data_source
stringclasses 8
values | prompt
listlengths 2
2
| ability
stringclasses 2
values | reward_model
dict | extra_info
dict |
|---|---|---|---|---|
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"
}
|
|
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"
}
|
|
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": "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"
}
|
|
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"
}
|
|
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": "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": "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"
}
|
|
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": "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": "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": "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": "2.1 Find $f(2013)$, if for any real $x$ and $y$ the equality holds\n\n$$\nf(x-y)=f(x)+f(y)-2xy\n$$",
"role": "user"
}
] |
{
"ground_truth": "4052169",
"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. (10 points) Two wheels rotate, meshed with each other, around fixed axes passing through the centers of wheels $A$ and $B$. The radii of the wheels differ by a factor of three. The smaller wheel makes 30 revolutions per minute. Determine how many seconds the larger wheel spends on one revolution?\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": "Determine the value of $2^{4}\\left(1+\\frac{1}{2}+\\frac{1}{2^{2}}+\\frac{1}{2^{3}}+\\frac{1}{2^{4}}\\right)$.",
"role": "user"
}
] |
{
"ground_truth": "31",
"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. If $x-y=12$, find the value of $x^{3}-y^{3}-36 x y$.\n(1 mark)\nIf $x-y=12$, find the value of $x^{3}-y^{3}-36 x y$.\n(1 mark)",
"role": "user"
}
] |
{
"ground_truth": "1728",
"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": "## 232. Math Puzzle $9 / 84$\n\nA motorcycle battery ( $6 \\mathrm{~V}$ ) is discharged through a lamp $6 \\mathrm{~V} / 0.5 \\mathrm{~W}$. The lamp burns for 48 hours.\n\nHow many Ah was the battery charged if we assume that the discharge current remains constant?",
"role": "user"
}
] |
{
"ground_truth": "4\\mathrm{Ah}",
"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. Determine the value of the sum\n$$\n\\frac{3}{1^{2} \\cdot 2^{2}}+\\frac{5}{2^{2} \\cdot 3^{2}}+\\frac{7}{3^{2} \\cdot 4^{2}}+\\cdots+\\frac{29}{14^{2} \\cdot 15^{2}} .\n$$",
"role": "user"
}
] |
{
"ground_truth": "\\frac{224}{225}",
"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 5.4. At the end-of-the-year school dance, there were twice as many boys as girls. Masha counted that there were 8 fewer girls, besides herself, than boys. How many boys came to the dance?",
"role": "user"
}
] |
{
"ground_truth": "14",
"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 $A$, $B$, $C$, $D$ be four points on a line in this order. Suppose that $AC = 25$, $BD = 40$, and $AD = 57$. Compute $AB \\cdot CD + AD \\cdot BC$.\n\n[i]Proposed by Evan Chen[/i]",
"role": "user"
}
] |
{
"ground_truth": "1000",
"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. An integer $x$ satisfies the inequality $x^{2} \\leq 729 \\leq-x^{3}$. $P$ and $Q$ are possible values of $x$. What is the maximum possible value of $10(P-Q)$ ?",
"role": "user"
}
] |
{
"ground_truth": "180",
"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": "Florián was thinking about what bouquet he would have tied for his mom for Mother's Day. In the florist's, according to the price list, he calculated that whether he buys 5 classic gerberas or 7 mini gerberas, the bouquet, when supplemented with a decorative ribbon, would cost the same, which is 295 crowns. However, if he bought only 2 mini gerberas and 1 classic gerbera without any additional items, he would pay 102 crowns.\n\nHow much does one ribbon cost? \n\n(L. Šimůnek)",
"role": "user"
}
] |
{
"ground_truth": "85",
