If applicable, include the answer in \\boxed{} for closed-form results like multiple choices or mathematical solutions.",
"role": "system"
},
{
"content": "18. Let $a_{k}$ be the coefficient of $x^{k}$ in the expansion of\n$$\n(x+1)+(x+1)^{2}+(x+1)^{3}+(x+1)^{4}+\\cdots+(x+1)^{99} \\text {. }\n$$\n\nDetermine the value of $\\left\\lfloor a_{4} / a_{3}\\right\\rfloor$.",
"role": "user"
}
] |
{
"ground_truth": "19",
"style": "rule"
}
|
{
"index": -1,
"split": "default"
}
|
|
olympiads
|
[
{
"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. If applicable, include the answer in \\boxed{} for closed-form results like multiple choices or mathematical solutions.",
"role": "system"
},
{
"content": "\\section*{Problem \\(6-330916=331016\\)}\n\nIt is known that \\(2^{10}=1024\\).\n\nFormulate a computer program that can determine the smallest natural exponent \\(p>10\\) for which the number \\(2^p\\) also ends in the digits ...024! Explain why the program you have formulated solves this problem!\n\nHint: Note that for the numbers involved in the calculations, there are limitations on the number of digits when using typical computer usage.",
"role": "user"
}
] |
{
"ground_truth": "110",
"style": "rule"
}
|
{
"index": -1,
"split": "default"
}
|
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