prompt
listlengths 2
2
| answer
stringlengths 3
48
| src
stringclasses 4
values | messages
listlengths 2
2
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[
{
"content": [
{
"text": "A user will ask you to solve a task. You should first draft your thinking process (inner monologue) until you have derived the final answer. Afterwards, write a self-contained summary of your thoughts (i.e. your summary should be succinct but contain all the critical steps you needed to reach the conclusion). You should use Markdown and Latex to format your response. Write both your thoughts and summary in the same language as the task posed by the user.\n\nYour thinking process must follow the template below:\n<think>\nYour thoughts or/and draft, like working through an exercise on scratch paper. Be as casual and as long as you want until you are confident to generate a correct answer.\n</think>\n\nHere, provide a concise summary that reflects your reasoning and presents a clear final answer to the user.\n\n\n\nYou will be given a problem. Please reason step by step, and put your final answer within \\boxed{}.",
"type": "text"
}
],
"role": "system"
},
{
"content": [
{
"text": "A circle is inscribed in quadrilateral $ABCD$ , tangent to $\\overline{AB}$ at $P$ and to $\\overline{CD}$ at $Q$ . Given that $AP=19$ , $PB=26$ , $CQ=37$ , and $QD=23$ , find the square of the radius of the circle.",
"type": "text"
}
],
"role": "user"
}
] |
$647$
|
di-zhang-fdu/AIME_1983_2024
|
[
{
"content": [
{
"path": "",
"text": "A user will ask you to solve a task. You should first draft your thinking process (inner monologue) until you have derived the final answer. Afterwards, write a self-contained summary of your thoughts (i.e. your summary should be succinct but contain all the critical steps you needed to reach the conclusion). You should use Markdown and Latex to format your response. Write both your thoughts and summary in the same language as the task posed by the user.\n\nYour thinking process must follow the template below:\n<think>\nYour thoughts or/and draft, like working through an exercise on scratch paper. Be as casual and as long as you want until you are confident to generate a correct answer.\n</think>\n\nHere, provide a concise summary that reflects your reasoning and presents a clear final answer to the user.\n\n\n\nYou will be given a problem. Please reason step by step, and put your final answer within \\boxed{}.",
"type": "text",
"url": null
}
],
"role": "system"
},
{
"content": [
{
"path": "",
"text": "A circle is inscribed in quadrilateral $ABCD$ , tangent to $\\overline{AB}$ at $P$ and to $\\overline{CD}$ at $Q$ . Given that $AP=19$ , $PB=26$ , $CQ=37$ , and $QD=23$ , find the square of the radius of the circle.",
"type": "text",
"url": null
}
],
"role": "user"
}
] |
[
{
"content": [
{
"text": "A user will ask you to solve a task. You should first draft your thinking process (inner monologue) until you have derived the final answer. Afterwards, write a self-contained summary of your thoughts (i.e. your summary should be succinct but contain all the critical steps you needed to reach the conclusion). You should use Markdown and Latex to format your response. Write both your thoughts and summary in the same language as the task posed by the user.\n\nYour thinking process must follow the template below:\n<think>\nYour thoughts or/and draft, like working through an exercise on scratch paper. Be as casual and as long as you want until you are confident to generate a correct answer.\n</think>\n\nHere, provide a concise summary that reflects your reasoning and presents a clear final answer to the user.\n\n",
"type": "text"
}
],
"role": "system"
},
{
"content": [
{
"text": "You will be given a problem. Please reason step by step, and put your final answer within \\boxed{}:\nFor some integer $m$ , the polynomial $x^3 - 2011x + m$ has the three integer roots $a$ , $b$ , and $c$ . Find $|a| + |b| + |c|$ .",
"type": "text"
}
],
"role": "user"
}
] |
$98$
|
di-zhang-fdu/AIME_1983_2024
|
[
{
"content": [
{
"path": "",
"text": "A user will ask you to solve a task. You should first draft your thinking process (inner monologue) until you have derived the final answer. Afterwards, write a self-contained summary of your thoughts (i.e. your summary should be succinct but contain all the critical steps you needed to reach the conclusion). You should use Markdown and Latex to format your response. Write both your thoughts and summary in the same language as the task posed by the user.\n\nYour thinking process must follow the template below:\n<think>\nYour thoughts or/and draft, like working through an exercise on scratch paper. Be as casual and as long as you want until you are confident to generate a correct answer.\n</think>\n\nHere, provide a concise summary that reflects your reasoning and presents a clear final answer to the user.\n\n",
"type": "text",
"url": null
}
],
"role": "system"
},
{
"content": [
{
"path": "",
"text": "You will be given a problem. Please reason step by step, and put your final answer within \\boxed{}:\nFor some integer $m$ , the polynomial $x^3 - 2011x + m$ has the three integer roots $a$ , $b$ , and $c$ . Find $|a| + |b| + |c|$ .",
"type": "text",
"url": null
}
],
"role": "user"
}
] |
[
{
"content": [
{
"text": "A user will ask you to solve a task. You should first draft your thinking process (inner monologue) until you have derived the final answer. Afterwards, write a self-contained summary of your thoughts (i.e. your summary should be succinct but contain all the critical steps you needed to reach the conclusion). You should use Markdown and Latex to format your response. Write both your thoughts and summary in the same language as the task posed by the user.\n\nYour thinking process must follow the template below:\n<think>\nYour thoughts or/and draft, like working through an exercise on scratch paper. Be as casual and as long as you want until you are confident to generate a correct answer.\n</think>\n\nHere, provide a concise summary that reflects your reasoning and presents a clear final answer to the user.\n\n\n\nYou will be given a problem. Please reason step by step, and put your final answer within \\boxed{}.",
"type": "text"
}
],
"role": "system"
},
{
"content": [
{
"text": "Let $S^{}_{}$ be a subset of $\\{1,2,3^{}_{},\\ldots,1989\\}$ such that no two members of $S^{}_{}$ differ by $4^{}_{}$ or $7^{}_{}$ . What is the largest number of elements $S^{}_{}$ can have?",
"type": "text"
}
],
"role": "user"
}
] |
$905$
|
di-zhang-fdu/AIME_1983_2024
|
[
{
"content": [
{
"path": "",
"text": "A user will ask you to solve a task. You should first draft your thinking process (inner monologue) until you have derived the final answer. Afterwards, write a self-contained summary of your thoughts (i.e. your summary should be succinct but contain all the critical steps you needed to reach the conclusion). You should use Markdown and Latex to format your response. Write both your thoughts and summary in the same language as the task posed by the user.\n\nYour thinking process must follow the template below:\n<think>\nYour thoughts or/and draft, like working through an exercise on scratch paper. Be as casual and as long as you want until you are confident to generate a correct answer.\n</think>\n\nHere, provide a concise summary that reflects your reasoning and presents a clear final answer to the user.\n\n\n\nYou will be given a problem. Please reason step by step, and put your final answer within \\boxed{}.",
"type": "text",
"url": null
}
],
"role": "system"
},
{
"content": [
{
"path": "",
"text": "Let $S^{}_{}$ be a subset of $\\{1,2,3^{}_{},\\ldots,1989\\}$ such that no two members of $S^{}_{}$ differ by $4^{}_{}$ or $7^{}_{}$ . What is the largest number of elements $S^{}_{}$ can have?",
"type": "text",
"url": null
}
],
"role": "user"
}
] |
[
{
"content": [
{
"text": "A user will ask you to solve a task. You should first draft your thinking process (inner monologue) until you have derived the final answer. Afterwards, write a self-contained summary of your thoughts (i.e. your summary should be succinct but contain all the critical steps you needed to reach the conclusion). You should use Markdown and Latex to format your response. Write both your thoughts and summary in the same language as the task posed by the user.\n\nYour thinking process must follow the template below:\n<think>\nYour thoughts or/and draft, like working through an exercise on scratch paper. Be as casual and as long as you want until you are confident to generate a correct answer.\n</think>\n\nHere, provide a concise summary that reflects your reasoning and presents a clear final answer to the user.\n\n",
"type": "text"
}
],
"role": "system"
},
{
"content": [
{
"text": "You will be given a problem. Please reason step by step, and put your final answer within \\boxed{}:\nWhen a certain biased coin is flipped five times, the probability of getting heads exactly once is not equal to $0$ and is the same as that of getting heads exactly twice. Let $\\frac ij^{}_{}$ , in lowest terms, be the probability that the coin comes up heads in exactly $3$ out of $5$ flips. Find $i+j^{}_{}$ .",
"type": "text"
}
],
"role": "user"
}
] |
$283$
|
di-zhang-fdu/AIME_1983_2024
|
[
{
"content": [
{
"path": "",
"text": "A user will ask you to solve a task. You should first draft your thinking process (inner monologue) until you have derived the final answer. Afterwards, write a self-contained summary of your thoughts (i.e. your summary should be succinct but contain all the critical steps you needed to reach the conclusion). You should use Markdown and Latex to format your response. Write both your thoughts and summary in the same language as the task posed by the user.\n\nYour thinking process must follow the template below:\n<think>\nYour thoughts or/and draft, like working through an exercise on scratch paper. Be as casual and as long as you want until you are confident to generate a correct answer.\n</think>\n\nHere, provide a concise summary that reflects your reasoning and presents a clear final answer to the user.\n\n",
"type": "text",
"url": null
}
],
"role": "system"
},
{
"content": [
{
"path": "",
"text": "You will be given a problem. Please reason step by step, and put your final answer within \\boxed{}:\nWhen a certain biased coin is flipped five times, the probability of getting heads exactly once is not equal to $0$ and is the same as that of getting heads exactly twice. Let $\\frac ij^{}_{}$ , in lowest terms, be the probability that the coin comes up heads in exactly $3$ out of $5$ flips. Find $i+j^{}_{}$ .",
"type": "text",
"url": null
}
],
"role": "user"
}
] |
[
{
"content": [
{
"text": "A user will ask you to solve a task. You should first draft your thinking process (inner monologue) until you have derived the final answer. Afterwards, write a self-contained summary of your thoughts (i.e. your summary should be succinct but contain all the critical steps you needed to reach the conclusion). You should use Markdown and Latex to format your response. Write both your thoughts and summary in the same language as the task posed by the user.\n\nYour thinking process must follow the template below:\n<think>\nYour thoughts or/and draft, like working through an exercise on scratch paper. Be as casual and as long as you want until you are confident to generate a correct answer.\n</think>\n\nHere, provide a concise summary that reflects your reasoning and presents a clear final answer to the user.\n\n",
"type": "text"
}
],
"role": "system"
},
{
"content": [
{
"text": "You will be given a problem. Please reason step by step, and put your final answer within \\boxed{}:\nA plane $\\mathcal{P}$ intersects a rectangular prism at a hexagon which has side lengths $45,66,63,55,54$, and 77, in that order. Compute the distance from the center of the rectangular prism to $\\mathcal{P}$.",
"type": "text"
}
],
"role": "user"
}
] |
$\sqrt{\frac{95}{24}}$
|
MathArena/hmmt_feb_2025
|
[
{
"content": [
{
"path": "",
"text": "A user will ask you to solve a task. You should first draft your thinking process (inner monologue) until you have derived the final answer. Afterwards, write a self-contained summary of your thoughts (i.e. your summary should be succinct but contain all the critical steps you needed to reach the conclusion). You should use Markdown and Latex to format your response. Write both your thoughts and summary in the same language as the task posed by the user.\n\nYour thinking process must follow the template below:\n<think>\nYour thoughts or/and draft, like working through an exercise on scratch paper. Be as casual and as long as you want until you are confident to generate a correct answer.\n</think>\n\nHere, provide a concise summary that reflects your reasoning and presents a clear final answer to the user.\n\n",
"type": "text",
"url": null
}
],
"role": "system"
},
{
"content": [
{
"path": "",
"text": "You will be given a problem. Please reason step by step, and put your final answer within \\boxed{}:\nA plane $\\mathcal{P}$ intersects a rectangular prism at a hexagon which has side lengths $45,66,63,55,54$, and 77, in that order. Compute the distance from the center of the rectangular prism to $\\mathcal{P}$.",
"type": "text",
"url": null
}
],
"role": "user"
}
] |
[
{
"content": [
{
"text": "A user will ask you to solve a task. You should first draft your thinking process (inner monologue) until you have derived the final answer. Afterwards, write a self-contained summary of your thoughts (i.e. your summary should be succinct but contain all the critical steps you needed to reach the conclusion). You should use Markdown and Latex to format your response. Write both your thoughts and summary in the same language as the task posed by the user.\n\nYour thinking process must follow the template below:\n<think>\nYour thoughts or/and draft, like working through an exercise on scratch paper. Be as casual and as long as you want until you are confident to generate a correct answer.\n</think>\n\nHere, provide a concise summary that reflects your reasoning and presents a clear final answer to the user.\n\n",
"type": "text"
}
],
"role": "system"
},
{
"content": [
{
"text": "You will be given a problem. Please reason step by step, and put your final answer within \\boxed{}:\nFind the number of second-degree polynomials $f(x)$ with integer coefficients and integer zeros for which $f(0)=2010$ .",
"type": "text"
}
],
"role": "user"
}
] |
$163$
|
di-zhang-fdu/AIME_1983_2024
|
[
{
"content": [
{
"path": "",
"text": "A user will ask you to solve a task. You should first draft your thinking process (inner monologue) until you have derived the final answer. Afterwards, write a self-contained summary of your thoughts (i.e. your summary should be succinct but contain all the critical steps you needed to reach the conclusion). You should use Markdown and Latex to format your response. Write both your thoughts and summary in the same language as the task posed by the user.\n\nYour thinking process must follow the template below:\n<think>\nYour thoughts or/and draft, like working through an exercise on scratch paper. Be as casual and as long as you want until you are confident to generate a correct answer.\n</think>\n\nHere, provide a concise summary that reflects your reasoning and presents a clear final answer to the user.\n\n",
"type": "text",
"url": null
}
],
"role": "system"
},
{
"content": [
{
"path": "",
"text": "You will be given a problem. Please reason step by step, and put your final answer within \\boxed{}:\nFind the number of second-degree polynomials $f(x)$ with integer coefficients and integer zeros for which $f(0)=2010$ .",
"type": "text",
"url": null
}
],
"role": "user"
}
] |
[
{
"content": [
{
"text": "A user will ask you to solve a task. You should first draft your thinking process (inner monologue) until you have derived the final answer. Afterwards, write a self-contained summary of your thoughts (i.e. your summary should be succinct but contain all the critical steps you needed to reach the conclusion). You should use Markdown and Latex to format your response. Write both your thoughts and summary in the same language as the task posed by the user.\n\nYour thinking process must follow the template below:\n<think>\nYour thoughts or/and draft, like working through an exercise on scratch paper. Be as casual and as long as you want until you are confident to generate a correct answer.\n</think>\n\nHere, provide a concise summary that reflects your reasoning and presents a clear final answer to the user.\n\n",
"type": "text"
}
],
"role": "system"
},
{
"content": [
{
"text": "You will be given a problem. Please reason step by step, and put your final answer within \\boxed{}:\nSeven teams play a soccer tournament in which each team plays every other team exactly once. No ties occur, each team has a $50\\%$ chance of winning each game it plays, and the outcomes of the games are independent. In each game, the winner is awarded a point and the loser gets 0 points. The total points are accumulated to decide the ranks of the teams. In the first game of the tournament, team $A$ beats team $B.$ The probability that team $A$ finishes with more points than team $B$ is $m/n,$ where $m$ and $n$ are relatively prime positive integers. Find $m+n.$",
"type": "text"
}
],
"role": "user"
}
] |
$831$
|
di-zhang-fdu/AIME_1983_2024
|
[
{
"content": [
{
"path": "",
"text": "A user will ask you to solve a task. You should first draft your thinking process (inner monologue) until you have derived the final answer. Afterwards, write a self-contained summary of your thoughts (i.e. your summary should be succinct but contain all the critical steps you needed to reach the conclusion). You should use Markdown and Latex to format your response. Write both your thoughts and summary in the same language as the task posed by the user.\n\nYour thinking process must follow the template below:\n<think>\nYour thoughts or/and draft, like working through an exercise on scratch paper. Be as casual and as long as you want until you are confident to generate a correct answer.\n</think>\n\nHere, provide a concise summary that reflects your reasoning and presents a clear final answer to the user.\n\n",
"type": "text",
"url": null
}
],
"role": "system"
},
{
"content": [
{
"path": "",
"text": "You will be given a problem. Please reason step by step, and put your final answer within \\boxed{}:\nSeven teams play a soccer tournament in which each team plays every other team exactly once. No ties occur, each team has a $50\\%$ chance of winning each game it plays, and the outcomes of the games are independent. In each game, the winner is awarded a point and the loser gets 0 points. The total points are accumulated to decide the ranks of the teams. In the first game of the tournament, team $A$ beats team $B.$ The probability that team $A$ finishes with more points than team $B$ is $m/n,$ where $m$ and $n$ are relatively prime positive integers. Find $m+n.$",
"type": "text",
"url": null
}
],
"role": "user"
}
] |
[
{
"content": [
{
"text": "A user will ask you to solve a task. You should first draft your thinking process (inner monologue) until you have derived the final answer. Afterwards, write a self-contained summary of your thoughts (i.e. your summary should be succinct but contain all the critical steps you needed to reach the conclusion). You should use Markdown and Latex to format your response. Write both your thoughts and summary in the same language as the task posed by the user.\n\nYour thinking process must follow the template below:\n<think>\nYour thoughts or/and draft, like working through an exercise on scratch paper. Be as casual and as long as you want until you are confident to generate a correct answer.\n</think>\n\nHere, provide a concise summary that reflects your reasoning and presents a clear final answer to the user.\n\n\n\nYou will be given a problem. Please reason step by step, and put your final answer within \\boxed{}.",
"type": "text"
}
],
"role": "system"
},
{
"content": [
{
"text": "For each permutation $a_1,a_2,a_3,\\cdots,a_{10}$ of the integers $1,2,3,\\cdots,10$ , form the sum $|a_1-a_2|+|a_3-a_4|+|a_5-a_6|+|a_7-a_8|+|a_9-a_{10}|$ . The average value of all such sums can be written in the form $\\dfrac{p}{q}$ , where $p$ and $q$ are relatively prime positive integers. Find $p+q$ .",
"type": "text"
}
],
"role": "user"
}
] |
$58$
|
di-zhang-fdu/AIME_1983_2024
|
[
{
"content": [
{
"path": "",
"text": "A user will ask you to solve a task. You should first draft your thinking process (inner monologue) until you have derived the final answer. Afterwards, write a self-contained summary of your thoughts (i.e. your summary should be succinct but contain all the critical steps you needed to reach the conclusion). You should use Markdown and Latex to format your response. Write both your thoughts and summary in the same language as the task posed by the user.\n\nYour thinking process must follow the template below:\n<think>\nYour thoughts or/and draft, like working through an exercise on scratch paper. Be as casual and as long as you want until you are confident to generate a correct answer.\n</think>\n\nHere, provide a concise summary that reflects your reasoning and presents a clear final answer to the user.\n\n\n\nYou will be given a problem. Please reason step by step, and put your final answer within \\boxed{}.",
"type": "text",
"url": null
}
],
"role": "system"
},
{
"content": [
{
"path": "",
"text": "For each permutation $a_1,a_2,a_3,\\cdots,a_{10}$ of the integers $1,2,3,\\cdots,10$ , form the sum $|a_1-a_2|+|a_3-a_4|+|a_5-a_6|+|a_7-a_8|+|a_9-a_{10}|$ . The average value of all such sums can be written in the form $\\dfrac{p}{q}$ , where $p$ and $q$ are relatively prime positive integers. Find $p+q$ .",
"type": "text",
"url": null
}
],
"role": "user"
}
] |
[
{
"content": [
{
"text": "A user will ask you to solve a task. You should first draft your thinking process (inner monologue) until you have derived the final answer. Afterwards, write a self-contained summary of your thoughts (i.e. your summary should be succinct but contain all the critical steps you needed to reach the conclusion). You should use Markdown and Latex to format your response. Write both your thoughts and summary in the same language as the task posed by the user.\n\nYour thinking process must follow the template below:\n<think>\nYour thoughts or/and draft, like working through an exercise on scratch paper. Be as casual and as long as you want until you are confident to generate a correct answer.\n</think>\n\nHere, provide a concise summary that reflects your reasoning and presents a clear final answer to the user.\n\n",
"type": "text"
}
],
"role": "system"
},
{
"content": [
{
"text": "You will be given a problem. Please reason step by step, and put your final answer within \\boxed{}:\nLet $a, b$, and $c$ be pairwise distinct complex numbers such that\n$$\na^{2}=b+6, \\quad b^{2}=c+6, \\quad \\text { and } \\quad c^{2}=a+6\n$$\n\nCompute the two possible values of $a+b+c$. In your answer, list the two values in a comma-separated list of two valid \\LaTeX expressions.",
"type": "text"
}
],
"role": "user"
}
] |
$\frac{-1+\sqrt{17}}{2}, \frac{-1-\sqrt{17}}{2}$
|
MathArena/hmmt_feb_2025
|
[
{
"content": [
{
"path": "",
"text": "A user will ask you to solve a task. You should first draft your thinking process (inner monologue) until you have derived the final answer. Afterwards, write a self-contained summary of your thoughts (i.e. your summary should be succinct but contain all the critical steps you needed to reach the conclusion). You should use Markdown and Latex to format your response. Write both your thoughts and summary in the same language as the task posed by the user.\n\nYour thinking process must follow the template below:\n<think>\nYour thoughts or/and draft, like working through an exercise on scratch paper. Be as casual and as long as you want until you are confident to generate a correct answer.\n</think>\n\nHere, provide a concise summary that reflects your reasoning and presents a clear final answer to the user.\n\n",
"type": "text",
"url": null
}
],
"role": "system"
},
{
"content": [
{
"path": "",
"text": "You will be given a problem. Please reason step by step, and put your final answer within \\boxed{}:\nLet $a, b$, and $c$ be pairwise distinct complex numbers such that\n$$\na^{2}=b+6, \\quad b^{2}=c+6, \\quad \\text { and } \\quad c^{2}=a+6\n$$\n\nCompute the two possible values of $a+b+c$. In your answer, list the two values in a comma-separated list of two valid \\LaTeX expressions.",
"type": "text",
"url": null
}
],
"role": "user"
}
] |
[
{
"content": [
{
"text": "A user will ask you to solve a task. You should first draft your thinking process (inner monologue) until you have derived the final answer. Afterwards, write a self-contained summary of your thoughts (i.e. your summary should be succinct but contain all the critical steps you needed to reach the conclusion). You should use Markdown and Latex to format your response. Write both your thoughts and summary in the same language as the task posed by the user.\n\nYour thinking process must follow the template below:\n<think>\nYour thoughts or/and draft, like working through an exercise on scratch paper. Be as casual and as long as you want until you are confident to generate a correct answer.\n</think>\n\nHere, provide a concise summary that reflects your reasoning and presents a clear final answer to the user.\n\n",
"type": "text"
}
],
"role": "system"
},
{
"content": [
{
"text": "You will be given a problem. Please reason step by step, and put your final answer within \\boxed{}:\nThe sum of the areas of all triangles whose vertices are also vertices of a 1 by 1 by 1 cube is $m + \\sqrt{n} + \\sqrt{p},$ where $m, n,$ and $p$ are integers. Find $m + n + p.$",
"type": "text"
}
],
"role": "user"
}
] |
$348$
|
di-zhang-fdu/AIME_1983_2024
|
[
{
"content": [
{
"path": "",
"text": "A user will ask you to solve a task. You should first draft your thinking process (inner monologue) until you have derived the final answer. Afterwards, write a self-contained summary of your thoughts (i.e. your summary should be succinct but contain all the critical steps you needed to reach the conclusion). You should use Markdown and Latex to format your response. Write both your thoughts and summary in the same language as the task posed by the user.\n\nYour thinking process must follow the template below:\n<think>\nYour thoughts or/and draft, like working through an exercise on scratch paper. Be as casual and as long as you want until you are confident to generate a correct answer.\n</think>\n\nHere, provide a concise summary that reflects your reasoning and presents a clear final answer to the user.\n\n",
"type": "text",
"url": null
}
],
"role": "system"
},
{
"content": [
{
"path": "",
"text": "You will be given a problem. Please reason step by step, and put your final answer within \\boxed{}:\nThe sum of the areas of all triangles whose vertices are also vertices of a 1 by 1 by 1 cube is $m + \\sqrt{n} + \\sqrt{p},$ where $m, n,$ and $p$ are integers. Find $m + n + p.$",
"type": "text",
"url": null
}
],
"role": "user"
}
] |
[
{
"content": [
{
"text": "A user will ask you to solve a task. You should first draft your thinking process (inner monologue) until you have derived the final answer. Afterwards, write a self-contained summary of your thoughts (i.e. your summary should be succinct but contain all the critical steps you needed to reach the conclusion). You should use Markdown and Latex to format your response. Write both your thoughts and summary in the same language as the task posed by the user.\n\nYour thinking process must follow the template below:\n<think>\nYour thoughts or/and draft, like working through an exercise on scratch paper. Be as casual and as long as you want until you are confident to generate a correct answer.\n</think>\n\nHere, provide a concise summary that reflects your reasoning and presents a clear final answer to the user.\n\n",
"type": "text"
}
],
"role": "system"
},
{
"content": [
{
"text": "You will be given a problem. Please reason step by step, and put your final answer within \\boxed{}:\nCircles of radius $3$ and $6$ are externally tangent to each other and are internally tangent to a circle of radius $9$ . The circle of radius $9$ has a chord that is a common external tangent of the other two circles. Find the square of the length of this chord.",
"type": "text"
}
],
"role": "user"
}
] |
$224$
|
di-zhang-fdu/AIME_1983_2024
|
[
{
"content": [
{
"path": "",
"text": "A user will ask you to solve a task. You should first draft your thinking process (inner monologue) until you have derived the final answer. Afterwards, write a self-contained summary of your thoughts (i.e. your summary should be succinct but contain all the critical steps you needed to reach the conclusion). You should use Markdown and Latex to format your response. Write both your thoughts and summary in the same language as the task posed by the user.\n\nYour thinking process must follow the template below:\n<think>\nYour thoughts or/and draft, like working through an exercise on scratch paper. Be as casual and as long as you want until you are confident to generate a correct answer.\n</think>\n\nHere, provide a concise summary that reflects your reasoning and presents a clear final answer to the user.\n\n",
"type": "text",
"url": null
}
],
"role": "system"
},
{
"content": [
{
"path": "",
"text": "You will be given a problem. Please reason step by step, and put your final answer within \\boxed{}:\nCircles of radius $3$ and $6$ are externally tangent to each other and are internally tangent to a circle of radius $9$ . The circle of radius $9$ has a chord that is a common external tangent of the other two circles. Find the square of the length of this chord.",
"type": "text",
"url": null
}
],
"role": "user"
}
] |
[
{
"content": [
{
"text": "A user will ask you to solve a task. You should first draft your thinking process (inner monologue) until you have derived the final answer. Afterwards, write a self-contained summary of your thoughts (i.e. your summary should be succinct but contain all the critical steps you needed to reach the conclusion). You should use Markdown and Latex to format your response. Write both your thoughts and summary in the same language as the task posed by the user.\n\nYour thinking process must follow the template below:\n<think>\nYour thoughts or/and draft, like working through an exercise on scratch paper. Be as casual and as long as you want until you are confident to generate a correct answer.\n</think>\n\nHere, provide a concise summary that reflects your reasoning and presents a clear final answer to the user.\n\n",
"type": "text"
}
],
"role": "system"
},
{
"content": [
{
"text": "You will be given a problem. Please reason step by step, and put your final answer within \\boxed{}:\nA chord of a circle is perpendicular to a radius at the midpoint of the radius. The ratio of the area of the larger of the two regions into which the chord divides the circle to the smaller can be expressed in the form $\\frac{a\\pi+b\\sqrt{c}}{d\\pi-e\\sqrt{f}},$ where $a, b, c, d, e,$ and $f$ are positive integers, $a$ and $e$ are relatively prime, and neither $c$ nor $f$ is divisible by the square of any prime. Find the remainder when the product $abcdef$ is divided by 1000.",
"type": "text"
}
],
"role": "user"
}
] |
$592$
|
di-zhang-fdu/AIME_1983_2024
|
[
{
"content": [
{
"path": "",
"text": "A user will ask you to solve a task. You should first draft your thinking process (inner monologue) until you have derived the final answer. Afterwards, write a self-contained summary of your thoughts (i.e. your summary should be succinct but contain all the critical steps you needed to reach the conclusion). You should use Markdown and Latex to format your response. Write both your thoughts and summary in the same language as the task posed by the user.\n\nYour thinking process must follow the template below:\n<think>\nYour thoughts or/and draft, like working through an exercise on scratch paper. Be as casual and as long as you want until you are confident to generate a correct answer.\n</think>\n\nHere, provide a concise summary that reflects your reasoning and presents a clear final answer to the user.\n\n",
"type": "text",
"url": null
}
],
"role": "system"
},
{
"content": [
{
"path": "",
"text": "You will be given a problem. Please reason step by step, and put your final answer within \\boxed{}:\nA chord of a circle is perpendicular to a radius at the midpoint of the radius. The ratio of the area of the larger of the two regions into which the chord divides the circle to the smaller can be expressed in the form $\\frac{a\\pi+b\\sqrt{c}}{d\\pi-e\\sqrt{f}},$ where $a, b, c, d, e,$ and $f$ are positive integers, $a$ and $e$ are relatively prime, and neither $c$ nor $f$ is divisible by the square of any prime. Find the remainder when the product $abcdef$ is divided by 1000.",
"type": "text",
"url": null
}
],
"role": "user"
}
] |
[
{
"content": [
{
"text": "A user will ask you to solve a task. You should first draft your thinking process (inner monologue) until you have derived the final answer. Afterwards, write a self-contained summary of your thoughts (i.e. your summary should be succinct but contain all the critical steps you needed to reach the conclusion). You should use Markdown and Latex to format your response. Write both your thoughts and summary in the same language as the task posed by the user.\n\nYour thinking process must follow the template below:\n<think>\nYour thoughts or/and draft, like working through an exercise on scratch paper. Be as casual and as long as you want until you are confident to generate a correct answer.\n</think>\n\nHere, provide a concise summary that reflects your reasoning and presents a clear final answer to the user.\n\n",
"type": "text"
}
],
"role": "system"
},
{
"content": [
{
"text": "You will be given a problem. Please reason step by step, and put your final answer within \\boxed{}:\nFind the area of the region enclosed by the graph of $|x-60|+|y|=\\left|\\frac{x}{4}\\right|.$",
"type": "text"
}
],
"role": "user"
}
] |
$480$
|
di-zhang-fdu/AIME_1983_2024
|
[
{
"content": [
{
"path": "",
"text": "A user will ask you to solve a task. You should first draft your thinking process (inner monologue) until you have derived the final answer. Afterwards, write a self-contained summary of your thoughts (i.e. your summary should be succinct but contain all the critical steps you needed to reach the conclusion). You should use Markdown and Latex to format your response. Write both your thoughts and summary in the same language as the task posed by the user.\n\nYour thinking process must follow the template below:\n<think>\nYour thoughts or/and draft, like working through an exercise on scratch paper. Be as casual and as long as you want until you are confident to generate a correct answer.\n</think>\n\nHere, provide a concise summary that reflects your reasoning and presents a clear final answer to the user.\n\n",
"type": "text",
"url": null
}
],
"role": "system"
},
{
"content": [
{
"path": "",
"text": "You will be given a problem. Please reason step by step, and put your final answer within \\boxed{}:\nFind the area of the region enclosed by the graph of $|x-60|+|y|=\\left|\\frac{x}{4}\\right|.$",
"type": "text",
"url": null
}
],
"role": "user"
}
] |
[
{
"content": [
{
"text": "A user will ask you to solve a task. You should first draft your thinking process (inner monologue) until you have derived the final answer. Afterwards, write a self-contained summary of your thoughts (i.e. your summary should be succinct but contain all the critical steps you needed to reach the conclusion). You should use Markdown and Latex to format your response. Write both your thoughts and summary in the same language as the task posed by the user.\n\nYour thinking process must follow the template below:\n<think>\nYour thoughts or/and draft, like working through an exercise on scratch paper. Be as casual and as long as you want until you are confident to generate a correct answer.\n</think>\n\nHere, provide a concise summary that reflects your reasoning and presents a clear final answer to the user.\n\n",