"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": "19) The inhabitants of an island are divided into two categories: those who are always truthful and those who always lie. Among three inhabitants of the island, Andrea, Barbara, and Ciro, the following conversation takes place: Andrea says: \"Barbara is truthful\", Barbara says: \"Andrea and Ciro are truthful\", Ciro says: \"Andrea is a liar\". We can conclude that\n\n(A) they are all three truthful, (B) they are all three liars, (C) Andrea and Barbara are truthful and Ciro is a liar, (D) Andrea and Barbara are liars and Ciro is truthful, (E) Andrea is truthful and Ciro and Barbara are liars.",
"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": "10. (3 points) The sum of two numbers $A$ and $B$ is 1812, and the quotient of the larger number divided by the smaller number is 7 with a remainder of 4. Then, the difference between the larger and smaller numbers is",
"role": "user"
}
] |
{
"ground_truth": "1360",
"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": "## 29. Leonie and Cats\n\nWhen old lady Leonie is asked how many cats she has, she melancholically replies: “Four fifths of my cats plus four fifths of a cat.” How many cats does she have?\n\n",
"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": "1. Consider the sequence 10, 13, 16, 19, .... Calculate the 2016th term of the sequence.",
"role": "user"
}
] |
{
"ground_truth": "6055",
"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": "Line segment $A D$ is divided into three segments by points $B$ and $C$, so that $A B: B C=1: 2$ and $B C: C D=6: 5$. The length of $A D$ is 56 units. What is the length of $A B$ ?\n\n",
"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": "The graph shows the fuel used per $100 \\mathrm{~km}$ of driving for five different vehicles. Which vehicle would travel the farthest using 50 litres of fuel?\n(A) $U$\n(B) $V$\n(C) $W$\n(D) $X$\n(E) $Y$\n\n",
"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": "If $x=\\frac{1}{4}$, which of the following has the largest value?\n(A) $x$\n(B) $x^{2}$\n(C) $\\frac{1}{2} x$\n(D) $\\frac{1}{x}$\n(E) $\\sqrt{x}$",
"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. (8 points) The calculation result of the expression $210+6-12-19$ is\n\n保留了源文本的换行和格式，但请注意，最后一句“保留了源文本的换行和格式”是说明性质的，不应包含在翻译结果中。正确的翻译结果如下：\n\n1. (8 points) The calculation result of the expression $210+6-12-19$ is",
"role": "user"
}
] |
{
"ground_truth": "185",
"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": "110. Find the general solution of the equation $y^{\\prime \\prime}=4 x$.",
"role": "user"
}
] |
{
"ground_truth": "\\frac{2}{3}x^{3}+C_{1}x+C_{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. The area of a rectangle is 180 units $^{2}$ and the perimeter is 54 units. If the length of each side of the rectangle is increased by six units, what is the area of the resulting rectangle?",
"role": "user"
}
] |
{
"ground_truth": "378",
"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. The volume of a cube in cubic metres and its surface area in square metres is numerically equal to four-thirds of the sum of the lengths of its edges in metres.\nWhat is the total volume in cubic metres of twenty-seven such cubes?",
"role": "user"
}
] |
{
"ground_truth": "216",
"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. Using this picture we can observe that\n$$\n1+3+5+7=4 \\times 4 \\text {. }\n$$\n\nWhat is the value of\n$$\n1+3+5+7+9+11+13+15+17+19+21 ?\n$$",
"role": "user"
}
] |
{
"ground_truth": "121",
"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": "A [i]normal magic square[/i] of order $n$ is an arrangement of the integers from $1$ to $n^2$ in a square such that the $n$ numbers in each row, each column, and each of the two diagonals sum to a constant, called the [i]magic sum[/i] of the magic square. Compute the magic sum of a normal magic square of order $8$.",
"role": "user"
}
] |
{
"ground_truth": "260",
"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": "$\\frac{1}{4}$ of 100 is equal to\n(A) $20 \\%$ of 200\n(B) $10 \\%$ of 250\n(C) $15 \\%$ of 100\n(D) $25 \\%$ of 50\n(E) $5 \\%$ of 300",
