On-Policy Self-Distillation for Reasoning Compression
Paper • 2603.05433 • Published • 9
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problem stringlengths 259 3.43k | answer stringlengths 1 23 | metadata stringlengths 131 3.48k | concise_instruction stringclasses 1
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Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.
In an acute triangle $ABC$, the lines tangent to the circumcircle of $ABC$ at $A$ and $B$ intersect at point $D$. Let $E$ and $F$ be points on... | 267 | {"dataset_name": "dapo_math", "question": "In an acute triangle $ABC$, the lines tangent to the circumcircle of $ABC$ at $A$ and $B$ intersect at point $D$. Let $E$ and $F$ be points on $CA$ and $CB$ such that $DECF$ forms a parallelogram. Given that $AB = 20$, $CA=25$, and $\\tan C = \\frac{4\\sqrt{21}}{17}$, the valu... | Solve the following math problem concisely and correctly. Be direct - avoid unnecessary elaboration, redundant steps, or restating the problem. Focus only on the key reasoning steps needed to reach the answer.
The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the an... |
Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.
设一个袋子里有红、黄、蓝色小球各一个. 现每次从袋子里取出一个球（取出某色球的概率均相同), 确定颜色后放回, 直到连续两次均取出红球时为止, 记此时取出球的次数为 $\xi$. 则 $\xi$ 的数学期望为 $\qquad$.
Remember to put your answ... | 12 | {"dataset_name": "dapo_math", "question": "\u8bbe\u4e00\u4e2a\u888b\u5b50\u91cc\u6709\u7ea2\u3001\u9ec4\u3001\u84dd\u8272\u5c0f\u7403\u5404\u4e00\u4e2a. \u73b0\u6bcf\u6b21\u4ece\u888b\u5b50\u91cc\u53d6\u51fa\u4e00\u4e2a\u7403\uff08\u53d6\u51fa\u67d0\u8272\u7403\u7684\u6982\u7387\u5747\u76f8\u540c), \u786e\u5b9a\u989c\u... | Solve the following math problem concisely and correctly. Be direct - avoid unnecessary elaboration, redundant steps, or restating the problem. Focus only on the key reasoning steps needed to reach the answer.
The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the an... |
Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.
Find the last three digits of the number $2003^{2002^{2001}}$.
Remember to put your answer on its own line after "Answer:". | 241 | {"dataset_name": "dapo_math", "question": "Find the last three digits of the number $2003^{2002^{2001}}$.\n\nRemember to put your answer on its own line after \"Answer:\"."} | Solve the following math problem concisely and correctly. Be direct - avoid unnecessary elaboration, redundant steps, or restating the problem. Focus only on the key reasoning steps needed to reach the answer.
The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the an... |
Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.
Let $x$ be a positive real number. Define
\[
A = \sum_{k=0}^{\infty} \frac{x^{3k}}{(3k)!}, \quad
B = \sum_{k=0}^{\infty} \frac{x^{3k+1}}{(... | 183 | {"dataset_name": "dapo_math", "question": "Let $x$ be a positive real number. Define\n\\[\n A = \\sum_{k=0}^{\\infty} \\frac{x^{3k}}{(3k)!}, \\quad\n B = \\sum_{k=0}^{\\infty} \\frac{x^{3k+1}}{(3k+1)!}, \\quad \\text{and} \\quad\n C = \\sum_{k=0}^{\\infty} \\frac{x^{3k+2}}{(3k+2)!}.\n\\] \nGiven that $A^3+B^3+C^3 + ... | Solve the following math problem concisely and correctly. Be direct - avoid unnecessary elaboration, redundant steps, or restating the problem. Focus only on the key reasoning steps needed to reach the answer.
The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the an... |
Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.
Find the minimum possible least common multiple of twenty natural numbers whose sum is $801$.
Remember to put your answer on its own line aft... | 42 | {"dataset_name": "dapo_math", "question": "Find the minimum possible least common multiple of twenty natural numbers whose sum is $801$.\n\nRemember to put your answer on its own line after \"Answer:\"."} | Solve the following math problem concisely and correctly. Be direct - avoid unnecessary elaboration, redundant steps, or restating the problem. Focus only on the key reasoning steps needed to reach the answer.
The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the an... |
Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.
在正方体中随机取 3 条棱, 它们两两异面的概率为 $\qquad$.
原始的答案是\frac{m}{n}的形式，其中m、n是互质的。请给出最终m + n的值
Remember to put your answer on its own line after "Answer:". | 57 | {"dataset_name": "dapo_math", "question": "\u5728\u6b63\u65b9\u4f53\u4e2d\u968f\u673a\u53d6 3 \u6761\u68f1, \u5b83\u4eec\u4e24\u4e24\u5f02\u9762\u7684\u6982\u7387\u4e3a $\\qquad$.\n\u539f\u59cb\u7684\u7b54\u6848\u662f\\frac{m}{n}\u7684\u5f62\u5f0f\uff0c\u5176\u4e2dm\u3001n\u662f\u4e92\u8d28\u7684\u3002\u8bf7\u7ed9\u51f... | Solve the following math problem concisely and correctly. Be direct - avoid unnecessary elaboration, redundant steps, or restating the problem. Focus only on the key reasoning steps needed to reach the answer.
The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the an... |
Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.
A positive integer $k$ is said to be \textit{good} if there exists a partition of $\{1, 2, 3, \ldots, 20\}$ into disjoint proper subsets such ... | 6 | {"dataset_name": "dapo_math", "question": "A positive integer $k$ is said to be \\textit{good} if there exists a partition of $\\{1, 2, 3, \\ldots, 20\\}$ into disjoint proper subsets such that the sum of the numbers in each subset of the partition is $k$. How many \\textit{good} numbers are there?\n\nRemember to put y... | Solve the following math problem concisely and correctly. Be direct - avoid unnecessary elaboration, redundant steps, or restating the problem. Focus only on the key reasoning steps needed to reach the answer.
The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the an... |
Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.
For a certain positive integer $n,$ there exist real numbers $x_1,$ $x_2,$ $\dots,$ $x_n$ such that
\begin{align*}
x_1 + x_2 + x_3 + \dots + x... | 125 | {"dataset_name": "dapo_math", "question": "For a certain positive integer $n,$ there exist real numbers $x_1,$ $x_2,$ $\\dots,$ $x_n$ such that\n\\begin{align*}\nx_1 + x_2 + x_3 + \\dots + x_n &= 1000, \\\\\nx_1^4 + x_2^4 + x_3^4 + \\dots + x_n^4 &= 512000.\n\\end{align*}Find the smallest positive integer $n$ for which... | Solve the following math problem concisely and correctly. Be direct - avoid unnecessary elaboration, redundant steps, or restating the problem. Focus only on the key reasoning steps needed to reach the answer.
The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the an... |
Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.
初始时黑板上有六个向量(1,0,0),\ (-1,0,0),\ (0,1,0),\ (0,-1,0),\ (0,0,1),\ (0,0,-1).一次操作可以将黑板上的两个向量 v,w 换为 \df{1}{\sqrt{2}}(v+w), \df{1}{\sqrt{2}}(v-w). 求... | 5 | {"dataset_name": "dapo_math", "question": "\u521d\u59cb\u65f6\u9ed1\u677f\u4e0a\u6709\u516d\u4e2a\u5411\u91cf(1,0,0),\\ (-1,0,0),\\ (0,1,0),\\ (0,-1,0),\\ (0,0,1),\\ (0,0,-1).\u4e00\u6b21\u64cd\u4f5c\u53ef\u4ee5\u5c06\u9ed1\u677f\u4e0a\u7684\u4e24\u4e2a\u5411\u91cf v,w \u6362\u4e3a \\df{1}{\\sqrt{2}}(v+w), \\df{1}{\\sq... | Solve the following math problem concisely and correctly. Be direct - avoid unnecessary elaboration, redundant steps, or restating the problem. Focus only on the key reasoning steps needed to reach the answer.
The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the an... |
Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.
In a 14-team baseball league, each team played every other team 10 times. At the end of the season, the number of games won by each team diffe... | 52 | {"dataset_name": "dapo_math", "question": "In a 14-team baseball league, each team played every other team 10 times. At the end of the season, the number of games won by each team differed from those won by the team immediately following it by the same amount. Determine the greatest number of games the last-place team ... | Solve the following math problem concisely and correctly. Be direct - avoid unnecessary elaboration, redundant steps, or restating the problem. Focus only on the key reasoning steps needed to reach the answer.
The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the an... |
Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.
求满足下面两个条件的所有实数序列 $\left\{b_{n}\right\} 、\left\{c_{n}\right\}(n \geqslant 1):$(1) 对于任意的正整数 $n$ ，均有 $b_{n} \leqslant c_{n}$ ；(2) 对于任意的正整数 $n$,均有... | 0 | {"dataset_name": "dapo_math", "question": "\u6c42\u6ee1\u8db3\u4e0b\u9762\u4e24\u4e2a\u6761\u4ef6\u7684\u6240\u6709\u5b9e\u6570\u5e8f\u5217 $\\left\\{b_{n}\\right\\} \u3001\\left\\{c_{n}\\right\\}(n \\geqslant 1):$(1) \u5bf9\u4e8e\u4efb\u610f\u7684\u6b63\u6574\u6570 $n$ \uff0c\u5747\u6709 $b_{n} \\leqslant c_{n}$ \uff1... | Solve the following math problem concisely and correctly. Be direct - avoid unnecessary elaboration, redundant steps, or restating the problem. Focus only on the key reasoning steps needed to reach the answer.
The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the an... |
Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.
On squared paper, a square is delimited, which comprises $25$ unit squares. How many rectangles are there in this square that contain one or m... | 225 | {"dataset_name": "dapo_math", "question": "On squared paper, a square is delimited, which comprises $25$ unit squares. How many rectangles are there in this square that contain one or more unit squares?\n\nRemember to put your answer on its own line after \"Answer:\"."} | Solve the following math problem concisely and correctly. Be direct - avoid unnecessary elaboration, redundant steps, or restating the problem. Focus only on the key reasoning steps needed to reach the answer.
The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the an... |
Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.