"type": "text"
}
],
"role": "system"
},
{
"content": [
{
"text": "You will be given a problem. Please reason step by step, and put your final answer within \\boxed{}:\nSuppose $x$ is in the interval $[0,\\pi/2]$ and $\\log_{24 \\sin x} (24 \\cos x) = \\frac{3}{2}$ . Find $24 \\cot^2 x$ .",
"type": "text"
}
],
"role": "user"
}
] |
$192$
|
di-zhang-fdu/AIME_1983_2024
|
[
{
"content": [
{
"path": "",
"text": "A user will ask you to solve a task. You should first draft your thinking process (inner monologue) until you have derived the final answer. Afterwards, write a self-contained summary of your thoughts (i.e. your summary should be succinct but contain all the critical steps you needed to reach the conclusion). You should use Markdown and Latex to format your response. Write both your thoughts and summary in the same language as the task posed by the user.\n\nYour thinking process must follow the template below:\n<think>\nYour thoughts or/and draft, like working through an exercise on scratch paper. Be as casual and as long as you want until you are confident to generate a correct answer.\n</think>\n\nHere, provide a concise summary that reflects your reasoning and presents a clear final answer to the user.\n\n",
"type": "text",
"url": null
}
],
"role": "system"
},
{
"content": [
{
"path": "",
"text": "You will be given a problem. Please reason step by step, and put your final answer within \\boxed{}:\nSuppose $x$ is in the interval $[0,\\pi/2]$ and $\\log_{24 \\sin x} (24 \\cos x) = \\frac{3}{2}$ . Find $24 \\cot^2 x$ .",
"type": "text",
"url": null
}
],
"role": "user"
}
] |
[
{
"content": [
{
"text": "A user will ask you to solve a task. You should first draft your thinking process (inner monologue) until you have derived the final answer. Afterwards, write a self-contained summary of your thoughts (i.e. your summary should be succinct but contain all the critical steps you needed to reach the conclusion). You should use Markdown and Latex to format your response. Write both your thoughts and summary in the same language as the task posed by the user.\n\nYour thinking process must follow the template below:\n<think>\nYour thoughts or/and draft, like working through an exercise on scratch paper. Be as casual and as long as you want until you are confident to generate a correct answer.\n</think>\n\nHere, provide a concise summary that reflects your reasoning and presents a clear final answer to the user.\n\n\n\nYou will be given a problem. Please reason step by step, and put your final answer within \\boxed{}.",
"type": "text"
}
],
"role": "system"
},
{
"content": [
{
"text": "If $\\{a_1,a_2,a_3,\\ldots,a_n\\}$ is a set of real numbers , indexed so that $a_1 < a_2 < a_3 < \\cdots < a_n,$ its complex power sum is defined to be $a_1i + a_2i^2+ a_3i^3 + \\cdots + a_ni^n,$ where $i^2 = - 1.$ Let $S_n$ be the sum of the complex power sums of all nonempty subsets of $\\{1,2,\\ldots,n\\}.$ Given that $S_8 = - 176 - 64i$ and $S_9 = p + qi,$ where $p$ and $q$ are integers, find $|p| + |q|.$",
"type": "text"
}
],
"role": "user"
}
] |
$368$
|
di-zhang-fdu/AIME_1983_2024
|
[
{
"content": [
{
"path": "",
"text": "A user will ask you to solve a task. You should first draft your thinking process (inner monologue) until you have derived the final answer. Afterwards, write a self-contained summary of your thoughts (i.e. your summary should be succinct but contain all the critical steps you needed to reach the conclusion). You should use Markdown and Latex to format your response. Write both your thoughts and summary in the same language as the task posed by the user.\n\nYour thinking process must follow the template below:\n<think>\nYour thoughts or/and draft, like working through an exercise on scratch paper. Be as casual and as long as you want until you are confident to generate a correct answer.\n</think>\n\nHere, provide a concise summary that reflects your reasoning and presents a clear final answer to the user.\n\n\n\nYou will be given a problem. Please reason step by step, and put your final answer within \\boxed{}.",
"type": "text",
"url": null
}
],
"role": "system"
},
{
"content": [
{
"path": "",
"text": "If $\\{a_1,a_2,a_3,\\ldots,a_n\\}$ is a set of real numbers , indexed so that $a_1 < a_2 < a_3 < \\cdots < a_n,$ its complex power sum is defined to be $a_1i + a_2i^2+ a_3i^3 + \\cdots + a_ni^n,$ where $i^2 = - 1.$ Let $S_n$ be the sum of the complex power sums of all nonempty subsets of $\\{1,2,\\ldots,n\\}.$ Given that $S_8 = - 176 - 64i$ and $S_9 = p + qi,$ where $p$ and $q$ are integers, find $|p| + |q|.$",
"type": "text",
"url": null
}
],
"role": "user"
}
] |
[
{
"content": [
{
"text": "A user will ask you to solve a task. You should first draft your thinking process (inner monologue) until you have derived the final answer. Afterwards, write a self-contained summary of your thoughts (i.e. your summary should be succinct but contain all the critical steps you needed to reach the conclusion). You should use Markdown and Latex to format your response. Write both your thoughts and summary in the same language as the task posed by the user.\n\nYour thinking process must follow the template below:\n<think>\nYour thoughts or/and draft, like working through an exercise on scratch paper. Be as casual and as long as you want until you are confident to generate a correct answer.\n</think>\n\nHere, provide a concise summary that reflects your reasoning and presents a clear final answer to the user.\n\n\n\nYou will be given a problem. Please reason step by step, and put your final answer within \\boxed{}.",
"type": "text"
}
],
"role": "system"
},
{
"content": [
{
"text": "The workers in a factory produce widgets and whoosits. For each product, production time is constant and identical for all workers, but not necessarily equal for the two products. In one hour, $100$ workers can produce $300$ widgets and $200$ whoosits. In two hours, $60$ workers can produce $240$ widgets and $300$ whoosits. In three hours, $50$ workers can produce $150$ widgets and $m$ whoosits. Find $m$ .",
"type": "text"
}
],
"role": "user"
}
] |
$450$
|
di-zhang-fdu/AIME_1983_2024
|
[
{
"content": [
{
"path": "",
"text": "A user will ask you to solve a task. You should first draft your thinking process (inner monologue) until you have derived the final answer. Afterwards, write a self-contained summary of your thoughts (i.e. your summary should be succinct but contain all the critical steps you needed to reach the conclusion). You should use Markdown and Latex to format your response. Write both your thoughts and summary in the same language as the task posed by the user.\n\nYour thinking process must follow the template below:\n<think>\nYour thoughts or/and draft, like working through an exercise on scratch paper. Be as casual and as long as you want until you are confident to generate a correct answer.\n</think>\n\nHere, provide a concise summary that reflects your reasoning and presents a clear final answer to the user.\n\n\n\nYou will be given a problem. Please reason step by step, and put your final answer within \\boxed{}.",
"type": "text",
"url": null
}
],
"role": "system"
},
{
"content": [
{
"path": "",
"text": "The workers in a factory produce widgets and whoosits. For each product, production time is constant and identical for all workers, but not necessarily equal for the two products. In one hour, $100$ workers can produce $300$ widgets and $200$ whoosits. In two hours, $60$ workers can produce $240$ widgets and $300$ whoosits. In three hours, $50$ workers can produce $150$ widgets and $m$ whoosits. Find $m$ .",
"type": "text",
"url": null
}
],
"role": "user"
}
] |
[
{
"content": [
{
"text": "A user will ask you to solve a task. You should first draft your thinking process (inner monologue) until you have derived the final answer. Afterwards, write a self-contained summary of your thoughts (i.e. your summary should be succinct but contain all the critical steps you needed to reach the conclusion). You should use Markdown and Latex to format your response. Write both your thoughts and summary in the same language as the task posed by the user.\n\nYour thinking process must follow the template below:\n<think>\nYour thoughts or/and draft, like working through an exercise on scratch paper. Be as casual and as long as you want until you are confident to generate a correct answer.\n</think>\n\nHere, provide a concise summary that reflects your reasoning and presents a clear final answer to the user.\n\n\n\nYou will be given a problem. Please reason step by step, and put your final answer within \\boxed{}.",
"type": "text"
}
],
"role": "system"
},
{
"content": [
{
"text": "Lines $l_1^{}$ and $l_2^{}$ both pass through the origin and make first-quadrant angles of $\\frac{\\pi}{70}$ and $\\frac{\\pi}{54}$ radians, respectively, with the positive x-axis. For any line $l^{}_{}$ , the transformation $R(l)^{}_{}$ produces another line as follows: $l^{}_{}$ is reflected in $l_1^{}$ , and the resulting line is reflected in $l_2^{}$ . Let $R^{(1)}(l)=R(l)^{}_{}$ and $R^{(n)}(l)^{}_{}=R\\left(R^{(n-1)}(l)\\right)$ . Given that $l^{}_{}$ is the line $y=\\frac{19}{92}x^{}_{}$ , find the smallest positive integer $m^{}_{}$ for which $R^{(m)}(l)=l^{}_{}$ .",
"type": "text"
}
],
"role": "user"
}
] |
$945$
|
di-zhang-fdu/AIME_1983_2024
|
[
{
"content": [
{
"path": "",
"text": "A user will ask you to solve a task. You should first draft your thinking process (inner monologue) until you have derived the final answer. Afterwards, write a self-contained summary of your thoughts (i.e. your summary should be succinct but contain all the critical steps you needed to reach the conclusion). You should use Markdown and Latex to format your response. Write both your thoughts and summary in the same language as the task posed by the user.\n\nYour thinking process must follow the template below:\n<think>\nYour thoughts or/and draft, like working through an exercise on scratch paper. Be as casual and as long as you want until you are confident to generate a correct answer.\n</think>\n\nHere, provide a concise summary that reflects your reasoning and presents a clear final answer to the user.\n\n\n\nYou will be given a problem. Please reason step by step, and put your final answer within \\boxed{}.",
"type": "text",
"url": null
}
],
"role": "system"
},
{
"content": [
{
"path": "",
"text": "Lines $l_1^{}$ and $l_2^{}$ both pass through the origin and make first-quadrant angles of $\\frac{\\pi}{70}$ and $\\frac{\\pi}{54}$ radians, respectively, with the positive x-axis. For any line $l^{}_{}$ , the transformation $R(l)^{}_{}$ produces another line as follows: $l^{}_{}$ is reflected in $l_1^{}$ , and the resulting line is reflected in $l_2^{}$ . Let $R^{(1)}(l)=R(l)^{}_{}$ and $R^{(n)}(l)^{}_{}=R\\left(R^{(n-1)}(l)\\right)$ . Given that $l^{}_{}$ is the line $y=\\frac{19}{92}x^{}_{}$ , find the smallest positive integer $m^{}_{}$ for which $R^{(m)}(l)=l^{}_{}$ .",
"type": "text",
"url": null
}
],
"role": "user"
}
] |
[
{
"content": [
{
"text": "A user will ask you to solve a task. You should first draft your thinking process (inner monologue) until you have derived the final answer. Afterwards, write a self-contained summary of your thoughts (i.e. your summary should be succinct but contain all the critical steps you needed to reach the conclusion). You should use Markdown and Latex to format your response. Write both your thoughts and summary in the same language as the task posed by the user.\n\nYour thinking process must follow the template below:\n<think>\nYour thoughts or/and draft, like working through an exercise on scratch paper. Be as casual and as long as you want until you are confident to generate a correct answer.\n</think>\n\nHere, provide a concise summary that reflects your reasoning and presents a clear final answer to the user.\n\n\n\nYou will be given a problem. Please reason step by step, and put your final answer within \\boxed{}.",
"type": "text"
}
],
"role": "system"
},
{
"content": [
{
"text": "A triangle has vertices $P_{}^{}=(-8,5)$ , $Q_{}^{}=(-15,-19)$ , and $R_{}^{}=(1,-7)$ . The equation of the bisector of $\\angle P$ can be written in the form $ax+2y+c=0_{}^{}$ . Find $a+c_{}^{}$ .",
"type": "text"
}
],
"role": "user"
}
] |
$89$
|
di-zhang-fdu/AIME_1983_2024
|
[
{
"content": [
{
"path": "",
"text": "A user will ask you to solve a task. You should first draft your thinking process (inner monologue) until you have derived the final answer. Afterwards, write a self-contained summary of your thoughts (i.e. your summary should be succinct but contain all the critical steps you needed to reach the conclusion). You should use Markdown and Latex to format your response. Write both your thoughts and summary in the same language as the task posed by the user.\n\nYour thinking process must follow the template below:\n<think>\nYour thoughts or/and draft, like working through an exercise on scratch paper. Be as casual and as long as you want until you are confident to generate a correct answer.\n</think>\n\nHere, provide a concise summary that reflects your reasoning and presents a clear final answer to the user.\n\n\n\nYou will be given a problem. Please reason step by step, and put your final answer within \\boxed{}.",
"type": "text",
"url": null
}
],
"role": "system"
},
{
"content": [
{
"path": "",
"text": "A triangle has vertices $P_{}^{}=(-8,5)$ , $Q_{}^{}=(-15,-19)$ , and $R_{}^{}=(1,-7)$ . The equation of the bisector of $\\angle P$ can be written in the form $ax+2y+c=0_{}^{}$ . Find $a+c_{}^{}$ .",
"type": "text",
"url": null
}
],
"role": "user"
}
] |
[
{
"content": [
{
"text": "A user will ask you to solve a task. You should first draft your thinking process (inner monologue) until you have derived the final answer. Afterwards, write a self-contained summary of your thoughts (i.e. your summary should be succinct but contain all the critical steps you needed to reach the conclusion). You should use Markdown and Latex to format your response. Write both your thoughts and summary in the same language as the task posed by the user.\n\nYour thinking process must follow the template below:\n<think>\nYour thoughts or/and draft, like working through an exercise on scratch paper. Be as casual and as long as you want until you are confident to generate a correct answer.\n</think>\n\nHere, provide a concise summary that reflects your reasoning and presents a clear final answer to the user.\n\n",
"type": "text"
}
],
"role": "system"
},
{
"content": [
{
"text": "You will be given a problem. Please reason step by step, and put your final answer within \\boxed{}:\nThe parabola with equation $y = x^2 - 4$ is rotated $60^\\circ$ counterclockwise around the origin. The unique point in the fourth quadrant where the original parabola and its image intersect has $y$-coordinate $\\frac{a - \\sqrt{b}}{c}$, where $a$, $b$, and $c$ are positive integers, and $a$ and $c$ are relatively prime. Find $a + b + c$.",
"type": "text"
}
],
"role": "user"
}
] |
$62$
|
MathArena/aime_2025_I
|
[
{
"content": [
{
"path": "",
"text": "A user will ask you to solve a task. You should first draft your thinking process (inner monologue) until you have derived the final answer. Afterwards, write a self-contained summary of your thoughts (i.e. your summary should be succinct but contain all the critical steps you needed to reach the conclusion). You should use Markdown and Latex to format your response. Write both your thoughts and summary in the same language as the task posed by the user.\n\nYour thinking process must follow the template below:\n<think>\nYour thoughts or/and draft, like working through an exercise on scratch paper. Be as casual and as long as you want until you are confident to generate a correct answer.\n</think>\n\nHere, provide a concise summary that reflects your reasoning and presents a clear final answer to the user.\n\n",
"type": "text",
"url": null
}
],
"role": "system"
},
{
"content": [
{
"path": "",
"text": "You will be given a problem. Please reason step by step, and put your final answer within \\boxed{}:\nThe parabola with equation $y = x^2 - 4$ is rotated $60^\\circ$ counterclockwise around the origin. The unique point in the fourth quadrant where the original parabola and its image intersect has $y$-coordinate $\\frac{a - \\sqrt{b}}{c}$, where $a$, $b$, and $c$ are positive integers, and $a$ and $c$ are relatively prime. Find $a + b + c$.",
"type": "text",
"url": null
}
],
"role": "user"
}
] |
[
{
"content": [
{
"text": "A user will ask you to solve a task. You should first draft your thinking process (inner monologue) until you have derived the final answer. Afterwards, write a self-contained summary of your thoughts (i.e. your summary should be succinct but contain all the critical steps you needed to reach the conclusion). You should use Markdown and Latex to format your response. Write both your thoughts and summary in the same language as the task posed by the user.\n\nYour thinking process must follow the template below:\n<think>\nYour thoughts or/and draft, like working through an exercise on scratch paper. Be as casual and as long as you want until you are confident to generate a correct answer.\n</think>\n\nHere, provide a concise summary that reflects your reasoning and presents a clear final answer to the user.\n\n\n\nYou will be given a problem. Please reason step by step, and put your final answer within \\boxed{}.",
"type": "text"
}
],
"role": "system"
},
{
"content": [
{
"text": "Six men and some number of women stand in a line in random order. Let $p$ be the probability that a group of at least four men stand together in the line, given that every man stands next to at least one other man. Find the least number of women in the line such that $p$ does not exceed 1 percent.",
"type": "text"
}
],
"role": "user"
}
] |
$594$
|
di-zhang-fdu/AIME_1983_2024
|
[
{
"content": [
{
"path": "",
"text": "A user will ask you to solve a task. You should first draft your thinking process (inner monologue) until you have derived the final answer. Afterwards, write a self-contained summary of your thoughts (i.e. your summary should be succinct but contain all the critical steps you needed to reach the conclusion). You should use Markdown and Latex to format your response. Write both your thoughts and summary in the same language as the task posed by the user.\n\nYour thinking process must follow the template below:\n<think>\nYour thoughts or/and draft, like working through an exercise on scratch paper. Be as casual and as long as you want until you are confident to generate a correct answer.\n</think>\n\nHere, provide a concise summary that reflects your reasoning and presents a clear final answer to the user.\n\n\n\nYou will be given a problem. Please reason step by step, and put your final answer within \\boxed{}.",
"type": "text",
"url": null
}
],
"role": "system"
},
{
"content": [
{
"path": "",
"text": "Six men and some number of women stand in a line in random order. Let $p$ be the probability that a group of at least four men stand together in the line, given that every man stands next to at least one other man. Find the least number of women in the line such that $p$ does not exceed 1 percent.",
"type": "text",
"url": null
}
],
"role": "user"
}
] |
[
{
"content": [
{
"text": "A user will ask you to solve a task. You should first draft your thinking process (inner monologue) until you have derived the final answer. Afterwards, write a self-contained summary of your thoughts (i.e. your summary should be succinct but contain all the critical steps you needed to reach the conclusion). You should use Markdown and Latex to format your response. Write both your thoughts and summary in the same language as the task posed by the user.\n\nYour thinking process must follow the template below:\n<think>\nYour thoughts or/and draft, like working through an exercise on scratch paper. Be as casual and as long as you want until you are confident to generate a correct answer.\n</think>\n\nHere, provide a concise summary that reflects your reasoning and presents a clear final answer to the user.\n\n",
"type": "text"
}
],
"role": "system"
},
{
"content": [
{
"text": "You will be given a problem. Please reason step by step, and put your final answer within \\boxed{}:\nFind the smallest prime that is the fifth term of an increasing arithmetic sequence, all four preceding terms also being prime. ",
"type": "text"
}
],
"role": "user"
}
] |
$29$
|
di-zhang-fdu/AIME_1983_2024
|
[
{
"content": [
{
"path": "",
"text": "A user will ask you to solve a task. You should first draft your thinking process (inner monologue) until you have derived the final answer. Afterwards, write a self-contained summary of your thoughts (i.e. your summary should be succinct but contain all the critical steps you needed to reach the conclusion). You should use Markdown and Latex to format your response. Write both your thoughts and summary in the same language as the task posed by the user.\n\nYour thinking process must follow the template below:\n<think>\nYour thoughts or/and draft, like working through an exercise on scratch paper. Be as casual and as long as you want until you are confident to generate a correct answer.\n</think>\n\nHere, provide a concise summary that reflects your reasoning and presents a clear final answer to the user.\n\n",
"type": "text",
"url": null
}
],
"role": "system"
},
{
"content": [
{
"path": "",
"text": "You will be given a problem. Please reason step by step, and put your final answer within \\boxed{}:\nFind the smallest prime that is the fifth term of an increasing arithmetic sequence, all four preceding terms also being prime. ",
"type": "text",
"url": null
}
],
"role": "user"
}
] |
[
{
"content": [
{
"text": "A user will ask you to solve a task. You should first draft your thinking process (inner monologue) until you have derived the final answer. Afterwards, write a self-contained summary of your thoughts (i.e. your summary should be succinct but contain all the critical steps you needed to reach the conclusion). You should use Markdown and Latex to format your response. Write both your thoughts and summary in the same language as the task posed by the user.\n\nYour thinking process must follow the template below:\n<think>\nYour thoughts or/and draft, like working through an exercise on scratch paper. Be as casual and as long as you want until you are confident to generate a correct answer.\n</think>\n\nHere, provide a concise summary that reflects your reasoning and presents a clear final answer to the user.\n\n\n\nYou will be given a problem. Please reason step by step, and put your final answer within \\boxed{}.",
"type": "text"
}
],
"role": "system"
},
{
"content": [
{
"text": "A convex quadrilateral has area $30$ and side lengths $5, 6, 9,$ and $7,$ in that order. Denote by $\\theta$ the measure of the acute angle formed by the diagonals of the quadrilateral. Then $\\tan \\theta$ can be written in the form $\\tfrac{m}{n}$ , where $m$ and $n$ are relatively prime positive integers. Find $m + n$ .",
"type": "text"
}
],
"role": "user"
}
] |
$47$
|
di-zhang-fdu/AIME_1983_2024
|
[
{
"content": [
{
"path": "",
"text": "A user will ask you to solve a task. You should first draft your thinking process (inner monologue) until you have derived the final answer. Afterwards, write a self-contained summary of your thoughts (i.e. your summary should be succinct but contain all the critical steps you needed to reach the conclusion). You should use Markdown and Latex to format your response. Write both your thoughts and summary in the same language as the task posed by the user.\n\nYour thinking process must follow the template below:\n<think>\nYour thoughts or/and draft, like working through an exercise on scratch paper. Be as casual and as long as you want until you are confident to generate a correct answer.\n</think>\n\nHere, provide a concise summary that reflects your reasoning and presents a clear final answer to the user.\n\n\n\nYou will be given a problem. Please reason step by step, and put your final answer within \\boxed{}.",
"type": "text",
"url": null
}
],
"role": "system"
},
{
"content": [
{
"path": "",
"text": "A convex quadrilateral has area $30$ and side lengths $5, 6, 9,$ and $7,$ in that order. Denote by $\\theta$ the measure of the acute angle formed by the diagonals of the quadrilateral. Then $\\tan \\theta$ can be written in the form $\\tfrac{m}{n}$ , where $m$ and $n$ are relatively prime positive integers. Find $m + n$ .",
"type": "text",
"url": null
}
],
"role": "user"
}
] |
[
{
"content": [
{
"text": "A user will ask you to solve a task. You should first draft your thinking process (inner monologue) until you have derived the final answer. Afterwards, write a self-contained summary of your thoughts (i.e. your summary should be succinct but contain all the critical steps you needed to reach the conclusion). You should use Markdown and Latex to format your response. Write both your thoughts and summary in the same language as the task posed by the user.\n\nYour thinking process must follow the template below:\n<think>\nYour thoughts or/and draft, like working through an exercise on scratch paper. Be as casual and as long as you want until you are confident to generate a correct answer.\n</think>\n\nHere, provide a concise summary that reflects your reasoning and presents a clear final answer to the user.\n\n",
"type": "text"
}
],
"role": "system"
},
{
"content": [
{
"text": "You will be given a problem. Please reason step by step, and put your final answer within \\boxed{}:\nOne base of a trapezoid is $100$ units longer than the other base. The segment that joins the midpoints of the legs divides the trapezoid into two regions whose areas are in the ratio $2: 3$ . Let $x$ be the length of the segment joining the legs of the trapezoid that is parallel to the bases and that divides the trapezoid into two regions of equal area. Find the greatest integer that does not exceed $x^2/100$ .",
"type": "text"
}
],
"role": "user"
}
] |
$181$
|
di-zhang-fdu/AIME_1983_2024
|
[
{
"content": [
{
"path": "",
"text": "A user will ask you to solve a task. You should first draft your thinking process (inner monologue) until you have derived the final answer. Afterwards, write a self-contained summary of your thoughts (i.e. your summary should be succinct but contain all the critical steps you needed to reach the conclusion). You should use Markdown and Latex to format your response. Write both your thoughts and summary in the same language as the task posed by the user.\n\nYour thinking process must follow the template below:\n<think>\nYour thoughts or/and draft, like working through an exercise on scratch paper. Be as casual and as long as you want until you are confident to generate a correct answer.\n</think>\n\nHere, provide a concise summary that reflects your reasoning and presents a clear final answer to the user.\n\n",
"type": "text",
"url": null
}
],
"role": "system"
},
{
"content": [
{
"path": "",
"text": "You will be given a problem. Please reason step by step, and put your final answer within \\boxed{}:\nOne base of a trapezoid is $100$ units longer than the other base. The segment that joins the midpoints of the legs divides the trapezoid into two regions whose areas are in the ratio $2: 3$ . Let $x$ be the length of the segment joining the legs of the trapezoid that is parallel to the bases and that divides the trapezoid into two regions of equal area. Find the greatest integer that does not exceed $x^2/100$ .",
"type": "text",
"url": null
}
],
"role": "user"
}
] |
[
{
"content": [
{
"text": "A user will ask you to solve a task. You should first draft your thinking process (inner monologue) until you have derived the final answer. Afterwards, write a self-contained summary of your thoughts (i.e. your summary should be succinct but contain all the critical steps you needed to reach the conclusion). You should use Markdown and Latex to format your response. Write both your thoughts and summary in the same language as the task posed by the user.\n\nYour thinking process must follow the template below:\n<think>\nYour thoughts or/and draft, like working through an exercise on scratch paper. Be as casual and as long as you want until you are confident to generate a correct answer.\n</think>\n\nHere, provide a concise summary that reflects your reasoning and presents a clear final answer to the user.\n\n\n\nYou will be given a problem. Please reason step by step, and put your final answer within \\boxed{}.",
"type": "text"
}
],
"role": "system"
},
{
"content": [
{
"text": "Six cards numbered $1$ through $6$ are to be lined up in a row. Find the number of arrangements of these six cards where one of the cards can be removed leaving the remaining five cards in either ascending or descending order.",
"type": "text"
}
],
"role": "user"
}
] |
$52$
|
di-zhang-fdu/AIME_1983_2024
|
[
{
"content": [
{
"path": "",
"text": "A user will ask you to solve a task. You should first draft your thinking process (inner monologue) until you have derived the final answer. Afterwards, write a self-contained summary of your thoughts (i.e. your summary should be succinct but contain all the critical steps you needed to reach the conclusion). You should use Markdown and Latex to format your response. Write both your thoughts and summary in the same language as the task posed by the user.\n\nYour thinking process must follow the template below:\n<think>\nYour thoughts or/and draft, like working through an exercise on scratch paper. Be as casual and as long as you want until you are confident to generate a correct answer.\n</think>\n\nHere, provide a concise summary that reflects your reasoning and presents a clear final answer to the user.\n\n\n\nYou will be given a problem. Please reason step by step, and put your final answer within \\boxed{}.",
"type": "text",
"url": null
}
],
"role": "system"
},
{
"content": [
{
"path": "",
"text": "Six cards numbered $1$ through $6$ are to be lined up in a row. Find the number of arrangements of these six cards where one of the cards can be removed leaving the remaining five cards in either ascending or descending order.",
"type": "text",
"url": null
}
],
"role": "user"
}
] |
[
{
"content": [
{
"text": "A user will ask you to solve a task. You should first draft your thinking process (inner monologue) until you have derived the final answer. Afterwards, write a self-contained summary of your thoughts (i.e. your summary should be succinct but contain all the critical steps you needed to reach the conclusion). You should use Markdown and Latex to format your response. Write both your thoughts and summary in the same language as the task posed by the user.\n\nYour thinking process must follow the template below:\n<think>\nYour thoughts or/and draft, like working through an exercise on scratch paper. Be as casual and as long as you want until you are confident to generate a correct answer.\n</think>\n\nHere, provide a concise summary that reflects your reasoning and presents a clear final answer to the user.\n\n",
"type": "text"
}
],
"role": "system"
},
{
"content": [
{
"text": "You will be given a problem. Please reason step by step, and put your final answer within \\boxed{}:\nIn the adjoining figure, two circles with radii $8$ and $6$ are drawn with their centers $12$ units apart. At $P$ , one of the points of intersection, a line is drawn in such a way that the chords $QP$ and $PR$ have equal length. Find the square of the length of $QP$ . [asy]size(160); defaultpen(linewidth(.8pt)+fontsize(11pt)); dotfactor=3; pair O1=(0,0), O2=(12,0); path C1=Circle(O1,8), C2=Circle(O2,6); pair P=intersectionpoints(C1,C2)[0]; path C3=Circle(P,sqrt(130)); pair Q=intersectionpoints(C3,C1)[0]; pair R=intersectionpoints(C3,C2)[1]; draw(C1); draw(C2); draw(O2--O1); dot(O1); dot(O2); draw(Q--R); label(\"$Q$\",Q,NW); label(\"$P$\",P,1.5*dir(80)); label(\"$R$\",R,NE); label(\"12\",waypoint(O1--O2,0.4),S);[/asy]",
"type": "text"
}
],
"role": "user"
}
] |
$130$
|
di-zhang-fdu/AIME_1983_2024
|
[
{
"content": [
{
"path": "",
"text": "A user will ask you to solve a task. You should first draft your thinking process (inner monologue) until you have derived the final answer. Afterwards, write a self-contained summary of your thoughts (i.e. your summary should be succinct but contain all the critical steps you needed to reach the conclusion). You should use Markdown and Latex to format your response. Write both your thoughts and summary in the same language as the task posed by the user.\n\nYour thinking process must follow the template below:\n<think>\nYour thoughts or/and draft, like working through an exercise on scratch paper. Be as casual and as long as you want until you are confident to generate a correct answer.\n</think>\n\nHere, provide a concise summary that reflects your reasoning and presents a clear final answer to the user.\n\n",
"type": "text",
"url": null
}
],
"role": "system"
},
{
"content": [
{
"path": "",
"text": "You will be given a problem. Please reason step by step, and put your final answer within \\boxed{}:\nIn the adjoining figure, two circles with radii $8$ and $6$ are drawn with their centers $12$ units apart. At $P$ , one of the points of intersection, a line is drawn in such a way that the chords $QP$ and $PR$ have equal length. Find the square of the length of $QP$ . [asy]size(160); defaultpen(linewidth(.8pt)+fontsize(11pt)); dotfactor=3; pair O1=(0,0), O2=(12,0); path C1=Circle(O1,8), C2=Circle(O2,6); pair P=intersectionpoints(C1,C2)[0]; path C3=Circle(P,sqrt(130)); pair Q=intersectionpoints(C3,C1)[0]; pair R=intersectionpoints(C3,C2)[1]; draw(C1); draw(C2); draw(O2--O1); dot(O1); dot(O2); draw(Q--R); label(\"$Q$\",Q,NW); label(\"$P$\",P,1.5*dir(80)); label(\"$R$\",R,NE); label(\"12\",waypoint(O1--O2,0.4),S);[/asy]",
"type": "text",
"url": null
}
],
"role": "user"
}
] |
[
{
"content": [
{
"text": "A user will ask you to solve a task. You should first draft your thinking process (inner monologue) until you have derived the final answer. Afterwards, write a self-contained summary of your thoughts (i.e. your summary should be succinct but contain all the critical steps you needed to reach the conclusion). You should use Markdown and Latex to format your response. Write both your thoughts and summary in the same language as the task posed by the user.\n\nYour thinking process must follow the template below:\n<think>\nYour thoughts or/and draft, like working through an exercise on scratch paper. Be as casual and as long as you want until you are confident to generate a correct answer.\n</think>\n\nHere, provide a concise summary that reflects your reasoning and presents a clear final answer to the user.\n\n\n\nYou will be given a problem. Please reason step by step, and put your final answer within \\boxed{}.",
"type": "text"
}
],
"role": "system"
},
{
"content": [
{
"text": "Define a domino to be an ordered pair of distinct positive integers. A proper sequence of dominos is a list of distinct dominos in which the first coordinate of each pair after the first equals the second coordinate of the immediately preceding pair, and in which $(i,j)$ and $(j,i)$ do not both appear for any $i$ and $j$ . Let $D_{40}$ be the set of all dominos whose coordinates are no larger than 40. Find the length of the longest proper sequence of dominos that can be formed using the dominos of $D_{40}.$",
"type": "text"
}
],
"role": "user"
}
] |
$761$
|
di-zhang-fdu/AIME_1983_2024
|
[
{
"content": [
{
"path": "",
"text": "A user will ask you to solve a task. You should first draft your thinking process (inner monologue) until you have derived the final answer. Afterwards, write a self-contained summary of your thoughts (i.e. your summary should be succinct but contain all the critical steps you needed to reach the conclusion). You should use Markdown and Latex to format your response. Write both your thoughts and summary in the same language as the task posed by the user.\n\nYour thinking process must follow the template below:\n<think>\nYour thoughts or/and draft, like working through an exercise on scratch paper. Be as casual and as long as you want until you are confident to generate a correct answer.\n</think>\n\nHere, provide a concise summary that reflects your reasoning and presents a clear final answer to the user.\n\n\n\nYou will be given a problem. Please reason step by step, and put your final answer within \\boxed{}.",