"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": "## Task 4 - 240624\n\nRita is experimenting with a balance scale.\n\n(With such a scale, it can be determined whether the content of one pan weighs as much as the content of the other pan or which of the two contents weighs more than the other.)\n\nRita has 17 balls, 6 cubes, and 1 pyramid. She observes:\n\n(1) Each ball weighs as much as each of the other balls.\n\n(2) Each cube weighs as much as each of the other cubes.\n\n(3) The pyramid and 5 cubes together weigh as much as 14 balls.\n\n(4) A cube and 8 balls together weigh as much as the pyramid.\n\nRolf asks Rita, after she has made these observations:\n\n\"How many balls weigh as much as the pyramid?\"\n\nProve that Rolf's question can already be answered uniquely using observations (1), (2), (3), (4), without the need for any further weighing! What is the answer?",
"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": "146. From a group of 15 people, four participants for the relay race $800+400+200+100$ are selected. In how many ways can the athletes be arranged for the relay stages?",
"role": "user"
}
] |
{
"ground_truth": "32760",
"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. If $f(x)=\\frac{1}{x}$ has a domain $A$, and $g(x)=f(x+1)-f(x)$ has a domain $B$, then ( ).\n(A) $A \\cup B=\\mathbf{R}$\n(B) $A \\supsetneqq B$\n(C) $A \\subseteq B$\n(D) $A \\cap B=\\varnothing$",
"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": "106. Calculate the sum:\n\n$$\nS=\\frac{1}{1 \\cdot 2}+\\frac{1}{2 \\cdot 3}+\\frac{1}{3 \\cdot 4}+\\cdots+\\frac{1}{99 \\cdot 100}\n$$",
"role": "user"
}
] |
{
"ground_truth": "0.99",
"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 past Mathematical Olympiad the maximum possible score on a problem was 5. The average score of boys was 4, the average score of girls was 3.25, and the overall average score was 3.60. Find the total number of participants, knowing that it was in the range from 31 to 50.",
"role": "user"
}
] |
{
"ground_truth": "45",
"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": "(solved by Alice Héliou). The sum of twenty consecutive integers is 1030. What is the smallest of these integers?",
"role": "user"
}
] |
{
"ground_truth": "42",
"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 $x=\\frac{a-b}{a+b}$, and $a \\neq 0$, then $\\frac{b}{a}$ equals ( ).\n(A) $\\frac{1-x}{1+x}$\n(B) $\\frac{1+x}{1-x}$\n(C) $\\frac{x-1}{x+1}$\n(D) $\\frac{x+1}{x-1}$",
"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": "3.1.1. (12 points) Calculate $\\sin (\\alpha+\\beta)$, if $\\sin \\alpha+\\cos \\beta=\\frac{1}{4}$ and $\\cos \\alpha+\\sin \\beta=-\\frac{8}{5}$. Answer: $\\frac{249}{800} \\approx 0.31$.",
"role": "user"
}
] |
{
"ground_truth": "\\frac{249}{800}",
"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 area of the figure bounded by the graphs of the functions:\n\n$$\nx=\\frac{1}{y \\sqrt{1+\\ln y}}, x=0, y=1, y=e^{3}\n$$",
"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": "Example 1 The graph of the function $y=f(x)$ is symmetric to the graph of the function $g(x)=\\log _{2} x(x>0)$ with respect to the origin, then the expression for $f(x)$ is ().\n(A) $f(x)=\\frac{1}{\\log _{2} x}(x>0)$\n(B) $f(x)=\\log _{2}(-x)(x>0)$\n(C) $f(x)=-\\log _{2} x(x<0)$\n(D) $f(x)=-\\log _{2}(-x)(x<0)$",
"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": "Example 1. Find $\\int e^{x^{2}} \\cdot x d x$.",
"role": "user"
}
] |
{
"ground_truth": "\\frac{1}{2}e^{x^{2}}+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": "## Task 3\n\nCalculate in writing: $438+8006+98+728$",
"role": "user"
}
] |
{
"ground_truth": "9270",
"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": "On the plane, nine parallel lines intersect with $n$ other parallel lines, all of which are perpendicular to the first nine. The lines together form a total of 756 rectangles. What is the value of $n$?",
"role": "user"
}
] |
{
"ground_truth": "7",
"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. Use square tiles of the same size to pave a square floor, with white tiles around the edges and black tiles in the middle (as shown in Fig. 1 and Fig. 2). When 80 white tiles are used around the square floor, the number of black tiles needed is $\\qquad$.\n\n保留源文本的换行和格式，直接输出翻译结果如下：\n\n5. Use square tiles of the same size to pave a square floor, with white tiles around the edges and black tiles in the middle (as shown in Fig. 1 and Fig. 2). When 80 white tiles are used around the square floor, the number of black tiles needed is $\\qquad$.",