Alice is planning a trip from the Bay Area to one of $5$ possible destinations, each serviced by only $1$ airport. She wants to book two fligh... | 45 | {"dataset_name": "dapo_math", "question": "Alice is planning a trip from the Bay Area to one of $5$ possible destinations, each serviced by only $1$ airport. She wants to book two flights: one to her destination and one returning. There are $3$ airports within the Bay Area from which she may leave and to which she may ... | Solve the following math problem concisely and correctly. Be direct - avoid unnecessary elaboration, redundant steps, or restating the problem. Focus only on the key reasoning steps needed to reach the answer.
The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the an... |
Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.
随机生成一个长度为 4 的由 0,1,2 构成的数列，则其中任意相邻两数之差的绝对值都小于 2 的概率是________.原始的答案是\frac{m}{n}的形式，其中m、n是互质的。请给出最终m + n的值
Remember to put your answer on its o... | 122 | {"dataset_name": "dapo_math", "question": "\u968f\u673a\u751f\u6210\u4e00\u4e2a\u957f\u5ea6\u4e3a 4 \u7684\u7531 0,1,2 \u6784\u6210\u7684\u6570\u5217\uff0c\u5219\u5176\u4e2d\u4efb\u610f\u76f8\u90bb\u4e24\u6570\u4e4b\u5dee\u7684\u7edd\u5bf9\u503c\u90fd\u5c0f\u4e8e 2 \u7684\u6982\u7387\u662f________.\u539f\u59cb\u7684\u7... | Solve the following math problem concisely and correctly. Be direct - avoid unnecessary elaboration, redundant steps, or restating the problem. Focus only on the key reasoning steps needed to reach the answer.
The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the an... |
Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.
Let $ABCD$ be a square with side length $2$. Let $M$ and $N$ be the midpoints of $\overline{BC}$ and $\overline{CD}$ respectively, and let $X$... | 3225 | {"dataset_name": "dapo_math", "question": "Let $ABCD$ be a square with side length $2$. Let $M$ and $N$ be the midpoints of $\\overline{BC}$ and $\\overline{CD}$ respectively, and let $X$ and $Y$ be the feet of the perpendiculars from $A$ to $\\overline{MD}$ and $\\overline{NB}$, also respectively. The square of the le... | Solve the following math problem concisely and correctly. Be direct - avoid unnecessary elaboration, redundant steps, or restating the problem. Focus only on the key reasoning steps needed to reach the answer.
The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the an... |
Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.
If $A$ is an angle such that $\tan A + \sec A = 2,$ enter all possible values of $\cos A,$ separated by commas.The answer is in the form rac{... | 9 | {"dataset_name": "dapo_math", "question": "If $A$ is an angle such that $\\tan A + \\sec A = 2,$ enter all possible values of $\\cos A,$ separated by commas.The answer is in the form \frac{m}{n}, where gcd(m, n) = 1. Please provide the value of m + n.\n\nRemember to put your answer on its own line after \"Answer:\"."} | Solve the following math problem concisely and correctly. Be direct - avoid unnecessary elaboration, redundant steps, or restating the problem. Focus only on the key reasoning steps needed to reach the answer.
The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the an... |
Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.
Two non-decreasing sequences of nonnegative integers have different first terms. Each sequence has the property that each term beginning with ... | 104 | {"dataset_name": "dapo_math", "question": "Two non-decreasing sequences of nonnegative integers have different first terms. Each sequence has the property that each term beginning with the third is the sum of the previous two terms, and the seventh term of each sequence is $N$. Find the smallest possible value of $N$.\... | Solve the following math problem concisely and correctly. Be direct - avoid unnecessary elaboration, redundant steps, or restating the problem. Focus only on the key reasoning steps needed to reach the answer.
The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the an... |
Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.
设动圆圆心在抛物线 $y=\frac{1}{4} x^{2}$ 上, 半径等于该圆圆心的纵坐标. 求所有这样的圆上点的集合的边界条件。请给出边界条件中最大y值的答案。
Remember to put your answer on its own line after "Answer... | 2 | {"dataset_name": "dapo_math", "question": "\u8bbe\u52a8\u5706\u5706\u5fc3\u5728\u629b\u7269\u7ebf $y=\\frac{1}{4} x^{2}$ \u4e0a, \u534a\u5f84\u7b49\u4e8e\u8be5\u5706\u5706\u5fc3\u7684\u7eb5\u5750\u6807. \u6c42\u6240\u6709\u8fd9\u6837\u7684\u5706\u4e0a\u70b9\u7684\u96c6\u5408\u7684\u8fb9\u754c\u6761\u4ef6\u3002\u8bf7\u7... | Solve the following math problem concisely and correctly. Be direct - avoid unnecessary elaboration, redundant steps, or restating the problem. Focus only on the key reasoning steps needed to reach the answer.
The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the an... |
Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.
In the diagram, the centre of the circle is $O.$ The area of the shaded region is $20\%$ of the area of the circle. What is the value of $x?$ ... | 72 | {"dataset_name": "dapo_math", "question": "In the diagram, the centre of the circle is $O.$ The area of the shaded region is $20\\%$ of the area of the circle. What is the value of $x?$ [asy]\nfilldraw(Circle((0,0),1),gray(0.8),linewidth(1));\nfilldraw((cos(pi/5),sin(pi/5))--(0,0)--(cos(-pi/5),sin(-pi/5))..(-1,0)..cycl... | Solve the following math problem concisely and correctly. Be direct - avoid unnecessary elaboration, redundant steps, or restating the problem. Focus only on the key reasoning steps needed to reach the answer.
The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the an... |
Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.
There are real numbers $x$, $y$, and $z$ such that the value of \(x + y + z - \left(\frac{x^2}{5} + \frac{y^2}{6} + \frac{z^2}{7}\right)\) rea... | 20 | {"dataset_name": "dapo_math", "question": "There are real numbers $x$, $y$, and $z$ such that the value of \\(x + y + z - \\left(\\frac{x^2}{5} + \\frac{y^2}{6} + \\frac{z^2}{7}\\right)\\) reaches its maximum of \\(\\frac{m}{n}\\), where \\(m\\) and \\(n\\) are relatively prime positive integers. Find \\(m + n + x + y ... | Solve the following math problem concisely and correctly. Be direct - avoid unnecessary elaboration, redundant steps, or restating the problem. Focus only on the key reasoning steps needed to reach the answer.
The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the an... |
Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.
数列 $\left\{a_{n}\right\}$ 满足: $a_{0}=\sqrt{6}, a_{n+1}=\left[a_{n}\right]+\frac{1}{\left\{a_{n}\right\}}$ (其中 $\left[a_{n}\right]$ 和 $\left\{a... | 3 | {"dataset_name": "dapo_math", "question": "\u6570\u5217 $\\left\\{a_{n}\\right\\}$ \u6ee1\u8db3: $a_{0}=\\sqrt{6}, a_{n+1}=\\left[a_{n}\\right]+\\frac{1}{\\left\\{a_{n}\\right\\}}$ (\u5176\u4e2d $\\left[a_{n}\\right]$ \u548c $\\left\\{a_{n}\\right\\}$ \u5206\u522b\u8868\u793a\u5b9e\u6570 $a_{n}$ \u7684\u6574\u6570\u90e... | Solve the following math problem concisely and correctly. Be direct - avoid unnecessary elaboration, redundant steps, or restating the problem. Focus only on the key reasoning steps needed to reach the answer.
The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the an... |
Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.
In triangle $ABC$, $AB = AC = 100$, and $BC = 56$. Circle $P$ has radius $16$ and is tangent to $\overline{AC}$ and $\overline{BC}$. Circle $Q... | 254 | {"dataset_name": "dapo_math", "question": "In triangle $ABC$, $AB = AC = 100$, and $BC = 56$. Circle $P$ has radius $16$ and is tangent to $\\overline{AC}$ and $\\overline{BC}$. Circle $Q$ is externally tangent to $P$ and is tangent to $\\overline{AB}$ and $\\overline{BC}$. No point of circle $Q$ lies outside of $\\tri... | Solve the following math problem concisely and correctly. Be direct - avoid unnecessary elaboration, redundant steps, or restating the problem. Focus only on the key reasoning steps needed to reach the answer.
The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the an... |
Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.
Find the value of $|xy|$ given that $x$ and $y$ are integers and $6x^2y^2 + 5x^2 - 18y^2 = 17253$.
Remember to put your answer on its own lin... | 54 | {"dataset_name": "dapo_math", "question": "Find the value of $|xy|$ given that $x$ and $y$ are integers and $6x^2y^2 + 5x^2 - 18y^2 = 17253$.\n\nRemember to put your answer on its own line after \"Answer:\"."} | Solve the following math problem concisely and correctly. Be direct - avoid unnecessary elaboration, redundant steps, or restating the problem. Focus only on the key reasoning steps needed to reach the answer.
The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the an... |
Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.
The work team was working at a rate fast enough to process $1250$ items in ten hours. But after working for six hours, the team was given an a... | 30 | {"dataset_name": "dapo_math", "question": "The work team was working at a rate fast enough to process $1250$ items in ten hours. But after working for six hours, the team was given an additional $165$ items to process. By what percent does the team need to increase its rate so that it can still complete its work within... | Solve the following math problem concisely and correctly. Be direct - avoid unnecessary elaboration, redundant steps, or restating the problem. Focus only on the key reasoning steps needed to reach the answer.
The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the an... |
Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.
设实数 $x_{1}, x_{2}, \cdots, x_{21}$ 满足 $0 \leqslant x_{i} \leqslant 1(1,2, \cdots, 21)$, 求 $\sum_{i=1}^{21} \sum_{k=1}^{21}\left|x_{i}-x_{k}\ri... | 220 | {"dataset_name": "dapo_math", "question": "\u8bbe\u5b9e\u6570 $x_{1}, x_{2}, \\cdots, x_{21}$ \u6ee1\u8db3 $0 \\leqslant x_{i} \\leqslant 1(1,2, \\cdots, 21)$, \u6c42 $\\sum_{i=1}^{21} \\sum_{k=1}^{21}\\left|x_{i}-x_{k}\\right|$ \u7684\u6700\u5927\u503c\u3002\n\nRemember to put your answer on its own line after \"Answe... | Solve the following math problem concisely and correctly. Be direct - avoid unnecessary elaboration, redundant steps, or restating the problem. Focus only on the key reasoning steps needed to reach the answer.