"type": "text",
"url": null
}
],
"role": "system"
},
{
"content": [
{
"path": "",
"text": "Define a domino to be an ordered pair of distinct positive integers. A proper sequence of dominos is a list of distinct dominos in which the first coordinate of each pair after the first equals the second coordinate of the immediately preceding pair, and in which $(i,j)$ and $(j,i)$ do not both appear for any $i$ and $j$ . Let $D_{40}$ be the set of all dominos whose coordinates are no larger than 40. Find the length of the longest proper sequence of dominos that can be formed using the dominos of $D_{40}.$",
"type": "text",
"url": null
}
],
"role": "user"
}
] |
[
{
"content": [
{
"text": "A user will ask you to solve a task. You should first draft your thinking process (inner monologue) until you have derived the final answer. Afterwards, write a self-contained summary of your thoughts (i.e. your summary should be succinct but contain all the critical steps you needed to reach the conclusion). You should use Markdown and Latex to format your response. Write both your thoughts and summary in the same language as the task posed by the user.\n\nYour thinking process must follow the template below:\n<think>\nYour thoughts or/and draft, like working through an exercise on scratch paper. Be as casual and as long as you want until you are confident to generate a correct answer.\n</think>\n\nHere, provide a concise summary that reflects your reasoning and presents a clear final answer to the user.\n\n",
"type": "text"
}
],
"role": "system"
},
{
"content": [
{
"text": "You will be given a problem. Please reason step by step, and put your final answer within \\boxed{}:\nNine delegates, three each from three different countries, randomly select chairs at a round table that seats nine people. Let the probability that each delegate sits next to at least one delegate from another country be $\\frac{m}{n}$ , where $m$ and $n$ are relatively prime positive integers. Find $m + n$ . ",
"type": "text"
}
],
"role": "user"
}
] |
$97$
|
di-zhang-fdu/AIME_1983_2024
|
[
{
"content": [
{
"path": "",
"text": "A user will ask you to solve a task. You should first draft your thinking process (inner monologue) until you have derived the final answer. Afterwards, write a self-contained summary of your thoughts (i.e. your summary should be succinct but contain all the critical steps you needed to reach the conclusion). You should use Markdown and Latex to format your response. Write both your thoughts and summary in the same language as the task posed by the user.\n\nYour thinking process must follow the template below:\n<think>\nYour thoughts or/and draft, like working through an exercise on scratch paper. Be as casual and as long as you want until you are confident to generate a correct answer.\n</think>\n\nHere, provide a concise summary that reflects your reasoning and presents a clear final answer to the user.\n\n",
"type": "text",
"url": null
}
],
"role": "system"
},
{
"content": [
{
"path": "",
"text": "You will be given a problem. Please reason step by step, and put your final answer within \\boxed{}:\nNine delegates, three each from three different countries, randomly select chairs at a round table that seats nine people. Let the probability that each delegate sits next to at least one delegate from another country be $\\frac{m}{n}$ , where $m$ and $n$ are relatively prime positive integers. Find $m + n$ . ",
"type": "text",
"url": null
}
],
"role": "user"
}
] |
[
{
"content": [
{
"text": "A user will ask you to solve a task. You should first draft your thinking process (inner monologue) until you have derived the final answer. Afterwards, write a self-contained summary of your thoughts (i.e. your summary should be succinct but contain all the critical steps you needed to reach the conclusion). You should use Markdown and Latex to format your response. Write both your thoughts and summary in the same language as the task posed by the user.\n\nYour thinking process must follow the template below:\n<think>\nYour thoughts or/and draft, like working through an exercise on scratch paper. Be as casual and as long as you want until you are confident to generate a correct answer.\n</think>\n\nHere, provide a concise summary that reflects your reasoning and presents a clear final answer to the user.\n\n",
"type": "text"
}
],
"role": "system"
},
{
"content": [
{
"text": "You will be given a problem. Please reason step by step, and put your final answer within \\boxed{}:\nTriangle $ABC$ has side lengths $AB=7,BC=8,$ and $CA=9.$ Circle $\\omega_1$ passes through $B$ and is tangent to line $AC$ at $A.$ Circle $\\omega_2$ passes through $C$ and is tangent to line $AB$ at $A.$ Let $K$ be the intersection of circles $\\omega_1$ and $\\omega_2$ not equal to $A.$ Then $AK=\\tfrac{m}{n},$ where $m$ and $n$ are relatively prime positive integers. Find $m+n.$",
"type": "text"
}
],
"role": "user"
}
] |
$11$
|
di-zhang-fdu/AIME_1983_2024
|
[
{
"content": [
{
"path": "",
"text": "A user will ask you to solve a task. You should first draft your thinking process (inner monologue) until you have derived the final answer. Afterwards, write a self-contained summary of your thoughts (i.e. your summary should be succinct but contain all the critical steps you needed to reach the conclusion). You should use Markdown and Latex to format your response. Write both your thoughts and summary in the same language as the task posed by the user.\n\nYour thinking process must follow the template below:\n<think>\nYour thoughts or/and draft, like working through an exercise on scratch paper. Be as casual and as long as you want until you are confident to generate a correct answer.\n</think>\n\nHere, provide a concise summary that reflects your reasoning and presents a clear final answer to the user.\n\n",
"type": "text",
"url": null
}
],
"role": "system"
},
{
"content": [
{
"path": "",
"text": "You will be given a problem. Please reason step by step, and put your final answer within \\boxed{}:\nTriangle $ABC$ has side lengths $AB=7,BC=8,$ and $CA=9.$ Circle $\\omega_1$ passes through $B$ and is tangent to line $AC$ at $A.$ Circle $\\omega_2$ passes through $C$ and is tangent to line $AB$ at $A.$ Let $K$ be the intersection of circles $\\omega_1$ and $\\omega_2$ not equal to $A.$ Then $AK=\\tfrac{m}{n},$ where $m$ and $n$ are relatively prime positive integers. Find $m+n.$",
"type": "text",
"url": null
}
],
"role": "user"
}
] |
[
{
"content": [
{
"text": "A user will ask you to solve a task. You should first draft your thinking process (inner monologue) until you have derived the final answer. Afterwards, write a self-contained summary of your thoughts (i.e. your summary should be succinct but contain all the critical steps you needed to reach the conclusion). You should use Markdown and Latex to format your response. Write both your thoughts and summary in the same language as the task posed by the user.\n\nYour thinking process must follow the template below:\n<think>\nYour thoughts or/and draft, like working through an exercise on scratch paper. Be as casual and as long as you want until you are confident to generate a correct answer.\n</think>\n\nHere, provide a concise summary that reflects your reasoning and presents a clear final answer to the user.\n\n",
"type": "text"
}
],
"role": "system"
},
{
"content": [
{
"text": "You will be given a problem. Please reason step by step, and put your final answer within \\boxed{}:\nA right prism with height $h$ has bases that are regular hexagons with sides of length $12$ . A vertex $A$ of the prism and its three adjacent vertices are the vertices of a triangular pyramid. The dihedral angle (the angle between the two planes) formed by the face of the pyramid that lies in a base of the prism and the face of the pyramid that does not contain $A$ measures $60^\\circ$ . Find $h^2$ .",
"type": "text"
}
],
"role": "user"
}
] |
$108$
|
di-zhang-fdu/AIME_1983_2024
|
[
{
"content": [
{
"path": "",
"text": "A user will ask you to solve a task. You should first draft your thinking process (inner monologue) until you have derived the final answer. Afterwards, write a self-contained summary of your thoughts (i.e. your summary should be succinct but contain all the critical steps you needed to reach the conclusion). You should use Markdown and Latex to format your response. Write both your thoughts and summary in the same language as the task posed by the user.\n\nYour thinking process must follow the template below:\n<think>\nYour thoughts or/and draft, like working through an exercise on scratch paper. Be as casual and as long as you want until you are confident to generate a correct answer.\n</think>\n\nHere, provide a concise summary that reflects your reasoning and presents a clear final answer to the user.\n\n",
"type": "text",
"url": null
}
],
"role": "system"
},
{
"content": [
{
"path": "",
"text": "You will be given a problem. Please reason step by step, and put your final answer within \\boxed{}:\nA right prism with height $h$ has bases that are regular hexagons with sides of length $12$ . A vertex $A$ of the prism and its three adjacent vertices are the vertices of a triangular pyramid. The dihedral angle (the angle between the two planes) formed by the face of the pyramid that lies in a base of the prism and the face of the pyramid that does not contain $A$ measures $60^\\circ$ . Find $h^2$ .",
"type": "text",
"url": null
}
],
"role": "user"
}
] |
[
{
"content": [
{
"text": "A user will ask you to solve a task. You should first draft your thinking process (inner monologue) until you have derived the final answer. Afterwards, write a self-contained summary of your thoughts (i.e. your summary should be succinct but contain all the critical steps you needed to reach the conclusion). You should use Markdown and Latex to format your response. Write both your thoughts and summary in the same language as the task posed by the user.\n\nYour thinking process must follow the template below:\n<think>\nYour thoughts or/and draft, like working through an exercise on scratch paper. Be as casual and as long as you want until you are confident to generate a correct answer.\n</think>\n\nHere, provide a concise summary that reflects your reasoning and presents a clear final answer to the user.\n\n\n\nYou will be given a problem. Please reason step by step, and put your final answer within \\boxed{}.",
"type": "text"
}
],
"role": "system"
},
{
"content": [
{
"text": "On $\\triangle ABC$ points $A, D, E$, and $B$ lie in that order on side $\\overline{AB}$ with $AD = 4$, $DE = 16$, $EB = 8$. Points $A, F, G$ and $C$ lie in that order on side $\\overline{AC}$ with $AF = 13$, $FG = 52$, and $GC = 26$. Let $M$ be the reflection of $D$ through $F$, and let $N$ be the reflection of $G$ through $E$. Quadrilateral $DEGF$ has area $288$. Find the area of heptagon $AFNBCEM$.\n\n\\begin{tikzpicture}[scale=0.07, line join=round, line cap=round, >=stealth]\n\n \\coordinate (A) at (100,100);\n\n \\coordinate (D) at (95,80);\n \\coordinate (F) at (130,80);\n \\coordinate (M) at (165,80);\n\n \\coordinate (N) at (0,50);\n \\coordinate (E) at (87.5,50);\n \\coordinate (G) at (175,50);\n\n \\coordinate (B) at ($(D)!2!(E)$);\n \\coordinate (C) at ($(F)!2!(G)$);\n \n \\fill[draw=black, fill=gray!20] (N) -- (E) -- (M) -- (F) -- cycle;\n \\fill[draw=black, fill=gray!20] (N) -- (E) -- (C) -- (B) -- cycle;\n \\fill[draw=black, fill=gray!20] (A) -- (F) -- (M) -- cycle;\n \n \\draw[line width=0.5mm] (A) -- (B) -- (C) -- cycle;\n\n \\draw (D) -- (M);\n \\draw (G) -- (N);\n \n \\foreach \\point in {A,B,C,D,E,F,G,M,N}\n \\filldraw [black] (\\point) circle (20pt);\n \n \\node[above] at (A) {$A$};\n \\node[below] at (B) {$B$};\n \\node[below] at (C) {$C$};\n \\node[left] at (D) {$D$};\n \\node[above left] at (E) {$E$};\n \\node[below] at (F) {$F$};\n \\node[below left] at (G) {$G$};\n \\node[right] at (M) {$M$};\n \\node[left] at (N) {$N$};\n \n\\end{tikzpicture}\n",
"type": "text"
}
],
"role": "user"
}
] |
$588$
|
MathArena/aime_2025_I
|
[
{
"content": [
{
"path": "",
"text": "A user will ask you to solve a task. You should first draft your thinking process (inner monologue) until you have derived the final answer. Afterwards, write a self-contained summary of your thoughts (i.e. your summary should be succinct but contain all the critical steps you needed to reach the conclusion). You should use Markdown and Latex to format your response. Write both your thoughts and summary in the same language as the task posed by the user.\n\nYour thinking process must follow the template below:\n<think>\nYour thoughts or/and draft, like working through an exercise on scratch paper. Be as casual and as long as you want until you are confident to generate a correct answer.\n</think>\n\nHere, provide a concise summary that reflects your reasoning and presents a clear final answer to the user.\n\n\n\nYou will be given a problem. Please reason step by step, and put your final answer within \\boxed{}.",
"type": "text",
"url": null
}
],
"role": "system"
},
{
"content": [
{
"path": "",
"text": "On $\\triangle ABC$ points $A, D, E$, and $B$ lie in that order on side $\\overline{AB}$ with $AD = 4$, $DE = 16$, $EB = 8$. Points $A, F, G$ and $C$ lie in that order on side $\\overline{AC}$ with $AF = 13$, $FG = 52$, and $GC = 26$. Let $M$ be the reflection of $D$ through $F$, and let $N$ be the reflection of $G$ through $E$. Quadrilateral $DEGF$ has area $288$. Find the area of heptagon $AFNBCEM$.\n\n\\begin{tikzpicture}[scale=0.07, line join=round, line cap=round, >=stealth]\n\n \\coordinate (A) at (100,100);\n\n \\coordinate (D) at (95,80);\n \\coordinate (F) at (130,80);\n \\coordinate (M) at (165,80);\n\n \\coordinate (N) at (0,50);\n \\coordinate (E) at (87.5,50);\n \\coordinate (G) at (175,50);\n\n \\coordinate (B) at ($(D)!2!(E)$);\n \\coordinate (C) at ($(F)!2!(G)$);\n \n \\fill[draw=black, fill=gray!20] (N) -- (E) -- (M) -- (F) -- cycle;\n \\fill[draw=black, fill=gray!20] (N) -- (E) -- (C) -- (B) -- cycle;\n \\fill[draw=black, fill=gray!20] (A) -- (F) -- (M) -- cycle;\n \n \\draw[line width=0.5mm] (A) -- (B) -- (C) -- cycle;\n\n \\draw (D) -- (M);\n \\draw (G) -- (N);\n \n \\foreach \\point in {A,B,C,D,E,F,G,M,N}\n \\filldraw [black] (\\point) circle (20pt);\n \n \\node[above] at (A) {$A$};\n \\node[below] at (B) {$B$};\n \\node[below] at (C) {$C$};\n \\node[left] at (D) {$D$};\n \\node[above left] at (E) {$E$};\n \\node[below] at (F) {$F$};\n \\node[below left] at (G) {$G$};\n \\node[right] at (M) {$M$};\n \\node[left] at (N) {$N$};\n \n\\end{tikzpicture}\n",
"type": "text",
"url": null
}
],
"role": "user"
}
] |
[
{
"content": [
{
"text": "A user will ask you to solve a task. You should first draft your thinking process (inner monologue) until you have derived the final answer. Afterwards, write a self-contained summary of your thoughts (i.e. your summary should be succinct but contain all the critical steps you needed to reach the conclusion). You should use Markdown and Latex to format your response. Write both your thoughts and summary in the same language as the task posed by the user.\n\nYour thinking process must follow the template below:\n<think>\nYour thoughts or/and draft, like working through an exercise on scratch paper. Be as casual and as long as you want until you are confident to generate a correct answer.\n</think>\n\nHere, provide a concise summary that reflects your reasoning and presents a clear final answer to the user.\n\n",
"type": "text"
}
],
"role": "system"
},
{
"content": [
{
"text": "You will be given a problem. Please reason step by step, and put your final answer within \\boxed{}:\nThere are nonzero integers $a$ , $b$ , $r$ , and $s$ such that the complex number $r+si$ is a zero of the polynomial $P(x)={x}^{3}-a{x}^{2}+bx-65$ . For each possible combination of $a$ and $b$ , let ${p}_{a,b}$ be the sum of the zeros of $P(x)$ . Find the sum of the ${p}_{a,b}$ 's for all possible combinations of $a$ and $b$ .",
"type": "text"
}
],
"role": "user"
}
] |
$80$
|
di-zhang-fdu/AIME_1983_2024
|
[
{
"content": [
{
"path": "",
"text": "A user will ask you to solve a task. You should first draft your thinking process (inner monologue) until you have derived the final answer. Afterwards, write a self-contained summary of your thoughts (i.e. your summary should be succinct but contain all the critical steps you needed to reach the conclusion). You should use Markdown and Latex to format your response. Write both your thoughts and summary in the same language as the task posed by the user.\n\nYour thinking process must follow the template below:\n<think>\nYour thoughts or/and draft, like working through an exercise on scratch paper. Be as casual and as long as you want until you are confident to generate a correct answer.\n</think>\n\nHere, provide a concise summary that reflects your reasoning and presents a clear final answer to the user.\n\n",
"type": "text",
"url": null
}
],
"role": "system"
},
{
"content": [
{
"path": "",
"text": "You will be given a problem. Please reason step by step, and put your final answer within \\boxed{}:\nThere are nonzero integers $a$ , $b$ , $r$ , and $s$ such that the complex number $r+si$ is a zero of the polynomial $P(x)={x}^{3}-a{x}^{2}+bx-65$ . For each possible combination of $a$ and $b$ , let ${p}_{a,b}$ be the sum of the zeros of $P(x)$ . Find the sum of the ${p}_{a,b}$ 's for all possible combinations of $a$ and $b$ .",
"type": "text",
"url": null
}
],
"role": "user"
}
] |
[
{
"content": [
{
"text": "A user will ask you to solve a task. You should first draft your thinking process (inner monologue) until you have derived the final answer. Afterwards, write a self-contained summary of your thoughts (i.e. your summary should be succinct but contain all the critical steps you needed to reach the conclusion). You should use Markdown and Latex to format your response. Write both your thoughts and summary in the same language as the task posed by the user.\n\nYour thinking process must follow the template below:\n<think>\nYour thoughts or/and draft, like working through an exercise on scratch paper. Be as casual and as long as you want until you are confident to generate a correct answer.\n</think>\n\nHere, provide a concise summary that reflects your reasoning and presents a clear final answer to the user.\n\n",
"type": "text"
}
],
"role": "system"
},
{
"content": [
{
"text": "You will be given a problem. Please reason step by step, and put your final answer within \\boxed{}:\nFind the arithmetic mean of all the three-digit palindromes. (Recall that a palindrome is a number that reads the same forward and backward, such as $777$ or $383$ .)",
"type": "text"
}
],
"role": "user"
}
] |
$550$
|
di-zhang-fdu/AIME_1983_2024
|
[
{
"content": [
{
"path": "",
"text": "A user will ask you to solve a task. You should first draft your thinking process (inner monologue) until you have derived the final answer. Afterwards, write a self-contained summary of your thoughts (i.e. your summary should be succinct but contain all the critical steps you needed to reach the conclusion). You should use Markdown and Latex to format your response. Write both your thoughts and summary in the same language as the task posed by the user.\n\nYour thinking process must follow the template below:\n<think>\nYour thoughts or/and draft, like working through an exercise on scratch paper. Be as casual and as long as you want until you are confident to generate a correct answer.\n</think>\n\nHere, provide a concise summary that reflects your reasoning and presents a clear final answer to the user.\n\n",
"type": "text",
"url": null
}
],
"role": "system"
},
{
"content": [
{
"path": "",
"text": "You will be given a problem. Please reason step by step, and put your final answer within \\boxed{}:\nFind the arithmetic mean of all the three-digit palindromes. (Recall that a palindrome is a number that reads the same forward and backward, such as $777$ or $383$ .)",
"type": "text",
"url": null
}
],
"role": "user"
}
] |
[
{
"content": [
{
"text": "A user will ask you to solve a task. You should first draft your thinking process (inner monologue) until you have derived the final answer. Afterwards, write a self-contained summary of your thoughts (i.e. your summary should be succinct but contain all the critical steps you needed to reach the conclusion). You should use Markdown and Latex to format your response. Write both your thoughts and summary in the same language as the task posed by the user.\n\nYour thinking process must follow the template below:\n<think>\nYour thoughts or/and draft, like working through an exercise on scratch paper. Be as casual and as long as you want until you are confident to generate a correct answer.\n</think>\n\nHere, provide a concise summary that reflects your reasoning and presents a clear final answer to the user.\n\n",
"type": "text"
}
],
"role": "system"
},
{
"content": [
{
"text": "You will be given a problem. Please reason step by step, and put your final answer within \\boxed{}:\nLet $F(z)=\\frac{z+i}{z-i}$ for all complex numbers $z\\not= i$ , and let $z_n=F(z_{n-1})$ for all positive integers $n$ . Given that $z_0=\\frac 1{137}+i$ and $z_{2002}=a+bi$ , where $a$ and $b$ are real numbers, find $a+b$ .",
"type": "text"
}
],
"role": "user"
}
] |
$275$
|
di-zhang-fdu/AIME_1983_2024
|
[
{
"content": [
{
"path": "",
"text": "A user will ask you to solve a task. You should first draft your thinking process (inner monologue) until you have derived the final answer. Afterwards, write a self-contained summary of your thoughts (i.e. your summary should be succinct but contain all the critical steps you needed to reach the conclusion). You should use Markdown and Latex to format your response. Write both your thoughts and summary in the same language as the task posed by the user.\n\nYour thinking process must follow the template below:\n<think>\nYour thoughts or/and draft, like working through an exercise on scratch paper. Be as casual and as long as you want until you are confident to generate a correct answer.\n</think>\n\nHere, provide a concise summary that reflects your reasoning and presents a clear final answer to the user.\n\n",
"type": "text",
"url": null
}
],
"role": "system"
},
{
"content": [
{
"path": "",
"text": "You will be given a problem. Please reason step by step, and put your final answer within \\boxed{}:\nLet $F(z)=\\frac{z+i}{z-i}$ for all complex numbers $z\\not= i$ , and let $z_n=F(z_{n-1})$ for all positive integers $n$ . Given that $z_0=\\frac 1{137}+i$ and $z_{2002}=a+bi$ , where $a$ and $b$ are real numbers, find $a+b$ .",
"type": "text",
"url": null
}
],
"role": "user"
}
] |
[
{
"content": [
{
"text": "A user will ask you to solve a task. You should first draft your thinking process (inner monologue) until you have derived the final answer. Afterwards, write a self-contained summary of your thoughts (i.e. your summary should be succinct but contain all the critical steps you needed to reach the conclusion). You should use Markdown and Latex to format your response. Write both your thoughts and summary in the same language as the task posed by the user.\n\nYour thinking process must follow the template below:\n<think>\nYour thoughts or/and draft, like working through an exercise on scratch paper. Be as casual and as long as you want until you are confident to generate a correct answer.\n</think>\n\nHere, provide a concise summary that reflects your reasoning and presents a clear final answer to the user.\n\n\n\nYou will be given a problem. Please reason step by step, and put your final answer within \\boxed{}.",
"type": "text"
}
],
"role": "system"
},
{
"content": [
{
"text": "Let $N$ be the number of positive integers that are less than or equal to 2003 and whose base-2 representation has more 1's than 0's. Find the remainder when $N$ is divided by 1000.",
"type": "text"
}
],
"role": "user"
}
] |
$155$
|
di-zhang-fdu/AIME_1983_2024
|
[
{
"content": [
{
"path": "",
"text": "A user will ask you to solve a task. You should first draft your thinking process (inner monologue) until you have derived the final answer. Afterwards, write a self-contained summary of your thoughts (i.e. your summary should be succinct but contain all the critical steps you needed to reach the conclusion). You should use Markdown and Latex to format your response. Write both your thoughts and summary in the same language as the task posed by the user.\n\nYour thinking process must follow the template below:\n<think>\nYour thoughts or/and draft, like working through an exercise on scratch paper. Be as casual and as long as you want until you are confident to generate a correct answer.\n</think>\n\nHere, provide a concise summary that reflects your reasoning and presents a clear final answer to the user.\n\n\n\nYou will be given a problem. Please reason step by step, and put your final answer within \\boxed{}.",
"type": "text",
"url": null
}
],
"role": "system"
},
{
"content": [
{
"path": "",
"text": "Let $N$ be the number of positive integers that are less than or equal to 2003 and whose base-2 representation has more 1's than 0's. Find the remainder when $N$ is divided by 1000.",
"type": "text",
"url": null
}
],
"role": "user"
}
] |
[
{
"content": [
{
"text": "A user will ask you to solve a task. You should first draft your thinking process (inner monologue) until you have derived the final answer. Afterwards, write a self-contained summary of your thoughts (i.e. your summary should be succinct but contain all the critical steps you needed to reach the conclusion). You should use Markdown and Latex to format your response. Write both your thoughts and summary in the same language as the task posed by the user.\n\nYour thinking process must follow the template below:\n<think>\nYour thoughts or/and draft, like working through an exercise on scratch paper. Be as casual and as long as you want until you are confident to generate a correct answer.\n</think>\n\nHere, provide a concise summary that reflects your reasoning and presents a clear final answer to the user.\n\n\n\nYou will be given a problem. Please reason step by step, and put your final answer within \\boxed{}.",
"type": "text"
}
],
"role": "system"
},
{
"content": [
{
"text": "Let $\\triangle ABC$ be an acute triangle with circumcircle $\\omega,$ and let $H$ be the intersection of the altitudes of $\\triangle ABC.$ Suppose the tangent to the circumcircle of $\\triangle HBC$ at $H$ intersects $\\omega$ at points $X$ and $Y$ with $HA=3,HX=2,$ and $HY=6.$ The area of $\\triangle ABC$ can be written in the form $m\\sqrt{n},$ where $m$ and $n$ are positive integers, and $n$ is not divisible by the square of any prime. Find $m+n.$",
"type": "text"
}
],
"role": "user"
}
] |
$58$
|
di-zhang-fdu/AIME_1983_2024
|
[
{
"content": [
{
"path": "",
"text": "A user will ask you to solve a task. You should first draft your thinking process (inner monologue) until you have derived the final answer. Afterwards, write a self-contained summary of your thoughts (i.e. your summary should be succinct but contain all the critical steps you needed to reach the conclusion). You should use Markdown and Latex to format your response. Write both your thoughts and summary in the same language as the task posed by the user.\n\nYour thinking process must follow the template below:\n<think>\nYour thoughts or/and draft, like working through an exercise on scratch paper. Be as casual and as long as you want until you are confident to generate a correct answer.\n</think>\n\nHere, provide a concise summary that reflects your reasoning and presents a clear final answer to the user.\n\n\n\nYou will be given a problem. Please reason step by step, and put your final answer within \\boxed{}.",
"type": "text",
"url": null
}
],
"role": "system"
},
{
"content": [
{
"path": "",
"text": "Let $\\triangle ABC$ be an acute triangle with circumcircle $\\omega,$ and let $H$ be the intersection of the altitudes of $\\triangle ABC.$ Suppose the tangent to the circumcircle of $\\triangle HBC$ at $H$ intersects $\\omega$ at points $X$ and $Y$ with $HA=3,HX=2,$ and $HY=6.$ The area of $\\triangle ABC$ can be written in the form $m\\sqrt{n},$ where $m$ and $n$ are positive integers, and $n$ is not divisible by the square of any prime. Find $m+n.$",
"type": "text",
"url": null
}
],
"role": "user"
}
] |
[
{
"content": [
{
"text": "A user will ask you to solve a task. You should first draft your thinking process (inner monologue) until you have derived the final answer. Afterwards, write a self-contained summary of your thoughts (i.e. your summary should be succinct but contain all the critical steps you needed to reach the conclusion). You should use Markdown and Latex to format your response. Write both your thoughts and summary in the same language as the task posed by the user.\n\nYour thinking process must follow the template below:\n<think>\nYour thoughts or/and draft, like working through an exercise on scratch paper. Be as casual and as long as you want until you are confident to generate a correct answer.\n</think>\n\nHere, provide a concise summary that reflects your reasoning and presents a clear final answer to the user.\n\n",
"type": "text"
}
],
"role": "system"
},
{
"content": [
{
"text": "You will be given a problem. Please reason step by step, and put your final answer within \\boxed{}:\nTwo squares of a $7\\times 7$ checkerboard are painted yellow, and the rest are painted green. Two color schemes are equivalent if one can be obtained from the other by applying a rotation in the plane board. How many inequivalent color schemes are possible?",
"type": "text"
}
],
"role": "user"
}
] |
$300$
|
di-zhang-fdu/AIME_1983_2024
|
[
{
"content": [
{
"path": "",
"text": "A user will ask you to solve a task. You should first draft your thinking process (inner monologue) until you have derived the final answer. Afterwards, write a self-contained summary of your thoughts (i.e. your summary should be succinct but contain all the critical steps you needed to reach the conclusion). You should use Markdown and Latex to format your response. Write both your thoughts and summary in the same language as the task posed by the user.\n\nYour thinking process must follow the template below:\n<think>\nYour thoughts or/and draft, like working through an exercise on scratch paper. Be as casual and as long as you want until you are confident to generate a correct answer.\n</think>\n\nHere, provide a concise summary that reflects your reasoning and presents a clear final answer to the user.\n\n",
"type": "text",
"url": null
}
],
"role": "system"
},
{
"content": [
{
"path": "",
"text": "You will be given a problem. Please reason step by step, and put your final answer within \\boxed{}:\nTwo squares of a $7\\times 7$ checkerboard are painted yellow, and the rest are painted green. Two color schemes are equivalent if one can be obtained from the other by applying a rotation in the plane board. How many inequivalent color schemes are possible?",
"type": "text",
"url": null
}
],
"role": "user"
}
] |
[
{
"content": [
{
"text": "A user will ask you to solve a task. You should first draft your thinking process (inner monologue) until you have derived the final answer. Afterwards, write a self-contained summary of your thoughts (i.e. your summary should be succinct but contain all the critical steps you needed to reach the conclusion). You should use Markdown and Latex to format your response. Write both your thoughts and summary in the same language as the task posed by the user.\n\nYour thinking process must follow the template below:\n<think>\nYour thoughts or/and draft, like working through an exercise on scratch paper. Be as casual and as long as you want until you are confident to generate a correct answer.\n</think>\n\nHere, provide a concise summary that reflects your reasoning and presents a clear final answer to the user.\n\n\n\nYou will be given a problem. Please reason step by step, and put your final answer within \\boxed{}.",
"type": "text"
}
],
"role": "system"
},
{
"content": [
{
"text": "An integer is called parity-monotonic if its decimal representation $a_{1}a_{2}a_{3}\\cdots a_{k}$ satisfies $a_{i}<a_{i+1}$ if $a_{i}$ is odd , and $a_{i}>a_{i+1}$ if $a_{i}$ is even . How many four-digit parity-monotonic integers are there?",
"type": "text"
}
],
"role": "user"
}
] |
$640$
|
di-zhang-fdu/AIME_1983_2024
|
[
{
"content": [
{
"path": "",
"text": "A user will ask you to solve a task. You should first draft your thinking process (inner monologue) until you have derived the final answer. Afterwards, write a self-contained summary of your thoughts (i.e. your summary should be succinct but contain all the critical steps you needed to reach the conclusion). You should use Markdown and Latex to format your response. Write both your thoughts and summary in the same language as the task posed by the user.\n\nYour thinking process must follow the template below:\n<think>\nYour thoughts or/and draft, like working through an exercise on scratch paper. Be as casual and as long as you want until you are confident to generate a correct answer.\n</think>\n\nHere, provide a concise summary that reflects your reasoning and presents a clear final answer to the user.\n\n\n\nYou will be given a problem. Please reason step by step, and put your final answer within \\boxed{}.",
"type": "text",
"url": null
}
],
"role": "system"
},
{
"content": [
{
"path": "",
"text": "An integer is called parity-monotonic if its decimal representation $a_{1}a_{2}a_{3}\\cdots a_{k}$ satisfies $a_{i}<a_{i+1}$ if $a_{i}$ is odd , and $a_{i}>a_{i+1}$ if $a_{i}$ is even . How many four-digit parity-monotonic integers are there?",
"type": "text",
"url": null
}
],
"role": "user"
}
] |
[
{
"content": [
{
"text": "A user will ask you to solve a task. You should first draft your thinking process (inner monologue) until you have derived the final answer. Afterwards, write a self-contained summary of your thoughts (i.e. your summary should be succinct but contain all the critical steps you needed to reach the conclusion). You should use Markdown and Latex to format your response. Write both your thoughts and summary in the same language as the task posed by the user.\n\nYour thinking process must follow the template below:\n<think>\nYour thoughts or/and draft, like working through an exercise on scratch paper. Be as casual and as long as you want until you are confident to generate a correct answer.\n</think>\n\nHere, provide a concise summary that reflects your reasoning and presents a clear final answer to the user.\n\n",
"type": "text"
}
],
"role": "system"
},
{
"content": [
{
"text": "You will be given a problem. Please reason step by step, and put your final answer within \\boxed{}:\nIn acute triangle $ABC,$ points $P$ and $Q$ are the feet of the perpendiculars from $C$ to $\\overline{AB}$ and from $B$ to $\\overline{AC}$ , respectively. Line $PQ$ intersects the circumcircle of $\\triangle ABC$ in two distinct points, $X$ and $Y$ . Suppose $XP=10$ , $PQ=25$ , and $QY=15$ . The value of $AB\\cdot AC$ can be written in the form $m\\sqrt n$ where $m$ and $n$ are positive integers, and $n$ is not divisible by the square of any prime. Find $m+n$ .",
"type": "text"
}
],
"role": "user"
}
] |
$574$
|
di-zhang-fdu/AIME_1983_2024
|
[
{
"content": [
{
"path": "",
"text": "A user will ask you to solve a task. You should first draft your thinking process (inner monologue) until you have derived the final answer. Afterwards, write a self-contained summary of your thoughts (i.e. your summary should be succinct but contain all the critical steps you needed to reach the conclusion). You should use Markdown and Latex to format your response. Write both your thoughts and summary in the same language as the task posed by the user.\n\nYour thinking process must follow the template below:\n<think>\nYour thoughts or/and draft, like working through an exercise on scratch paper. Be as casual and as long as you want until you are confident to generate a correct answer.\n</think>\n\nHere, provide a concise summary that reflects your reasoning and presents a clear final answer to the user.\n\n",