"role": "user"
}
] |
{
"ground_truth": "361",
"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": "[ Coordinate method on the plane ] $\\left[\\begin{array}{l}\\text { [Properties and characteristics of the tangent] }\\end{array}\\right.$\n\nCompose the equation of the circle with the center at point $M(3 ; 2)$, touching the line $y=2 x+6$.",
"role": "user"
}
] |
{
"ground_truth": "(x-3)^{2}+(y-2)^{2}=20",
"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. Aljmez\n\nOn the planet Aljmez, a day is called NAD, an hour is called TAS, a minute is called NIM, and a second is called KES. One NAD lasts ten TAS, one TAS lasts ten NIM, and one NIM lasts eight KES. How many Earth seconds does one Aljmezian KES last, if one NAD lasts as long as one day?\n\nResult: $\\quad \\mathbf{1 0 8}$",
"role": "user"
}
] |
{
"ground_truth": "108",
"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": "## Task 5 - 210835\n\nSomeone withdraws a certain amount of money from their savings account. They receive this amount paid out in a total of 29 banknotes, exclusively in 10-mark notes, 20-mark notes, and 50-mark notes. The number of 10-mark notes is 1 less than the number of 20-mark notes. The number of 50-mark notes is greater than twice but less than three times the number of 20-mark notes.\n\nDetermine the amount of money withdrawn!",
"role": "user"
}
] |
{
"ground_truth": "1000\\mathrm{M}",
"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. (Average/Difficult) A geometric sequence has a nonzero first term, distinct terms, and a positive common ratio. If the second, fourth, and fifth terms form an arithmetic sequence, find the common ratio of the geometric sequence.",
"role": "user"
}
] |
{
"ground_truth": "\\frac{1+\\sqrt{5}}{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": "2. The students went to see an exhibition and had to pay 120 EUR for the bus fare. Since three students fell ill, each of the remaining students had to pay an additional 2 EUR for the transport. How many students signed up for the exhibition?",
"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": "4. In triangle $ABC$, it holds that $\\frac{h_{a} h_{b}}{h_{c}}=c$, where $h_{a}, h_{b}, h_{c}$ are the lengths of the altitudes, and $c$ is the length of one side of the triangle. Determine one of the angles of this triangle.",
"role": "user"
}
] |
{
"ground_truth": "90",
"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": "60. Meteorological observations. At a weather station, it was noticed that during a certain period of time, if it rained in the morning, it was clear in the evening, and if it rained in the evening, it was clear in the morning. In total, there were 9 rainy days, with clear evenings 6 times and clear mornings 7 times. How many days did this entire period cover?",
"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": "How many perfect squares are there between 2 and 150 ?",
"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": "18. Master Li made 8 identical rabbit lanterns in 3 days, making at least 1 lantern each day. Master Li has ( ) different ways to do this.",
"role": "user"
}
] |
{
"ground_truth": "21",
"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": "Task B-1.2. Write as a power with base 5:\n\n$$\n3\\left(5^{n}-5\\right)\\left(5^{n}+5\\right)+2\\left(25+5^{2 n}\\right)+25^{n+1}: 5^{2 n}\n$$",
"role": "user"
}
] |
{
"ground_truth": "5^{2n+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": "4. While working on fruit harvesting, class 5A collected 560 kg of apples, 5B - 595 kg, and 5V - 735 kg. All the collected apples were packed into boxes, with each box containing the same maximum possible number of kilograms. How many such boxes were required for each class?",
"role": "user"
}
] |
{
"ground_truth": "16,17,21",
"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": "Basil needs to solve an exercise on summing two fractions $\\dfrac{a}{b}$ and $\\dfrac{c}{d}$, where $a$, $b$, $c$, $d$ are some non-zero real numbers. But instead of summing he performed multiplication (correctly). It appears that Basil's answer coincides with the correct answer to given exercise. Find the value of $\\dfrac{b}{a} + \\dfrac{d}{c}$.",