The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the an... |
Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.
Let $a$ and $b$ be positive real numbers with $a > b$. Find the smallest possible value of
$$S = 2a + 3 + \frac{32}{(a - b)(2b + 3)^2}.$$
Re... | 8 | {"dataset_name": "dapo_math", "question": "Let $a$ and $b$ be positive real numbers with $a > b$. Find the smallest possible value of \n$$S = 2a + 3 + \\frac{32}{(a - b)(2b + 3)^2}.$$\n\nRemember to put your answer on its own line after \"Answer:\"."} | Solve the following math problem concisely and correctly. Be direct - avoid unnecessary elaboration, redundant steps, or restating the problem. Focus only on the key reasoning steps needed to reach the answer.
The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the an... |
Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.
For each integer $n \geq 3$, let $f(n)$ be the number of $3$-element subsets of the vertices of the regular $n$-gon that are the vertices of a... | 245 | {"dataset_name": "dapo_math", "question": "For each integer $n \\geq 3$, let $f(n)$ be the number of $3$-element subsets of the vertices of the regular $n$-gon that are the vertices of an isosceles triangle (including equilateral triangles). Find the sum of all values of $n$ such that $f(n+1)=f(n)+78$.\n\nRemember to p... | Solve the following math problem concisely and correctly. Be direct - avoid unnecessary elaboration, redundant steps, or restating the problem. Focus only on the key reasoning steps needed to reach the answer.
The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the an... |
Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.
In a magic square, the sum of the three entries in any row, column, or diagonal is the same value. The figure below shows four of the entries ... | 200 | {"dataset_name": "dapo_math", "question": "In a magic square, the sum of the three entries in any row, column, or diagonal is the same value. The figure below shows four of the entries of a magic square. Find $x$.\n[asy]\nsize(2cm);\nfor (int i=0; i<=3; ++i) draw((i,0)--(i,3)^^(0,i)--(3,i));\nlabel(\"$x$\",(0.5,2.5));l... | Solve the following math problem concisely and correctly. Be direct - avoid unnecessary elaboration, redundant steps, or restating the problem. Focus only on the key reasoning steps needed to reach the answer.
The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the an... |
Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.
Let $N$ be the number of positive divisors of $2010^{2010}$ that end in the digit 2. What is the remainder when $N$ is divided by 2010?
Remem... | 503 | {"dataset_name": "dapo_math", "question": "Let $N$ be the number of positive divisors of $2010^{2010}$ that end in the digit 2. What is the remainder when $N$ is divided by 2010?\n\nRemember to put your answer on its own line after \"Answer:\"."} | Solve the following math problem concisely and correctly. Be direct - avoid unnecessary elaboration, redundant steps, or restating the problem. Focus only on the key reasoning steps needed to reach the answer.
The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the an... |
Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.
Find the maximum integral value of $k$ such that $0 \le k \le 2019$ and $|e^{2\pi i \frac{k}{2019}} - 1|$ is maximal.
Remember to put your an... | 1010 | {"dataset_name": "dapo_math", "question": "Find the maximum integral value of $k$ such that $0 \\le k \\le 2019$ and $|e^{2\\pi i \\frac{k}{2019}} - 1|$ is maximal.\n\nRemember to put your answer on its own line after \"Answer:\"."} | Solve the following math problem concisely and correctly. Be direct - avoid unnecessary elaboration, redundant steps, or restating the problem. Focus only on the key reasoning steps needed to reach the answer.
The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the an... |
Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.
Denote by $\mathbb{N}$ the set of all positive integers. Find all functions $f: \mathbb{N} \to \mathbb{N}$ such that for all positive integers... | 4 | {"dataset_name": "dapo_math", "question": "Denote by $\\mathbb{N}$ the set of all positive integers. Find all functions $f: \\mathbb{N} \\to \\mathbb{N}$ such that for all positive integers $m$ and $n$, the integer $f(m)+f(n)-mn$ is nonzero and divides $mf(m)+nf(n).$ Please provide the value of $f(n)$ when $n=2$. Direc... | Solve the following math problem concisely and correctly. Be direct - avoid unnecessary elaboration, redundant steps, or restating the problem. Focus only on the key reasoning steps needed to reach the answer.
The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the an... |
Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.
Matilda drew $12$ quadrilaterals. The first quadrilateral is a rectangle with integer sides, where the width is $7$ times the length. Every ti... | 2023 | {"dataset_name": "dapo_math", "question": "Matilda drew $12$ quadrilaterals. The first quadrilateral is a rectangle with integer sides, where the width is $7$ times the length. Every time she drew a quadrilateral, she joined the midpoints of each pair of consecutive sides with a segment. It is known that the last quadr... | Solve the following math problem concisely and correctly. Be direct - avoid unnecessary elaboration, redundant steps, or restating the problem. Focus only on the key reasoning steps needed to reach the answer.
The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the an... |
Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.
Let $V$ be the set of vertices of a regular $25$ sided polygon with center at point $C.$ How many triangles have vertices in $ V$ and contain ... | 650 | {"dataset_name": "dapo_math", "question": "Let $V$ be the set of vertices of a regular $25$ sided polygon with center at point $C.$ How many triangles have vertices in $ V$ and contain the point $C$ in the interior of the triangle?\n\nRemember to put your answer on its own line after \"Answer:\"."} | Solve the following math problem concisely and correctly. Be direct - avoid unnecessary elaboration, redundant steps, or restating the problem. Focus only on the key reasoning steps needed to reach the answer.
The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the an... |
Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.
A [i]substring [/i] of a number $n$ is a number formed by removing some digits from the beginning and end of $n$ (possibly a different number ... | 576 | {"dataset_name": "dapo_math", "question": "A [i]substring [/i] of a number $n$ is a number formed by removing some digits from the beginning and end of $n$ (possibly a different number of digits is removed from each side). Find the sum of all prime numbers $p$ that have the property that any substring of $p$ is also pr... | Solve the following math problem concisely and correctly. Be direct - avoid unnecessary elaboration, redundant steps, or restating the problem. Focus only on the key reasoning steps needed to reach the answer.
The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the an... |
Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.
If the integers $m,n,k$ satisfy the equation $221m + 247n + 323k = 2001$, find the smallest possible value of $k$ greater than $100$.
Remembe... | 111 | {"dataset_name": "dapo_math", "question": "If the integers $m,n,k$ satisfy the equation $221m + 247n + 323k = 2001$, find the smallest possible value of $k$ greater than $100$.\n\nRemember to put your answer on its own line after \"Answer:\"."} | Solve the following math problem concisely and correctly. Be direct - avoid unnecessary elaboration, redundant steps, or restating the problem. Focus only on the key reasoning steps needed to reach the answer.
The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the an... |
Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.
During the weekends, Eli delivers milk in the complex plane. On Saturday, he begins at $z$ and delivers milk to houses located at $z^3,z^5,z^7... | 2011 | {"dataset_name": "dapo_math", "question": "During the weekends, Eli delivers milk in the complex plane. On Saturday, he begins at $z$ and delivers milk to houses located at $z^3,z^5,z^7,\\ldots,z^{2013}$ in that order; on Sunday, he begins at $1$ and delivers milk to houses located at $z^2,z^4,z^6,\\ldots,z^{2012}$ in ... | Solve the following math problem concisely and correctly. Be direct - avoid unnecessary elaboration, redundant steps, or restating the problem. Focus only on the key reasoning steps needed to reach the answer.
The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the an... |
Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.
Let $\omega$ be a nonreal root of $x^3 = 1,$ and let
\[\mathbf{M} = \begin{pmatrix} -\omega^2 & - \omega \\ 1 & 0 \end{pmatrix}.\]Find the sum... | 4018 | {"dataset_name": "dapo_math", "question": "Let $\\omega$ be a nonreal root of $x^3 = 1,$ and let\n\\[\\mathbf{M} = \\begin{pmatrix} -\\omega^2 & - \\omega \\\\ 1 & 0 \\end{pmatrix}.\\]Find the sum of the entries of $\\mathbf{M} + \\mathbf{M}^2 + \\mathbf{M}^3 + \\dots + \\mathbf{M}^{2009}.$\n\nRemember to put your answ... | Solve the following math problem concisely and correctly. Be direct - avoid unnecessary elaboration, redundant steps, or restating the problem. Focus only on the key reasoning steps needed to reach the answer.
The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the an... |
Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.
Let \[ \begin{array}{ccccccccccc} A &=& 5 \cdot 6 &-& 6 \cdot 7 &+& 7 \cdot 8 &-& \cdots &+& 2003 \cdot 2004, \\ B &=& 1 \cdot 10 &-& 2 \cdot ... | 20 | {"dataset_name": "dapo_math", "question": "Let \\[ \\begin{array}{ccccccccccc} A &=& 5 \\cdot 6 &-& 6 \\cdot 7 &+& 7 \\cdot 8 &-& \\cdots &+& 2003 \\cdot 2004, \\\\ B &=& 1 \\cdot 10 &-& 2 \\cdot 11 &+& 3 \\cdot 12 &-& \\cdots &+& 1999 \\cdot 2008. \\end{array} \\] \nFind the value of $A-B$.\n\nRemember to put your ans... | Solve the following math problem concisely and correctly. Be direct - avoid unnecessary elaboration, redundant steps, or restating the problem. Focus only on the key reasoning steps needed to reach the answer.
The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the an... |
Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.
在平面直角坐标系 $x O y$ 中， $F_{1} 、 F_{2}$ 分别是椭圆 $\frac{x^{2}}{2}+y^{2}=1$ 的左、右焦点. 设不经过焦点 $F_{1}$ 的直线 $l$ 与椭圆交于两个不同的点 $A 、 B$, 焦点 $F_{2}$ 到直线 $l$ 的距离... | 5 | {"dataset_name": "dapo_math", "question": "\u5728\u5e73\u9762\u76f4\u89d2\u5750\u6807\u7cfb $x O y$ \u4e2d\uff0c $F_{1} \u3001 F_{2}$ \u5206\u522b\u662f\u692d\u5706 $\\frac{x^{2}}{2}+y^{2}=1$ \u7684\u5de6\u3001\u53f3\u7126\u70b9. \u8bbe\u4e0d\u7ecf\u8fc7\u7126\u70b9 $F_{1}$ \u7684\u76f4\u7ebf $l$ \u4e0e\u692d\u5706\u4e... | Solve the following math problem concisely and correctly. Be direct - avoid unnecessary elaboration, redundant steps, or restating the problem. Focus only on the key reasoning steps needed to reach the answer.