"type": "text",
"url": null
}
],
"role": "system"
},
{
"content": [
{
"path": "",
"text": "You will be given a problem. Please reason step by step, and put your final answer within \\boxed{}:\nIn acute triangle $ABC,$ points $P$ and $Q$ are the feet of the perpendiculars from $C$ to $\\overline{AB}$ and from $B$ to $\\overline{AC}$ , respectively. Line $PQ$ intersects the circumcircle of $\\triangle ABC$ in two distinct points, $X$ and $Y$ . Suppose $XP=10$ , $PQ=25$ , and $QY=15$ . The value of $AB\\cdot AC$ can be written in the form $m\\sqrt n$ where $m$ and $n$ are positive integers, and $n$ is not divisible by the square of any prime. Find $m+n$ .",
"type": "text",
"url": null
}
],
"role": "user"
}
] |
[
{
"content": [
{
"text": "A user will ask you to solve a task. You should first draft your thinking process (inner monologue) until you have derived the final answer. Afterwards, write a self-contained summary of your thoughts (i.e. your summary should be succinct but contain all the critical steps you needed to reach the conclusion). You should use Markdown and Latex to format your response. Write both your thoughts and summary in the same language as the task posed by the user.\n\nYour thinking process must follow the template below:\n<think>\nYour thoughts or/and draft, like working through an exercise on scratch paper. Be as casual and as long as you want until you are confident to generate a correct answer.\n</think>\n\nHere, provide a concise summary that reflects your reasoning and presents a clear final answer to the user.\n\n",
"type": "text"
}
],
"role": "system"
},
{
"content": [
{
"text": "You will be given a problem. Please reason step by step, and put your final answer within \\boxed{}:\nFind the smallest positive integer whose cube ends in $888$ .",
"type": "text"
}
],
"role": "user"
}
] |
$192$
|
di-zhang-fdu/AIME_1983_2024
|
[
{
"content": [
{
"path": "",
"text": "A user will ask you to solve a task. You should first draft your thinking process (inner monologue) until you have derived the final answer. Afterwards, write a self-contained summary of your thoughts (i.e. your summary should be succinct but contain all the critical steps you needed to reach the conclusion). You should use Markdown and Latex to format your response. Write both your thoughts and summary in the same language as the task posed by the user.\n\nYour thinking process must follow the template below:\n<think>\nYour thoughts or/and draft, like working through an exercise on scratch paper. Be as casual and as long as you want until you are confident to generate a correct answer.\n</think>\n\nHere, provide a concise summary that reflects your reasoning and presents a clear final answer to the user.\n\n",
"type": "text",
"url": null
}
],
"role": "system"
},
{
"content": [
{
"path": "",
"text": "You will be given a problem. Please reason step by step, and put your final answer within \\boxed{}:\nFind the smallest positive integer whose cube ends in $888$ .",
"type": "text",
"url": null
}
],
"role": "user"
}
] |
[
{
"content": [
{
"text": "A user will ask you to solve a task. You should first draft your thinking process (inner monologue) until you have derived the final answer. Afterwards, write a self-contained summary of your thoughts (i.e. your summary should be succinct but contain all the critical steps you needed to reach the conclusion). You should use Markdown and Latex to format your response. Write both your thoughts and summary in the same language as the task posed by the user.\n\nYour thinking process must follow the template below:\n<think>\nYour thoughts or/and draft, like working through an exercise on scratch paper. Be as casual and as long as you want until you are confident to generate a correct answer.\n</think>\n\nHere, provide a concise summary that reflects your reasoning and presents a clear final answer to the user.\n\n",
"type": "text"
}
],
"role": "system"
},
{
"content": [
{
"text": "You will be given a problem. Please reason step by step, and put your final answer within \\boxed{}:\nConvex pentagon $ABCDE$ has side lengths $AB=5$ , $BC=CD=DE=6$ , and $EA=7$ . Moreover, the pentagon has an inscribed circle (a circle tangent to each side of the pentagon). Find the area of $ABCDE$ .",
"type": "text"
}
],
"role": "user"
}
] |
$60$
|
di-zhang-fdu/AIME_1983_2024
|
[
{
"content": [
{
"path": "",
"text": "A user will ask you to solve a task. You should first draft your thinking process (inner monologue) until you have derived the final answer. Afterwards, write a self-contained summary of your thoughts (i.e. your summary should be succinct but contain all the critical steps you needed to reach the conclusion). You should use Markdown and Latex to format your response. Write both your thoughts and summary in the same language as the task posed by the user.\n\nYour thinking process must follow the template below:\n<think>\nYour thoughts or/and draft, like working through an exercise on scratch paper. Be as casual and as long as you want until you are confident to generate a correct answer.\n</think>\n\nHere, provide a concise summary that reflects your reasoning and presents a clear final answer to the user.\n\n",
"type": "text",
"url": null
}
],
"role": "system"
},
{
"content": [
{
"path": "",
"text": "You will be given a problem. Please reason step by step, and put your final answer within \\boxed{}:\nConvex pentagon $ABCDE$ has side lengths $AB=5$ , $BC=CD=DE=6$ , and $EA=7$ . Moreover, the pentagon has an inscribed circle (a circle tangent to each side of the pentagon). Find the area of $ABCDE$ .",
"type": "text",
"url": null
}
],
"role": "user"
}
] |
[
{
"content": [
{
"text": "A user will ask you to solve a task. You should first draft your thinking process (inner monologue) until you have derived the final answer. Afterwards, write a self-contained summary of your thoughts (i.e. your summary should be succinct but contain all the critical steps you needed to reach the conclusion). You should use Markdown and Latex to format your response. Write both your thoughts and summary in the same language as the task posed by the user.\n\nYour thinking process must follow the template below:\n<think>\nYour thoughts or/and draft, like working through an exercise on scratch paper. Be as casual and as long as you want until you are confident to generate a correct answer.\n</think>\n\nHere, provide a concise summary that reflects your reasoning and presents a clear final answer to the user.\n\n\n\nYou will be given a problem. Please reason step by step, and put your final answer within \\boxed{}.",
"type": "text"
}
],
"role": "system"
},
{
"content": [
{
"text": "Polyhedron $ABCDEFG$ has six faces. Face $ABCD$ is a square with $AB = 12;$ face $ABFG$ is a trapezoid with $\\overline{AB}$ parallel to $\\overline{GF},$ $BF = AG = 8,$ and $GF = 6;$ and face $CDE$ has $CE = DE = 14.$ The other three faces are $ADEG, BCEF,$ and $EFG.$ The distance from $E$ to face $ABCD$ is 12. Given that $EG^2 = p - q\\sqrt {r},$ where $p, q,$ and $r$ are positive integers and $r$ is not divisible by the square of any prime, find $p + q + r.$",
"type": "text"
}
],
"role": "user"
}
] |
$163$
|
di-zhang-fdu/AIME_1983_2024
|
[
{
"content": [
{
"path": "",
"text": "A user will ask you to solve a task. You should first draft your thinking process (inner monologue) until you have derived the final answer. Afterwards, write a self-contained summary of your thoughts (i.e. your summary should be succinct but contain all the critical steps you needed to reach the conclusion). You should use Markdown and Latex to format your response. Write both your thoughts and summary in the same language as the task posed by the user.\n\nYour thinking process must follow the template below:\n<think>\nYour thoughts or/and draft, like working through an exercise on scratch paper. Be as casual and as long as you want until you are confident to generate a correct answer.\n</think>\n\nHere, provide a concise summary that reflects your reasoning and presents a clear final answer to the user.\n\n\n\nYou will be given a problem. Please reason step by step, and put your final answer within \\boxed{}.",
"type": "text",
"url": null
}
],
"role": "system"
},
{
"content": [
{
"path": "",
"text": "Polyhedron $ABCDEFG$ has six faces. Face $ABCD$ is a square with $AB = 12;$ face $ABFG$ is a trapezoid with $\\overline{AB}$ parallel to $\\overline{GF},$ $BF = AG = 8,$ and $GF = 6;$ and face $CDE$ has $CE = DE = 14.$ The other three faces are $ADEG, BCEF,$ and $EFG.$ The distance from $E$ to face $ABCD$ is 12. Given that $EG^2 = p - q\\sqrt {r},$ where $p, q,$ and $r$ are positive integers and $r$ is not divisible by the square of any prime, find $p + q + r.$",
"type": "text",
"url": null
}
],
"role": "user"
}
] |
[
{
"content": [
{
"text": "A user will ask you to solve a task. You should first draft your thinking process (inner monologue) until you have derived the final answer. Afterwards, write a self-contained summary of your thoughts (i.e. your summary should be succinct but contain all the critical steps you needed to reach the conclusion). You should use Markdown and Latex to format your response. Write both your thoughts and summary in the same language as the task posed by the user.\n\nYour thinking process must follow the template below:\n<think>\nYour thoughts or/and draft, like working through an exercise on scratch paper. Be as casual and as long as you want until you are confident to generate a correct answer.\n</think>\n\nHere, provide a concise summary that reflects your reasoning and presents a clear final answer to the user.\n\n",
"type": "text"
}
],
"role": "system"
},
{
"content": [
{
"text": "You will be given a problem. Please reason step by step, and put your final answer within \\boxed{}:\nRhombus $ABCD$ has $\\angle BAD < 90^\\circ.$ There is a point $P$ on the incircle of the rhombus such that the distances from $P$ to the lines $DA,AB,$ and $BC$ are $9,5,$ and $16,$ respectively. Find the perimeter of $ABCD.$",
"type": "text"
}
],
"role": "user"
}
] |
$125$
|
di-zhang-fdu/AIME_1983_2024
|
[
{
"content": [
{
"path": "",
"text": "A user will ask you to solve a task. You should first draft your thinking process (inner monologue) until you have derived the final answer. Afterwards, write a self-contained summary of your thoughts (i.e. your summary should be succinct but contain all the critical steps you needed to reach the conclusion). You should use Markdown and Latex to format your response. Write both your thoughts and summary in the same language as the task posed by the user.\n\nYour thinking process must follow the template below:\n<think>\nYour thoughts or/and draft, like working through an exercise on scratch paper. Be as casual and as long as you want until you are confident to generate a correct answer.\n</think>\n\nHere, provide a concise summary that reflects your reasoning and presents a clear final answer to the user.\n\n",
"type": "text",
"url": null
}
],
"role": "system"
},
{
"content": [
{
"path": "",
"text": "You will be given a problem. Please reason step by step, and put your final answer within \\boxed{}:\nRhombus $ABCD$ has $\\angle BAD < 90^\\circ.$ There is a point $P$ on the incircle of the rhombus such that the distances from $P$ to the lines $DA,AB,$ and $BC$ are $9,5,$ and $16,$ respectively. Find the perimeter of $ABCD.$",
"type": "text",
"url": null
}
],
"role": "user"
}
] |
[
{
"content": [
{
"text": "A user will ask you to solve a task. You should first draft your thinking process (inner monologue) until you have derived the final answer. Afterwards, write a self-contained summary of your thoughts (i.e. your summary should be succinct but contain all the critical steps you needed to reach the conclusion). You should use Markdown and Latex to format your response. Write both your thoughts and summary in the same language as the task posed by the user.\n\nYour thinking process must follow the template below:\n<think>\nYour thoughts or/and draft, like working through an exercise on scratch paper. Be as casual and as long as you want until you are confident to generate a correct answer.\n</think>\n\nHere, provide a concise summary that reflects your reasoning and presents a clear final answer to the user.\n\n\n\nYou will be given a problem. Please reason step by step, and put your final answer within \\boxed{}.",
"type": "text"
}
],
"role": "system"
},
{
"content": [
{
"text": "Let $S$ be the set of all ordered triple of integers $(a_1,a_2,a_3)$ with $1 \\le a_1,a_2,a_3 \\le 10$ . Each ordered triple in $S$ generates a sequence according to the rule $a_n=a_{n-1}\\cdot | a_{n-2}-a_{n-3} |$ for all $n\\ge 4$ . Find the number of such sequences for which $a_n=0$ for some $n$ .",
"type": "text"
}
],
"role": "user"
}
] |
$494$
|
di-zhang-fdu/AIME_1983_2024
|
[
{
"content": [
{
"path": "",
"text": "A user will ask you to solve a task. You should first draft your thinking process (inner monologue) until you have derived the final answer. Afterwards, write a self-contained summary of your thoughts (i.e. your summary should be succinct but contain all the critical steps you needed to reach the conclusion). You should use Markdown and Latex to format your response. Write both your thoughts and summary in the same language as the task posed by the user.\n\nYour thinking process must follow the template below:\n<think>\nYour thoughts or/and draft, like working through an exercise on scratch paper. Be as casual and as long as you want until you are confident to generate a correct answer.\n</think>\n\nHere, provide a concise summary that reflects your reasoning and presents a clear final answer to the user.\n\n\n\nYou will be given a problem. Please reason step by step, and put your final answer within \\boxed{}.",
"type": "text",
"url": null
}
],
"role": "system"
},
{
"content": [
{
"path": "",
"text": "Let $S$ be the set of all ordered triple of integers $(a_1,a_2,a_3)$ with $1 \\le a_1,a_2,a_3 \\le 10$ . Each ordered triple in $S$ generates a sequence according to the rule $a_n=a_{n-1}\\cdot | a_{n-2}-a_{n-3} |$ for all $n\\ge 4$ . Find the number of such sequences for which $a_n=0$ for some $n$ .",
"type": "text",
"url": null
}
],
"role": "user"
}
] |
[
{
"content": [
{
"text": "A user will ask you to solve a task. You should first draft your thinking process (inner monologue) until you have derived the final answer. Afterwards, write a self-contained summary of your thoughts (i.e. your summary should be succinct but contain all the critical steps you needed to reach the conclusion). You should use Markdown and Latex to format your response. Write both your thoughts and summary in the same language as the task posed by the user.\n\nYour thinking process must follow the template below:\n<think>\nYour thoughts or/and draft, like working through an exercise on scratch paper. Be as casual and as long as you want until you are confident to generate a correct answer.\n</think>\n\nHere, provide a concise summary that reflects your reasoning and presents a clear final answer to the user.\n\n\n\nYou will be given a problem. Please reason step by step, and put your final answer within \\boxed{}.",
"type": "text"
}
],
"role": "system"
},
{
"content": [
{
"text": "Find the number of four-element subsets of $\\{1,2,3,4,\\dots, 20\\}$ with the property that two distinct elements of a subset have a sum of $16$ , and two distinct elements of a subset have a sum of $24$ . For example, $\\{3,5,13,19\\}$ and $\\{6,10,20,18\\}$ are two such subsets.",
"type": "text"
}
],
"role": "user"
}
] |
$210$
|
di-zhang-fdu/AIME_1983_2024
|
[
{
"content": [
{
"path": "",
"text": "A user will ask you to solve a task. You should first draft your thinking process (inner monologue) until you have derived the final answer. Afterwards, write a self-contained summary of your thoughts (i.e. your summary should be succinct but contain all the critical steps you needed to reach the conclusion). You should use Markdown and Latex to format your response. Write both your thoughts and summary in the same language as the task posed by the user.\n\nYour thinking process must follow the template below:\n<think>\nYour thoughts or/and draft, like working through an exercise on scratch paper. Be as casual and as long as you want until you are confident to generate a correct answer.\n</think>\n\nHere, provide a concise summary that reflects your reasoning and presents a clear final answer to the user.\n\n\n\nYou will be given a problem. Please reason step by step, and put your final answer within \\boxed{}.",
"type": "text",
"url": null
}
],
"role": "system"
},
{
"content": [
{
"path": "",
"text": "Find the number of four-element subsets of $\\{1,2,3,4,\\dots, 20\\}$ with the property that two distinct elements of a subset have a sum of $16$ , and two distinct elements of a subset have a sum of $24$ . For example, $\\{3,5,13,19\\}$ and $\\{6,10,20,18\\}$ are two such subsets.",
"type": "text",
"url": null
}
],
"role": "user"
}
] |
[
{
"content": [
{
"text": "A user will ask you to solve a task. You should first draft your thinking process (inner monologue) until you have derived the final answer. Afterwards, write a self-contained summary of your thoughts (i.e. your summary should be succinct but contain all the critical steps you needed to reach the conclusion). You should use Markdown and Latex to format your response. Write both your thoughts and summary in the same language as the task posed by the user.\n\nYour thinking process must follow the template below:\n<think>\nYour thoughts or/and draft, like working through an exercise on scratch paper. Be as casual and as long as you want until you are confident to generate a correct answer.\n</think>\n\nHere, provide a concise summary that reflects your reasoning and presents a clear final answer to the user.\n\n",
"type": "text"
}
],
"role": "system"
},
{
"content": [
{
"text": "You will be given a problem. Please reason step by step, and put your final answer within \\boxed{}:\nTriangle $ABC$ has $BC=20.$ The incircle of the triangle evenly trisects the median $AD.$ If the area of the triangle is $m \\sqrt{n}$ where $m$ and $n$ are integers and $n$ is not divisible by the square of a prime, find $m+n.$",
"type": "text"
}
],
"role": "user"
}
] |
$38$
|
di-zhang-fdu/AIME_1983_2024
|
[
{
"content": [
{
"path": "",
"text": "A user will ask you to solve a task. You should first draft your thinking process (inner monologue) until you have derived the final answer. Afterwards, write a self-contained summary of your thoughts (i.e. your summary should be succinct but contain all the critical steps you needed to reach the conclusion). You should use Markdown and Latex to format your response. Write both your thoughts and summary in the same language as the task posed by the user.\n\nYour thinking process must follow the template below:\n<think>\nYour thoughts or/and draft, like working through an exercise on scratch paper. Be as casual and as long as you want until you are confident to generate a correct answer.\n</think>\n\nHere, provide a concise summary that reflects your reasoning and presents a clear final answer to the user.\n\n",
"type": "text",
"url": null
}
],
"role": "system"
},
{
"content": [
{
"path": "",
"text": "You will be given a problem. Please reason step by step, and put your final answer within \\boxed{}:\nTriangle $ABC$ has $BC=20.$ The incircle of the triangle evenly trisects the median $AD.$ If the area of the triangle is $m \\sqrt{n}$ where $m$ and $n$ are integers and $n$ is not divisible by the square of a prime, find $m+n.$",
"type": "text",
"url": null
}
],
"role": "user"
}
] |
[
{
"content": [
{
"text": "A user will ask you to solve a task. You should first draft your thinking process (inner monologue) until you have derived the final answer. Afterwards, write a self-contained summary of your thoughts (i.e. your summary should be succinct but contain all the critical steps you needed to reach the conclusion). You should use Markdown and Latex to format your response. Write both your thoughts and summary in the same language as the task posed by the user.\n\nYour thinking process must follow the template below:\n<think>\nYour thoughts or/and draft, like working through an exercise on scratch paper. Be as casual and as long as you want until you are confident to generate a correct answer.\n</think>\n\nHere, provide a concise summary that reflects your reasoning and presents a clear final answer to the user.\n\n\n\nYou will be given a problem. Please reason step by step, and put your final answer within \\boxed{}.",
"type": "text"
}
],
"role": "system"
},
{
"content": [
{
"text": "An ant makes a sequence of moves on a cube where a move consists of walking from one vertex to an adjacent vertex along an edge of the cube. Initially the ant is at a vertex of the bottom face of the cube and chooses one of the three adjacent vertices to move to as its first move. For all moves after the first move, the ant does not return to its previous vertex, but chooses to move to one of the other two adjacent vertices. All choices are selected at random so that each of the possible moves is equally likely. The probability that after exactly $8$ moves that ant is at a vertex of the top face on the cube is $\\frac{m}{n}$ , where $m$ and $n$ are relatively prime positive integers. Find $m + n.$",
"type": "text"
}
],
"role": "user"
}
] |
$49$
|
di-zhang-fdu/AIME_1983_2024
|
[
{
"content": [
{
"path": "",
"text": "A user will ask you to solve a task. You should first draft your thinking process (inner monologue) until you have derived the final answer. Afterwards, write a self-contained summary of your thoughts (i.e. your summary should be succinct but contain all the critical steps you needed to reach the conclusion). You should use Markdown and Latex to format your response. Write both your thoughts and summary in the same language as the task posed by the user.\n\nYour thinking process must follow the template below:\n<think>\nYour thoughts or/and draft, like working through an exercise on scratch paper. Be as casual and as long as you want until you are confident to generate a correct answer.\n</think>\n\nHere, provide a concise summary that reflects your reasoning and presents a clear final answer to the user.\n\n\n\nYou will be given a problem. Please reason step by step, and put your final answer within \\boxed{}.",
"type": "text",
"url": null
}
],
"role": "system"
},
{
"content": [
{
"path": "",
"text": "An ant makes a sequence of moves on a cube where a move consists of walking from one vertex to an adjacent vertex along an edge of the cube. Initially the ant is at a vertex of the bottom face of the cube and chooses one of the three adjacent vertices to move to as its first move. For all moves after the first move, the ant does not return to its previous vertex, but chooses to move to one of the other two adjacent vertices. All choices are selected at random so that each of the possible moves is equally likely. The probability that after exactly $8$ moves that ant is at a vertex of the top face on the cube is $\\frac{m}{n}$ , where $m$ and $n$ are relatively prime positive integers. Find $m + n.$",
"type": "text",
"url": null
}
],
"role": "user"
}
] |
[
{
"content": [
{
"text": "A user will ask you to solve a task. You should first draft your thinking process (inner monologue) until you have derived the final answer. Afterwards, write a self-contained summary of your thoughts (i.e. your summary should be succinct but contain all the critical steps you needed to reach the conclusion). You should use Markdown and Latex to format your response. Write both your thoughts and summary in the same language as the task posed by the user.\n\nYour thinking process must follow the template below:\n<think>\nYour thoughts or/and draft, like working through an exercise on scratch paper. Be as casual and as long as you want until you are confident to generate a correct answer.\n</think>\n\nHere, provide a concise summary that reflects your reasoning and presents a clear final answer to the user.\n\n",
"type": "text"
}
],
"role": "system"
},
{
"content": [
{
"text": "You will be given a problem. Please reason step by step, and put your final answer within \\boxed{}:\nThe vertices of $\\triangle ABC$ are $A = (0,0)\\,$ , $B = (0,420)\\,$ , and $C = (560,0)\\,$ . The six faces of a die are labeled with two $A\\,$ 's, two $B\\,$ 's, and two $C\\,$ 's. Point $P_1 = (k,m)\\,$ is chosen in the interior of $\\triangle ABC$ , and points $P_2\\,$ , $P_3\\,$ , $P_4, \\dots$ are generated by rolling the die repeatedly and applying the rule: If the die shows label $L\\,$ , where $L \\in \\{A, B, C\\}$ , and $P_n\\,$ is the most recently obtained point, then $P_{n + 1}^{}$ is the midpoint of $\\overline{P_n L}$ . Given that $P_7 = (14,92)\\,$ , what is $k + m\\,$ ?",
"type": "text"
}
],
"role": "user"
}
] |
$344$
|
di-zhang-fdu/AIME_1983_2024
|
[
{
"content": [
{
"path": "",
"text": "A user will ask you to solve a task. You should first draft your thinking process (inner monologue) until you have derived the final answer. Afterwards, write a self-contained summary of your thoughts (i.e. your summary should be succinct but contain all the critical steps you needed to reach the conclusion). You should use Markdown and Latex to format your response. Write both your thoughts and summary in the same language as the task posed by the user.\n\nYour thinking process must follow the template below:\n<think>\nYour thoughts or/and draft, like working through an exercise on scratch paper. Be as casual and as long as you want until you are confident to generate a correct answer.\n</think>\n\nHere, provide a concise summary that reflects your reasoning and presents a clear final answer to the user.\n\n",
"type": "text",
"url": null
}
],
"role": "system"
},
{
"content": [
{
"path": "",
"text": "You will be given a problem. Please reason step by step, and put your final answer within \\boxed{}:\nThe vertices of $\\triangle ABC$ are $A = (0,0)\\,$ , $B = (0,420)\\,$ , and $C = (560,0)\\,$ . The six faces of a die are labeled with two $A\\,$ 's, two $B\\,$ 's, and two $C\\,$ 's. Point $P_1 = (k,m)\\,$ is chosen in the interior of $\\triangle ABC$ , and points $P_2\\,$ , $P_3\\,$ , $P_4, \\dots$ are generated by rolling the die repeatedly and applying the rule: If the die shows label $L\\,$ , where $L \\in \\{A, B, C\\}$ , and $P_n\\,$ is the most recently obtained point, then $P_{n + 1}^{}$ is the midpoint of $\\overline{P_n L}$ . Given that $P_7 = (14,92)\\,$ , what is $k + m\\,$ ?",
"type": "text",
"url": null
}
],
"role": "user"
}
] |
[
{
"content": [
{
"text": "A user will ask you to solve a task. You should first draft your thinking process (inner monologue) until you have derived the final answer. Afterwards, write a self-contained summary of your thoughts (i.e. your summary should be succinct but contain all the critical steps you needed to reach the conclusion). You should use Markdown and Latex to format your response. Write both your thoughts and summary in the same language as the task posed by the user.\n\nYour thinking process must follow the template below:\n<think>\nYour thoughts or/and draft, like working through an exercise on scratch paper. Be as casual and as long as you want until you are confident to generate a correct answer.\n</think>\n\nHere, provide a concise summary that reflects your reasoning and presents a clear final answer to the user.\n\n\n\nYou will be given a problem. Please reason step by step, and put your final answer within \\boxed{}.",
"type": "text"
}
],
"role": "system"
},
{
"content": [
{
"text": "There is a unique angle $\\theta$ between $0^\\circ$ and $90^\\circ$ such that for nonnegative integers $n,$ the value of $\\tan(2^n\\theta)$ is positive when $n$ is a multiple of $3$ , and negative otherwise. The degree measure of $\\theta$ is $\\tfrac{p}{q}$ , where $p$ and $q$ are relatively prime positive integers. Find $p+q$ .",
"type": "text"
}
],
"role": "user"
}
] |
$547$
|
di-zhang-fdu/AIME_1983_2024
|
[
{
"content": [
{
"path": "",
"text": "A user will ask you to solve a task. You should first draft your thinking process (inner monologue) until you have derived the final answer. Afterwards, write a self-contained summary of your thoughts (i.e. your summary should be succinct but contain all the critical steps you needed to reach the conclusion). You should use Markdown and Latex to format your response. Write both your thoughts and summary in the same language as the task posed by the user.\n\nYour thinking process must follow the template below:\n<think>\nYour thoughts or/and draft, like working through an exercise on scratch paper. Be as casual and as long as you want until you are confident to generate a correct answer.\n</think>\n\nHere, provide a concise summary that reflects your reasoning and presents a clear final answer to the user.\n\n\n\nYou will be given a problem. Please reason step by step, and put your final answer within \\boxed{}.",
"type": "text",
"url": null
}
],
"role": "system"
},
{
"content": [
{
"path": "",
"text": "There is a unique angle $\\theta$ between $0^\\circ$ and $90^\\circ$ such that for nonnegative integers $n,$ the value of $\\tan(2^n\\theta)$ is positive when $n$ is a multiple of $3$ , and negative otherwise. The degree measure of $\\theta$ is $\\tfrac{p}{q}$ , where $p$ and $q$ are relatively prime positive integers. Find $p+q$ .",
"type": "text",
"url": null
}
],
"role": "user"
}
] |
[
{
"content": [
{
"text": "A user will ask you to solve a task. You should first draft your thinking process (inner monologue) until you have derived the final answer. Afterwards, write a self-contained summary of your thoughts (i.e. your summary should be succinct but contain all the critical steps you needed to reach the conclusion). You should use Markdown and Latex to format your response. Write both your thoughts and summary in the same language as the task posed by the user.\n\nYour thinking process must follow the template below:\n<think>\nYour thoughts or/and draft, like working through an exercise on scratch paper. Be as casual and as long as you want until you are confident to generate a correct answer.\n</think>\n\nHere, provide a concise summary that reflects your reasoning and presents a clear final answer to the user.\n\n\n\nYou will be given a problem. Please reason step by step, and put your final answer within \\boxed{}.",
"type": "text"
}
],
"role": "system"
},
{
"content": [
{
"text": "Let $x$ , $y$ and $z$ all exceed $1$ and let $w$ be a positive number such that $\\log_xw=24$ , $\\log_y w = 40$ and $\\log_{xyz}w=12$ . Find $\\log_zw$ .",
"type": "text"
}
],
"role": "user"
}
] |
$60$
|
di-zhang-fdu/AIME_1983_2024
|
[
{
"content": [
{
"path": "",
"text": "A user will ask you to solve a task. You should first draft your thinking process (inner monologue) until you have derived the final answer. Afterwards, write a self-contained summary of your thoughts (i.e. your summary should be succinct but contain all the critical steps you needed to reach the conclusion). You should use Markdown and Latex to format your response. Write both your thoughts and summary in the same language as the task posed by the user.\n\nYour thinking process must follow the template below:\n<think>\nYour thoughts or/and draft, like working through an exercise on scratch paper. Be as casual and as long as you want until you are confident to generate a correct answer.\n</think>\n\nHere, provide a concise summary that reflects your reasoning and presents a clear final answer to the user.\n\n\n\nYou will be given a problem. Please reason step by step, and put your final answer within \\boxed{}.",
"type": "text",
"url": null
}
],
"role": "system"
},
{
"content": [
{
"path": "",
"text": "Let $x$ , $y$ and $z$ all exceed $1$ and let $w$ be a positive number such that $\\log_xw=24$ , $\\log_y w = 40$ and $\\log_{xyz}w=12$ . Find $\\log_zw$ .",
"type": "text",
"url": null
}
],
"role": "user"
}
] |
[
{
"content": [
{
"text": "A user will ask you to solve a task. You should first draft your thinking process (inner monologue) until you have derived the final answer. Afterwards, write a self-contained summary of your thoughts (i.e. your summary should be succinct but contain all the critical steps you needed to reach the conclusion). You should use Markdown and Latex to format your response. Write both your thoughts and summary in the same language as the task posed by the user.\n\nYour thinking process must follow the template below:\n<think>\nYour thoughts or/and draft, like working through an exercise on scratch paper. Be as casual and as long as you want until you are confident to generate a correct answer.\n</think>\n\nHere, provide a concise summary that reflects your reasoning and presents a clear final answer to the user.\n\n\n\nYou will be given a problem. Please reason step by step, and put your final answer within \\boxed{}.",
"type": "text"
}
],
"role": "system"
},
{
"content": [
{
"text": "Alice chooses a set $A$ of positive integers. Then Bob lists all finite nonempty sets $B$ of positive integers with the property that the maximum element of $B$ belongs to $A$ . Bob's list has $2024$ sets. Find the sum of the elements of $A$ .",
"type": "text"
}
],
"role": "user"
}
] |
$55$
|
di-zhang-fdu/AIME_1983_2024
|
[
{
"content": [
{
"path": "",
"text": "A user will ask you to solve a task. You should first draft your thinking process (inner monologue) until you have derived the final answer. Afterwards, write a self-contained summary of your thoughts (i.e. your summary should be succinct but contain all the critical steps you needed to reach the conclusion). You should use Markdown and Latex to format your response. Write both your thoughts and summary in the same language as the task posed by the user.\n\nYour thinking process must follow the template below:\n<think>\nYour thoughts or/and draft, like working through an exercise on scratch paper. Be as casual and as long as you want until you are confident to generate a correct answer.\n</think>\n\nHere, provide a concise summary that reflects your reasoning and presents a clear final answer to the user.\n\n\n\nYou will be given a problem. Please reason step by step, and put your final answer within \\boxed{}.",
"type": "text",
"url": null
}
],
"role": "system"
},
{
"content": [
{
"path": "",
"text": "Alice chooses a set $A$ of positive integers. Then Bob lists all finite nonempty sets $B$ of positive integers with the property that the maximum element of $B$ belongs to $A$ . Bob's list has $2024$ sets. Find the sum of the elements of $A$ .",
"type": "text",
"url": null
}
],
"role": "user"
}
] |
[
{
"content": [
{
"text": "A user will ask you to solve a task. You should first draft your thinking process (inner monologue) until you have derived the final answer. Afterwards, write a self-contained summary of your thoughts (i.e. your summary should be succinct but contain all the critical steps you needed to reach the conclusion). You should use Markdown and Latex to format your response. Write both your thoughts and summary in the same language as the task posed by the user.\n\nYour thinking process must follow the template below:\n<think>\nYour thoughts or/and draft, like working through an exercise on scratch paper. Be as casual and as long as you want until you are confident to generate a correct answer.\n</think>\n\nHere, provide a concise summary that reflects your reasoning and presents a clear final answer to the user.\n\n\n\nYou will be given a problem. Please reason step by step, and put your final answer within \\boxed{}.",
"type": "text"
}
],
"role": "system"
},
{
"content": [
{
"text": "Lily pads $1,2,3,\\ldots$ lie in a row on a pond. A frog makes a sequence of jumps starting on pad $1$ . From any pad $k$ the frog jumps to either pad $k+1$ or pad $k+2$ chosen randomly with probability $\\tfrac{1}{2}$ and independently of other jumps. The probability that the frog visits pad $7$ is $\\tfrac{p}{q}$ , where $p$ and $q$ are relatively prime positive integers. Find $p+q$ .",
"type": "text"
}
],
"role": "user"
}
] |
$107$
|
di-zhang-fdu/AIME_1983_2024
|
[
{
"content": [
{
"path": "",