"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": "## Task 1 - 110611\n\nTwo cars of the \"Wartburg\" type covered one a distance of $1200 \\mathrm{~km}$, the other a distance of $800 \\mathrm{~km}$. It is assumed that each of the two cars consumed the same amount of fuel per kilometer. The second car consumed 36 liters less fuel than the first.\n\nCalculate how many liters of fuel both cars together consumed for the distances mentioned above!",
"role": "user"
}
] |
{
"ground_truth": "180",
"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": "Kathy owns more cats than Alice and more dogs than Bruce. Alice owns more dogs than Kathy and fewer cats than Bruce. Which of the statements must be true?\n\n(A) Bruce owns the fewest cats.\n\n(B) Bruce owns the most cats.\n\n(C) Kathy owns the most cats.\n\n(D) Alice owns the most dogs.\n\n(E) Kathy owns the fewest dogs.",
"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": "2. (8 points) Shuaishuai finished memorizing English words in five days. It is known that in the first three days, he memorized $\\frac{1}{2}$ of all the words, and in the last three days, he memorized $\\frac{2}{3}$ of all the words, and he memorized 120 fewer words in the first three days than in the last three days. Therefore, Shuaishuai memorized $\\qquad$ English words on the third day.",
"role": "user"
}
] |
{
"ground_truth": "120",
"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. (6 points) The figure is a rectangle. To divide it into 7 parts, at least $\\qquad$ straight lines need to be drawn.\n\n",
"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": "(Application of the algorithm)\n\nFind the GCD $d$ of the integers 663 and 182 and integers $u, v \\in \\mathbb{Z}$ such that $d=663 u+182 v$.",
"role": "user"
}
] |
{
"ground_truth": "13==11\\times182-3\\times663",
"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": "93. A small train puzzle. The express from Basltown to Ironchester travels at a speed of 60 km/h, and the express from Ironchester to Basltown, which departs simultaneously with it, travels at a speed of 40 km/h.\n\nHow far apart will they be one hour before meeting?\n\nI couldn't find these cities on any map or in any reference, so I don't know the exact distance between them. Let's assume it does not exceed 250 km.",
"role": "user"
}
] |
{
"ground_truth": "100",
"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 function:\n\n$\\lim _{x \\rightarrow 1} \\frac{2 x^{2}-x-1}{x^{3}+2 x^{2}-x-2}$",
"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": "Daddy decided to give his son Mojmir a monthly allowance. Mojmir received his first allowance in January. Daddy increased the allowance by 4 Kč every month. If Mojmir didn't spend any, he would have 900 Kč after the twelfth allowance before Christmas. How many Kč did Mojmir receive for his first allowance in January?\n\n(L. Hozová)",
"role": "user"
}
] |
{
"ground_truth": "53",
"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 6 Let $x y=1$, and $x>y>0$. Find the minimum value of $\\frac{x^{2}+y^{2}}{x-y}$.\n\n untranslated text is retained in its original format and directly output the translation result.",
"role": "user"
}
] |
{
"ground_truth": "2 \\sqrt{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": "1. $a, b$ are positive integer divisors of 1995, then the number of ordered pairs $(a, b)$ is ().\n(A) 16\n(B) 32\n(C) 64\n(D) 256",
"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": "\\section*{Exercise 1 - 081221}\n\nGive all prime numbers \\(p\\) for which both \\(p+10\\) and \\(p+14\\) are also prime numbers!",
"role": "user"
}
] |
{
"ground_truth": "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": "5. It is known that after 100 years, cadmium retains $95.76 \\%$ of its original mass. Let the remaining mass of a mass of 1 after $x$ years be $y$, then the functional relationship between $x$ and $y$ is ( ).\n(A) $y=(0.9576)^{\\frac{x}{100}}$\n(B) $y=(0.9576)^{100 x}$\n(C) $y=\\left(\\frac{0.9576}{100}\\right)^{x}$\n(D) $y=1-(0.0424)^{\\frac{x}{100}}$",