The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the an... |
Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.
Five distinct 2-digit numbers are in a geometric progression. Find the middle term.
Remember to put your answer on its own line after "Answer... | 36 | {"dataset_name": "dapo_math", "question": "Five distinct 2-digit numbers are in a geometric progression. Find the middle term.\n\nRemember to put your answer on its own line after \"Answer:\"."} | Solve the following math problem concisely and correctly. Be direct - avoid unnecessary elaboration, redundant steps, or restating the problem. Focus only on the key reasoning steps needed to reach the answer.
The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the an... |
Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.
已知正实数 $a, b$ 满足 $a^{b}=(8 a)^{9 b}$, 则 $\log _{a}\left(4 a^{2}\right)$ 的值为 $\qquad$.原始的答案是\frac{m}{n}的形式，其中m、n是互质的。请给出最终m + n的值
Remember to p... | 65 | {"dataset_name": "dapo_math", "question": "\u5df2\u77e5\u6b63\u5b9e\u6570 $a, b$ \u6ee1\u8db3 $a^{b}=(8 a)^{9 b}$, \u5219 $\\log _{a}\\left(4 a^{2}\\right)$ \u7684\u503c\u4e3a $\\qquad$.\u539f\u59cb\u7684\u7b54\u6848\u662f\\frac{m}{n}\u7684\u5f62\u5f0f\uff0c\u5176\u4e2dm\u3001n\u662f\u4e92\u8d28\u7684\u3002\u8bf7\u7ed9... | Solve the following math problem concisely and correctly. Be direct - avoid unnecessary elaboration, redundant steps, or restating the problem. Focus only on the key reasoning steps needed to reach the answer.
The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the an... |
Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.
设平面向量 $\boldsymbol{a} 、 \boldsymbol{b}$ 满足: $|\boldsymbol{a}|=1,|\boldsymbol{b}|=2$, $\boldsymbol{a} \perp \boldsymbol{b}. O 、 A 、 B$ 为平面上的三个点... | 7 | {"dataset_name": "dapo_math", "question": "\u8bbe\u5e73\u9762\u5411\u91cf $\\boldsymbol{a} \u3001 \\boldsymbol{b}$ \u6ee1\u8db3: $|\\boldsymbol{a}|=1,|\\boldsymbol{b}|=2$, $\\boldsymbol{a} \\perp \\boldsymbol{b}. O \u3001 A \u3001 B$ \u4e3a\u5e73\u9762\u4e0a\u7684\u4e09\u4e2a\u70b9\uff0c\u6ee1\u8db3: $\\overrightarrow{... | Solve the following math problem concisely and correctly. Be direct - avoid unnecessary elaboration, redundant steps, or restating the problem. Focus only on the key reasoning steps needed to reach the answer.
The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the an... |
Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.
How many of the first $1000$ positive integers can be expressed in the form
\[\lfloor 2x \rfloor + \lfloor 4x \rfloor + \lfloor 6x \rfloor + \... | 600 | {"dataset_name": "dapo_math", "question": "How many of the first $1000$ positive integers can be expressed in the form\n\\[\\lfloor 2x \\rfloor + \\lfloor 4x \\rfloor + \\lfloor 6x \\rfloor + \\lfloor 8x \\rfloor\\]where $x$ is a real number, and $\\lfloor z \\rfloor$ denotes the greatest integer less than or equal to ... | Solve the following math problem concisely and correctly. Be direct - avoid unnecessary elaboration, redundant steps, or restating the problem. Focus only on the key reasoning steps needed to reach the answer.
The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the an... |
Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.
A sequence of three real numbers forms an arithmetic progression with a first term of $9$. If $2$ is added to the second term and $20$ is adde... | 1 | {"dataset_name": "dapo_math", "question": "A sequence of three real numbers forms an arithmetic progression with a first term of $9$. If $2$ is added to the second term and $20$ is added to the third term, the three resulting numbers form a geometric progression. What is the smallest possible value for the third term i... | Solve the following math problem concisely and correctly. Be direct - avoid unnecessary elaboration, redundant steps, or restating the problem. Focus only on the key reasoning steps needed to reach the answer.
The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the an... |
Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.
Find all pairs $(k,n)$ of positive integers for which $7^k-3^n$ divides $k^4+n^2$. Please provide the sum of all values of $k$ and $n$ in the ... | 4 | {"dataset_name": "dapo_math", "question": "Find all pairs $(k,n)$ of positive integers for which $7^k-3^n$ divides $k^4+n^2$. Please provide the sum of all values of $k$ and $n$ in the pairs.\n\nRemember to put your answer on its own line after \"Answer:\"."} | Solve the following math problem concisely and correctly. Be direct - avoid unnecessary elaboration, redundant steps, or restating the problem. Focus only on the key reasoning steps needed to reach the answer.
The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the an... |
Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.
设三位数 $n=abc$，若以 $a, b, c$ 为三条边长可以构成一个等腰（含等边）三角形，则这样的三位数 $n$ 有多少个？
Remember to put your answer on its own line after "Answer:". | 165 | {"dataset_name": "dapo_math", "question": "\u8bbe\u4e09\u4f4d\u6570 $n=abc$\uff0c\u82e5\u4ee5 $a, b, c$ \u4e3a\u4e09\u6761\u8fb9\u957f\u53ef\u4ee5\u6784\u6210\u4e00\u4e2a\u7b49\u8170\uff08\u542b\u7b49\u8fb9\uff09\u4e09\u89d2\u5f62\uff0c\u5219\u8fd9\u6837\u7684\u4e09\u4f4d\u6570 $n$ \u6709\u591a\u5c11\u4e2a\uff1f\n\nRem... | Solve the following math problem concisely and correctly. Be direct - avoid unnecessary elaboration, redundant steps, or restating the problem. Focus only on the key reasoning steps needed to reach the answer.
The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the an... |
Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.
设非负实数 a,b,c,d 满足 a+b+c+d=4. 求\df{a}{b^3+4}+\df{b}{c^3+4}+\df{c}{d^3+4}+\df{d}{a^3+4}的最小值.原始的答案是\frac{m}{n}的形式，其中m、n是互质的。请给出最终m + n的值
Remember... | 5 | {"dataset_name": "dapo_math", "question": "\u8bbe\u975e\u8d1f\u5b9e\u6570 a,b,c,d \u6ee1\u8db3 a+b+c+d=4. \u6c42\\df{a}{b^3+4}+\\df{b}{c^3+4}+\\df{c}{d^3+4}+\\df{d}{a^3+4}\u7684\u6700\u5c0f\u503c.\u539f\u59cb\u7684\u7b54\u6848\u662f\\frac{m}{n}\u7684\u5f62\u5f0f\uff0c\u5176\u4e2dm\u3001n\u662f\u4e92\u8d28\u7684\u3002\u... | Solve the following math problem concisely and correctly. Be direct - avoid unnecessary elaboration, redundant steps, or restating the problem. Focus only on the key reasoning steps needed to reach the answer.
The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the an... |
Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.
定义函数 A(x)=\ds{m=1}{\infty}\ds{n=0}{\infty}\df{m!n!}{(m+n+1)!}x^m，计算 [100A(\frac{2}{3})].
Remember to put your answer on its own line after "A... | 109 | {"dataset_name": "dapo_math", "question": "\u5b9a\u4e49\u51fd\u6570 A(x)=\\ds{m=1}{\\infty}\\ds{n=0}{\\infty}\\df{m!n!}{(m+n+1)!}x^m\uff0c\u8ba1\u7b97 [100A(\\frac{2}{3})].\n\nRemember to put your answer on its own line after \"Answer:\"."} | Solve the following math problem concisely and correctly. Be direct - avoid unnecessary elaboration, redundant steps, or restating the problem. Focus only on the key reasoning steps needed to reach the answer.
The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the an... |
Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.
Triangle $ABC$ satisfies $\angle ABC = \angle ACB = 78^\circ$. Points $D$ and $E$ lie on $AB$ and $AC$ respectively, and satisfy $\angle BCD =... | 12 | {"dataset_name": "dapo_math", "question": "Triangle $ABC$ satisfies $\\angle ABC = \\angle ACB = 78^\\circ$. Points $D$ and $E$ lie on $AB$ and $AC$ respectively, and satisfy $\\angle BCD = 24^\\circ$ and $\\angle CBE = 51^\\circ$. If $\\angle BED = x^\\circ$, find $x$.\n\nRemember to put your answer on its own line af... | Solve the following math problem concisely and correctly. Be direct - avoid unnecessary elaboration, redundant steps, or restating the problem. Focus only on the key reasoning steps needed to reach the answer.
The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the an... |
Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.
若 $A+B=\frac{2 \pi}{3}$，求 $\cos ^{2} A+\cos ^{2} B$ 的最小值 $m$ 和最大值 $M$。请分别给出 $m$ 和 $M$ 的值。答案的形式为：最小值为\frac{m}{n}，最大值为\frac{p}{q}，请计算m+n+p+q的值。
... | 8 | {"dataset_name": "dapo_math", "question": "\u82e5 $A+B=\\frac{2 \\pi}{3}$\uff0c\u6c42 $\\cos ^{2} A+\\cos ^{2} B$ \u7684\u6700\u5c0f\u503c $m$ \u548c\u6700\u5927\u503c $M$\u3002\u8bf7\u5206\u522b\u7ed9\u51fa $m$ \u548c $M$ \u7684\u503c\u3002\u7b54\u6848\u7684\u5f62\u5f0f\u4e3a\uff1a\u6700\u5c0f\u503c\u4e3a\\frac{m}{n}\... | Solve the following math problem concisely and correctly. Be direct - avoid unnecessary elaboration, redundant steps, or restating the problem. Focus only on the key reasoning steps needed to reach the answer.
The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the an... |
Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.