"text": "A user will ask you to solve a task. You should first draft your thinking process (inner monologue) until you have derived the final answer. Afterwards, write a self-contained summary of your thoughts (i.e. your summary should be succinct but contain all the critical steps you needed to reach the conclusion). You should use Markdown and Latex to format your response. Write both your thoughts and summary in the same language as the task posed by the user.\n\nYour thinking process must follow the template below:\n<think>\nYour thoughts or/and draft, like working through an exercise on scratch paper. Be as casual and as long as you want until you are confident to generate a correct answer.\n</think>\n\nHere, provide a concise summary that reflects your reasoning and presents a clear final answer to the user.\n\n\n\nYou will be given a problem. Please reason step by step, and put your final answer within \\boxed{}.",
"type": "text",
"url": null
}
],
"role": "system"
},
{
"content": [
{
"path": "",
"text": "Lily pads $1,2,3,\\ldots$ lie in a row on a pond. A frog makes a sequence of jumps starting on pad $1$ . From any pad $k$ the frog jumps to either pad $k+1$ or pad $k+2$ chosen randomly with probability $\\tfrac{1}{2}$ and independently of other jumps. The probability that the frog visits pad $7$ is $\\tfrac{p}{q}$ , where $p$ and $q$ are relatively prime positive integers. Find $p+q$ .",
"type": "text",
"url": null
}
],
"role": "user"
}
] |
[
{
"content": [
{
"text": "A user will ask you to solve a task. You should first draft your thinking process (inner monologue) until you have derived the final answer. Afterwards, write a self-contained summary of your thoughts (i.e. your summary should be succinct but contain all the critical steps you needed to reach the conclusion). You should use Markdown and Latex to format your response. Write both your thoughts and summary in the same language as the task posed by the user.\n\nYour thinking process must follow the template below:\n<think>\nYour thoughts or/and draft, like working through an exercise on scratch paper. Be as casual and as long as you want until you are confident to generate a correct answer.\n</think>\n\nHere, provide a concise summary that reflects your reasoning and presents a clear final answer to the user.\n\n\n\nYou will be given a problem. Please reason step by step, and put your final answer within \\boxed{}.",
"type": "text"
}
],
"role": "system"
},
{
"content": [
{
"text": "In a regular tetrahedron, the centers of the four faces are the vertices of a smaller tetrahedron. The ratio of the volume of the smaller tetrahedron to that of the larger is $m/n$ , where $m$ and $n$ are relatively prime positive integers. Find $m+n$ . ",
"type": "text"
}
],
"role": "user"
}
] |
$28$
|
di-zhang-fdu/AIME_1983_2024
|
[
{
"content": [
{
"path": "",
"text": "A user will ask you to solve a task. You should first draft your thinking process (inner monologue) until you have derived the final answer. Afterwards, write a self-contained summary of your thoughts (i.e. your summary should be succinct but contain all the critical steps you needed to reach the conclusion). You should use Markdown and Latex to format your response. Write both your thoughts and summary in the same language as the task posed by the user.\n\nYour thinking process must follow the template below:\n<think>\nYour thoughts or/and draft, like working through an exercise on scratch paper. Be as casual and as long as you want until you are confident to generate a correct answer.\n</think>\n\nHere, provide a concise summary that reflects your reasoning and presents a clear final answer to the user.\n\n\n\nYou will be given a problem. Please reason step by step, and put your final answer within \\boxed{}.",
"type": "text",
"url": null
}
],
"role": "system"
},
{
"content": [
{
"path": "",
"text": "In a regular tetrahedron, the centers of the four faces are the vertices of a smaller tetrahedron. The ratio of the volume of the smaller tetrahedron to that of the larger is $m/n$ , where $m$ and $n$ are relatively prime positive integers. Find $m+n$ . ",
"type": "text",
"url": null
}
],
"role": "user"
}
] |
[
{
"content": [
{
"text": "A user will ask you to solve a task. You should first draft your thinking process (inner monologue) until you have derived the final answer. Afterwards, write a self-contained summary of your thoughts (i.e. your summary should be succinct but contain all the critical steps you needed to reach the conclusion). You should use Markdown and Latex to format your response. Write both your thoughts and summary in the same language as the task posed by the user.\n\nYour thinking process must follow the template below:\n<think>\nYour thoughts or/and draft, like working through an exercise on scratch paper. Be as casual and as long as you want until you are confident to generate a correct answer.\n</think>\n\nHere, provide a concise summary that reflects your reasoning and presents a clear final answer to the user.\n\n\n\nYou will be given a problem. Please reason step by step, and put your final answer within \\boxed{}.",
"type": "text"
}
],
"role": "system"
},
{
"content": [
{
"text": "Let $x,y$ and $z$ be positive real numbers that satisfy the following system of equations: \\[\\log_2\\left({x \\over yz}\\right) = {1 \\over 2}\\] \\[\\log_2\\left({y \\over xz}\\right) = {1 \\over 3}\\] \\[\\log_2\\left({z \\over xy}\\right) = {1 \\over 4}\\] Then the value of $\\left|\\log_2(x^4y^3z^2)\\right|$ is $\\tfrac{m}{n}$ where $m$ and $n$ are relatively prime positive integers. Find $m+n$ .",
"type": "text"
}
],
"role": "user"
}
] |
$33$
|
di-zhang-fdu/AIME_1983_2024
|
[
{
"content": [
{
"path": "",
"text": "A user will ask you to solve a task. You should first draft your thinking process (inner monologue) until you have derived the final answer. Afterwards, write a self-contained summary of your thoughts (i.e. your summary should be succinct but contain all the critical steps you needed to reach the conclusion). You should use Markdown and Latex to format your response. Write both your thoughts and summary in the same language as the task posed by the user.\n\nYour thinking process must follow the template below:\n<think>\nYour thoughts or/and draft, like working through an exercise on scratch paper. Be as casual and as long as you want until you are confident to generate a correct answer.\n</think>\n\nHere, provide a concise summary that reflects your reasoning and presents a clear final answer to the user.\n\n\n\nYou will be given a problem. Please reason step by step, and put your final answer within \\boxed{}.",
"type": "text",
"url": null
}
],
"role": "system"
},
{
"content": [
{
"path": "",
"text": "Let $x,y$ and $z$ be positive real numbers that satisfy the following system of equations: \\[\\log_2\\left({x \\over yz}\\right) = {1 \\over 2}\\] \\[\\log_2\\left({y \\over xz}\\right) = {1 \\over 3}\\] \\[\\log_2\\left({z \\over xy}\\right) = {1 \\over 4}\\] Then the value of $\\left|\\log_2(x^4y^3z^2)\\right|$ is $\\tfrac{m}{n}$ where $m$ and $n$ are relatively prime positive integers. Find $m+n$ .",
"type": "text",
"url": null
}
],
"role": "user"
}
] |
[
{
"content": [
{
"text": "A user will ask you to solve a task. You should first draft your thinking process (inner monologue) until you have derived the final answer. Afterwards, write a self-contained summary of your thoughts (i.e. your summary should be succinct but contain all the critical steps you needed to reach the conclusion). You should use Markdown and Latex to format your response. Write both your thoughts and summary in the same language as the task posed by the user.\n\nYour thinking process must follow the template below:\n<think>\nYour thoughts or/and draft, like working through an exercise on scratch paper. Be as casual and as long as you want until you are confident to generate a correct answer.\n</think>\n\nHere, provide a concise summary that reflects your reasoning and presents a clear final answer to the user.\n\n",
"type": "text"
}
],
"role": "system"
},
{
"content": [
{
"text": "You will be given a problem. Please reason step by step, and put your final answer within \\boxed{}:\nFind the sum of all positive integers $n$ for which $n^2-19n+99$ is a perfect square.",
"type": "text"
}
],
"role": "user"
}
] |
$38$
|
di-zhang-fdu/AIME_1983_2024
|
[
{
"content": [
{
"path": "",
"text": "A user will ask you to solve a task. You should first draft your thinking process (inner monologue) until you have derived the final answer. Afterwards, write a self-contained summary of your thoughts (i.e. your summary should be succinct but contain all the critical steps you needed to reach the conclusion). You should use Markdown and Latex to format your response. Write both your thoughts and summary in the same language as the task posed by the user.\n\nYour thinking process must follow the template below:\n<think>\nYour thoughts or/and draft, like working through an exercise on scratch paper. Be as casual and as long as you want until you are confident to generate a correct answer.\n</think>\n\nHere, provide a concise summary that reflects your reasoning and presents a clear final answer to the user.\n\n",
"type": "text",
"url": null
}
],
"role": "system"
},
{
"content": [
{
"path": "",
"text": "You will be given a problem. Please reason step by step, and put your final answer within \\boxed{}:\nFind the sum of all positive integers $n$ for which $n^2-19n+99$ is a perfect square.",
"type": "text",
"url": null
}
],
"role": "user"
}
] |
[
{
"content": [
{
"text": "A user will ask you to solve a task. You should first draft your thinking process (inner monologue) until you have derived the final answer. Afterwards, write a self-contained summary of your thoughts (i.e. your summary should be succinct but contain all the critical steps you needed to reach the conclusion). You should use Markdown and Latex to format your response. Write both your thoughts and summary in the same language as the task posed by the user.\n\nYour thinking process must follow the template below:\n<think>\nYour thoughts or/and draft, like working through an exercise on scratch paper. Be as casual and as long as you want until you are confident to generate a correct answer.\n</think>\n\nHere, provide a concise summary that reflects your reasoning and presents a clear final answer to the user.\n\n",
"type": "text"
}
],
"role": "system"
},
{
"content": [
{
"text": "You will be given a problem. Please reason step by step, and put your final answer within \\boxed{}:\n$ABCD$ is a rectangular sheet of paper that has been folded so that corner $B$ is matched with point $B'$ on edge $AD.$ The crease is $EF,$ where $E$ is on $AB$ and $F$ is on $CD.$ The dimensions $AE=8, BE=17,$ and $CF=3$ are given. The perimeter of rectangle $ABCD$ is $m/n,$ where $m$ and $n$ are relatively prime positive integers. Find $m+n.$ [asy] size(200); defaultpen(linewidth(0.7)+fontsize(10)); pair A=origin, B=(25,0), C=(25,70/3), D=(0,70/3), E=(8,0), F=(22,70/3), Bp=reflect(E,F)*B, Cp=reflect(E,F)*C; draw(F--D--A--E); draw(E--B--C--F, linetype(\"4 4\")); filldraw(E--F--Cp--Bp--cycle, white, black); pair point=( 12.5, 35/3 ); label(\"$A$\", A, dir(point--A)); label(\"$B$\", B, dir(point--B)); label(\"$C$\", C, dir(point--C)); label(\"$D$\", D, dir(point--D)); label(\"$E$\", E, dir(point--E)); label(\"$F$\", F, dir(point--F)); label(\"$B^\\prime$\", Bp, dir(point--Bp)); label(\"$C^\\prime$\", Cp, dir(point--Cp));[/asy]",
"type": "text"
}
],
"role": "user"
}
] |
$293$
|
di-zhang-fdu/AIME_1983_2024
|
[
{
"content": [
{
"path": "",
"text": "A user will ask you to solve a task. You should first draft your thinking process (inner monologue) until you have derived the final answer. Afterwards, write a self-contained summary of your thoughts (i.e. your summary should be succinct but contain all the critical steps you needed to reach the conclusion). You should use Markdown and Latex to format your response. Write both your thoughts and summary in the same language as the task posed by the user.\n\nYour thinking process must follow the template below:\n<think>\nYour thoughts or/and draft, like working through an exercise on scratch paper. Be as casual and as long as you want until you are confident to generate a correct answer.\n</think>\n\nHere, provide a concise summary that reflects your reasoning and presents a clear final answer to the user.\n\n",
"type": "text",
"url": null
}
],
"role": "system"
},
{
"content": [
{
"path": "",
"text": "You will be given a problem. Please reason step by step, and put your final answer within \\boxed{}:\n$ABCD$ is a rectangular sheet of paper that has been folded so that corner $B$ is matched with point $B'$ on edge $AD.$ The crease is $EF,$ where $E$ is on $AB$ and $F$ is on $CD.$ The dimensions $AE=8, BE=17,$ and $CF=3$ are given. The perimeter of rectangle $ABCD$ is $m/n,$ where $m$ and $n$ are relatively prime positive integers. Find $m+n.$ [asy] size(200); defaultpen(linewidth(0.7)+fontsize(10)); pair A=origin, B=(25,0), C=(25,70/3), D=(0,70/3), E=(8,0), F=(22,70/3), Bp=reflect(E,F)*B, Cp=reflect(E,F)*C; draw(F--D--A--E); draw(E--B--C--F, linetype(\"4 4\")); filldraw(E--F--Cp--Bp--cycle, white, black); pair point=( 12.5, 35/3 ); label(\"$A$\", A, dir(point--A)); label(\"$B$\", B, dir(point--B)); label(\"$C$\", C, dir(point--C)); label(\"$D$\", D, dir(point--D)); label(\"$E$\", E, dir(point--E)); label(\"$F$\", F, dir(point--F)); label(\"$B^\\prime$\", Bp, dir(point--Bp)); label(\"$C^\\prime$\", Cp, dir(point--Cp));[/asy]",
"type": "text",
"url": null
}
],
"role": "user"
}
] |
[
{
"content": [
{
"text": "A user will ask you to solve a task. You should first draft your thinking process (inner monologue) until you have derived the final answer. Afterwards, write a self-contained summary of your thoughts (i.e. your summary should be succinct but contain all the critical steps you needed to reach the conclusion). You should use Markdown and Latex to format your response. Write both your thoughts and summary in the same language as the task posed by the user.\n\nYour thinking process must follow the template below:\n<think>\nYour thoughts or/and draft, like working through an exercise on scratch paper. Be as casual and as long as you want until you are confident to generate a correct answer.\n</think>\n\nHere, provide a concise summary that reflects your reasoning and presents a clear final answer to the user.\n\n\n\nYou will be given a problem. Please reason step by step, and put your final answer within \\boxed{}.",
"type": "text"
}
],
"role": "system"
},
{
"content": [
{
"text": "Ten points in the plane are given, with no three collinear. Four distinct segments joining pairs of these points are chosen at random, all such segments being equally likely. The probability that some three of the segments form a triangle whose vertices are among the ten given points is $m/n,$ where $m_{}$ and $n_{}$ are relatively prime positive integers. Find $m+n.$ ",
"type": "text"
}
],
"role": "user"
}
] |
$489$
|
di-zhang-fdu/AIME_1983_2024
|
[
{
"content": [
{
"path": "",
"text": "A user will ask you to solve a task. You should first draft your thinking process (inner monologue) until you have derived the final answer. Afterwards, write a self-contained summary of your thoughts (i.e. your summary should be succinct but contain all the critical steps you needed to reach the conclusion). You should use Markdown and Latex to format your response. Write both your thoughts and summary in the same language as the task posed by the user.\n\nYour thinking process must follow the template below:\n<think>\nYour thoughts or/and draft, like working through an exercise on scratch paper. Be as casual and as long as you want until you are confident to generate a correct answer.\n</think>\n\nHere, provide a concise summary that reflects your reasoning and presents a clear final answer to the user.\n\n\n\nYou will be given a problem. Please reason step by step, and put your final answer within \\boxed{}.",
"type": "text",
"url": null
}
],
"role": "system"
},
{
"content": [
{
"path": "",
"text": "Ten points in the plane are given, with no three collinear. Four distinct segments joining pairs of these points are chosen at random, all such segments being equally likely. The probability that some three of the segments form a triangle whose vertices are among the ten given points is $m/n,$ where $m_{}$ and $n_{}$ are relatively prime positive integers. Find $m+n.$ ",
"type": "text",
"url": null
}
],
"role": "user"
}
] |
[
{
"content": [
{
"text": "A user will ask you to solve a task. You should first draft your thinking process (inner monologue) until you have derived the final answer. Afterwards, write a self-contained summary of your thoughts (i.e. your summary should be succinct but contain all the critical steps you needed to reach the conclusion). You should use Markdown and Latex to format your response. Write both your thoughts and summary in the same language as the task posed by the user.\n\nYour thinking process must follow the template below:\n<think>\nYour thoughts or/and draft, like working through an exercise on scratch paper. Be as casual and as long as you want until you are confident to generate a correct answer.\n</think>\n\nHere, provide a concise summary that reflects your reasoning and presents a clear final answer to the user.\n\n",
"type": "text"
}
],
"role": "system"
},
{
"content": [
{
"text": "You will be given a problem. Please reason step by step, and put your final answer within \\boxed{}:\nA sample of 121 integers is given, each between 1 and 1000 inclusive, with repetitions allowed. The sample has a unique mode (most frequent value). Let $D^{}_{}$ be the difference between the mode and the arithmetic mean of the sample. What is the largest possible value of $\\lfloor D^{}_{}\\rfloor$ ? (For real $x^{}_{}$ , $\\lfloor x^{}_{}\\rfloor$ is the greatest integer less than or equal to $x^{}_{}$ .)",
"type": "text"
}
],
"role": "user"
}
] |
$947$
|
di-zhang-fdu/AIME_1983_2024
|
[
{
"content": [
{
"path": "",
"text": "A user will ask you to solve a task. You should first draft your thinking process (inner monologue) until you have derived the final answer. Afterwards, write a self-contained summary of your thoughts (i.e. your summary should be succinct but contain all the critical steps you needed to reach the conclusion). You should use Markdown and Latex to format your response. Write both your thoughts and summary in the same language as the task posed by the user.\n\nYour thinking process must follow the template below:\n<think>\nYour thoughts or/and draft, like working through an exercise on scratch paper. Be as casual and as long as you want until you are confident to generate a correct answer.\n</think>\n\nHere, provide a concise summary that reflects your reasoning and presents a clear final answer to the user.\n\n",
"type": "text",
"url": null
}
],
"role": "system"
},
{
"content": [
{
"path": "",
"text": "You will be given a problem. Please reason step by step, and put your final answer within \\boxed{}:\nA sample of 121 integers is given, each between 1 and 1000 inclusive, with repetitions allowed. The sample has a unique mode (most frequent value). Let $D^{}_{}$ be the difference between the mode and the arithmetic mean of the sample. What is the largest possible value of $\\lfloor D^{}_{}\\rfloor$ ? (For real $x^{}_{}$ , $\\lfloor x^{}_{}\\rfloor$ is the greatest integer less than or equal to $x^{}_{}$ .)",
"type": "text",
"url": null
}
],
"role": "user"
}
] |
[
{
"content": [
{
"text": "A user will ask you to solve a task. You should first draft your thinking process (inner monologue) until you have derived the final answer. Afterwards, write a self-contained summary of your thoughts (i.e. your summary should be succinct but contain all the critical steps you needed to reach the conclusion). You should use Markdown and Latex to format your response. Write both your thoughts and summary in the same language as the task posed by the user.\n\nYour thinking process must follow the template below:\n<think>\nYour thoughts or/and draft, like working through an exercise on scratch paper. Be as casual and as long as you want until you are confident to generate a correct answer.\n</think>\n\nHere, provide a concise summary that reflects your reasoning and presents a clear final answer to the user.\n\n\n\nYou will be given a problem. Please reason step by step, and put your final answer within \\boxed{}.",
"type": "text"
}
],
"role": "system"
},
{
"content": [
{
"text": "Let $m$ be a positive integer, and let $a_0, a_1,\\ldots,a_m$ be a sequence of reals such that $a_0 = 37, a_1 = 72, a_m = 0,$ and $a_{k+1} = a_{k-1} - \\frac 3{a_k}$ for $k = 1,2,\\ldots, m-1.$ Find $m.$",
"type": "text"
}
],
"role": "user"
}
] |
$889$
|
di-zhang-fdu/AIME_1983_2024
|
[
{
"content": [
{
"path": "",
"text": "A user will ask you to solve a task. You should first draft your thinking process (inner monologue) until you have derived the final answer. Afterwards, write a self-contained summary of your thoughts (i.e. your summary should be succinct but contain all the critical steps you needed to reach the conclusion). You should use Markdown and Latex to format your response. Write both your thoughts and summary in the same language as the task posed by the user.\n\nYour thinking process must follow the template below:\n<think>\nYour thoughts or/and draft, like working through an exercise on scratch paper. Be as casual and as long as you want until you are confident to generate a correct answer.\n</think>\n\nHere, provide a concise summary that reflects your reasoning and presents a clear final answer to the user.\n\n\n\nYou will be given a problem. Please reason step by step, and put your final answer within \\boxed{}.",
"type": "text",
"url": null
}
],
"role": "system"
},
{
"content": [
{
"path": "",
"text": "Let $m$ be a positive integer, and let $a_0, a_1,\\ldots,a_m$ be a sequence of reals such that $a_0 = 37, a_1 = 72, a_m = 0,$ and $a_{k+1} = a_{k-1} - \\frac 3{a_k}$ for $k = 1,2,\\ldots, m-1.$ Find $m.$",
"type": "text",
"url": null
}
],
"role": "user"
}
] |
[
{
"content": [
{
"text": "A user will ask you to solve a task. You should first draft your thinking process (inner monologue) until you have derived the final answer. Afterwards, write a self-contained summary of your thoughts (i.e. your summary should be succinct but contain all the critical steps you needed to reach the conclusion). You should use Markdown and Latex to format your response. Write both your thoughts and summary in the same language as the task posed by the user.\n\nYour thinking process must follow the template below:\n<think>\nYour thoughts or/and draft, like working through an exercise on scratch paper. Be as casual and as long as you want until you are confident to generate a correct answer.\n</think>\n\nHere, provide a concise summary that reflects your reasoning and presents a clear final answer to the user.\n\n",
"type": "text"
}
],
"role": "system"
},
{
"content": [
{
"text": "You will be given a problem. Please reason step by step, and put your final answer within \\boxed{}:\nLet $x$ be a real number such that $\\sin^{10}x+\\cos^{10} x = \\tfrac{11}{36}$ . Then $\\sin^{12}x+\\cos^{12} x = \\tfrac{m}{n}$ where $m$ and $n$ are relatively prime positive integers. Find $m+n$ .",
"type": "text"
}
],
"role": "user"
}
] |
$67$
|
di-zhang-fdu/AIME_1983_2024
|
[
{
"content": [
{
"path": "",
"text": "A user will ask you to solve a task. You should first draft your thinking process (inner monologue) until you have derived the final answer. Afterwards, write a self-contained summary of your thoughts (i.e. your summary should be succinct but contain all the critical steps you needed to reach the conclusion). You should use Markdown and Latex to format your response. Write both your thoughts and summary in the same language as the task posed by the user.\n\nYour thinking process must follow the template below:\n<think>\nYour thoughts or/and draft, like working through an exercise on scratch paper. Be as casual and as long as you want until you are confident to generate a correct answer.\n</think>\n\nHere, provide a concise summary that reflects your reasoning and presents a clear final answer to the user.\n\n",
"type": "text",
"url": null
}
],
"role": "system"
},
{
"content": [
{
"path": "",
"text": "You will be given a problem. Please reason step by step, and put your final answer within \\boxed{}:\nLet $x$ be a real number such that $\\sin^{10}x+\\cos^{10} x = \\tfrac{11}{36}$ . Then $\\sin^{12}x+\\cos^{12} x = \\tfrac{m}{n}$ where $m$ and $n$ are relatively prime positive integers. Find $m+n$ .",
"type": "text",
"url": null
}
],
"role": "user"
}
] |
[
{
"content": [
{
"text": "A user will ask you to solve a task. You should first draft your thinking process (inner monologue) until you have derived the final answer. Afterwards, write a self-contained summary of your thoughts (i.e. your summary should be succinct but contain all the critical steps you needed to reach the conclusion). You should use Markdown and Latex to format your response. Write both your thoughts and summary in the same language as the task posed by the user.\n\nYour thinking process must follow the template below:\n<think>\nYour thoughts or/and draft, like working through an exercise on scratch paper. Be as casual and as long as you want until you are confident to generate a correct answer.\n</think>\n\nHere, provide a concise summary that reflects your reasoning and presents a clear final answer to the user.\n\n\n\nYou will be given a problem. Please reason step by step, and put your final answer within \\boxed{}.",
"type": "text"
}
],
"role": "system"
},
{
"content": [
{
"text": "In $\\triangle ABC, AB = 360, BC = 507,$ and $CA = 780.$ Let $M$ be the midpoint of $\\overline{CA},$ and let $D$ be the point on $\\overline{CA}$ such that $\\overline{BD}$ bisects angle $ABC.$ Let $F$ be the point on $\\overline{BC}$ such that $\\overline{DF} \\perp \\overline{BD}.$ Suppose that $\\overline{DF}$ meets $\\overline{BM}$ at $E.$ The ratio $DE: EF$ can be written in the form $m/n,$ where $m$ and $n$ are relatively prime positive integers. Find $m + n.$",
"type": "text"
}
],
"role": "user"
}
] |
$289$
|
di-zhang-fdu/AIME_1983_2024
|
[
{
"content": [
{
"path": "",
"text": "A user will ask you to solve a task. You should first draft your thinking process (inner monologue) until you have derived the final answer. Afterwards, write a self-contained summary of your thoughts (i.e. your summary should be succinct but contain all the critical steps you needed to reach the conclusion). You should use Markdown and Latex to format your response. Write both your thoughts and summary in the same language as the task posed by the user.\n\nYour thinking process must follow the template below:\n<think>\nYour thoughts or/and draft, like working through an exercise on scratch paper. Be as casual and as long as you want until you are confident to generate a correct answer.\n</think>\n\nHere, provide a concise summary that reflects your reasoning and presents a clear final answer to the user.\n\n\n\nYou will be given a problem. Please reason step by step, and put your final answer within \\boxed{}.",
"type": "text",
"url": null
}
],
"role": "system"
},
{
"content": [
{
"path": "",
"text": "In $\\triangle ABC, AB = 360, BC = 507,$ and $CA = 780.$ Let $M$ be the midpoint of $\\overline{CA},$ and let $D$ be the point on $\\overline{CA}$ such that $\\overline{BD}$ bisects angle $ABC.$ Let $F$ be the point on $\\overline{BC}$ such that $\\overline{DF} \\perp \\overline{BD}.$ Suppose that $\\overline{DF}$ meets $\\overline{BM}$ at $E.$ The ratio $DE: EF$ can be written in the form $m/n,$ where $m$ and $n$ are relatively prime positive integers. Find $m + n.$",
"type": "text",
"url": null
}
],
"role": "user"
}
] |
[
{
"content": [
{
"text": "A user will ask you to solve a task. You should first draft your thinking process (inner monologue) until you have derived the final answer. Afterwards, write a self-contained summary of your thoughts (i.e. your summary should be succinct but contain all the critical steps you needed to reach the conclusion). You should use Markdown and Latex to format your response. Write both your thoughts and summary in the same language as the task posed by the user.\n\nYour thinking process must follow the template below:\n<think>\nYour thoughts or/and draft, like working through an exercise on scratch paper. Be as casual and as long as you want until you are confident to generate a correct answer.\n</think>\n\nHere, provide a concise summary that reflects your reasoning and presents a clear final answer to the user.\n\n",
"type": "text"
}
],
"role": "system"
},
{
"content": [
{
"text": "You will be given a problem. Please reason step by step, and put your final answer within \\boxed{}:\nLet $m$ be the least positive integer divisible by $17$ whose digits sum to $17$ . Find $m$ .",
"type": "text"
}
],
"role": "user"
}
] |
$476$
|
di-zhang-fdu/AIME_1983_2024
|
[
{
"content": [
{
"path": "",
"text": "A user will ask you to solve a task. You should first draft your thinking process (inner monologue) until you have derived the final answer. Afterwards, write a self-contained summary of your thoughts (i.e. your summary should be succinct but contain all the critical steps you needed to reach the conclusion). You should use Markdown and Latex to format your response. Write both your thoughts and summary in the same language as the task posed by the user.\n\nYour thinking process must follow the template below:\n<think>\nYour thoughts or/and draft, like working through an exercise on scratch paper. Be as casual and as long as you want until you are confident to generate a correct answer.\n</think>\n\nHere, provide a concise summary that reflects your reasoning and presents a clear final answer to the user.\n\n",
"type": "text",
"url": null
}
],
"role": "system"
},
{
"content": [
{
"path": "",
"text": "You will be given a problem. Please reason step by step, and put your final answer within \\boxed{}:\nLet $m$ be the least positive integer divisible by $17$ whose digits sum to $17$ . Find $m$ .",
"type": "text",
"url": null
}
],
"role": "user"
}
] |
[
{
"content": [
{
"text": "A user will ask you to solve a task. You should first draft your thinking process (inner monologue) until you have derived the final answer. Afterwards, write a self-contained summary of your thoughts (i.e. your summary should be succinct but contain all the critical steps you needed to reach the conclusion). You should use Markdown and Latex to format your response. Write both your thoughts and summary in the same language as the task posed by the user.\n\nYour thinking process must follow the template below:\n<think>\nYour thoughts or/and draft, like working through an exercise on scratch paper. Be as casual and as long as you want until you are confident to generate a correct answer.\n</think>\n\nHere, provide a concise summary that reflects your reasoning and presents a clear final answer to the user.\n\n\n\nYou will be given a problem. Please reason step by step, and put your final answer within \\boxed{}.",
"type": "text"
}
],
"role": "system"
},
{
"content": [
{
"text": "Let $z$ be a complex number with $|z|=2014$ . Let $P$ be the polygon in the complex plane whose vertices are $z$ and every $w$ such that $\\frac{1}{z+w}=\\frac{1}{z}+\\frac{1}{w}$ . Then the area enclosed by $P$ can be written in the form $n\\sqrt{3}$ , where $n$ is an integer. Find the remainder when $n$ is divided by $1000$ .",
"type": "text"
}
],
"role": "user"
}
] |
$147$
|
di-zhang-fdu/AIME_1983_2024
|
[
{
"content": [
{
"path": "",
"text": "A user will ask you to solve a task. You should first draft your thinking process (inner monologue) until you have derived the final answer. Afterwards, write a self-contained summary of your thoughts (i.e. your summary should be succinct but contain all the critical steps you needed to reach the conclusion). You should use Markdown and Latex to format your response. Write both your thoughts and summary in the same language as the task posed by the user.\n\nYour thinking process must follow the template below:\n<think>\nYour thoughts or/and draft, like working through an exercise on scratch paper. Be as casual and as long as you want until you are confident to generate a correct answer.\n</think>\n\nHere, provide a concise summary that reflects your reasoning and presents a clear final answer to the user.\n\n\n\nYou will be given a problem. Please reason step by step, and put your final answer within \\boxed{}.",
"type": "text",
"url": null
}
],
"role": "system"
},
{
"content": [
{
"path": "",
"text": "Let $z$ be a complex number with $|z|=2014$ . Let $P$ be the polygon in the complex plane whose vertices are $z$ and every $w$ such that $\\frac{1}{z+w}=\\frac{1}{z}+\\frac{1}{w}$ . Then the area enclosed by $P$ can be written in the form $n\\sqrt{3}$ , where $n$ is an integer. Find the remainder when $n$ is divided by $1000$ .",
"type": "text",
"url": null
}
],
"role": "user"
}
] |
[
{
"content": [
{
"text": "A user will ask you to solve a task. You should first draft your thinking process (inner monologue) until you have derived the final answer. Afterwards, write a self-contained summary of your thoughts (i.e. your summary should be succinct but contain all the critical steps you needed to reach the conclusion). You should use Markdown and Latex to format your response. Write both your thoughts and summary in the same language as the task posed by the user.\n\nYour thinking process must follow the template below:\n<think>\nYour thoughts or/and draft, like working through an exercise on scratch paper. Be as casual and as long as you want until you are confident to generate a correct answer.\n</think>\n\nHere, provide a concise summary that reflects your reasoning and presents a clear final answer to the user.\n\n\n\nYou will be given a problem. Please reason step by step, and put your final answer within \\boxed{}.",
"type": "text"
}
],
"role": "system"
},
{
"content": [
{
"text": "Gary purchased a large beverage, but only drank $m/n$ of it, where $m$ and $n$ are relatively prime positive integers. If he had purchased half as much and drunk twice as much, he would have wasted only $2/9$ as much beverage. Find $m+n$ .",
"type": "text"
}
],
"role": "user"
}
] |
$37$
|
di-zhang-fdu/AIME_1983_2024
|
[
{
"content": [
{
"path": "",
"text": "A user will ask you to solve a task. You should first draft your thinking process (inner monologue) until you have derived the final answer. Afterwards, write a self-contained summary of your thoughts (i.e. your summary should be succinct but contain all the critical steps you needed to reach the conclusion). You should use Markdown and Latex to format your response. Write both your thoughts and summary in the same language as the task posed by the user.\n\nYour thinking process must follow the template below:\n<think>\nYour thoughts or/and draft, like working through an exercise on scratch paper. Be as casual and as long as you want until you are confident to generate a correct answer.\n</think>\n\nHere, provide a concise summary that reflects your reasoning and presents a clear final answer to the user.\n\n\n\nYou will be given a problem. Please reason step by step, and put your final answer within \\boxed{}.",
"type": "text",
"url": null
}
],
"role": "system"
},
{
"content": [
{
"path": "",
"text": "Gary purchased a large beverage, but only drank $m/n$ of it, where $m$ and $n$ are relatively prime positive integers. If he had purchased half as much and drunk twice as much, he would have wasted only $2/9$ as much beverage. Find $m+n$ .",
"type": "text",
"url": null
}
],
"role": "user"
}
] |
[
{
"content": [
{
"text": "A user will ask you to solve a task. You should first draft your thinking process (inner monologue) until you have derived the final answer. Afterwards, write a self-contained summary of your thoughts (i.e. your summary should be succinct but contain all the critical steps you needed to reach the conclusion). You should use Markdown and Latex to format your response. Write both your thoughts and summary in the same language as the task posed by the user.\n\nYour thinking process must follow the template below:\n<think>\nYour thoughts or/and draft, like working through an exercise on scratch paper. Be as casual and as long as you want until you are confident to generate a correct answer.\n</think>\n\nHere, provide a concise summary that reflects your reasoning and presents a clear final answer to the user.\n\n\n\nYou will be given a problem. Please reason step by step, and put your final answer within \\boxed{}.",