"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": "Knowing that $a b c=8$, with $a, b, c$ positive, what is the minimum value of $a+b+c$?",
"role": "user"
}
] |
{
"ground_truth": "6",
"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": "Triangle $ABC$ lies in the first quadrant. Points $A$, $B$, and $C$ are reflected across the line $y=x$ to points $A'$, $B'$, and $C'$, respectively. Assume that none of the vertices of the triangle lie on the line $y=x$. Which of the following statements is not always true?\n$\\textbf{(A) }$ Triangle $A'B'C'$ lies in the first quadrant.\n$\\textbf{(B) }$ Triangles $ABC$ and $A'B'C'$ have the same area.\n$\\textbf{(C) }$ The slope of line $AA'$ is $-1$.\n$\\textbf{(D) }$ The slopes of lines $AA'$ and $CC'$ are the same.\n$\\textbf{(E) }$ Lines $AB$ and $A'B'$ are perpendicular to each other.",
"role": "user"
}
] |
{
"ground_truth": "\\textbf{(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": "49. It's winter vacation, and in the first week, Xi Xi completed $\\frac{1}{5}$ of all the questions in the *Winter Vacation Homework*. In the second week, she completed 30% of all the questions, which was 15 more questions than in the first week. Therefore, the total number of questions in Xi Xi's *Winter Vacation Homework* is $\\qquad$ questions.",
"role": "user"
}
] |
{
"ground_truth": "150",
"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. The positive integer solution of the system of equations $\\left\\{\\begin{array}{l}\\frac{z^{y}}{y}=y^{2 x}, \\\\ 2^{z}=2 \\cdot 4^{x}, \\\\ x+y+z=12\\end{array}\\right.$ is $\\qquad$",
"role": "user"
}
] |
{
"ground_truth": "x=2, y=5, z=5",
"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・3 If $a=(-3)^{-4}, b=-3^{4}, c=-3^{-4}$, then the incorrect conclusion among the following is\n(A) $\\log _{3} a=-4$.\n(B) $\\lg b c=0$.\n(C) $a, c$ are opposite numbers.\n(D) $a, b$ are reciprocals.\n(China Sichuan Province Junior High School Mathematics League, 1989)",
"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": "2. Inside the area of $\\measuredangle A O B$, a ray $O C$ is drawn such that $\\measuredangle A O C$ is $40^{\\circ}$ less than $\\measuredangle C O B$ and is equal to one third of $\\measuredangle A O B$. Determine $\\measuredangle A O B$.\n\n翻译完成，保留了原文的换行和格式。",
"role": "user"
}
] |
{
"ground_truth": "120",
"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 function:\n\n$\\lim _{x \\rightarrow 3} \\frac{\\sqrt[3]{5+x}-2}{\\sin \\pi x}$",
"role": "user"
}
] |
{
"ground_truth": "-\\frac{1}{12\\pi}",
"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": "14. $\\log _{\\frac{\\sqrt{3}}{3}}\\left(\\log _{8} \\frac{\\sqrt{2}}{2}-\\log _{3} \\frac{\\sqrt{3}}{3}\\right)$.\n\nIn № $15-27$ solve the equations:",
"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": "7. Let $[x]$ denote the greatest integer not exceeding the real number $x$, and $\\{x\\}=x-[x]$. Then\n$$\n\\left\\{\\frac{2015!}{2017}\\right\\}=\n$$\n$\\qquad$",
"role": "user"
}
] |
{
"ground_truth": "\\frac{1}{2017}",
"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": "1.1. Masha thought of a 10-digit number and told Vasya that the remainder of dividing this number by 9 is 3. Then Masha crossed out one digit and told Vasya that the remainder of dividing the resulting 9-digit number by 9 is 7. Help Vasya guess the digit that Masha crossed out. Write this digit in the answer.",
"role": "user"
}
] |
{
"ground_truth": "5",
"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 non-zero integers $x$ and $y$ we define $x \\nabla y=x^{y}+4 x$. For example, $2 \\nabla 3=2^{3}+4(2)=16$. Determine all real numbers $x$ such that $x \\nabla 2=12$.",
"role": "user"
}
] |
{
"ground_truth": "-6,2",
"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": "# Problem 3.\n\nA square with a side of 75 mm was cut by two parallel cuts into three rectangles. It turned out that the perimeter of one of these rectangles is half the sum of the perimeters of the other two. What is this perimeter? Give your answer in centimeters.",
"role": "user"
}
] |
{
"ground_truth": "20",