设集合 $T=\{\left(a,b,c\right)|a,b,c\in\mathbf{Z}_{+}$,且 $a、b、c$ 可构成某个三角形的三边长\}.则$\sum_{(a,b,c)\in T}\frac{2^a}{3^b\times5^c}$的值为一个分数，分子和分母分别为$m$... | 38 | {"dataset_name": "dapo_math", "question": "\u8bbe\u96c6\u5408 $T=\\{\\left(a,b,c\\right)|a,b,c\\in\\mathbf{Z}_{+}$,\u4e14 $a\u3001b\u3001c$ \u53ef\u6784\u6210\u67d0\u4e2a\u4e09\u89d2\u5f62\u7684\u4e09\u8fb9\u957f\\}.\u5219$\\sum_{(a,b,c)\\in T}\\frac{2^a}{3^b\\times5^c}$\u7684\u503c\u4e3a\u4e00\u4e2a\u5206\u6570\uff0c\... | Solve the following math problem concisely and correctly. Be direct - avoid unnecessary elaboration, redundant steps, or restating the problem. Focus only on the key reasoning steps needed to reach the answer.
The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the an... |
Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.
Let $m, n \in \mathbb{N}^*$. Find the least $n$ for which there exists $m$, such that the rectangle $(3m + 2) \times (4m + 3)$ can be covered ... | 8 | {"dataset_name": "dapo_math", "question": "Let $m, n \\in \\mathbb{N}^*$. Find the least $n$ for which there exists $m$, such that the rectangle $(3m + 2) \\times (4m + 3)$ can be covered with $\\frac{n(n + 1)}{2}$ squares, among which there are $n$ squares of length $1$, $n - 1$ squares of length $2$, ..., and $1$ squ... | Solve the following math problem concisely and correctly. Be direct - avoid unnecessary elaboration, redundant steps, or restating the problem. Focus only on the key reasoning steps needed to reach the answer.
The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the an... |
Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.
Let $a, b, c$, and $d$ be prime numbers with $a \le b \le c \le d > 0$.
Suppose $a^2 + 2b^2 + c^2 + 2d^2 = 2(ab + bc - cd + da)$. Find $4a + ... | 51 | {"dataset_name": "dapo_math", "question": "Let $a, b, c$, and $d$ be prime numbers with $a \\le b \\le c \\le d > 0$. \nSuppose $a^2 + 2b^2 + c^2 + 2d^2 = 2(ab + bc - cd + da)$. Find $4a + 3b + 2c + d$.\n\nRemember to put your answer on its own line after \"Answer:\"."} | Solve the following math problem concisely and correctly. Be direct - avoid unnecessary elaboration, redundant steps, or restating the problem. Focus only on the key reasoning steps needed to reach the answer.
The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the an... |
Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.
$AL$, $BM$, and $CN$ are the medians of $\triangle ABC$. $K$ is the intersection of the medians. If $C, K, L, M$ are concyclic and $AB = \sqrt... | 5 | {"dataset_name": "dapo_math", "question": "$AL$, $BM$, and $CN$ are the medians of $\\triangle ABC$. $K$ is the intersection of the medians. If $C, K, L, M$ are concyclic and $AB = \\sqrt{3}$, find the length of the median $CN$. The original answer is in the form \\(\\frac{k\\sqrt{3}}{n}\\), where k and n are integers.... | Solve the following math problem concisely and correctly. Be direct - avoid unnecessary elaboration, redundant steps, or restating the problem. Focus only on the key reasoning steps needed to reach the answer.
The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the an... |
Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.
Let $a$, $b$, $c$, $d$, and $e$ be distinct integers such that
\[ (6 - a)(6 - b)(6 - c)(6 - d)(6 - e) = 45. \]
Find the value of $a + b + c + ... | 25 | {"dataset_name": "dapo_math", "question": "Let $a$, $b$, $c$, $d$, and $e$ be distinct integers such that\n\\[ (6 - a)(6 - b)(6 - c)(6 - d)(6 - e) = 45. \\]\nFind the value of $a + b + c + d + e$.\n\nRemember to put your answer on its own line after \"Answer:\"."} | Solve the following math problem concisely and correctly. Be direct - avoid unnecessary elaboration, redundant steps, or restating the problem. Focus only on the key reasoning steps needed to reach the answer.
The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the an... |
Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.
A penny in a corner. A circle moves so that it is continually in contact with all three coordinate planes of an ordinary rectangular system. F... | 3 | {"dataset_name": "dapo_math", "question": "A penny in a corner. A circle moves so that it is continually in contact with all three coordinate planes of an ordinary rectangular system. Find the locus of the center of the circle. Please provide the num of the possible condition that $x_{i}^{2} \\leq r^{2}$. \n\nRemember ... | Solve the following math problem concisely and correctly. Be direct - avoid unnecessary elaboration, redundant steps, or restating the problem. Focus only on the key reasoning steps needed to reach the answer.
The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the an... |
Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.
在直角坐标系 xoy 中，点 $A\left(x_{1}, y_{1}\right)$ 和点 $B\left(x_{2}, y_{2}\right)$ 的坐标均为一位的正整数。 $O A$ 与 $x$ 轴正方向的夹角大于 $45^{\circ}, O B$ 与 $x$ 轴正方向的夹角... | 1985 | {"dataset_name": "dapo_math", "question": "\u5728\u76f4\u89d2\u5750\u6807\u7cfb xoy \u4e2d\uff0c\u70b9 $A\\left(x_{1}, y_{1}\\right)$ \u548c\u70b9 $B\\left(x_{2}, y_{2}\\right)$ \u7684\u5750\u6807\u5747\u4e3a\u4e00\u4f4d\u7684\u6b63\u6574\u6570\u3002 $O A$ \u4e0e $x$ \u8f74\u6b63\u65b9\u5411\u7684\u5939\u89d2\u5927\u4e... | Solve the following math problem concisely and correctly. Be direct - avoid unnecessary elaboration, redundant steps, or restating the problem. Focus only on the key reasoning steps needed to reach the answer.
The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the an... |
Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.
Let $X = \{1, 2, 3, 4, 5, 6, 7, 8, 9, 10\}$ and $A = \{1, 2, 3, 4\}$. Find the number of $4$-element subsets $Y$ of $X$ such that $10 \in Y$ a... | 74 | {"dataset_name": "dapo_math", "question": "Let $X = \\{1, 2, 3, 4, 5, 6, 7, 8, 9, 10\\}$ and $A = \\{1, 2, 3, 4\\}$. Find the number of $4$-element subsets $Y$ of $X$ such that $10 \\in Y$ and the intersection of $Y$ and $A$ is not empty.\n\nRemember to put your answer on its own line after \"Answer:\"."} | Solve the following math problem concisely and correctly. Be direct - avoid unnecessary elaboration, redundant steps, or restating the problem. Focus only on the key reasoning steps needed to reach the answer.
The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the an... |
Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.
已知 $X^{\lg X} Y^{\lg Y} Z^{\lg Z}=5, X^{\lg Y} Y^{\lg Z} Z^{\lg X}=\sqrt{2}$, 求 $X Y Z$ 的可能取值. 请给出 X Y Z 可能取值的和的整数部分。
Remember to put your an... | 10 | {"dataset_name": "dapo_math", "question": "\u5df2\u77e5 $X^{\\lg X} Y^{\\lg Y} Z^{\\lg Z}=5, X^{\\lg Y} Y^{\\lg Z} Z^{\\lg X}=\\sqrt{2}$, \u6c42 $X Y Z$ \u7684\u53ef\u80fd\u53d6\u503c. \u8bf7\u7ed9\u51fa X Y Z \u53ef\u80fd\u53d6\u503c\u7684\u548c\u7684\u6574\u6570\u90e8\u5206\u3002\n\nRemember to put your answer on its... | Solve the following math problem concisely and correctly. Be direct - avoid unnecessary elaboration, redundant steps, or restating the problem. Focus only on the key reasoning steps needed to reach the answer.
The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the an... |
Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.
Annie's soccer team is conducting a passing drill in which each of the 11 members of the soccer team must pass the ball to each of the other m... | 330 | {"dataset_name": "dapo_math", "question": "Annie's soccer team is conducting a passing drill in which each of the 11 members of the soccer team must pass the ball to each of the other members exactly three times. How many times must the ball be passed before the passing drill is over?\n\nRemember to put your answer on ... | Solve the following math problem concisely and correctly. Be direct - avoid unnecessary elaboration, redundant steps, or restating the problem. Focus only on the key reasoning steps needed to reach the answer.
The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the an... |
Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.
数列 $\left\{a_{n}\right\}$ 满足 $a_{1}=2, a_{n+1}=\frac{2(n+2)}{n+1} a_{n}\left(n \in \mathbb{N}^{*}\right)$, 则 $\frac{a_{2014}}{a_{1}+a_{2}+\cdo... | 4028 | {"dataset_name": "dapo_math", "question": "\u6570\u5217 $\\left\\{a_{n}\\right\\}$ \u6ee1\u8db3 $a_{1}=2, a_{n+1}=\\frac{2(n+2)}{n+1} a_{n}\\left(n \\in \\mathbb{N}^{*}\\right)$, \u5219 $\\frac{a_{2014}}{a_{1}+a_{2}+\\cdots+a_{2013}}=$\n$\\qquad$.\n\u539f\u59cb\u7684\u7b54\u6848\u662f\\frac{m}{n}\u7684\u5f62\u5f0f\uff0... | Solve the following math problem concisely and correctly. Be direct - avoid unnecessary elaboration, redundant steps, or restating the problem. Focus only on the key reasoning steps needed to reach the answer.
The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the an... |
Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.
Consider the sequences of six positive integers $a_1,a_2,a_3,a_4,a_5,a_6$ with the properties that $a_1=1$, and if for some $j > 1$, $a_j = m ... | 203 | {"dataset_name": "dapo_math", "question": "Consider the sequences of six positive integers $a_1,a_2,a_3,a_4,a_5,a_6$ with the properties that $a_1=1$, and if for some $j > 1$, $a_j = m > 1$, then $m-1$ appears in the sequence $a_1,a_2,\\dots,a_{j-1}$. Such sequences include $1,1,2,1,3,2$ and $1,2,3,1,4,1$ but not $1,2,... | Solve the following math problem concisely and correctly. Be direct - avoid unnecessary elaboration, redundant steps, or restating the problem. Focus only on the key reasoning steps needed to reach the answer.
The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the an... |
Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.
What is the remainder when $2^3 \cdot 4^5 \cdot 6^7 \cdot 8^9$ is divided by 13?