"type": "text"
}
],
"role": "system"
},
{
"content": [
{
"text": "Find the number of functions $f(x)$ from $\\{1, 2, 3, 4, 5\\}$ to $\\{1, 2, 3, 4, 5\\}$ that satisfy $f(f(x)) = f(f(f(x)))$ for all $x$ in $\\{1, 2, 3, 4, 5\\}$ .",
"type": "text"
}
],
"role": "user"
}
] |
$756$
|
di-zhang-fdu/AIME_1983_2024
|
[
{
"content": [
{
"path": "",
"text": "A user will ask you to solve a task. You should first draft your thinking process (inner monologue) until you have derived the final answer. Afterwards, write a self-contained summary of your thoughts (i.e. your summary should be succinct but contain all the critical steps you needed to reach the conclusion). You should use Markdown and Latex to format your response. Write both your thoughts and summary in the same language as the task posed by the user.\n\nYour thinking process must follow the template below:\n<think>\nYour thoughts or/and draft, like working through an exercise on scratch paper. Be as casual and as long as you want until you are confident to generate a correct answer.\n</think>\n\nHere, provide a concise summary that reflects your reasoning and presents a clear final answer to the user.\n\n\n\nYou will be given a problem. Please reason step by step, and put your final answer within \\boxed{}.",
"type": "text",
"url": null
}
],
"role": "system"
},
{
"content": [
{
"path": "",
"text": "Find the number of functions $f(x)$ from $\\{1, 2, 3, 4, 5\\}$ to $\\{1, 2, 3, 4, 5\\}$ that satisfy $f(f(x)) = f(f(f(x)))$ for all $x$ in $\\{1, 2, 3, 4, 5\\}$ .",
"type": "text",
"url": null
}
],
"role": "user"
}
] |
[
{
"content": [
{
"text": "A user will ask you to solve a task. You should first draft your thinking process (inner monologue) until you have derived the final answer. Afterwards, write a self-contained summary of your thoughts (i.e. your summary should be succinct but contain all the critical steps you needed to reach the conclusion). You should use Markdown and Latex to format your response. Write both your thoughts and summary in the same language as the task posed by the user.\n\nYour thinking process must follow the template below:\n<think>\nYour thoughts or/and draft, like working through an exercise on scratch paper. Be as casual and as long as you want until you are confident to generate a correct answer.\n</think>\n\nHere, provide a concise summary that reflects your reasoning and presents a clear final answer to the user.\n\n",
"type": "text"
}
],
"role": "system"
},
{
"content": [
{
"text": "You will be given a problem. Please reason step by step, and put your final answer within \\boxed{}:\nLet $\\triangle ABC$ be an equilateral triangle with side length $55.$ Points $D,$ $E,$ and $F$ lie on $\\overline{BC},$ $\\overline{CA},$ and $\\overline{AB},$ respectively, with $BD = 7,$ $CE=30,$ and $AF=40.$ Point $P$ inside $\\triangle ABC$ has the property that \\[\\angle AEP = \\angle BFP = \\angle CDP.\\] Find $\\tan^2(\\angle AEP).$",
"type": "text"
}
],
"role": "user"
}
] |
$75$
|
di-zhang-fdu/AIME_1983_2024
|
[
{
"content": [
{
"path": "",
"text": "A user will ask you to solve a task. You should first draft your thinking process (inner monologue) until you have derived the final answer. Afterwards, write a self-contained summary of your thoughts (i.e. your summary should be succinct but contain all the critical steps you needed to reach the conclusion). You should use Markdown and Latex to format your response. Write both your thoughts and summary in the same language as the task posed by the user.\n\nYour thinking process must follow the template below:\n<think>\nYour thoughts or/and draft, like working through an exercise on scratch paper. Be as casual and as long as you want until you are confident to generate a correct answer.\n</think>\n\nHere, provide a concise summary that reflects your reasoning and presents a clear final answer to the user.\n\n",
"type": "text",
"url": null
}
],
"role": "system"
},
{
"content": [
{
"path": "",
"text": "You will be given a problem. Please reason step by step, and put your final answer within \\boxed{}:\nLet $\\triangle ABC$ be an equilateral triangle with side length $55.$ Points $D,$ $E,$ and $F$ lie on $\\overline{BC},$ $\\overline{CA},$ and $\\overline{AB},$ respectively, with $BD = 7,$ $CE=30,$ and $AF=40.$ Point $P$ inside $\\triangle ABC$ has the property that \\[\\angle AEP = \\angle BFP = \\angle CDP.\\] Find $\\tan^2(\\angle AEP).$",
"type": "text",
"url": null
}
],
"role": "user"
}
] |
[
{
"content": [
{
"text": "A user will ask you to solve a task. You should first draft your thinking process (inner monologue) until you have derived the final answer. Afterwards, write a self-contained summary of your thoughts (i.e. your summary should be succinct but contain all the critical steps you needed to reach the conclusion). You should use Markdown and Latex to format your response. Write both your thoughts and summary in the same language as the task posed by the user.\n\nYour thinking process must follow the template below:\n<think>\nYour thoughts or/and draft, like working through an exercise on scratch paper. Be as casual and as long as you want until you are confident to generate a correct answer.\n</think>\n\nHere, provide a concise summary that reflects your reasoning and presents a clear final answer to the user.\n\n\n\nYou will be given a problem. Please reason step by step, and put your final answer within \\boxed{}.",
"type": "text"
}
],
"role": "system"
},
{
"content": [
{
"text": "Triangle $ABC$ has positive integer side lengths with $AB=AC$ . Let $I$ be the intersection of the bisectors of $\\angle B$ and $\\angle C$ . Suppose $BI=8$ . Find the smallest possible perimeter of $\\triangle ABC$ .",
"type": "text"
}
],
"role": "user"
}
] |
$108$
|
di-zhang-fdu/AIME_1983_2024
|
[
{
"content": [
{
"path": "",
"text": "A user will ask you to solve a task. You should first draft your thinking process (inner monologue) until you have derived the final answer. Afterwards, write a self-contained summary of your thoughts (i.e. your summary should be succinct but contain all the critical steps you needed to reach the conclusion). You should use Markdown and Latex to format your response. Write both your thoughts and summary in the same language as the task posed by the user.\n\nYour thinking process must follow the template below:\n<think>\nYour thoughts or/and draft, like working through an exercise on scratch paper. Be as casual and as long as you want until you are confident to generate a correct answer.\n</think>\n\nHere, provide a concise summary that reflects your reasoning and presents a clear final answer to the user.\n\n\n\nYou will be given a problem. Please reason step by step, and put your final answer within \\boxed{}.",
"type": "text",
"url": null
}
],
"role": "system"
},
{
"content": [
{
"path": "",
"text": "Triangle $ABC$ has positive integer side lengths with $AB=AC$ . Let $I$ be the intersection of the bisectors of $\\angle B$ and $\\angle C$ . Suppose $BI=8$ . Find the smallest possible perimeter of $\\triangle ABC$ .",
"type": "text",
"url": null
}
],
"role": "user"
}
] |
[
{
"content": [
{
"text": "A user will ask you to solve a task. You should first draft your thinking process (inner monologue) until you have derived the final answer. Afterwards, write a self-contained summary of your thoughts (i.e. your summary should be succinct but contain all the critical steps you needed to reach the conclusion). You should use Markdown and Latex to format your response. Write both your thoughts and summary in the same language as the task posed by the user.\n\nYour thinking process must follow the template below:\n<think>\nYour thoughts or/and draft, like working through an exercise on scratch paper. Be as casual and as long as you want until you are confident to generate a correct answer.\n</think>\n\nHere, provide a concise summary that reflects your reasoning and presents a clear final answer to the user.\n\n",
"type": "text"
}
],
"role": "system"
},
{
"content": [
{
"text": "You will be given a problem. Please reason step by step, and put your final answer within \\boxed{}:\nJon and Steve ride their bicycles along a path that parallels two side-by-side train tracks running the east/west direction. Jon rides east at $20$ miles per hour, and Steve rides west at $20$ miles per hour. Two trains of equal length, traveling in opposite directions at constant but different speeds each pass the two riders. Each train takes exactly $1$ minute to go past Jon. The westbound train takes $10$ times as long as the eastbound train to go past Steve. The length of each train is $\\tfrac{m}{n}$ miles, where $m$ and $n$ are relatively prime positive integers. Find $m+n$ .",
"type": "text"
}
],
"role": "user"
}
] |
$49$
|
di-zhang-fdu/AIME_1983_2024
|
[
{
"content": [
{
"path": "",
"text": "A user will ask you to solve a task. You should first draft your thinking process (inner monologue) until you have derived the final answer. Afterwards, write a self-contained summary of your thoughts (i.e. your summary should be succinct but contain all the critical steps you needed to reach the conclusion). You should use Markdown and Latex to format your response. Write both your thoughts and summary in the same language as the task posed by the user.\n\nYour thinking process must follow the template below:\n<think>\nYour thoughts or/and draft, like working through an exercise on scratch paper. Be as casual and as long as you want until you are confident to generate a correct answer.\n</think>\n\nHere, provide a concise summary that reflects your reasoning and presents a clear final answer to the user.\n\n",
"type": "text",
"url": null
}
],
"role": "system"
},
{
"content": [
{
"path": "",
"text": "You will be given a problem. Please reason step by step, and put your final answer within \\boxed{}:\nJon and Steve ride their bicycles along a path that parallels two side-by-side train tracks running the east/west direction. Jon rides east at $20$ miles per hour, and Steve rides west at $20$ miles per hour. Two trains of equal length, traveling in opposite directions at constant but different speeds each pass the two riders. Each train takes exactly $1$ minute to go past Jon. The westbound train takes $10$ times as long as the eastbound train to go past Steve. The length of each train is $\\tfrac{m}{n}$ miles, where $m$ and $n$ are relatively prime positive integers. Find $m+n$ .",
"type": "text",
"url": null
}
],
"role": "user"
}
] |
[
{
"content": [
{
"text": "A user will ask you to solve a task. You should first draft your thinking process (inner monologue) until you have derived the final answer. Afterwards, write a self-contained summary of your thoughts (i.e. your summary should be succinct but contain all the critical steps you needed to reach the conclusion). You should use Markdown and Latex to format your response. Write both your thoughts and summary in the same language as the task posed by the user.\n\nYour thinking process must follow the template below:\n<think>\nYour thoughts or/and draft, like working through an exercise on scratch paper. Be as casual and as long as you want until you are confident to generate a correct answer.\n</think>\n\nHere, provide a concise summary that reflects your reasoning and presents a clear final answer to the user.\n\n\n\nYou will be given a problem. Please reason step by step, and put your final answer within \\boxed{}.",
"type": "text"
}
],
"role": "system"
},
{
"content": [
{
"text": "David found four sticks of different lengths that can be used to form three non-congruent convex cyclic quadrilaterals, $A,\\text{ }B,\\text{ }C$ , which can each be inscribed in a circle with radius $1$ . Let $\\varphi_A$ denote the measure of the acute angle made by the diagonals of quadrilateral $A$ , and define $\\varphi_B$ and $\\varphi_C$ similarly. Suppose that $\\sin\\varphi_A=\\frac{2}{3}$ , $\\sin\\varphi_B=\\frac{3}{5}$ , and $\\sin\\varphi_C=\\frac{6}{7}$ . All three quadrilaterals have the same area $K$ , which can be written in the form $\\dfrac{m}{n}$ , where $m$ and $n$ are relatively prime positive integers. Find $m+n$ .",
"type": "text"
}
],
"role": "user"
}
] |
$59$
|
di-zhang-fdu/AIME_1983_2024
|
[
{
"content": [
{
"path": "",
"text": "A user will ask you to solve a task. You should first draft your thinking process (inner monologue) until you have derived the final answer. Afterwards, write a self-contained summary of your thoughts (i.e. your summary should be succinct but contain all the critical steps you needed to reach the conclusion). You should use Markdown and Latex to format your response. Write both your thoughts and summary in the same language as the task posed by the user.\n\nYour thinking process must follow the template below:\n<think>\nYour thoughts or/and draft, like working through an exercise on scratch paper. Be as casual and as long as you want until you are confident to generate a correct answer.\n</think>\n\nHere, provide a concise summary that reflects your reasoning and presents a clear final answer to the user.\n\n\n\nYou will be given a problem. Please reason step by step, and put your final answer within \\boxed{}.",
"type": "text",
"url": null
}
],
"role": "system"
},
{
"content": [
{
"path": "",
"text": "David found four sticks of different lengths that can be used to form three non-congruent convex cyclic quadrilaterals, $A,\\text{ }B,\\text{ }C$ , which can each be inscribed in a circle with radius $1$ . Let $\\varphi_A$ denote the measure of the acute angle made by the diagonals of quadrilateral $A$ , and define $\\varphi_B$ and $\\varphi_C$ similarly. Suppose that $\\sin\\varphi_A=\\frac{2}{3}$ , $\\sin\\varphi_B=\\frac{3}{5}$ , and $\\sin\\varphi_C=\\frac{6}{7}$ . All three quadrilaterals have the same area $K$ , which can be written in the form $\\dfrac{m}{n}$ , where $m$ and $n$ are relatively prime positive integers. Find $m+n$ .",
"type": "text",
"url": null
}
],
"role": "user"
}
] |
[
{
"content": [
{
"text": "A user will ask you to solve a task. You should first draft your thinking process (inner monologue) until you have derived the final answer. Afterwards, write a self-contained summary of your thoughts (i.e. your summary should be succinct but contain all the critical steps you needed to reach the conclusion). You should use Markdown and Latex to format your response. Write both your thoughts and summary in the same language as the task posed by the user.\n\nYour thinking process must follow the template below:\n<think>\nYour thoughts or/and draft, like working through an exercise on scratch paper. Be as casual and as long as you want until you are confident to generate a correct answer.\n</think>\n\nHere, provide a concise summary that reflects your reasoning and presents a clear final answer to the user.\n\n",
"type": "text"
}
],
"role": "system"
},
{
"content": [
{
"text": "You will be given a problem. Please reason step by step, and put your final answer within \\boxed{}:\nSquare $ABCD$ has center $O, AB=900, E$ and $F$ are on $AB$ with $AE<BF$ and $E$ between $A$ and $F, m\\angle EOF =45^\\circ,$ and $EF=400.$ Given that $BF=p+q\\sqrt{r},$ where $p,q,$ and $r$ are positive integers and $r$ is not divisible by the square of any prime, find $p+q+r.$",
"type": "text"
}
],
"role": "user"
}
] |
$307$
|
di-zhang-fdu/AIME_1983_2024
|
[
{
"content": [
{
"path": "",
"text": "A user will ask you to solve a task. You should first draft your thinking process (inner monologue) until you have derived the final answer. Afterwards, write a self-contained summary of your thoughts (i.e. your summary should be succinct but contain all the critical steps you needed to reach the conclusion). You should use Markdown and Latex to format your response. Write both your thoughts and summary in the same language as the task posed by the user.\n\nYour thinking process must follow the template below:\n<think>\nYour thoughts or/and draft, like working through an exercise on scratch paper. Be as casual and as long as you want until you are confident to generate a correct answer.\n</think>\n\nHere, provide a concise summary that reflects your reasoning and presents a clear final answer to the user.\n\n",
"type": "text",
"url": null
}
],
"role": "system"
},
{
"content": [
{
"path": "",
"text": "You will be given a problem. Please reason step by step, and put your final answer within \\boxed{}:\nSquare $ABCD$ has center $O, AB=900, E$ and $F$ are on $AB$ with $AE<BF$ and $E$ between $A$ and $F, m\\angle EOF =45^\\circ,$ and $EF=400.$ Given that $BF=p+q\\sqrt{r},$ where $p,q,$ and $r$ are positive integers and $r$ is not divisible by the square of any prime, find $p+q+r.$",
"type": "text",
"url": null
}
],
"role": "user"
}
] |
[
{
"content": [
{
"text": "A user will ask you to solve a task. You should first draft your thinking process (inner monologue) until you have derived the final answer. Afterwards, write a self-contained summary of your thoughts (i.e. your summary should be succinct but contain all the critical steps you needed to reach the conclusion). You should use Markdown and Latex to format your response. Write both your thoughts and summary in the same language as the task posed by the user.\n\nYour thinking process must follow the template below:\n<think>\nYour thoughts or/and draft, like working through an exercise on scratch paper. Be as casual and as long as you want until you are confident to generate a correct answer.\n</think>\n\nHere, provide a concise summary that reflects your reasoning and presents a clear final answer to the user.\n\n",
"type": "text"
}
],
"role": "system"
},
{
"content": [
{
"text": "You will be given a problem. Please reason step by step, and put your final answer within \\boxed{}:\nLet $r$ , $s$ , and $t$ be the three roots of the equation \\[8x^3 + 1001x + 2008 = 0.\\] Find $(r + s)^3 + (s + t)^3 + (t + r)^3$ .",
"type": "text"
}
],
"role": "user"
}
] |
$753$
|
di-zhang-fdu/AIME_1983_2024
|
[
{
"content": [
{
"path": "",
"text": "A user will ask you to solve a task. You should first draft your thinking process (inner monologue) until you have derived the final answer. Afterwards, write a self-contained summary of your thoughts (i.e. your summary should be succinct but contain all the critical steps you needed to reach the conclusion). You should use Markdown and Latex to format your response. Write both your thoughts and summary in the same language as the task posed by the user.\n\nYour thinking process must follow the template below:\n<think>\nYour thoughts or/and draft, like working through an exercise on scratch paper. Be as casual and as long as you want until you are confident to generate a correct answer.\n</think>\n\nHere, provide a concise summary that reflects your reasoning and presents a clear final answer to the user.\n\n",
"type": "text",
"url": null
}
],
"role": "system"
},
{
"content": [
{
"path": "",
"text": "You will be given a problem. Please reason step by step, and put your final answer within \\boxed{}:\nLet $r$ , $s$ , and $t$ be the three roots of the equation \\[8x^3 + 1001x + 2008 = 0.\\] Find $(r + s)^3 + (s + t)^3 + (t + r)^3$ .",
"type": "text",
"url": null
}
],
"role": "user"
}
] |
[
{
"content": [
{
"text": "A user will ask you to solve a task. You should first draft your thinking process (inner monologue) until you have derived the final answer. Afterwards, write a self-contained summary of your thoughts (i.e. your summary should be succinct but contain all the critical steps you needed to reach the conclusion). You should use Markdown and Latex to format your response. Write both your thoughts and summary in the same language as the task posed by the user.\n\nYour thinking process must follow the template below:\n<think>\nYour thoughts or/and draft, like working through an exercise on scratch paper. Be as casual and as long as you want until you are confident to generate a correct answer.\n</think>\n\nHere, provide a concise summary that reflects your reasoning and presents a clear final answer to the user.\n\n\n\nYou will be given a problem. Please reason step by step, and put your final answer within \\boxed{}.",
"type": "text"
}
],
"role": "system"
},
{
"content": [
{
"text": "Compute the sum of the positive divisors (including $1$) of $9!$ that have units digit $1$.",
"type": "text"
}
],
"role": "user"
}
] |
$103$
|
MathArena/hmmt_feb_2025
|
[
{
"content": [
{
"path": "",
"text": "A user will ask you to solve a task. You should first draft your thinking process (inner monologue) until you have derived the final answer. Afterwards, write a self-contained summary of your thoughts (i.e. your summary should be succinct but contain all the critical steps you needed to reach the conclusion). You should use Markdown and Latex to format your response. Write both your thoughts and summary in the same language as the task posed by the user.\n\nYour thinking process must follow the template below:\n<think>\nYour thoughts or/and draft, like working through an exercise on scratch paper. Be as casual and as long as you want until you are confident to generate a correct answer.\n</think>\n\nHere, provide a concise summary that reflects your reasoning and presents a clear final answer to the user.\n\n\n\nYou will be given a problem. Please reason step by step, and put your final answer within \\boxed{}.",
"type": "text",
"url": null
}
],
"role": "system"
},
{
"content": [
{
"path": "",
"text": "Compute the sum of the positive divisors (including $1$) of $9!$ that have units digit $1$.",
"type": "text",
"url": null
}
],
"role": "user"
}
] |
[
{
"content": [
{
"text": "A user will ask you to solve a task. You should first draft your thinking process (inner monologue) until you have derived the final answer. Afterwards, write a self-contained summary of your thoughts (i.e. your summary should be succinct but contain all the critical steps you needed to reach the conclusion). You should use Markdown and Latex to format your response. Write both your thoughts and summary in the same language as the task posed by the user.\n\nYour thinking process must follow the template below:\n<think>\nYour thoughts or/and draft, like working through an exercise on scratch paper. Be as casual and as long as you want until you are confident to generate a correct answer.\n</think>\n\nHere, provide a concise summary that reflects your reasoning and presents a clear final answer to the user.\n\n",
"type": "text"
}
],
"role": "system"
},
{
"content": [
{
"text": "You will be given a problem. Please reason step by step, and put your final answer within \\boxed{}:\nTen chairs are arranged in a circle. Find the number of subsets of this set of chairs that contain at least three adjacent chairs. ",
"type": "text"
}
],
"role": "user"
}
] |
$581$
|
di-zhang-fdu/AIME_1983_2024
|
[
{
"content": [
{
"path": "",
"text": "A user will ask you to solve a task. You should first draft your thinking process (inner monologue) until you have derived the final answer. Afterwards, write a self-contained summary of your thoughts (i.e. your summary should be succinct but contain all the critical steps you needed to reach the conclusion). You should use Markdown and Latex to format your response. Write both your thoughts and summary in the same language as the task posed by the user.\n\nYour thinking process must follow the template below:\n<think>\nYour thoughts or/and draft, like working through an exercise on scratch paper. Be as casual and as long as you want until you are confident to generate a correct answer.\n</think>\n\nHere, provide a concise summary that reflects your reasoning and presents a clear final answer to the user.\n\n",
"type": "text",
"url": null
}
],
"role": "system"
},
{
"content": [
{
"path": "",
"text": "You will be given a problem. Please reason step by step, and put your final answer within \\boxed{}:\nTen chairs are arranged in a circle. Find the number of subsets of this set of chairs that contain at least three adjacent chairs. ",
"type": "text",
"url": null
}
],
"role": "user"
}
] |
[
{
"content": [
{
"text": "A user will ask you to solve a task. You should first draft your thinking process (inner monologue) until you have derived the final answer. Afterwards, write a self-contained summary of your thoughts (i.e. your summary should be succinct but contain all the critical steps you needed to reach the conclusion). You should use Markdown and Latex to format your response. Write both your thoughts and summary in the same language as the task posed by the user.\n\nYour thinking process must follow the template below:\n<think>\nYour thoughts or/and draft, like working through an exercise on scratch paper. Be as casual and as long as you want until you are confident to generate a correct answer.\n</think>\n\nHere, provide a concise summary that reflects your reasoning and presents a clear final answer to the user.\n\n\n\nYou will be given a problem. Please reason step by step, and put your final answer within \\boxed{}.",
"type": "text"
}
],
"role": "system"
},
{
"content": [
{
"text": "Triangle $ABC^{}_{}$ has $AB=9^{}_{}$ and $BC: AC=40: 41^{}_{}$ . What's the largest area that this triangle can have?",
"type": "text"
}
],
"role": "user"
}
] |
$820$
|
di-zhang-fdu/AIME_1983_2024
|
[
{
"content": [
{
"path": "",
"text": "A user will ask you to solve a task. You should first draft your thinking process (inner monologue) until you have derived the final answer. Afterwards, write a self-contained summary of your thoughts (i.e. your summary should be succinct but contain all the critical steps you needed to reach the conclusion). You should use Markdown and Latex to format your response. Write both your thoughts and summary in the same language as the task posed by the user.\n\nYour thinking process must follow the template below:\n<think>\nYour thoughts or/and draft, like working through an exercise on scratch paper. Be as casual and as long as you want until you are confident to generate a correct answer.\n</think>\n\nHere, provide a concise summary that reflects your reasoning and presents a clear final answer to the user.\n\n\n\nYou will be given a problem. Please reason step by step, and put your final answer within \\boxed{}.",
"type": "text",
"url": null
}
],
"role": "system"
},
{
"content": [
{
"path": "",
"text": "Triangle $ABC^{}_{}$ has $AB=9^{}_{}$ and $BC: AC=40: 41^{}_{}$ . What's the largest area that this triangle can have?",
"type": "text",
"url": null
}
],
"role": "user"
}
] |
[
{
"content": [
{
"text": "A user will ask you to solve a task. You should first draft your thinking process (inner monologue) until you have derived the final answer. Afterwards, write a self-contained summary of your thoughts (i.e. your summary should be succinct but contain all the critical steps you needed to reach the conclusion). You should use Markdown and Latex to format your response. Write both your thoughts and summary in the same language as the task posed by the user.\n\nYour thinking process must follow the template below:\n<think>\nYour thoughts or/and draft, like working through an exercise on scratch paper. Be as casual and as long as you want until you are confident to generate a correct answer.\n</think>\n\nHere, provide a concise summary that reflects your reasoning and presents a clear final answer to the user.\n\n\n\nYou will be given a problem. Please reason step by step, and put your final answer within \\boxed{}.",
"type": "text"
}
],
"role": "system"
},
{
"content": [
{
"text": "Let $A B C D$ be a rectangle with $B C=24$. Point $X$ lies inside the rectangle such that $\\angle A X B=90^{\\circ}$. Given that triangles $\\triangle A X D$ and $\\triangle B X C$ are both acute and have circumradii $13$ and $15$, respectively, compute $A B$.",
"type": "text"
}
],
"role": "user"
}
] |
$14+4\sqrt{37}$
|
MathArena/hmmt_feb_2025
|
[
{
"content": [
{
"path": "",
"text": "A user will ask you to solve a task. You should first draft your thinking process (inner monologue) until you have derived the final answer. Afterwards, write a self-contained summary of your thoughts (i.e. your summary should be succinct but contain all the critical steps you needed to reach the conclusion). You should use Markdown and Latex to format your response. Write both your thoughts and summary in the same language as the task posed by the user.\n\nYour thinking process must follow the template below:\n<think>\nYour thoughts or/and draft, like working through an exercise on scratch paper. Be as casual and as long as you want until you are confident to generate a correct answer.\n</think>\n\nHere, provide a concise summary that reflects your reasoning and presents a clear final answer to the user.\n\n\n\nYou will be given a problem. Please reason step by step, and put your final answer within \\boxed{}.",
"type": "text",
"url": null
}
],
"role": "system"
},
{
"content": [
{
"path": "",
"text": "Let $A B C D$ be a rectangle with $B C=24$. Point $X$ lies inside the rectangle such that $\\angle A X B=90^{\\circ}$. Given that triangles $\\triangle A X D$ and $\\triangle B X C$ are both acute and have circumradii $13$ and $15$, respectively, compute $A B$.",
"type": "text",
"url": null
}
],
"role": "user"
}
] |
[
{
"content": [
{
"text": "A user will ask you to solve a task. You should first draft your thinking process (inner monologue) until you have derived the final answer. Afterwards, write a self-contained summary of your thoughts (i.e. your summary should be succinct but contain all the critical steps you needed to reach the conclusion). You should use Markdown and Latex to format your response. Write both your thoughts and summary in the same language as the task posed by the user.\n\nYour thinking process must follow the template below:\n<think>\nYour thoughts or/and draft, like working through an exercise on scratch paper. Be as casual and as long as you want until you are confident to generate a correct answer.\n</think>\n\nHere, provide a concise summary that reflects your reasoning and presents a clear final answer to the user.\n\n\n\nYou will be given a problem. Please reason step by step, and put your final answer within \\boxed{}.",
"type": "text"
}
],
"role": "system"
},
{
"content": [
{
"text": "In $\\triangle PQR$ , $PR=15$ , $QR=20$ , and $PQ=25$ . Points $A$ and $B$ lie on $\\overline{PQ}$ , points $C$ and $D$ lie on $\\overline{QR}$ , and points $E$ and $F$ lie on $\\overline{PR}$ , with $PA=QB=QC=RD=RE=PF=5$ . Find the area of hexagon $ABCDEF$ .",
"type": "text"
}
],
"role": "user"
}
] |
$120$
|
di-zhang-fdu/AIME_1983_2024
|
[
{
"content": [
{
"path": "",
"text": "A user will ask you to solve a task. You should first draft your thinking process (inner monologue) until you have derived the final answer. Afterwards, write a self-contained summary of your thoughts (i.e. your summary should be succinct but contain all the critical steps you needed to reach the conclusion). You should use Markdown and Latex to format your response. Write both your thoughts and summary in the same language as the task posed by the user.\n\nYour thinking process must follow the template below:\n<think>\nYour thoughts or/and draft, like working through an exercise on scratch paper. Be as casual and as long as you want until you are confident to generate a correct answer.\n</think>\n\nHere, provide a concise summary that reflects your reasoning and presents a clear final answer to the user.\n\n\n\nYou will be given a problem. Please reason step by step, and put your final answer within \\boxed{}.",
"type": "text",
"url": null
}
],
"role": "system"
},
{
"content": [
{
"path": "",
"text": "In $\\triangle PQR$ , $PR=15$ , $QR=20$ , and $PQ=25$ . Points $A$ and $B$ lie on $\\overline{PQ}$ , points $C$ and $D$ lie on $\\overline{QR}$ , and points $E$ and $F$ lie on $\\overline{PR}$ , with $PA=QB=QC=RD=RE=PF=5$ . Find the area of hexagon $ABCDEF$ .",
"type": "text",
"url": null
}
],
"role": "user"
}
] |
[
{
"content": [
{
"text": "A user will ask you to solve a task. You should first draft your thinking process (inner monologue) until you have derived the final answer. Afterwards, write a self-contained summary of your thoughts (i.e. your summary should be succinct but contain all the critical steps you needed to reach the conclusion). You should use Markdown and Latex to format your response. Write both your thoughts and summary in the same language as the task posed by the user.\n\nYour thinking process must follow the template below:\n<think>\nYour thoughts or/and draft, like working through an exercise on scratch paper. Be as casual and as long as you want until you are confident to generate a correct answer.\n</think>\n\nHere, provide a concise summary that reflects your reasoning and presents a clear final answer to the user.\n\n\n\nYou will be given a problem. Please reason step by step, and put your final answer within \\boxed{}.",
"type": "text"
}
],
"role": "system"
},
{
"content": [
{
"text": "Find the number of positive integers less than or equal to $2017$ whose base-three representation contains no digit equal to $0$ .",
"type": "text"
}
],
"role": "user"
}
] |
$222$
|
di-zhang-fdu/AIME_1983_2024
|
[
{
"content": [
{
"path": "",
"text": "A user will ask you to solve a task. You should first draft your thinking process (inner monologue) until you have derived the final answer. Afterwards, write a self-contained summary of your thoughts (i.e. your summary should be succinct but contain all the critical steps you needed to reach the conclusion). You should use Markdown and Latex to format your response. Write both your thoughts and summary in the same language as the task posed by the user.\n\nYour thinking process must follow the template below:\n<think>\nYour thoughts or/and draft, like working through an exercise on scratch paper. Be as casual and as long as you want until you are confident to generate a correct answer.\n</think>\n\nHere, provide a concise summary that reflects your reasoning and presents a clear final answer to the user.\n\n\n\nYou will be given a problem. Please reason step by step, and put your final answer within \\boxed{}.",
"type": "text",
"url": null
}
],
"role": "system"
},
{
"content": [
{
"path": "",
"text": "Find the number of positive integers less than or equal to $2017$ whose base-three representation contains no digit equal to $0$ .",
"type": "text",
"url": null
}
],
"role": "user"
}
] |
[
{
"content": [
{
"text": "A user will ask you to solve a task. You should first draft your thinking process (inner monologue) until you have derived the final answer. Afterwards, write a self-contained summary of your thoughts (i.e. your summary should be succinct but contain all the critical steps you needed to reach the conclusion). You should use Markdown and Latex to format your response. Write both your thoughts and summary in the same language as the task posed by the user.\n\nYour thinking process must follow the template below:\n<think>\nYour thoughts or/and draft, like working through an exercise on scratch paper. Be as casual and as long as you want until you are confident to generate a correct answer.\n</think>\n\nHere, provide a concise summary that reflects your reasoning and presents a clear final answer to the user.\n\n",
"type": "text"
}
],
"role": "system"
},
{
"content": [
{
"text": "You will be given a problem. Please reason step by step, and put your final answer within \\boxed{}:\nFor every subset $T$ of $U = \\{ 1,2,3,\\ldots,18 \\}$ , let $s(T)$ be the sum of the elements of $T$ , with $s(\\emptyset)$ defined to be $0$ . If $T$ is chosen at random among all subsets of $U$ , the probability that $s(T)$ is divisible by $3$ is $\\frac{m}{n}$ , where $m$ and $n$ are relatively prime positive integers. Find $m$ .",
"type": "text"
}
],
"role": "user"
}
] |
$683$
|
di-zhang-fdu/AIME_1983_2024
|
[
{
"content": [
{
"path": "",