"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. The arithmetic mean of five data points is 18. What will be the arithmetic mean of the remaining data points after removing the data point with a value of 10?",
"role": "user"
}
] |
{
"ground_truth": "20",
"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": "24. \"Rzhev\" was a famous battlefield for tank battles during World War II. According to statistics, there were a total of 115 tanks. The number of German tanks was 2 more than twice the number of Allied tanks, and the number of Allied tanks was 1 more than three times the number of the third battalion. How many more tanks did the Germans have compared to the third battalion?",
"role": "user"
}
] |
{
"ground_truth": "59",
"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": "$3 \\cdot 2$ Find the sum of $1 \\cdot 1!+2 \\cdot 2!+3 \\cdot 3!+\\cdots+(n-1)(n-1)!+n \\cdot n!$, where $n!=n(n-1)(n-2) \\cdots 2 \\cdot 1$.",
"role": "user"
}
] |
{
"ground_truth": "(n+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": "11. (5 points) As shown in the figure, a cubic wooden block is placed on a table, with several points drawn on each face. The sum of the number of points on opposite faces is 13. Jingjing sees that the sum of the points on the front, left, and top faces is 16, while Qingqing sees that the sum of the points on the top, right, and back faces is 24. What is the number of points on the face touching the table? $\\qquad$ .",
"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": "Task B-2.4. Let $f(x)=x^{2}+b x+c, b, c \\in \\mathbb{R}$. If $f(0)+f(1)=\\frac{1}{2}$, calculate $f\\left(\\frac{1}{2}\\right)$.",
"role": "user"
}
] |
{
"ground_truth": "0",
"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": "Compute \\[\\left\\lfloor \\dfrac{2007!+2004!}{2006!+2005!}\\right\\rfloor.\\] (Note that $\\lfloor x \\rfloor$ denotes the greatest integer less than or equal to $x$.)",
"role": "user"
}
] |
{
"ground_truth": "2006",
"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 proportion of potassium nitrate, sulfur, and charcoal in the formulation of ancient Chinese \"black powder\" is $15: 2: 3$. Given 50 kilograms of charcoal, to prepare \"black powder\" weighing 1000 kilograms, how many more kilograms of charcoal are needed?",
"role": "user"
}
] |
{
"ground_truth": "100",
"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 2. Find the third-order derivative of the function $y=x^{2}+3 x+2$.",
"role": "user"
}
] |
{
"ground_truth": "0",
"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": "What is the largest possible distance between two points, one on the sphere of radius 19 with center $(-2, -10, 5)$ and the other on the sphere of radius 87 with center $(12, 8, -16)$?",
"role": "user"
}
] |
{
"ground_truth": "137",
"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": "Let $\\text{o}$ be an odd whole number and let $\\text{n}$ be any whole number. Which of the following statements about the whole number $(\\text{o}^2+\\text{no})$ is always true?\n$\\text{(A)}\\ \\text{it is always odd} \\qquad \\text{(B)}\\ \\text{it is always even}$\n$\\text{(C)}\\ \\text{it is even only if n is even} \\qquad \\text{(D)}\\ \\text{it is odd only if n is odd}$\n$\\text{(E)}\\ \\text{it is odd only if n is even}$",
"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": "Example 1-8: There are 5 Japanese books, 7 English books, and 10 Chinese books. If two books of different languages are taken, how many possibilities are there? If two books of the same language are taken, how many schemes are there? If two books are taken regardless of the language, how many possibilities are there?",
"role": "user"
}
] |
{
"ground_truth": "231",
"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. On each side of a cube, a natural number is written. At each vertex (corner) of the cube, the product of the three numbers written on the sides that form the vertex (corner) is written. The sum of the eight thus obtained products is 385. Determine the sum of the numbers written on the sides of the cube.",
"role": "user"
}
] |
{
"ground_truth": "23",
"style": "rule"
}
|
{
"index": -1,
"split": "default"
}
|
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