Remember to put your answer on its own line after "Answer:". | 8 | {"dataset_name": "dapo_math", "question": "What is the remainder when $2^3 \\cdot 4^5 \\cdot 6^7 \\cdot 8^9$ is divided by 13?\n\nRemember to put your answer on its own line after \"Answer:\"."} | Solve the following math problem concisely and correctly. Be direct - avoid unnecessary elaboration, redundant steps, or restating the problem. Focus only on the key reasoning steps needed to reach the answer.
The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the an... |
Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.
The points $A$, $B$ and $C$ lie on the surface of a sphere with center $O$ and radius $20$. It is given that $AB=13$, $BC=14$, $CA=15$, and th... | 118 | {"dataset_name": "dapo_math", "question": "The points $A$, $B$ and $C$ lie on the surface of a sphere with center $O$ and radius $20$. It is given that $AB=13$, $BC=14$, $CA=15$, and that the distance from $O$ to $\\triangle ABC$ is $\\frac{m\\sqrt{n}}k$, where $m$, $n$, and $k$ are positive integers, $m$ and $k$ are r... | Solve the following math problem concisely and correctly. Be direct - avoid unnecessary elaboration, redundant steps, or restating the problem. Focus only on the key reasoning steps needed to reach the answer.
The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the an... |
Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.
The line joining $(3,2)$ and $(6,0)$ divides the square shown into two parts. What fraction of the area of the square is above this line? Expr... | 5 | {"dataset_name": "dapo_math", "question": "The line joining $(3,2)$ and $(6,0)$ divides the square shown into two parts. What fraction of the area of the square is above this line? Express your answer as a common fraction.\n\n[asy]\ndraw((-2,0)--(7,0),linewidth(1),Arrows);\ndraw((0,-1)--(0,4),linewidth(1),Arrows);\n\nd... | Solve the following math problem concisely and correctly. Be direct - avoid unnecessary elaboration, redundant steps, or restating the problem. Focus only on the key reasoning steps needed to reach the answer.
The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the an... |
Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.
若实数 $\alpha, \beta, \gamma$ 构成以 2 为公比的等比数列， $\sin \alpha, \sin \beta, \sin \gamma$ 构成等比数列，则 $\cos \alpha$ 的值是以\frac{m}{n}格式给出，请给出m + n的值。
Rem... | 3 | {"dataset_name": "dapo_math", "question": "\u82e5\u5b9e\u6570 $\\alpha, \\beta, \\gamma$ \u6784\u6210\u4ee5 2 \u4e3a\u516c\u6bd4\u7684\u7b49\u6bd4\u6570\u5217\uff0c $\\sin \\alpha, \\sin \\beta, \\sin \\gamma$ \u6784\u6210\u7b49\u6bd4\u6570\u5217\uff0c\u5219 $\\cos \\alpha$ \u7684\u503c\u662f\u4ee5\\frac{m}{n}\u683c\u5... | Solve the following math problem concisely and correctly. Be direct - avoid unnecessary elaboration, redundant steps, or restating the problem. Focus only on the key reasoning steps needed to reach the answer.
The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the an... |
Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.
Find the smallest positive integer $n$ for which the polynomial \[x^n-x^{n-1}-x^{n-2}-\cdots -x-1\] has a real root greater than $1.999$.
Rem... | 10 | {"dataset_name": "dapo_math", "question": "Find the smallest positive integer $n$ for which the polynomial \\[x^n-x^{n-1}-x^{n-2}-\\cdots -x-1\\] has a real root greater than $1.999$.\n\nRemember to put your answer on its own line after \"Answer:\"."} | Solve the following math problem concisely and correctly. Be direct - avoid unnecessary elaboration, redundant steps, or restating the problem. Focus only on the key reasoning steps needed to reach the answer.
The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the an... |
Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.
Let $S$ be the set of positive real numbers. Let $f : S \to \mathbb{R}$ be a function such that
\[f(x) f(y) = f(xy) + 2005 \left( \frac{1}{x}... | 4013 | {"dataset_name": "dapo_math", "question": "Let $S$ be the set of positive real numbers. Let $f : S \\to \\mathbb{R}$ be a function such that\n\\[f(x) f(y) = f(xy) + 2005 \\left( \\frac{1}{x} + \\frac{1}{y} + 2004 \\right)\\]for all $x,$ $y > 0.$\n\nLet $n$ be the number of possible values of $f(2),$ and let $s$ be the... | Solve the following math problem concisely and correctly. Be direct - avoid unnecessary elaboration, redundant steps, or restating the problem. Focus only on the key reasoning steps needed to reach the answer.
The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the an... |
Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.
When Tim was Jim’s age, Kim was twice as old as Jim. When Kim was Tim’s age, Jim was 30. When Jim becomes Kim’s age, Tim will be 88. When J... | 221 | {"dataset_name": "dapo_math", "question": "When Tim was Jim\u2019s age, Kim was twice as old as Jim. When Kim was Tim\u2019s age, Jim was 30. When Jim becomes Kim\u2019s age, Tim will be 88. When Jim becomes Tim\u2019s age, what will be the sum of the ages of Tim, Jim, and Kim?\n\nRemember to put your answer on its ... | Solve the following math problem concisely and correctly. Be direct - avoid unnecessary elaboration, redundant steps, or restating the problem. Focus only on the key reasoning steps needed to reach the answer.
The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the an... |
Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.
In the regular hexagon $ABCDEF$, a point $X$ is marked on the diagonal $AD$ such that $\angle AEX = 65^\circ$. What is the degree measure of t... | 25 | {"dataset_name": "dapo_math", "question": "In the regular hexagon $ABCDEF$, a point $X$ is marked on the diagonal $AD$ such that $\\angle AEX = 65^\\circ$. What is the degree measure of the angle $\\angle XCD$?\n\nRemember to put your answer on its own line after \"Answer:\"."} | Solve the following math problem concisely and correctly. Be direct - avoid unnecessary elaboration, redundant steps, or restating the problem. Focus only on the key reasoning steps needed to reach the answer.
The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the an... |
Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.
已知 $\forall x \in R, f(x)=2 x^{4}+m x^{3}+(m+6) x^{2}+m x+2>0$, 求正整数 $m$ 的最大值.
Remember to put your answer on its own line after "Answer:". | 9 | {"dataset_name": "dapo_math", "question": "\u5df2\u77e5 $\\forall x \\in R, f(x)=2 x^{4}+m x^{3}+(m+6) x^{2}+m x+2>0$, \u6c42\u6b63\u6574\u6570 $m$ \u7684\u6700\u5927\u503c.\n\nRemember to put your answer on its own line after \"Answer:\"."} | Solve the following math problem concisely and correctly. Be direct - avoid unnecessary elaboration, redundant steps, or restating the problem. Focus only on the key reasoning steps needed to reach the answer.
The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the an... |
Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.
For how many integers $x \in [0, 2007]$ is $\frac{6x^3+53x^2+61x+7}{2x^2+17x+15}$ reducible?
Remember to put your answer on its own line afte... | 286 | {"dataset_name": "dapo_math", "question": "For how many integers $x \\in [0, 2007]$ is $\\frac{6x^3+53x^2+61x+7}{2x^2+17x+15}$ reducible?\n\nRemember to put your answer on its own line after \"Answer:\"."} | Solve the following math problem concisely and correctly. Be direct - avoid unnecessary elaboration, redundant steps, or restating the problem. Focus only on the key reasoning steps needed to reach the answer.
The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the an... |
Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.
Two boards, one four inches wide and the other six inches wide, are nailed together to form an X. The angle at which they cross is 60 degrees.... | 19 | {"dataset_name": "dapo_math", "question": "Two boards, one four inches wide and the other six inches wide, are nailed together to form an X. The angle at which they cross is 60 degrees. If this structure is painted and the boards are separated what is the area of the unpainted region on the four-inch board? (The holes ... | Solve the following math problem concisely and correctly. Be direct - avoid unnecessary elaboration, redundant steps, or restating the problem. Focus only on the key reasoning steps needed to reach the answer.
The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the an... |
Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.
Let $a_1=2021$ and for $n \ge 1$ let $a_{n+1}=\sqrt{4+a_n}$. Then $a_5$ can be written as $$\sqrt{\frac{m+\sqrt{n}}{2}}+\sqrt{\frac{m-\sqrt{n}... | 45 | {"dataset_name": "dapo_math", "question": "Let $a_1=2021$ and for $n \\ge 1$ let $a_{n+1}=\\sqrt{4+a_n}$. Then $a_5$ can be written as $$\\sqrt{\\frac{m+\\sqrt{n}}{2}}+\\sqrt{\\frac{m-\\sqrt{n}}{2}},$$ where $m$ and $n$ are positive integers. Find $10m+n$.\n\nRemember to put your answer on its own line after \"Answer:\... | Solve the following math problem concisely and correctly. Be direct - avoid unnecessary elaboration, redundant steps, or restating the problem. Focus only on the key reasoning steps needed to reach the answer.
The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the an... |
Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.
How many ordered pairs of integers $(x, y)$ satisfy the equation $x^{2020}+y^2=2y?$
Remember to put your answer on its own line after "Answer... | 4 | {"dataset_name": "dapo_math", "question": "How many ordered pairs of integers $(x, y)$ satisfy the equation $x^{2020}+y^2=2y?$\n\nRemember to put your answer on its own line after \"Answer:\"."} | Solve the following math problem concisely and correctly. Be direct - avoid unnecessary elaboration, redundant steps, or restating the problem. Focus only on the key reasoning steps needed to reach the answer.
The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the an... |
Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.
在平面直角坐标系 $x O y$ 中, 圆 $\Omega$ 与抛物线 $\Gamma: y^{2}=4 x$ 恰有一个公共点, 且圆 $\Omega$ 与 $x$轴相切于 $\Gamma$ 的焦点 $F$ 。求圆 $\Gamma$ 的半径。原始答案为 $\frac{m \sqrt{... | 13 | {"dataset_name": "dapo_math", "question": "\u5728\u5e73\u9762\u76f4\u89d2\u5750\u6807\u7cfb $x O y$ \u4e2d, \u5706 $\\Omega$ \u4e0e\u629b\u7269\u7ebf $\\Gamma: y^{2}=4 x$ \u6070\u6709\u4e00\u4e2a\u516c\u5171\u70b9, \u4e14\u5706 $\\Omega$ \u4e0e $x$\u8f74\u76f8\u5207\u4e8e $\\Gamma$ \u7684\u7126\u70b9 $F$ \u3002\u6c42\u... | Solve the following math problem concisely and correctly. Be direct - avoid unnecessary elaboration, redundant steps, or restating the problem. Focus only on the key reasoning steps needed to reach the answer.