"text": "A user will ask you to solve a task. You should first draft your thinking process (inner monologue) until you have derived the final answer. Afterwards, write a self-contained summary of your thoughts (i.e. your summary should be succinct but contain all the critical steps you needed to reach the conclusion). You should use Markdown and Latex to format your response. Write both your thoughts and summary in the same language as the task posed by the user.\n\nYour thinking process must follow the template below:\n<think>\nYour thoughts or/and draft, like working through an exercise on scratch paper. Be as casual and as long as you want until you are confident to generate a correct answer.\n</think>\n\nHere, provide a concise summary that reflects your reasoning and presents a clear final answer to the user.\n\n",
"type": "text",
"url": null
}
],
"role": "system"
},
{
"content": [
{
"path": "",
"text": "You will be given a problem. Please reason step by step, and put your final answer within \\boxed{}:\nFor every subset $T$ of $U = \\{ 1,2,3,\\ldots,18 \\}$ , let $s(T)$ be the sum of the elements of $T$ , with $s(\\emptyset)$ defined to be $0$ . If $T$ is chosen at random among all subsets of $U$ , the probability that $s(T)$ is divisible by $3$ is $\\frac{m}{n}$ , where $m$ and $n$ are relatively prime positive integers. Find $m$ .",
"type": "text",
"url": null
}
],
"role": "user"
}
] |
[
{
"content": [
{
"text": "A user will ask you to solve a task. You should first draft your thinking process (inner monologue) until you have derived the final answer. Afterwards, write a self-contained summary of your thoughts (i.e. your summary should be succinct but contain all the critical steps you needed to reach the conclusion). You should use Markdown and Latex to format your response. Write both your thoughts and summary in the same language as the task posed by the user.\n\nYour thinking process must follow the template below:\n<think>\nYour thoughts or/and draft, like working through an exercise on scratch paper. Be as casual and as long as you want until you are confident to generate a correct answer.\n</think>\n\nHere, provide a concise summary that reflects your reasoning and presents a clear final answer to the user.\n\n",
"type": "text"
}
],
"role": "system"
},
{
"content": [
{
"text": "You will be given a problem. Please reason step by step, and put your final answer within \\boxed{}:\nIn rectangle $ABCD$ , $AB = 12$ and $BC = 10$ . Points $E$ and $F$ lie inside rectangle $ABCD$ so that $BE = 9$ , $DF = 8$ , $\\overline{BE} \\parallel \\overline{DF}$ , $\\overline{EF} \\parallel \\overline{AB}$ , and line $BE$ intersects segment $\\overline{AD}$ . The length $EF$ can be expressed in the form $m \\sqrt{n} - p$ , where $m$ , $n$ , and $p$ are positive integers and $n$ is not divisible by the square of any prime. Find $m + n + p$ .",
"type": "text"
}
],
"role": "user"
}
] |
$36$
|
di-zhang-fdu/AIME_1983_2024
|
[
{
"content": [
{
"path": "",
"text": "A user will ask you to solve a task. You should first draft your thinking process (inner monologue) until you have derived the final answer. Afterwards, write a self-contained summary of your thoughts (i.e. your summary should be succinct but contain all the critical steps you needed to reach the conclusion). You should use Markdown and Latex to format your response. Write both your thoughts and summary in the same language as the task posed by the user.\n\nYour thinking process must follow the template below:\n<think>\nYour thoughts or/and draft, like working through an exercise on scratch paper. Be as casual and as long as you want until you are confident to generate a correct answer.\n</think>\n\nHere, provide a concise summary that reflects your reasoning and presents a clear final answer to the user.\n\n",
"type": "text",
"url": null
}
],
"role": "system"
},
{
"content": [
{
"path": "",
"text": "You will be given a problem. Please reason step by step, and put your final answer within \\boxed{}:\nIn rectangle $ABCD$ , $AB = 12$ and $BC = 10$ . Points $E$ and $F$ lie inside rectangle $ABCD$ so that $BE = 9$ , $DF = 8$ , $\\overline{BE} \\parallel \\overline{DF}$ , $\\overline{EF} \\parallel \\overline{AB}$ , and line $BE$ intersects segment $\\overline{AD}$ . The length $EF$ can be expressed in the form $m \\sqrt{n} - p$ , where $m$ , $n$ , and $p$ are positive integers and $n$ is not divisible by the square of any prime. Find $m + n + p$ .",
"type": "text",
"url": null
}
],
"role": "user"
}
] |
[
{
"content": [
{
"text": "A user will ask you to solve a task. You should first draft your thinking process (inner monologue) until you have derived the final answer. Afterwards, write a self-contained summary of your thoughts (i.e. your summary should be succinct but contain all the critical steps you needed to reach the conclusion). You should use Markdown and Latex to format your response. Write both your thoughts and summary in the same language as the task posed by the user.\n\nYour thinking process must follow the template below:\n<think>\nYour thoughts or/and draft, like working through an exercise on scratch paper. Be as casual and as long as you want until you are confident to generate a correct answer.\n</think>\n\nHere, provide a concise summary that reflects your reasoning and presents a clear final answer to the user.\n\n\n\nYou will be given a problem. Please reason step by step, and put your final answer within \\boxed{}.",
"type": "text"
}
],
"role": "system"
},
{
"content": [
{
"text": "Circle $C_0$ has radius $1$ , and the point $A_0$ is a point on the circle. Circle $C_1$ has radius $r<1$ and is internally tangent to $C_0$ at point $A_0$ . Point $A_1$ lies on circle $C_1$ so that $A_1$ is located $90^{\\circ}$ counterclockwise from $A_0$ on $C_1$ . Circle $C_2$ has radius $r^2$ and is internally tangent to $C_1$ at point $A_1$ . In this way a sequence of circles $C_1,C_2,C_3,\\ldots$ and a sequence of points on the circles $A_1,A_2,A_3,\\ldots$ are constructed, where circle $C_n$ has radius $r^n$ and is internally tangent to circle $C_{n-1}$ at point $A_{n-1}$ , and point $A_n$ lies on $C_n$ $90^{\\circ}$ counterclockwise from point $A_{n-1}$ , as shown in the figure below. There is one point $B$ inside all of these circles. When $r = \\frac{11}{60}$ , the distance from the center $C_0$ to $B$ is $\\frac{m}{n}$ , where $m$ and $n$ are relatively prime positive integers. Find $m+n$ . [asy] draw(Circle((0,0),125)); draw(Circle((25,0),100)); draw(Circle((25,20),80)); draw(Circle((9,20),64)); dot((125,0)); label(\"$A_0$\",(125,0),E); dot((25,100)); label(\"$A_1$\",(25,100),SE); dot((-55,20)); label(\"$A_2$\",(-55,20),E); [/asy]",
"type": "text"
}
],
"role": "user"
}
] |
$110$
|
di-zhang-fdu/AIME_1983_2024
|
[
{
"content": [
{
"path": "",
"text": "A user will ask you to solve a task. You should first draft your thinking process (inner monologue) until you have derived the final answer. Afterwards, write a self-contained summary of your thoughts (i.e. your summary should be succinct but contain all the critical steps you needed to reach the conclusion). You should use Markdown and Latex to format your response. Write both your thoughts and summary in the same language as the task posed by the user.\n\nYour thinking process must follow the template below:\n<think>\nYour thoughts or/and draft, like working through an exercise on scratch paper. Be as casual and as long as you want until you are confident to generate a correct answer.\n</think>\n\nHere, provide a concise summary that reflects your reasoning and presents a clear final answer to the user.\n\n\n\nYou will be given a problem. Please reason step by step, and put your final answer within \\boxed{}.",
"type": "text",
"url": null
}
],
"role": "system"
},
{
"content": [
{
"path": "",
"text": "Circle $C_0$ has radius $1$ , and the point $A_0$ is a point on the circle. Circle $C_1$ has radius $r<1$ and is internally tangent to $C_0$ at point $A_0$ . Point $A_1$ lies on circle $C_1$ so that $A_1$ is located $90^{\\circ}$ counterclockwise from $A_0$ on $C_1$ . Circle $C_2$ has radius $r^2$ and is internally tangent to $C_1$ at point $A_1$ . In this way a sequence of circles $C_1,C_2,C_3,\\ldots$ and a sequence of points on the circles $A_1,A_2,A_3,\\ldots$ are constructed, where circle $C_n$ has radius $r^n$ and is internally tangent to circle $C_{n-1}$ at point $A_{n-1}$ , and point $A_n$ lies on $C_n$ $90^{\\circ}$ counterclockwise from point $A_{n-1}$ , as shown in the figure below. There is one point $B$ inside all of these circles. When $r = \\frac{11}{60}$ , the distance from the center $C_0$ to $B$ is $\\frac{m}{n}$ , where $m$ and $n$ are relatively prime positive integers. Find $m+n$ . [asy] draw(Circle((0,0),125)); draw(Circle((25,0),100)); draw(Circle((25,20),80)); draw(Circle((9,20),64)); dot((125,0)); label(\"$A_0$\",(125,0),E); dot((25,100)); label(\"$A_1$\",(25,100),SE); dot((-55,20)); label(\"$A_2$\",(-55,20),E); [/asy]",
"type": "text",
"url": null
}
],
"role": "user"
}
] |
[
{
"content": [
{
"text": "A user will ask you to solve a task. You should first draft your thinking process (inner monologue) until you have derived the final answer. Afterwards, write a self-contained summary of your thoughts (i.e. your summary should be succinct but contain all the critical steps you needed to reach the conclusion). You should use Markdown and Latex to format your response. Write both your thoughts and summary in the same language as the task posed by the user.\n\nYour thinking process must follow the template below:\n<think>\nYour thoughts or/and draft, like working through an exercise on scratch paper. Be as casual and as long as you want until you are confident to generate a correct answer.\n</think>\n\nHere, provide a concise summary that reflects your reasoning and presents a clear final answer to the user.\n\n\n\nYou will be given a problem. Please reason step by step, and put your final answer within \\boxed{}.",
"type": "text"
}
],
"role": "system"
},
{
"content": [
{
"text": "Let $S$ be the set of all positive rational numbers $r$ such that when the two numbers $r$ and $55r$ are written as fractions in lowest terms, the sum of the numerator and denominator of one fraction is the same as the sum of the numerator and denominator of the other fraction. The sum of all the elements of $S$ can be expressed in the form $\\frac{p}{q},$ where $p$ and $q$ are relatively prime positive integers. Find $p+q.$",
"type": "text"
}
],
"role": "user"
}
] |
$719$
|
di-zhang-fdu/AIME_1983_2024
|
[
{
"content": [
{
"path": "",
"text": "A user will ask you to solve a task. You should first draft your thinking process (inner monologue) until you have derived the final answer. Afterwards, write a self-contained summary of your thoughts (i.e. your summary should be succinct but contain all the critical steps you needed to reach the conclusion). You should use Markdown and Latex to format your response. Write both your thoughts and summary in the same language as the task posed by the user.\n\nYour thinking process must follow the template below:\n<think>\nYour thoughts or/and draft, like working through an exercise on scratch paper. Be as casual and as long as you want until you are confident to generate a correct answer.\n</think>\n\nHere, provide a concise summary that reflects your reasoning and presents a clear final answer to the user.\n\n\n\nYou will be given a problem. Please reason step by step, and put your final answer within \\boxed{}.",
"type": "text",
"url": null
}
],
"role": "system"
},
{
"content": [
{
"path": "",
"text": "Let $S$ be the set of all positive rational numbers $r$ such that when the two numbers $r$ and $55r$ are written as fractions in lowest terms, the sum of the numerator and denominator of one fraction is the same as the sum of the numerator and denominator of the other fraction. The sum of all the elements of $S$ can be expressed in the form $\\frac{p}{q},$ where $p$ and $q$ are relatively prime positive integers. Find $p+q.$",
"type": "text",
"url": null
}
],
"role": "user"
}
] |
[
{
"content": [
{
"text": "A user will ask you to solve a task. You should first draft your thinking process (inner monologue) until you have derived the final answer. Afterwards, write a self-contained summary of your thoughts (i.e. your summary should be succinct but contain all the critical steps you needed to reach the conclusion). You should use Markdown and Latex to format your response. Write both your thoughts and summary in the same language as the task posed by the user.\n\nYour thinking process must follow the template below:\n<think>\nYour thoughts or/and draft, like working through an exercise on scratch paper. Be as casual and as long as you want until you are confident to generate a correct answer.\n</think>\n\nHere, provide a concise summary that reflects your reasoning and presents a clear final answer to the user.\n\n",
"type": "text"
}
],
"role": "system"
},
{
"content": [
{
"text": "You will be given a problem. Please reason step by step, and put your final answer within \\boxed{}:\nOn square $ABCD$ , point $E$ lies on side $AD$ and point $F$ lies on side $BC$ , so that $BE=EF=FD=30$ . Find the area of the square $ABCD$ .",
"type": "text"
}
],
"role": "user"
}
] |
$810$
|
di-zhang-fdu/AIME_1983_2024
|
[
{
"content": [
{
"path": "",
"text": "A user will ask you to solve a task. You should first draft your thinking process (inner monologue) until you have derived the final answer. Afterwards, write a self-contained summary of your thoughts (i.e. your summary should be succinct but contain all the critical steps you needed to reach the conclusion). You should use Markdown and Latex to format your response. Write both your thoughts and summary in the same language as the task posed by the user.\n\nYour thinking process must follow the template below:\n<think>\nYour thoughts or/and draft, like working through an exercise on scratch paper. Be as casual and as long as you want until you are confident to generate a correct answer.\n</think>\n\nHere, provide a concise summary that reflects your reasoning and presents a clear final answer to the user.\n\n",
"type": "text",
"url": null
}
],
"role": "system"
},
{
"content": [
{
"path": "",
"text": "You will be given a problem. Please reason step by step, and put your final answer within \\boxed{}:\nOn square $ABCD$ , point $E$ lies on side $AD$ and point $F$ lies on side $BC$ , so that $BE=EF=FD=30$ . Find the area of the square $ABCD$ .",
"type": "text",
"url": null
}
],
"role": "user"
}
] |
[
{
"content": [
{
"text": "A user will ask you to solve a task. You should first draft your thinking process (inner monologue) until you have derived the final answer. Afterwards, write a self-contained summary of your thoughts (i.e. your summary should be succinct but contain all the critical steps you needed to reach the conclusion). You should use Markdown and Latex to format your response. Write both your thoughts and summary in the same language as the task posed by the user.\n\nYour thinking process must follow the template below:\n<think>\nYour thoughts or/and draft, like working through an exercise on scratch paper. Be as casual and as long as you want until you are confident to generate a correct answer.\n</think>\n\nHere, provide a concise summary that reflects your reasoning and presents a clear final answer to the user.\n\n\n\nYou will be given a problem. Please reason step by step, and put your final answer within \\boxed{}.",
"type": "text"
}
],
"role": "system"
},
{
"content": [
{
"text": "In trapezoid $ABCD$ , leg $\\overline{BC}$ is perpendicular to bases $\\overline{AB}$ and $\\overline{CD}$ , and diagonals $\\overline{AC}$ and $\\overline{BD}$ are perpendicular. Given that $AB=\\sqrt{11}$ and $AD=\\sqrt{1001}$ , find $BC^2$ .",
"type": "text"
}
],
"role": "user"
}
] |
$110$
|
di-zhang-fdu/AIME_1983_2024
|
[
{
"content": [
{
"path": "",
"text": "A user will ask you to solve a task. You should first draft your thinking process (inner monologue) until you have derived the final answer. Afterwards, write a self-contained summary of your thoughts (i.e. your summary should be succinct but contain all the critical steps you needed to reach the conclusion). You should use Markdown and Latex to format your response. Write both your thoughts and summary in the same language as the task posed by the user.\n\nYour thinking process must follow the template below:\n<think>\nYour thoughts or/and draft, like working through an exercise on scratch paper. Be as casual and as long as you want until you are confident to generate a correct answer.\n</think>\n\nHere, provide a concise summary that reflects your reasoning and presents a clear final answer to the user.\n\n\n\nYou will be given a problem. Please reason step by step, and put your final answer within \\boxed{}.",
"type": "text",
"url": null
}
],
"role": "system"
},
{
"content": [
{
"path": "",
"text": "In trapezoid $ABCD$ , leg $\\overline{BC}$ is perpendicular to bases $\\overline{AB}$ and $\\overline{CD}$ , and diagonals $\\overline{AC}$ and $\\overline{BD}$ are perpendicular. Given that $AB=\\sqrt{11}$ and $AD=\\sqrt{1001}$ , find $BC^2$ .",
"type": "text",
"url": null
}
],
"role": "user"
}
] |
[
{
"content": [
{
"text": "A user will ask you to solve a task. You should first draft your thinking process (inner monologue) until you have derived the final answer. Afterwards, write a self-contained summary of your thoughts (i.e. your summary should be succinct but contain all the critical steps you needed to reach the conclusion). You should use Markdown and Latex to format your response. Write both your thoughts and summary in the same language as the task posed by the user.\n\nYour thinking process must follow the template below:\n<think>\nYour thoughts or/and draft, like working through an exercise on scratch paper. Be as casual and as long as you want until you are confident to generate a correct answer.\n</think>\n\nHere, provide a concise summary that reflects your reasoning and presents a clear final answer to the user.\n\n",
"type": "text"
}
],
"role": "system"
},
{
"content": [
{
"text": "You will be given a problem. Please reason step by step, and put your final answer within \\boxed{}:\nA soccer team has $22$ available players. A fixed set of $11$ players starts the game, while the other $11$ are available as substitutes. During the game, the coach may make as many as $3$ substitutions, where any one of the $11$ players in the game is replaced by one of the substitutes. No player removed from the game may reenter the game, although a substitute entering the game may be replaced later. No two substitutions can happen at the same time. The players involved and the order of the substitutions matter. Let $n$ be the number of ways the coach can make substitutions during the game (including the possibility of making no substitutions). Find the remainder when $n$ is divided by $1000$ .",
"type": "text"
}
],
"role": "user"
}
] |
$122$
|
di-zhang-fdu/AIME_1983_2024
|
[
{
"content": [
{
"path": "",
"text": "A user will ask you to solve a task. You should first draft your thinking process (inner monologue) until you have derived the final answer. Afterwards, write a self-contained summary of your thoughts (i.e. your summary should be succinct but contain all the critical steps you needed to reach the conclusion). You should use Markdown and Latex to format your response. Write both your thoughts and summary in the same language as the task posed by the user.\n\nYour thinking process must follow the template below:\n<think>\nYour thoughts or/and draft, like working through an exercise on scratch paper. Be as casual and as long as you want until you are confident to generate a correct answer.\n</think>\n\nHere, provide a concise summary that reflects your reasoning and presents a clear final answer to the user.\n\n",
"type": "text",
"url": null
}
],
"role": "system"
},
{
"content": [
{
"path": "",
"text": "You will be given a problem. Please reason step by step, and put your final answer within \\boxed{}:\nA soccer team has $22$ available players. A fixed set of $11$ players starts the game, while the other $11$ are available as substitutes. During the game, the coach may make as many as $3$ substitutions, where any one of the $11$ players in the game is replaced by one of the substitutes. No player removed from the game may reenter the game, although a substitute entering the game may be replaced later. No two substitutions can happen at the same time. The players involved and the order of the substitutions matter. Let $n$ be the number of ways the coach can make substitutions during the game (including the possibility of making no substitutions). Find the remainder when $n$ is divided by $1000$ .",
"type": "text",
"url": null
}
],
"role": "user"
}
] |
[
{
"content": [
{
"text": "A user will ask you to solve a task. You should first draft your thinking process (inner monologue) until you have derived the final answer. Afterwards, write a self-contained summary of your thoughts (i.e. your summary should be succinct but contain all the critical steps you needed to reach the conclusion). You should use Markdown and Latex to format your response. Write both your thoughts and summary in the same language as the task posed by the user.\n\nYour thinking process must follow the template below:\n<think>\nYour thoughts or/and draft, like working through an exercise on scratch paper. Be as casual and as long as you want until you are confident to generate a correct answer.\n</think>\n\nHere, provide a concise summary that reflects your reasoning and presents a clear final answer to the user.\n\n",
"type": "text"
}
],
"role": "system"
},
{
"content": [
{
"text": "You will be given a problem. Please reason step by step, and put your final answer within \\boxed{}:\nSquares $S_1$ and $S_2$ are inscribed in right triangle $ABC$ , as shown in the figures below. Find $AC + CB$ if area $(S_1) = 441$ and area $(S_2) = 440$ . AIME 1987 Problem 15.png",
"type": "text"
}
],
"role": "user"
}
] |
$462$
|
di-zhang-fdu/AIME_1983_2024
|
[
{
"content": [
{
"path": "",
"text": "A user will ask you to solve a task. You should first draft your thinking process (inner monologue) until you have derived the final answer. Afterwards, write a self-contained summary of your thoughts (i.e. your summary should be succinct but contain all the critical steps you needed to reach the conclusion). You should use Markdown and Latex to format your response. Write both your thoughts and summary in the same language as the task posed by the user.\n\nYour thinking process must follow the template below:\n<think>\nYour thoughts or/and draft, like working through an exercise on scratch paper. Be as casual and as long as you want until you are confident to generate a correct answer.\n</think>\n\nHere, provide a concise summary that reflects your reasoning and presents a clear final answer to the user.\n\n",
"type": "text",
"url": null
}
],
"role": "system"
},
{
"content": [
{
"path": "",
"text": "You will be given a problem. Please reason step by step, and put your final answer within \\boxed{}:\nSquares $S_1$ and $S_2$ are inscribed in right triangle $ABC$ , as shown in the figures below. Find $AC + CB$ if area $(S_1) = 441$ and area $(S_2) = 440$ . AIME 1987 Problem 15.png",
"type": "text",
"url": null
}
],
"role": "user"
}
] |
[
{
"content": [
{
"text": "A user will ask you to solve a task. You should first draft your thinking process (inner monologue) until you have derived the final answer. Afterwards, write a self-contained summary of your thoughts (i.e. your summary should be succinct but contain all the critical steps you needed to reach the conclusion). You should use Markdown and Latex to format your response. Write both your thoughts and summary in the same language as the task posed by the user.\n\nYour thinking process must follow the template below:\n<think>\nYour thoughts or/and draft, like working through an exercise on scratch paper. Be as casual and as long as you want until you are confident to generate a correct answer.\n</think>\n\nHere, provide a concise summary that reflects your reasoning and presents a clear final answer to the user.\n\n",
"type": "text"
}
],
"role": "system"
},
{
"content": [
{
"text": "You will be given a problem. Please reason step by step, and put your final answer within \\boxed{}:\nThe numbers in the sequence $101$ , $104$ , $109$ , $116$ , $\\ldots$ are of the form $a_n=100+n^2$ , where $n=1,2,3,\\ldots$ . For each $n$ , let $d_n$ be the greatest common divisor of $a_n$ and $a_{n+1}$ . Find the maximum value of $d_n$ as $n$ ranges through the positive integers .",
"type": "text"
}
],
"role": "user"
}
] |
$401$
|
di-zhang-fdu/AIME_1983_2024
|
[
{
"content": [
{
"path": "",
"text": "A user will ask you to solve a task. You should first draft your thinking process (inner monologue) until you have derived the final answer. Afterwards, write a self-contained summary of your thoughts (i.e. your summary should be succinct but contain all the critical steps you needed to reach the conclusion). You should use Markdown and Latex to format your response. Write both your thoughts and summary in the same language as the task posed by the user.\n\nYour thinking process must follow the template below:\n<think>\nYour thoughts or/and draft, like working through an exercise on scratch paper. Be as casual and as long as you want until you are confident to generate a correct answer.\n</think>\n\nHere, provide a concise summary that reflects your reasoning and presents a clear final answer to the user.\n\n",
"type": "text",
"url": null
}
],
"role": "system"
},
{
"content": [
{
"path": "",
"text": "You will be given a problem. Please reason step by step, and put your final answer within \\boxed{}:\nThe numbers in the sequence $101$ , $104$ , $109$ , $116$ , $\\ldots$ are of the form $a_n=100+n^2$ , where $n=1,2,3,\\ldots$ . For each $n$ , let $d_n$ be the greatest common divisor of $a_n$ and $a_{n+1}$ . Find the maximum value of $d_n$ as $n$ ranges through the positive integers .",
"type": "text",
"url": null
}
],
"role": "user"
}
] |
[
{
"content": [
{
"text": "A user will ask you to solve a task. You should first draft your thinking process (inner monologue) until you have derived the final answer. Afterwards, write a self-contained summary of your thoughts (i.e. your summary should be succinct but contain all the critical steps you needed to reach the conclusion). You should use Markdown and Latex to format your response. Write both your thoughts and summary in the same language as the task posed by the user.\n\nYour thinking process must follow the template below:\n<think>\nYour thoughts or/and draft, like working through an exercise on scratch paper. Be as casual and as long as you want until you are confident to generate a correct answer.\n</think>\n\nHere, provide a concise summary that reflects your reasoning and presents a clear final answer to the user.\n\n\n\nYou will be given a problem. Please reason step by step, and put your final answer within \\boxed{}.",
"type": "text"
}
],
"role": "system"
},
{
"content": [
{
"text": "A token starts at the point $(0,0)$ of an $xy$ -coordinate grid and then makes a sequence of six moves. Each move is 1 unit in a direction parallel to one of the coordinate axes. Each move is selected randomly from the four possible directions and independently of the other moves. The probability the token ends at a point on the graph of $|y|=|x|$ is $\\tfrac{m}{n}$ , where $m$ and $n$ are relatively prime positive integers. Find $m+n$ .",
"type": "text"
}
],
"role": "user"
}
] |
$391$
|
di-zhang-fdu/AIME_1983_2024
|
[
{
"content": [
{
"path": "",
"text": "A user will ask you to solve a task. You should first draft your thinking process (inner monologue) until you have derived the final answer. Afterwards, write a self-contained summary of your thoughts (i.e. your summary should be succinct but contain all the critical steps you needed to reach the conclusion). You should use Markdown and Latex to format your response. Write both your thoughts and summary in the same language as the task posed by the user.\n\nYour thinking process must follow the template below:\n<think>\nYour thoughts or/and draft, like working through an exercise on scratch paper. Be as casual and as long as you want until you are confident to generate a correct answer.\n</think>\n\nHere, provide a concise summary that reflects your reasoning and presents a clear final answer to the user.\n\n\n\nYou will be given a problem. Please reason step by step, and put your final answer within \\boxed{}.",
"type": "text",
"url": null
}
],
"role": "system"
},
{
"content": [
{
"path": "",
"text": "A token starts at the point $(0,0)$ of an $xy$ -coordinate grid and then makes a sequence of six moves. Each move is 1 unit in a direction parallel to one of the coordinate axes. Each move is selected randomly from the four possible directions and independently of the other moves. The probability the token ends at a point on the graph of $|y|=|x|$ is $\\tfrac{m}{n}$ , where $m$ and $n$ are relatively prime positive integers. Find $m+n$ .",
"type": "text",
"url": null
}
],
"role": "user"
}
] |
[
{
"content": [
{
"text": "A user will ask you to solve a task. You should first draft your thinking process (inner monologue) until you have derived the final answer. Afterwards, write a self-contained summary of your thoughts (i.e. your summary should be succinct but contain all the critical steps you needed to reach the conclusion). You should use Markdown and Latex to format your response. Write both your thoughts and summary in the same language as the task posed by the user.\n\nYour thinking process must follow the template below:\n<think>\nYour thoughts or/and draft, like working through an exercise on scratch paper. Be as casual and as long as you want until you are confident to generate a correct answer.\n</think>\n\nHere, provide a concise summary that reflects your reasoning and presents a clear final answer to the user.\n\n",
"type": "text"
}
],
"role": "system"
},
{
"content": [
{
"text": "You will be given a problem. Please reason step by step, and put your final answer within \\boxed{}:\nWhat is that largest positive integer $n$ for which $n^3+100$ is divisible by $n+10$ ?",
"type": "text"
}
],
"role": "user"
}
] |
$890$
|
di-zhang-fdu/AIME_1983_2024
|
[
{
"content": [
{
"path": "",
"text": "A user will ask you to solve a task. You should first draft your thinking process (inner monologue) until you have derived the final answer. Afterwards, write a self-contained summary of your thoughts (i.e. your summary should be succinct but contain all the critical steps you needed to reach the conclusion). You should use Markdown and Latex to format your response. Write both your thoughts and summary in the same language as the task posed by the user.\n\nYour thinking process must follow the template below:\n<think>\nYour thoughts or/and draft, like working through an exercise on scratch paper. Be as casual and as long as you want until you are confident to generate a correct answer.\n</think>\n\nHere, provide a concise summary that reflects your reasoning and presents a clear final answer to the user.\n\n",
"type": "text",
"url": null
}
],
"role": "system"
},
{
"content": [
{
"path": "",
"text": "You will be given a problem. Please reason step by step, and put your final answer within \\boxed{}:\nWhat is that largest positive integer $n$ for which $n^3+100$ is divisible by $n+10$ ?",
"type": "text",
"url": null
}
],
"role": "user"
}
] |
[
{
"content": [
{
"text": "A user will ask you to solve a task. You should first draft your thinking process (inner monologue) until you have derived the final answer. Afterwards, write a self-contained summary of your thoughts (i.e. your summary should be succinct but contain all the critical steps you needed to reach the conclusion). You should use Markdown and Latex to format your response. Write both your thoughts and summary in the same language as the task posed by the user.\n\nYour thinking process must follow the template below:\n<think>\nYour thoughts or/and draft, like working through an exercise on scratch paper. Be as casual and as long as you want until you are confident to generate a correct answer.\n</think>\n\nHere, provide a concise summary that reflects your reasoning and presents a clear final answer to the user.\n\n\n\nYou will be given a problem. Please reason step by step, and put your final answer within \\boxed{}.",
"type": "text"
}
],
"role": "system"
},
{
"content": [
{
"text": "There exist $r$ unique nonnegative integers $n_1 > n_2 > \\cdots > n_r$ and $r$ integers $a_k$ ( $1\\le k\\le r$ ) with each $a_k$ either $1$ or $- 1$ such that \\[a_13^{n_1} + a_23^{n_2} + \\cdots + a_r3^{n_r} = 2008.\\] Find $n_1 + n_2 + \\cdots + n_r$ .",
"type": "text"
}
],
"role": "user"
}
] |
$21$
|
di-zhang-fdu/AIME_1983_2024
|
[
{
"content": [
{
"path": "",
"text": "A user will ask you to solve a task. You should first draft your thinking process (inner monologue) until you have derived the final answer. Afterwards, write a self-contained summary of your thoughts (i.e. your summary should be succinct but contain all the critical steps you needed to reach the conclusion). You should use Markdown and Latex to format your response. Write both your thoughts and summary in the same language as the task posed by the user.\n\nYour thinking process must follow the template below:\n<think>\nYour thoughts or/and draft, like working through an exercise on scratch paper. Be as casual and as long as you want until you are confident to generate a correct answer.\n</think>\n\nHere, provide a concise summary that reflects your reasoning and presents a clear final answer to the user.\n\n\n\nYou will be given a problem. Please reason step by step, and put your final answer within \\boxed{}.",
"type": "text",
"url": null
}
],
"role": "system"
},
{
"content": [
{
"path": "",
"text": "There exist $r$ unique nonnegative integers $n_1 > n_2 > \\cdots > n_r$ and $r$ integers $a_k$ ( $1\\le k\\le r$ ) with each $a_k$ either $1$ or $- 1$ such that \\[a_13^{n_1} + a_23^{n_2} + \\cdots + a_r3^{n_r} = 2008.\\] Find $n_1 + n_2 + \\cdots + n_r$ .",
"type": "text",
"url": null
}
],
"role": "user"
}
] |
[
{
"content": [
{
"text": "A user will ask you to solve a task. You should first draft your thinking process (inner monologue) until you have derived the final answer. Afterwards, write a self-contained summary of your thoughts (i.e. your summary should be succinct but contain all the critical steps you needed to reach the conclusion). You should use Markdown and Latex to format your response. Write both your thoughts and summary in the same language as the task posed by the user.\n\nYour thinking process must follow the template below:\n<think>\nYour thoughts or/and draft, like working through an exercise on scratch paper. Be as casual and as long as you want until you are confident to generate a correct answer.\n</think>\n\nHere, provide a concise summary that reflects your reasoning and presents a clear final answer to the user.\n\n",
"type": "text"
}
],
"role": "system"
},
{
"content": [
{
"text": "You will be given a problem. Please reason step by step, and put your final answer within \\boxed{}:\nThere exists a unique positive integer $a$ for which the sum \\[U=\\sum_{n=1}^{2023}\\left\\lfloor\\dfrac{n^{2}-na}{5}\\right\\rfloor\\] is an integer strictly between $-1000$ and $1000$ . For that unique $a$ , find $a+U$ . (Note that $\\lfloor x\\rfloor$ denotes the greatest integer that is less than or equal to $x$ .)",
"type": "text"
}
],
"role": "user"
}
] |
$944$
|
di-zhang-fdu/AIME_1983_2024
|
[
{
"content": [
{
"path": "",
"text": "A user will ask you to solve a task. You should first draft your thinking process (inner monologue) until you have derived the final answer. Afterwards, write a self-contained summary of your thoughts (i.e. your summary should be succinct but contain all the critical steps you needed to reach the conclusion). You should use Markdown and Latex to format your response. Write both your thoughts and summary in the same language as the task posed by the user.\n\nYour thinking process must follow the template below:\n<think>\nYour thoughts or/and draft, like working through an exercise on scratch paper. Be as casual and as long as you want until you are confident to generate a correct answer.\n</think>\n\nHere, provide a concise summary that reflects your reasoning and presents a clear final answer to the user.\n\n",
"type": "text",
"url": null
}
],
"role": "system"
},
{
"content": [
{
"path": "",
"text": "You will be given a problem. Please reason step by step, and put your final answer within \\boxed{}:\nThere exists a unique positive integer $a$ for which the sum \\[U=\\sum_{n=1}^{2023}\\left\\lfloor\\dfrac{n^{2}-na}{5}\\right\\rfloor\\] is an integer strictly between $-1000$ and $1000$ . For that unique $a$ , find $a+U$ . (Note that $\\lfloor x\\rfloor$ denotes the greatest integer that is less than or equal to $x$ .)",
"type": "text",
"url": null
}
],
"role": "user"
}
] |
[
{
"content": [
{
"text": "A user will ask you to solve a task. You should first draft your thinking process (inner monologue) until you have derived the final answer. Afterwards, write a self-contained summary of your thoughts (i.e. your summary should be succinct but contain all the critical steps you needed to reach the conclusion). You should use Markdown and Latex to format your response. Write both your thoughts and summary in the same language as the task posed by the user.\n\nYour thinking process must follow the template below:\n<think>\nYour thoughts or/and draft, like working through an exercise on scratch paper. Be as casual and as long as you want until you are confident to generate a correct answer.\n</think>\n\nHere, provide a concise summary that reflects your reasoning and presents a clear final answer to the user.\n\n\n\nYou will be given a problem. Please reason step by step, and put your final answer within \\boxed{}.",
"type": "text"
}
],
"role": "system"
},
{
"content": [
{
"text": "Point $B$ is on $\\overline{AC}$ with $AB = 9$ and $BC = 21.$ Point $D$ is not on $\\overline{AC}$ so that $AD = CD,$ and $AD$ and $BD$ are integers. Let $s$ be the sum of all possible perimeters of $\\triangle ACD.$ Find $s.$",
"type": "text"
}
],
"role": "user"
}
] |
$380$
|
di-zhang-fdu/AIME_1983_2024
|
[
{
"content": [
{
"path": "",
"text": "A user will ask you to solve a task. You should first draft your thinking process (inner monologue) until you have derived the final answer. Afterwards, write a self-contained summary of your thoughts (i.e. your summary should be succinct but contain all the critical steps you needed to reach the conclusion). You should use Markdown and Latex to format your response. Write both your thoughts and summary in the same language as the task posed by the user.\n\nYour thinking process must follow the template below:\n<think>\nYour thoughts or/and draft, like working through an exercise on scratch paper. Be as casual and as long as you want until you are confident to generate a correct answer.\n</think>\n\nHere, provide a concise summary that reflects your reasoning and presents a clear final answer to the user.\n\n\n\nYou will be given a problem. Please reason step by step, and put your final answer within \\boxed{}.",
"type": "text",
"url": null
}
],
"role": "system"
},
{
"content": [
{
"path": "",
"text": "Point $B$ is on $\\overline{AC}$ with $AB = 9$ and $BC = 21.$ Point $D$ is not on $\\overline{AC}$ so that $AD = CD,$ and $AD$ and $BD$ are integers. Let $s$ be the sum of all possible perimeters of $\\triangle ACD.$ Find $s.$",
"type": "text",
"url": null
}
],
"role": "user"
}
] |
[
{
"content": [
{
"text": "A user will ask you to solve a task. You should first draft your thinking process (inner monologue) until you have derived the final answer. Afterwards, write a self-contained summary of your thoughts (i.e. your summary should be succinct but contain all the critical steps you needed to reach the conclusion). You should use Markdown and Latex to format your response. Write both your thoughts and summary in the same language as the task posed by the user.\n\nYour thinking process must follow the template below:\n<think>\nYour thoughts or/and draft, like working through an exercise on scratch paper. Be as casual and as long as you want until you are confident to generate a correct answer.\n</think>\n\nHere, provide a concise summary that reflects your reasoning and presents a clear final answer to the user.\n\n\n\nYou will be given a problem. Please reason step by step, and put your final answer within \\boxed{}.",
"type": "text"
}
],
"role": "system"
},
{
"content": [
{
"text": "Let $ABCD$ be a parallelogram with $\\angle BAD < 90^\\circ.$ A circle tangent to sides $\\overline{DA},$ $\\overline{AB},$ and $\\overline{BC}$ intersects diagonal $\\overline{AC}$ at points $P$ and $Q$ with $AP < AQ,$ as shown. Suppose that $AP=3,$ $PQ=9,$ and $QC=16.$ Then the area of $ABCD$ can be expressed in the form $m\\sqrt{n},$ where $m$ and $n$ are positive integers, and $n$ is not divisible by the square of any prime. Find $m+n.$ [asy] defaultpen(linewidth(0.6)+fontsize(11)); size(8cm); pair A,B,C,D,P,Q; A=(0,0); label(\"$A$\", A, SW); B=(6,15); label(\"$B$\", B, NW); C=(30,15); label(\"$C$\", C, NE); D=(24,0); label(\"$D$\", D, SE); P=(5.2,2.6); label(\"$P$\", (5.8,2.6), N); Q=(18.3,9.1); label(\"$Q$\", (18.1,9.7), W); draw(A--B--C--D--cycle); draw(C--A); draw(Circle((10.95,7.45), 7.45)); dot(A^^B^^C^^D^^P^^Q); [/asy]",
"type": "text"
}
],
"role": "user"
}
] |
$150$
|
di-zhang-fdu/AIME_1983_2024
|
[
{
"content": [
{
"path": "",
"text": "A user will ask you to solve a task. You should first draft your thinking process (inner monologue) until you have derived the final answer. Afterwards, write a self-contained summary of your thoughts (i.e. your summary should be succinct but contain all the critical steps you needed to reach the conclusion). You should use Markdown and Latex to format your response. Write both your thoughts and summary in the same language as the task posed by the user.\n\nYour thinking process must follow the template below:\n<think>\nYour thoughts or/and draft, like working through an exercise on scratch paper. Be as casual and as long as you want until you are confident to generate a correct answer.\n</think>\n\nHere, provide a concise summary that reflects your reasoning and presents a clear final answer to the user.\n\n\n\nYou will be given a problem. Please reason step by step, and put your final answer within \\boxed{}.",
"type": "text",
"url": null
}
],
"role": "system"
},
{
"content": [
{
"path": "",
"text": "Let $ABCD$ be a parallelogram with $\\angle BAD < 90^\\circ.$ A circle tangent to sides $\\overline{DA},$ $\\overline{AB},$ and $\\overline{BC}$ intersects diagonal $\\overline{AC}$ at points $P$ and $Q$ with $AP < AQ,$ as shown. Suppose that $AP=3,$ $PQ=9,$ and $QC=16.$ Then the area of $ABCD$ can be expressed in the form $m\\sqrt{n},$ where $m$ and $n$ are positive integers, and $n$ is not divisible by the square of any prime. Find $m+n.$ [asy] defaultpen(linewidth(0.6)+fontsize(11)); size(8cm); pair A,B,C,D,P,Q; A=(0,0); label(\"$A$\", A, SW); B=(6,15); label(\"$B$\", B, NW); C=(30,15); label(\"$C$\", C, NE); D=(24,0); label(\"$D$\", D, SE); P=(5.2,2.6); label(\"$P$\", (5.8,2.6), N); Q=(18.3,9.1); label(\"$Q$\", (18.1,9.7), W); draw(A--B--C--D--cycle); draw(C--A); draw(Circle((10.95,7.45), 7.45)); dot(A^^B^^C^^D^^P^^Q); [/asy]",
"type": "text",
"url": null
}
],
"role": "user"
}
] |
[
{
"content": [
{
"text": "A user will ask you to solve a task. You should first draft your thinking process (inner monologue) until you have derived the final answer. Afterwards, write a self-contained summary of your thoughts (i.e. your summary should be succinct but contain all the critical steps you needed to reach the conclusion). You should use Markdown and Latex to format your response. Write both your thoughts and summary in the same language as the task posed by the user.\n\nYour thinking process must follow the template below:\n<think>\nYour thoughts or/and draft, like working through an exercise on scratch paper. Be as casual and as long as you want until you are confident to generate a correct answer.\n</think>\n\nHere, provide a concise summary that reflects your reasoning and presents a clear final answer to the user.\n\n\n\nYou will be given a problem. Please reason step by step, and put your final answer within \\boxed{}.",
"type": "text"
}
],
"role": "system"
},
{
"content": [
{
"text": "Find $3x^2 y^2$ if $x$ and $y$ are integers such that $y^2 + 3x^2 y^2 = 30x^2 + 517$ .",
"type": "text"
}
],
"role": "user"
}
] |
$588$
|
di-zhang-fdu/AIME_1983_2024
|
[
{
"content": [
{
"path": "",
"text": "A user will ask you to solve a task. You should first draft your thinking process (inner monologue) until you have derived the final answer. Afterwards, write a self-contained summary of your thoughts (i.e. your summary should be succinct but contain all the critical steps you needed to reach the conclusion). You should use Markdown and Latex to format your response. Write both your thoughts and summary in the same language as the task posed by the user.\n\nYour thinking process must follow the template below:\n<think>\nYour thoughts or/and draft, like working through an exercise on scratch paper. Be as casual and as long as you want until you are confident to generate a correct answer.\n</think>\n\nHere, provide a concise summary that reflects your reasoning and presents a clear final answer to the user.\n\n\n\nYou will be given a problem. Please reason step by step, and put your final answer within \\boxed{}.",
"type": "text",
"url": null
}
],
"role": "system"
},
{
"content": [
{
"path": "",
"text": "Find $3x^2 y^2$ if $x$ and $y$ are integers such that $y^2 + 3x^2 y^2 = 30x^2 + 517$ .",
"type": "text",
"url": null
}
],
"role": "user"
}
] |
[
{
"content": [
{
"text": "A user will ask you to solve a task. You should first draft your thinking process (inner monologue) until you have derived the final answer. Afterwards, write a self-contained summary of your thoughts (i.e. your summary should be succinct but contain all the critical steps you needed to reach the conclusion). You should use Markdown and Latex to format your response. Write both your thoughts and summary in the same language as the task posed by the user.\n\nYour thinking process must follow the template below:\n<think>\nYour thoughts or/and draft, like working through an exercise on scratch paper. Be as casual and as long as you want until you are confident to generate a correct answer.\n</think>\n\nHere, provide a concise summary that reflects your reasoning and presents a clear final answer to the user.\n\n\n\nYou will be given a problem. Please reason step by step, and put your final answer within \\boxed{}.",
"type": "text"
}
],
"role": "system"
},
{
"content": [
{
"text": "A frog is positioned at the origin of the coordinate plane. From the point $(x, y)$ , the frog can jump to any of the points $(x + 1, y)$ , $(x + 2, y)$ , $(x, y + 1)$ , or $(x, y + 2)$ . Find the number of distinct sequences of jumps in which the frog begins at $(0, 0)$ and ends at $(4, 4)$ .",
"type": "text"
}
],
"role": "user"
}
] |
$556$
|
di-zhang-fdu/AIME_1983_2024
|
[
{
"content": [
{
"path": "",
"text": "A user will ask you to solve a task. You should first draft your thinking process (inner monologue) until you have derived the final answer. Afterwards, write a self-contained summary of your thoughts (i.e. your summary should be succinct but contain all the critical steps you needed to reach the conclusion). You should use Markdown and Latex to format your response. Write both your thoughts and summary in the same language as the task posed by the user.\n\nYour thinking process must follow the template below:\n<think>\nYour thoughts or/and draft, like working through an exercise on scratch paper. Be as casual and as long as you want until you are confident to generate a correct answer.\n</think>\n\nHere, provide a concise summary that reflects your reasoning and presents a clear final answer to the user.\n\n\n\nYou will be given a problem. Please reason step by step, and put your final answer within \\boxed{}.",
"type": "text",
"url": null
}
],
"role": "system"
},
{
"content": [
{
"path": "",
"text": "A frog is positioned at the origin of the coordinate plane. From the point $(x, y)$ , the frog can jump to any of the points $(x + 1, y)$ , $(x + 2, y)$ , $(x, y + 1)$ , or $(x, y + 2)$ . Find the number of distinct sequences of jumps in which the frog begins at $(0, 0)$ and ends at $(4, 4)$ .",
"type": "text",
"url": null
}
],
"role": "user"
}
] |
[
{
"content": [
{
"text": "A user will ask you to solve a task. You should first draft your thinking process (inner monologue) until you have derived the final answer. Afterwards, write a self-contained summary of your thoughts (i.e. your summary should be succinct but contain all the critical steps you needed to reach the conclusion). You should use Markdown and Latex to format your response. Write both your thoughts and summary in the same language as the task posed by the user.\n\nYour thinking process must follow the template below:\n<think>\nYour thoughts or/and draft, like working through an exercise on scratch paper. Be as casual and as long as you want until you are confident to generate a correct answer.\n</think>\n\nHere, provide a concise summary that reflects your reasoning and presents a clear final answer to the user.\n\n",
"type": "text"
}
],
"role": "system"
},
{
"content": [
{
"text": "You will be given a problem. Please reason step by step, and put your final answer within \\boxed{}:\nFor how many ordered pairs $(x,y)$ of integers is it true that $0 < x < y < 10^{6}$ and that the arithmetic mean of $x$ and $y$ is exactly $2$ more than the geometric mean of $x$ and $y$ ?",
"type": "text"
}
],
"role": "user"
}
] |
$997$
|
di-zhang-fdu/AIME_1983_2024
|
[
{
"content": [
{
"path": "",
"text": "A user will ask you to solve a task. You should first draft your thinking process (inner monologue) until you have derived the final answer. Afterwards, write a self-contained summary of your thoughts (i.e. your summary should be succinct but contain all the critical steps you needed to reach the conclusion). You should use Markdown and Latex to format your response. Write both your thoughts and summary in the same language as the task posed by the user.\n\nYour thinking process must follow the template below:\n<think>\nYour thoughts or/and draft, like working through an exercise on scratch paper. Be as casual and as long as you want until you are confident to generate a correct answer.\n</think>\n\nHere, provide a concise summary that reflects your reasoning and presents a clear final answer to the user.\n\n",
"type": "text",
"url": null
}
],
"role": "system"
},
{
"content": [
{
"path": "",
"text": "You will be given a problem. Please reason step by step, and put your final answer within \\boxed{}:\nFor how many ordered pairs $(x,y)$ of integers is it true that $0 < x < y < 10^{6}$ and that the arithmetic mean of $x$ and $y$ is exactly $2$ more than the geometric mean of $x$ and $y$ ?",
"type": "text",
"url": null
}
],
"role": "user"
}
] |
[
{
"content": [
{
"text": "A user will ask you to solve a task. You should first draft your thinking process (inner monologue) until you have derived the final answer. Afterwards, write a self-contained summary of your thoughts (i.e. your summary should be succinct but contain all the critical steps you needed to reach the conclusion). You should use Markdown and Latex to format your response. Write both your thoughts and summary in the same language as the task posed by the user.\n\nYour thinking process must follow the template below:\n<think>\nYour thoughts or/and draft, like working through an exercise on scratch paper. Be as casual and as long as you want until you are confident to generate a correct answer.\n</think>\n\nHere, provide a concise summary that reflects your reasoning and presents a clear final answer to the user.\n\n",
"type": "text"
}
],
"role": "system"
},
{
"content": [
{
"text": "You will be given a problem. Please reason step by step, and put your final answer within \\boxed{}:\nIn the diagram below, angle $ABC$ is a right angle. Point $D$ is on $\\overline{BC}$ , and $\\overline{AD}$ bisects angle $CAB$ . Points $E$ and $F$ are on $\\overline{AB}$ and $\\overline{AC}$ , respectively, so that $AE=3$ and $AF=10$ . Given that $EB=9$ and $FC=27$ , find the integer closest to the area of quadrilateral $DCFG$ . [asy] size(250); pair A=(0,12), E=(0,8), B=origin, C=(24*sqrt(2),0), D=(6*sqrt(2),0), F=A+10*dir(A--C), G=intersectionpoint(E--F, A--D); draw(A--B--C--A--D^^E--F); pair point=G+1*dir(250); label(\"$A$\", A, dir(point--A)); label(\"$B$\", B, dir(point--B)); label(\"$C$\", C, dir(point--C)); label(\"$D$\", D, dir(point--D)); label(\"$E$\", E, dir(point--E)); label(\"$F$\", F, dir(point--F)); label(\"$G$\", G, dir(point--G)); markscalefactor=0.1; draw(rightanglemark(A,B,C)); label(\"10\", A--F, dir(90)*dir(A--F)); label(\"27\", F--C, dir(90)*dir(F--C)); label(\"3\", (0,10), W); label(\"9\", (0,4), W); [/asy]",
"type": "text"
}
],
"role": "user"
}
] |
$148$
|
di-zhang-fdu/AIME_1983_2024
|
[
{
"content": [
{
"path": "",
"text": "A user will ask you to solve a task. You should first draft your thinking process (inner monologue) until you have derived the final answer. Afterwards, write a self-contained summary of your thoughts (i.e. your summary should be succinct but contain all the critical steps you needed to reach the conclusion). You should use Markdown and Latex to format your response. Write both your thoughts and summary in the same language as the task posed by the user.\n\nYour thinking process must follow the template below:\n<think>\nYour thoughts or/and draft, like working through an exercise on scratch paper. Be as casual and as long as you want until you are confident to generate a correct answer.\n</think>\n\nHere, provide a concise summary that reflects your reasoning and presents a clear final answer to the user.\n\n",
"type": "text",
"url": null
}
],
"role": "system"
},
{
"content": [
{
"path": "",
"text": "You will be given a problem. Please reason step by step, and put your final answer within \\boxed{}:\nIn the diagram below, angle $ABC$ is a right angle. Point $D$ is on $\\overline{BC}$ , and $\\overline{AD}$ bisects angle $CAB$ . Points $E$ and $F$ are on $\\overline{AB}$ and $\\overline{AC}$ , respectively, so that $AE=3$ and $AF=10$ . Given that $EB=9$ and $FC=27$ , find the integer closest to the area of quadrilateral $DCFG$ . [asy] size(250); pair A=(0,12), E=(0,8), B=origin, C=(24*sqrt(2),0), D=(6*sqrt(2),0), F=A+10*dir(A--C), G=intersectionpoint(E--F, A--D); draw(A--B--C--A--D^^E--F); pair point=G+1*dir(250); label(\"$A$\", A, dir(point--A)); label(\"$B$\", B, dir(point--B)); label(\"$C$\", C, dir(point--C)); label(\"$D$\", D, dir(point--D)); label(\"$E$\", E, dir(point--E)); label(\"$F$\", F, dir(point--F)); label(\"$G$\", G, dir(point--G)); markscalefactor=0.1; draw(rightanglemark(A,B,C)); label(\"10\", A--F, dir(90)*dir(A--F)); label(\"27\", F--C, dir(90)*dir(F--C)); label(\"3\", (0,10), W); label(\"9\", (0,4), W); [/asy]",
"type": "text",
"url": null
}
],
"role": "user"
}
] |
[
{
"content": [
{
"text": "A user will ask you to solve a task. You should first draft your thinking process (inner monologue) until you have derived the final answer. Afterwards, write a self-contained summary of your thoughts (i.e. your summary should be succinct but contain all the critical steps you needed to reach the conclusion). You should use Markdown and Latex to format your response. Write both your thoughts and summary in the same language as the task posed by the user.\n\nYour thinking process must follow the template below:\n<think>\nYour thoughts or/and draft, like working through an exercise on scratch paper. Be as casual and as long as you want until you are confident to generate a correct answer.\n</think>\n\nHere, provide a concise summary that reflects your reasoning and presents a clear final answer to the user.\n\n",
"type": "text"
}
],
"role": "system"
},
{
"content": [
{
"text": "You will be given a problem. Please reason step by step, and put your final answer within \\boxed{}:\nOctagon $ABCDEFGH$ with side lengths $AB = CD = EF = GH = 10$ and $BC = DE = FG = HA = 11$ is formed by removing 6-8-10 triangles from the corners of a $23$ $\\times$ $27$ rectangle with side $\\overline{AH}$ on a short side of the rectangle, as shown. Let $J$ be the midpoint of $\\overline{AH}$ , and partition the octagon into 7 triangles by drawing segments $\\overline{JB}$ , $\\overline{JC}$ , $\\overline{JD}$ , $\\overline{JE}$ , $\\overline{JF}$ , and $\\overline{JG}$ . Find the area of the convex polygon whose vertices are the centroids of these 7 triangles. [asy] unitsize(6); pair P = (0, 0), Q = (0, 23), R = (27, 23), SS = (27, 0); pair A = (0, 6), B = (8, 0), C = (19, 0), D = (27, 6), EE = (27, 17), F = (19, 23), G = (8, 23), J = (0, 23/2), H = (0, 17); draw(P--Q--R--SS--cycle); draw(J--B); draw(J--C); draw(J--D); draw(J--EE); draw(J--F); draw(J--G); draw(A--B); draw(H--G); real dark = 0.6; filldraw(A--B--P--cycle, gray(dark)); filldraw(H--G--Q--cycle, gray(dark)); filldraw(F--EE--R--cycle, gray(dark)); filldraw(D--C--SS--cycle, gray(dark)); dot(A); dot(B); dot(C); dot(D); dot(EE); dot(F); dot(G); dot(H); dot(J); dot(H); defaultpen(fontsize(10pt)); real r = 1.3; label(\"$A$\", A, W*r); label(\"$B$\", B, S*r); label(\"$C$\", C, S*r); label(\"$D$\", D, E*r); label(\"$E$\", EE, E*r); label(\"$F$\", F, N*r); label(\"$G$\", G, N*r); label(\"$H$\", H, W*r); label(\"$J$\", J, W*r); [/asy]",
"type": "text"
}
],
"role": "user"
}
] |
$184$
|
di-zhang-fdu/AIME_1983_2024
|
[
{
"content": [
{
"path": "",
"text": "A user will ask you to solve a task. You should first draft your thinking process (inner monologue) until you have derived the final answer. Afterwards, write a self-contained summary of your thoughts (i.e. your summary should be succinct but contain all the critical steps you needed to reach the conclusion). You should use Markdown and Latex to format your response. Write both your thoughts and summary in the same language as the task posed by the user.\n\nYour thinking process must follow the template below:\n<think>\nYour thoughts or/and draft, like working through an exercise on scratch paper. Be as casual and as long as you want until you are confident to generate a correct answer.\n</think>\n\nHere, provide a concise summary that reflects your reasoning and presents a clear final answer to the user.\n\n",
"type": "text",
"url": null
}
],
"role": "system"
},
{
"content": [
{
"path": "",
"text": "You will be given a problem. Please reason step by step, and put your final answer within \\boxed{}:\nOctagon $ABCDEFGH$ with side lengths $AB = CD = EF = GH = 10$ and $BC = DE = FG = HA = 11$ is formed by removing 6-8-10 triangles from the corners of a $23$ $\\times$ $27$ rectangle with side $\\overline{AH}$ on a short side of the rectangle, as shown. Let $J$ be the midpoint of $\\overline{AH}$ , and partition the octagon into 7 triangles by drawing segments $\\overline{JB}$ , $\\overline{JC}$ , $\\overline{JD}$ , $\\overline{JE}$ , $\\overline{JF}$ , and $\\overline{JG}$ . Find the area of the convex polygon whose vertices are the centroids of these 7 triangles. [asy] unitsize(6); pair P = (0, 0), Q = (0, 23), R = (27, 23), SS = (27, 0); pair A = (0, 6), B = (8, 0), C = (19, 0), D = (27, 6), EE = (27, 17), F = (19, 23), G = (8, 23), J = (0, 23/2), H = (0, 17); draw(P--Q--R--SS--cycle); draw(J--B); draw(J--C); draw(J--D); draw(J--EE); draw(J--F); draw(J--G); draw(A--B); draw(H--G); real dark = 0.6; filldraw(A--B--P--cycle, gray(dark)); filldraw(H--G--Q--cycle, gray(dark)); filldraw(F--EE--R--cycle, gray(dark)); filldraw(D--C--SS--cycle, gray(dark)); dot(A); dot(B); dot(C); dot(D); dot(EE); dot(F); dot(G); dot(H); dot(J); dot(H); defaultpen(fontsize(10pt)); real r = 1.3; label(\"$A$\", A, W*r); label(\"$B$\", B, S*r); label(\"$C$\", C, S*r); label(\"$D$\", D, E*r); label(\"$E$\", EE, E*r); label(\"$F$\", F, N*r); label(\"$G$\", G, N*r); label(\"$H$\", H, W*r); label(\"$J$\", J, W*r); [/asy]",
"type": "text",
"url": null
}
],
"role": "user"
}
] |
[
{
"content": [
{
"text": "A user will ask you to solve a task. You should first draft your thinking process (inner monologue) until you have derived the final answer. Afterwards, write a self-contained summary of your thoughts (i.e. your summary should be succinct but contain all the critical steps you needed to reach the conclusion). You should use Markdown and Latex to format your response. Write both your thoughts and summary in the same language as the task posed by the user.\n\nYour thinking process must follow the template below:\n<think>\nYour thoughts or/and draft, like working through an exercise on scratch paper. Be as casual and as long as you want until you are confident to generate a correct answer.\n</think>\n\nHere, provide a concise summary that reflects your reasoning and presents a clear final answer to the user.\n\n\n\nYou will be given a problem. Please reason step by step, and put your final answer within \\boxed{}.",
"type": "text"
}
],
"role": "system"
},
{
"content": [
{
"text": "Three numbers, $a_1, a_2, a_3$ , are drawn randomly and without replacement from the set $\\{1, 2, 3,\\ldots, 1000\\}$ . Three other numbers, $b_1, b_2, b_3$ , are then drawn randomly and without replacement from the remaining set of $997$ numbers. Let $p$ be the probability that, after suitable rotation, a brick of dimensions $a_1 \\times a_2 \\times a_3$ can be enclosed in a box of dimension $b_1 \\times b_2 \\times b_3$ , with the sides of the brick parallel to the sides of the box. If $p$ is written as a fraction in lowest terms, what is the sum of the numerator and denominator?",
"type": "text"
}
],
"role": "user"
}
] |
$5$
|
di-zhang-fdu/AIME_1983_2024
|
[
{
"content": [
{
"path": "",
"text": "A user will ask you to solve a task. You should first draft your thinking process (inner monologue) until you have derived the final answer. Afterwards, write a self-contained summary of your thoughts (i.e. your summary should be succinct but contain all the critical steps you needed to reach the conclusion). You should use Markdown and Latex to format your response. Write both your thoughts and summary in the same language as the task posed by the user.\n\nYour thinking process must follow the template below:\n<think>\nYour thoughts or/and draft, like working through an exercise on scratch paper. Be as casual and as long as you want until you are confident to generate a correct answer.\n</think>\n\nHere, provide a concise summary that reflects your reasoning and presents a clear final answer to the user.\n\n\n\nYou will be given a problem. Please reason step by step, and put your final answer within \\boxed{}.",
"type": "text",
"url": null
}
],
"role": "system"
},
{
"content": [
{
"path": "",
"text": "Three numbers, $a_1, a_2, a_3$ , are drawn randomly and without replacement from the set $\\{1, 2, 3,\\ldots, 1000\\}$ . Three other numbers, $b_1, b_2, b_3$ , are then drawn randomly and without replacement from the remaining set of $997$ numbers. Let $p$ be the probability that, after suitable rotation, a brick of dimensions $a_1 \\times a_2 \\times a_3$ can be enclosed in a box of dimension $b_1 \\times b_2 \\times b_3$ , with the sides of the brick parallel to the sides of the box. If $p$ is written as a fraction in lowest terms, what is the sum of the numerator and denominator?",
"type": "text",
"url": null
}
],
"role": "user"
}
] |
[
{
"content": [
{
"text": "A user will ask you to solve a task. You should first draft your thinking process (inner monologue) until you have derived the final answer. Afterwards, write a self-contained summary of your thoughts (i.e. your summary should be succinct but contain all the critical steps you needed to reach the conclusion). You should use Markdown and Latex to format your response. Write both your thoughts and summary in the same language as the task posed by the user.\n\nYour thinking process must follow the template below:\n<think>\nYour thoughts or/and draft, like working through an exercise on scratch paper. Be as casual and as long as you want until you are confident to generate a correct answer.\n</think>\n\nHere, provide a concise summary that reflects your reasoning and presents a clear final answer to the user.\n\n\n\nYou will be given a problem. Please reason step by step, and put your final answer within \\boxed{}.",
"type": "text"
}
],
"role": "system"
},
{
"content": [
{
"text": "A transformation of the first quadrant of the coordinate plane maps each point $(x,y)$ to the point $(\\sqrt{x},\\sqrt{y}).$ The vertices of quadrilateral $ABCD$ are $A=(900,300), B=(1800,600), C=(600,1800),$ and $D=(300,900).$ Let $k_{}$ be the area of the region enclosed by the image of quadrilateral $ABCD.$ Find the greatest integer that does not exceed $k_{}.$",
"type": "text"
}
],
"role": "user"
}
] |
$314$
|
di-zhang-fdu/AIME_1983_2024
|
[
{
"content": [
{
"path": "",
"text": "A user will ask you to solve a task. You should first draft your thinking process (inner monologue) until you have derived the final answer. Afterwards, write a self-contained summary of your thoughts (i.e. your summary should be succinct but contain all the critical steps you needed to reach the conclusion). You should use Markdown and Latex to format your response. Write both your thoughts and summary in the same language as the task posed by the user.\n\nYour thinking process must follow the template below:\n<think>\nYour thoughts or/and draft, like working through an exercise on scratch paper. Be as casual and as long as you want until you are confident to generate a correct answer.\n</think>\n\nHere, provide a concise summary that reflects your reasoning and presents a clear final answer to the user.\n\n\n\nYou will be given a problem. Please reason step by step, and put your final answer within \\boxed{}.",
"type": "text",
"url": null
}
],
"role": "system"
},
{
"content": [
{
"path": "",
"text": "A transformation of the first quadrant of the coordinate plane maps each point $(x,y)$ to the point $(\\sqrt{x},\\sqrt{y}).$ The vertices of quadrilateral $ABCD$ are $A=(900,300), B=(1800,600), C=(600,1800),$ and $D=(300,900).$ Let $k_{}$ be the area of the region enclosed by the image of quadrilateral $ABCD.$ Find the greatest integer that does not exceed $k_{}.$",
"type": "text",
"url": null
}
],
"role": "user"
}
] |
[
{
"content": [
{
"text": "A user will ask you to solve a task. You should first draft your thinking process (inner monologue) until you have derived the final answer. Afterwards, write a self-contained summary of your thoughts (i.e. your summary should be succinct but contain all the critical steps you needed to reach the conclusion). You should use Markdown and Latex to format your response. Write both your thoughts and summary in the same language as the task posed by the user.\n\nYour thinking process must follow the template below:\n<think>\nYour thoughts or/and draft, like working through an exercise on scratch paper. Be as casual and as long as you want until you are confident to generate a correct answer.\n</think>\n\nHere, provide a concise summary that reflects your reasoning and presents a clear final answer to the user.\n\n\n\nYou will be given a problem. Please reason step by step, and put your final answer within \\boxed{}.",
"type": "text"
}
],
"role": "system"
},
{
"content": [
{
"text": "Each unit square of a 3-by-3 unit-square grid is to be colored either blue or red. For each square, either color is equally likely to be used. The probability of obtaining a grid that does not have a 2-by-2 red square is $\\frac {m}{n}$ , where $m$ and $n$ are relatively prime positive integers. Find $m + n$ .",
"type": "text"
}
],
"role": "user"
}
] |
$929$
|
di-zhang-fdu/AIME_1983_2024
|
[
{
"content": [
{
"path": "",
"text": "A user will ask you to solve a task. You should first draft your thinking process (inner monologue) until you have derived the final answer. Afterwards, write a self-contained summary of your thoughts (i.e. your summary should be succinct but contain all the critical steps you needed to reach the conclusion). You should use Markdown and Latex to format your response. Write both your thoughts and summary in the same language as the task posed by the user.\n\nYour thinking process must follow the template below:\n<think>\nYour thoughts or/and draft, like working through an exercise on scratch paper. Be as casual and as long as you want until you are confident to generate a correct answer.\n</think>\n\nHere, provide a concise summary that reflects your reasoning and presents a clear final answer to the user.\n\n\n\nYou will be given a problem. Please reason step by step, and put your final answer within \\boxed{}.",
"type": "text",
"url": null
}
],
"role": "system"
},
{
"content": [
{
"path": "",
"text": "Each unit square of a 3-by-3 unit-square grid is to be colored either blue or red. For each square, either color is equally likely to be used. The probability of obtaining a grid that does not have a 2-by-2 red square is $\\frac {m}{n}$ , where $m$ and $n$ are relatively prime positive integers. Find $m + n$ .",
"type": "text",
"url": null
}
],
"role": "user"
}
] |
[
{
"content": [
{
"text": "A user will ask you to solve a task. You should first draft your thinking process (inner monologue) until you have derived the final answer. Afterwards, write a self-contained summary of your thoughts (i.e. your summary should be succinct but contain all the critical steps you needed to reach the conclusion). You should use Markdown and Latex to format your response. Write both your thoughts and summary in the same language as the task posed by the user.\n\nYour thinking process must follow the template below:\n<think>\nYour thoughts or/and draft, like working through an exercise on scratch paper. Be as casual and as long as you want until you are confident to generate a correct answer.\n</think>\n\nHere, provide a concise summary that reflects your reasoning and presents a clear final answer to the user.\n\n\n\nYou will be given a problem. Please reason step by step, and put your final answer within \\boxed{}.",
"type": "text"
}
],
"role": "system"
},
{
"content": [
{
"text": "The expressions $A$ = $1 \\times 2 + 3 \\times 4 + 5 \\times 6 + \\cdots + 37 \\times 38 + 39$ and $B$ = $1 + 2 \\times 3 + 4 \\times 5 + \\cdots + 36 \\times 37 + 38 \\times 39$ are obtained by writing multiplication and addition operators in an alternating pattern between successive integers. Find the positive difference between integers $A$ and $B$ .",
"type": "text"
}
],
"role": "user"
}
] |
$722$
|
di-zhang-fdu/AIME_1983_2024
|
[
{
"content": [
{
"path": "",
"text": "A user will ask you to solve a task. You should first draft your thinking process (inner monologue) until you have derived the final answer. Afterwards, write a self-contained summary of your thoughts (i.e. your summary should be succinct but contain all the critical steps you needed to reach the conclusion). You should use Markdown and Latex to format your response. Write both your thoughts and summary in the same language as the task posed by the user.\n\nYour thinking process must follow the template below:\n<think>\nYour thoughts or/and draft, like working through an exercise on scratch paper. Be as casual and as long as you want until you are confident to generate a correct answer.\n</think>\n\nHere, provide a concise summary that reflects your reasoning and presents a clear final answer to the user.\n\n\n\nYou will be given a problem. Please reason step by step, and put your final answer within \\boxed{}.",
"type": "text",
"url": null
}
],
"role": "system"
},
{
"content": [
{
"path": "",
"text": "The expressions $A$ = $1 \\times 2 + 3 \\times 4 + 5 \\times 6 + \\cdots + 37 \\times 38 + 39$ and $B$ = $1 + 2 \\times 3 + 4 \\times 5 + \\cdots + 36 \\times 37 + 38 \\times 39$ are obtained by writing multiplication and addition operators in an alternating pattern between successive integers. Find the positive difference between integers $A$ and $B$ .",
"type": "text",
"url": null
}
],
"role": "user"
}
] |
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