The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the an... |
Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.
Three clever monkeys divide a pile of bananas. The first monkey takes some bananas from the pile, keeps three-fourths of them, and divides the... | 408 | {"dataset_name": "dapo_math", "question": "Three clever monkeys divide a pile of bananas. The first monkey takes some bananas from the pile, keeps three-fourths of them, and divides the rest equally between the other two. The second monkey takes some bananas from the pile, keeps one-fourth of them, and divides the rest... | Solve the following math problem concisely and correctly. Be direct - avoid unnecessary elaboration, redundant steps, or restating the problem. Focus only on the key reasoning steps needed to reach the answer.
The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the an... |
Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.
There are $2n$ complex numbers that satisfy both $z^{28} - z^{8} - 1 = 0$ and $\mid z \mid = 1$. These numbers have the form $z_{m} = \cos\the... | 840 | {"dataset_name": "dapo_math", "question": "There are $2n$ complex numbers that satisfy both $z^{28} - z^{8} - 1 = 0$ and $\\mid z \\mid = 1$. These numbers have the form $z_{m} = \\cos\\theta_{m} + i\\sin\\theta_{m}$, where $0\\leq\\theta_{1} < \\theta_{2} < \\ldots < \\theta_{2n} < 360$ and angles are measured in degr... | Solve the following math problem concisely and correctly. Be direct - avoid unnecessary elaboration, redundant steps, or restating the problem. Focus only on the key reasoning steps needed to reach the answer.
The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the an... |
Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.
How many positive real solutions are there to $x^{10}+7x^9+14x^8+1729x^7-1379x^6=0$?
Remember to put your answer on its own line after "Answe... | 1 | {"dataset_name": "dapo_math", "question": "How many positive real solutions are there to $x^{10}+7x^9+14x^8+1729x^7-1379x^6=0$?\n\nRemember to put your answer on its own line after \"Answer:\"."} | Solve the following math problem concisely and correctly. Be direct - avoid unnecessary elaboration, redundant steps, or restating the problem. Focus only on the key reasoning steps needed to reach the answer.
The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the an... |
Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.
Let $p(x)$ be a monic quartic polynomial such that $p(1) = 2,$ $p(2) = 5,$ $p(3) = 10,$ and $p(4) = 17.$ Find $p(5).$
Remember to put your a... | 50 | {"dataset_name": "dapo_math", "question": "Let $p(x)$ be a monic quartic polynomial such that $p(1) = 2,$ $p(2) = 5,$ $p(3) = 10,$ and $p(4) = 17.$ Find $p(5).$\n\nRemember to put your answer on its own line after \"Answer:\"."} | Solve the following math problem concisely and correctly. Be direct - avoid unnecessary elaboration, redundant steps, or restating the problem. Focus only on the key reasoning steps needed to reach the answer.
The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the an... |
Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.
We are given 5040 balls in \(k\) different colors, where the number of balls of each color is the same. The balls are put into 2520 bags so th... | 6 | {"dataset_name": "dapo_math", "question": "We are given 5040 balls in \\(k\\) different colors, where the number of balls of each color is the same. The balls are put into 2520 bags so that each bag contains two balls of different colors. Find the smallest \\(k\\) such that, however the balls are distributed into the b... | Solve the following math problem concisely and correctly. Be direct - avoid unnecessary elaboration, redundant steps, or restating the problem. Focus only on the key reasoning steps needed to reach the answer.
The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the an... |
Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.
A grasshopper jumps on the plane from an integer point (point with integer coordinates) to another integer point according to the following ru... | 9 | {"dataset_name": "dapo_math", "question": "A grasshopper jumps on the plane from an integer point (point with integer coordinates) to another integer point according to the following rules: His first jump is of length $\\sqrt{98}$, his second jump is of length $\\sqrt{149}$, his next jump is of length $\\sqrt{98}$, and... | Solve the following math problem concisely and correctly. Be direct - avoid unnecessary elaboration, redundant steps, or restating the problem. Focus only on the key reasoning steps needed to reach the answer.
The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the an... |
Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.
In the diagram, the area of rectangle $ABCD$ is $40$. What is the area of $MBCN$? [asy]
import olympiad;
pair a = (0, 0); pair m = (4, 0); pai... | 15 | {"dataset_name": "dapo_math", "question": "In the diagram, the area of rectangle $ABCD$ is $40$. What is the area of $MBCN$? [asy]\nimport olympiad;\npair a = (0, 0); pair m = (4, 0); pair b = (8, 0); pair c = (8, -5); pair n = (6, -5); pair d = (0, -5);\ndraw(m--n);\ndraw(a--b--c--d--cycle);\nlabel(\"$A$\", a, NW); la... | Solve the following math problem concisely and correctly. Be direct - avoid unnecessary elaboration, redundant steps, or restating the problem. Focus only on the key reasoning steps needed to reach the answer.
The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the an... |
Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.
Four points are chosen uniformly and independently at random in the interior of a given circle. Find the probability that they are the vertice... | 47 | {"dataset_name": "dapo_math", "question": "Four points are chosen uniformly and independently at random in the interior of a given circle. Find the probability that they are the vertices of a convex quadrilateral. The original answer is in the format $1-\\frac{m}{n\\pi^2}$, please provide the value of m + n.\n\nRemembe... | Solve the following math problem concisely and correctly. Be direct - avoid unnecessary elaboration, redundant steps, or restating the problem. Focus only on the key reasoning steps needed to reach the answer.
The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the an... |
Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.
Study the convergence of a sequence defined by \( u_0 \ge 0 \) and \( u_{n+1} = \sqrt{u_n} + \frac{1}{n+1} \) for all \( n \in \mathbb{N}_0 \)... | 1 | {"dataset_name": "dapo_math", "question": "Study the convergence of a sequence defined by \\( u_0 \\ge 0 \\) and \\( u_{n+1} = \\sqrt{u_n} + \\frac{1}{n+1} \\) for all \\( n \\in \\mathbb{N}_0 \\).\n\nRemember to put your answer on its own line after \"Answer:\"."} | Solve the following math problem concisely and correctly. Be direct - avoid unnecessary elaboration, redundant steps, or restating the problem. Focus only on the key reasoning steps needed to reach the answer.
The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the an... |
Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.
A box contains six cards. Three of the cards are black on both sides, one card is black on one side and red on the other, and two of the cards... | 9 | {"dataset_name": "dapo_math", "question": "A box contains six cards. Three of the cards are black on both sides, one card is black on one side and red on the other, and two of the cards are red on both sides. You pick a card uniformly at random from the box and look at a random side. Given that the side you see is re... | Solve the following math problem concisely and correctly. Be direct - avoid unnecessary elaboration, redundant steps, or restating the problem. Focus only on the key reasoning steps needed to reach the answer.
The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the an... |
Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.
Let $D$ be the foot of the internal angle bisector of the angle $A$ of a triangle $ABC$. Let $E$ be a point on side $[AC]$ such that $|CE|= |C... | 19 | {"dataset_name": "dapo_math", "question": "Let $D$ be the foot of the internal angle bisector of the angle $A$ of a triangle $ABC$. Let $E$ be a point on side $[AC]$ such that $|CE|= |CD|$ and $|AE|=6\\sqrt{5}$; let $F$ be a point on the ray $[AB$ such that $|DB|=|BF|$ and $|AB|<|AF| = 8\\sqrt{5}$. The original answer ... | Solve the following math problem concisely and correctly. Be direct - avoid unnecessary elaboration, redundant steps, or restating the problem. Focus only on the key reasoning steps needed to reach the answer.
The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the an... |
Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.
Among all pairs of real numbers $(x, y)$ such that $\sin \sin x = \sin \sin y$ with $-10 \pi \le x, y \le 10 \pi$, Oleg randomly selected a pa... | 21 | {"dataset_name": "dapo_math", "question": "Among all pairs of real numbers $(x, y)$ such that $\\sin \\sin x = \\sin \\sin y$ with $-10 \\pi \\le x, y \\le 10 \\pi$, Oleg randomly selected a pair $(X, Y)$. Compute the probability that $X = Y$.The answer is in the form \frac{m}{n}, where gcd(m, n) = 1. Please provide t... | Solve the following math problem concisely and correctly. Be direct - avoid unnecessary elaboration, redundant steps, or restating the problem. Focus only on the key reasoning steps needed to reach the answer.
The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the an... |
Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.
What is the least possible sum of two positive integers $a$ and $b$ where $a \cdot b = 10!$?
Remember to put your answer on its own line afte... | 3810 | {"dataset_name": "dapo_math", "question": "What is the least possible sum of two positive integers $a$ and $b$ where $a \\cdot b = 10!$?\n\nRemember to put your answer on its own line after \"Answer:\"."} | Solve the following math problem concisely and correctly. Be direct - avoid unnecessary elaboration, redundant steps, or restating the problem. Focus only on the key reasoning steps needed to reach the answer.
The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the an... |
Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.
若 $z \in \mathbf{C}, \arg \left(z^{2}-4\right)=\frac{5 \pi}{6}, \arg \left(z^{2}+4\right)=\frac{\pi}{3}$, 请提供 $z$ 的两个解中实部和虚部之和。
Remember to p... | 0 | {"dataset_name": "dapo_math", "question": "\u82e5 $z \\in \\mathbf{C}, \\arg \\left(z^{2}-4\\right)=\\frac{5 \\pi}{6}, \\arg \\left(z^{2}+4\\right)=\\frac{\\pi}{3}$, \u8bf7\u63d0\u4f9b $z$ \u7684\u4e24\u4e2a\u89e3\u4e2d\u5b9e\u90e8\u548c\u865a\u90e8\u4e4b\u548c\u3002\n\nRemember to put your answer on its own line after... | Solve the following math problem concisely and correctly. Be direct - avoid unnecessary elaboration, redundant steps, or restating the problem. Focus only on the key reasoning steps needed to reach the answer.
The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the an... |
Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.
Let $a = \pi/2008$. Find the smallest positive integer $n$ such that\[2[\cos(a)\sin(a) + \cos(4a)\sin(2a) + \cos(9a)\sin(3a) + \cdots + \cos(n... | 251 | {"dataset_name": "dapo_math", "question": "Let $a = \\pi/2008$. Find the smallest positive integer $n$ such that\\[2[\\cos(a)\\sin(a) + \\cos(4a)\\sin(2a) + \\cos(9a)\\sin(3a) + \\cdots + \\cos(n^2a)\\sin(na)]\\]is an integer.\n\nRemember to put your answer on its own line after \"Answer:\"."} | Solve the following math problem concisely and correctly. Be direct - avoid unnecessary elaboration, redundant steps, or restating the problem. Focus only on the key reasoning steps needed to reach the answer.
The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the an... |
Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.
A quadratic polynomial $f(x)$ is called sparse if its degree is exactly 2 , if it has integer coefficients, and if there exists a nonzero poly... | 228 | {"dataset_name": "dapo_math", "question": "A quadratic polynomial $f(x)$ is called sparse if its degree is exactly 2 , if it has integer coefficients, and if there exists a nonzero polynomial $g(x)$ with integer coefficients such that $f(x) g(x)$ has degree at most 3 and $f(x) g(x)$ has at most two nonzero coefficients... | Solve the following math problem concisely and correctly. Be direct - avoid unnecessary elaboration, redundant steps, or restating the problem. Focus only on the key reasoning steps needed to reach the answer.
The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the an... |
Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.
In a rectangular plot of land, a man walks in a very peculiar fashion. Labeling the corners $ABCD$, he starts at $A$ and walks to $C$. Then, h... | 793 | {"dataset_name": "dapo_math", "question": "In a rectangular plot of land, a man walks in a very peculiar fashion. Labeling the corners $ABCD$, he starts at $A$ and walks to $C$. Then, he walks to the midpoint of side $AD$, say $A_1$. Then, he walks to the midpoint of side $CD$, say $C_1$, and then the midpoint of $A_1D... | Solve the following math problem concisely and correctly. Be direct - avoid unnecessary elaboration, redundant steps, or restating the problem. Focus only on the key reasoning steps needed to reach the answer.
The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the an... |
Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.
2018 little ducklings numbered 1 through 2018 are standing in a line, with each holding a slip of paper with a nonnegative number on it. It is... | 2000 | {"dataset_name": "dapo_math", "question": "2018 little ducklings numbered 1 through 2018 are standing in a line, with each holding a slip of paper with a nonnegative number on it. It is given that ducklings 1 and 2018 have the number zero. At some point, ducklings 2 through 2017 change their number to equal the average... | Solve the following math problem concisely and correctly. Be direct - avoid unnecessary elaboration, redundant steps, or restating the problem. Focus only on the key reasoning steps needed to reach the answer.
The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the an... |
Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.
Find the sum of all positive integers $n$ such that:
$$ \frac{\sqrt{n}}{2} + \frac{30}{\sqrt{n}} $$
is an integer.
Remember to put your ans... | 1040 | {"dataset_name": "dapo_math", "question": "Find the sum of all positive integers $n$ such that:\n\n$$ \\frac{\\sqrt{n}}{2} + \\frac{30}{\\sqrt{n}} $$\n\nis an integer.\n\nRemember to put your answer on its own line after \"Answer:\"."} | Solve the following math problem concisely and correctly. Be direct - avoid unnecessary elaboration, redundant steps, or restating the problem. Focus only on the key reasoning steps needed to reach the answer.
The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the an... |
Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.
设 $V=\{(x, y, z) \mid x+2 y+3 z \leqslant 1, x \geqslant 0, y \geqslant 0, z \geqslant 0\}$, 求 $V$ 的体积。原始答案是一个最简分数形式 \frac{k}{m}，请给出k+m的值。
Re... | 37 | {"dataset_name": "dapo_math", "question": "\u8bbe $V=\\{(x, y, z) \\mid x+2 y+3 z \\leqslant 1, x \\geqslant 0, y \\geqslant 0, z \\geqslant 0\\}$, \u6c42 $V$ \u7684\u4f53\u79ef\u3002\u539f\u59cb\u7b54\u6848\u662f\u4e00\u4e2a\u6700\u7b80\u5206\u6570\u5f62\u5f0f \\frac{k}{m}\uff0c\u8bf7\u7ed9\u51fak+m\u7684\u503c\u3002\... | Solve the following math problem concisely and correctly. Be direct - avoid unnecessary elaboration, redundant steps, or restating the problem. Focus only on the key reasoning steps needed to reach the answer.
The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the an... |
Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.
Compute the largest integer not exceeding $$\frac{2549^3}{2547\cdot 2548} - \frac{2547^3}{2548\cdot 2549}$$.
Remember to put your answer on i... | 8 | {"dataset_name": "dapo_math", "question": "Compute the largest integer not exceeding $$\\frac{2549^3}{2547\\cdot 2548} - \\frac{2547^3}{2548\\cdot 2549}$$.\n\nRemember to put your answer on its own line after \"Answer:\"."} | Solve the following math problem concisely and correctly. Be direct - avoid unnecessary elaboration, redundant steps, or restating the problem. Focus only on the key reasoning steps needed to reach the answer.
The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the an... |
Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.
平面上的 4027 个点称为一个哥伦比亚式点集，如果其中任意三点不共线，且有 2013 个点是红色的，2014 个点是蓝色的. 在平面上画出一组直线，可以将平面分成若干区域. 如果一组直线对于一个哥伦比亚式点集满足下述两个条件，我们就称这是一个好直线组：(1) 这些直线不经过该哥伦... | 2013 | {"dataset_name": "dapo_math", "question": "\u5e73\u9762\u4e0a\u7684 4027 \u4e2a\u70b9\u79f0\u4e3a\u4e00\u4e2a\u54e5\u4f26\u6bd4\u4e9a\u5f0f\u70b9\u96c6\uff0c\u5982\u679c\u5176\u4e2d\u4efb\u610f\u4e09\u70b9\u4e0d\u5171\u7ebf\uff0c\u4e14\u6709 2013 \u4e2a\u70b9\u662f\u7ea2\u8272\u7684\uff0c2014 \u4e2a\u70b9\u662f\u84dd\... | Solve the following math problem concisely and correctly. Be direct - avoid unnecessary elaboration, redundant steps, or restating the problem. Focus only on the key reasoning steps needed to reach the answer.
The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the an... |
Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.
Find the largest positive integer \(d\) for which there exists a degree $d$ polynomial $P$ with real coefficients such that there are at most ... | 3 | {"dataset_name": "dapo_math", "question": "Find the largest positive integer \\(d\\) for which there exists a degree $d$ polynomial $P$ with real coefficients such that there are at most $d$ different values among $P(0), P(1), \\ldots, P\\left(d^{2}-\\right.$ $d)$.\n\nRemember to put your answer on its own line after \... | Solve the following math problem concisely and correctly. Be direct - avoid unnecessary elaboration, redundant steps, or restating the problem. Focus only on the key reasoning steps needed to reach the answer.
The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the an... |
Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.
Three mutually tangent spheres of radius \(1\) rest on a horizontal plane. A sphere of radius \(2\) rests on them. Find the distance from the ... | 75 | {"dataset_name": "dapo_math", "question": "Three mutually tangent spheres of radius \\(1\\) rest on a horizontal plane. A sphere of radius \\(2\\) rests on them. Find the distance from the plane to the top of the larger sphere. The answer is in the form \\(k + \\frac{\\sqrt{m}}{n}\\), where \\(n\\) is not divisible by ... | Solve the following math problem concisely and correctly. Be direct - avoid unnecessary elaboration, redundant steps, or restating the problem. Focus only on the key reasoning steps needed to reach the answer.
The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the an... |
End of preview. Expand in Data Studio
CRISP training data (DAPO-Math-17k)
Training data for CRISP (Compressed Reasoning via Iterative Self-Policy Distillation), an on-policy self-distillation method that teaches reasoning models to be concise by distilling their own concise behavior back into themselves. The teacher is the same model conditioned on a conciseness instruction; no ground-truth answers or token budgets enter the loss.
Derived from DAPO-Math-17k (17,398 competition-level math problems). CRISP uses only the problem
statements to generate student rollouts — the answer column is not used by the training loss.
Files
| File | Concise instruction (concise_instruction column) |
|---|---|
dapo_math_17k_crisp_train_full_vocab_v1.parquet |
v1 — uniform. "Solve concisely and correctly. Be direct — avoid unnecessary elaboration, redundant steps, or restating the problem." |
dapo_math_17k_crisp_train_full_vocab_v2.parquet |
v2 — difficulty-aware (default). Adds a caveat to not over-compress hard/multi-step problems (keep case analysis, edge cases, a final check). |
Both files have 17,398 rows and identical schema.
Schema
| Column | Type | Description |
|---|---|---|
problem |
string | The student prompt (problem statement + answer-format instruction). |
answer |
string | Reference answer (for offline eval only; unused by the CRISP loss). |
metadata |
string (JSON) | Source metadata (dataset_name, question, source_id, …). |
concise_instruction |
string | The privileged conciseness instruction prepended to the teacher prompt (v1 or v2). This is the only CRISP-specific column. |
Usage
from datasets import load_dataset
ds_v2 = load_dataset("pb09204048/CRISP", data_files="dapo_math_17k_crisp_train_full_vocab_v2.parquet")["train"]
print(ds_v2[0]["concise_instruction"])
The teacher distribution is obtained by conditioning the base model on concise_instruction; the
student is the same model on problem alone. Training minimizes per-token reverse KL from student to
teacher on the student's own rollouts.
Paper
CRISP: Compressed Reasoning via Iterative Self-Policy Distillation — https://arxiv.org/abs/2603.05433
If you use this dataset, please cite:
@article{sang2026crisp,
title={Crisp: Compressed reasoning via iterative self-policy distillation},
author={Sang, Hejian and Xu, Yuanda and Zhou, Zhengze and He, Ran and Wang, Zhipeng and Sun, Jiachen},
journal={arXiv preprint arXiv:2603.05433},
year={2026}
}
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