mirror of https://github.com/inclusionAI/AReaL
11 lines
5.5 KiB
JSON
Executable File
11 lines
5.5 KiB
JSON
Executable File
{"prompt": "<\uff5cUser\uff5c>\nBaron Munchausen told a story. \"There were a whole crowd of us. We reached a crossroads. Then half of our group turned left, a third turned right, and a fifth went straight.\" \"But wait, the Duke remarked, the sum of half, a third, and a fifth isn't equal to one, so you are lying!\" The Baron replied, \"I'm not lying, I'm rounding. For example, there are 17 people. I say that a third turned. Should one person split in your opinion? No, with rounding, six people turned. From whole numbers, the closest to the fraction $17 / 3$ is 6. And if I say that half of the 17 people turned, it means 8 or 9 people.\" It is known that Baron Munchausen never lies. What is the largest number of people that could have been in the crowd?\nPlease reason step by step, and put your final answer within \\boxed{}.<\uff5cAssistant\uff5c><think>", "task": "math", "query_id": "00006d8f079c739f", "solutions": ["\\boxed{37}"]}
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{"prompt": "<\uff5cUser\uff5c>What is the unit digit of the product\n\n$$\n(5+1)\\left(5^{3}+1\\right)\\left(5^{6}+1\\right)\\left(5^{12}+1\\right) ?\n$$\n\n(a) 0 \n(b) 1 \n(c) 2 \n(d) 5 \n(e) 6\nPlease reason step by step, and put your final answer within \\boxed{}.<\uff5cAssistant\uff5c><think>", "task": "math", "query_id": "000316109ea516b3", "solutions": ["\\boxed{e}"]}
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{"prompt": "<\uff5cUser\uff5c>Given points \\( A(4,0) \\) and \\( B(2,2) \\) are inside the ellipse \\( \\frac{x^{2}}{25}+\\frac{y^{2}}{9}=1 \\), and \\( M \\) is a point on the ellipse, find the maximum value of \\( |MA| + |MB| \\).\nPlease reason step by step, and put your final answer within \\boxed{}.<\uff5cAssistant\uff5c><think>", "task": "math", "query_id": "000adcfa66ee4270", "solutions": ["\\boxed{10+2\\sqrt{10}}"]}
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{"prompt": "<\uff5cUser\uff5c>There is a schoolbag containing 12 cards labeled $1, 1, 2, 2, \\cdots, 6, 6$. A person draws one card at a time without replacement. If a card is drawn that has the same number as a previously drawn card, both cards are discarded. The process ends when the person has 3 single cards in hand or all cards in the schoolbag have been drawn. Find the probability that all cards in the schoolbag are drawn.\nPlease reason step by step, and put your final answer within \\boxed{}.<\uff5cAssistant\uff5c><think>", "task": "math", "query_id": "001354647264e663", "solutions": ["\\boxed{\\frac{9}{385}}"]}
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{"prompt": "<\uff5cUser\uff5c>For the sequence of numbers \\( n_{1}, n_{2}, n_{3}, \\ldots \\), the relation \\( n_{i} = 2 n_{i-1} + a \\) holds for all \\( i > 1 \\). If \\( n_{2} = 5 \\) and \\( n_{8} = 257 \\), what is \\( n_{5} \\)?\nPlease reason step by step, and put your final answer within \\boxed{}.<\uff5cAssistant\uff5c><think>", "task": "math", "query_id": "0014142e5f3c28a7", "solutions": ["\\boxed{33}"]}
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{"prompt": "<\uff5cUser\uff5c>Three players play tic-tac-toe together. In other words, the three players take turns placing an \"A\", \"B\", and \"C\", respectively, in one of the free spots of a \\(3 \\times 3\\) grid, and the first player to have three of their label in a row, column, or diagonal wins. How many possible final boards are there where the player who goes third wins the game? (Rotations and reflections are considered different boards, but the order of placement does not matter.)\nPlease reason step by step, and put your final answer within \\boxed{}.<\uff5cAssistant\uff5c><think>", "task": "math", "query_id": "0017c4e9f72d26eb", "solutions": ["\\boxed{148}"]}
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{"prompt": "<\uff5cUser\uff5c>Let \\( a_{1}, a_{2}, \\cdots, a_{2014} \\) be a permutation of the positive integers \\( 1, 2, \\cdots, 2014 \\). Define\n\\[ S_{k} = a_{1} + a_{2} + \\cdots + a_{k} \\quad (k=1, 2, \\cdots, 2014). \\]\n\nWhat is the maximum number of odd numbers among \\( S_{1}, S_{2}, \\cdots, S_{2014} \\)?\nPlease reason step by step, and put your final answer within \\boxed{}.<\uff5cAssistant\uff5c><think>", "task": "math", "query_id": "00231541a71983cd", "solutions": ["\\boxed{1511}"]}
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{"prompt": "<\uff5cUser\uff5c>\nThe polynomial \\( G(x) \\) with real coefficients takes the value 2022 at exactly five distinct points \\( x_{1}<x_{2}<x_{3}<x_{4}<x_{5} \\). It is known that the graph of the function \\( y=G(x) \\) is symmetric with respect to the line \\( x=-7 \\).\n\n(a) Find \\( x_{1}+x_{3}+x_{5} \\).\n\n(b) What is the minimum degree that \\( G(x) \\) can have?\nPlease reason step by step, and put your final answer within \\boxed{}.<\uff5cAssistant\uff5c><think>", "task": "math", "query_id": "002ba4c0d1ad1b54", "solutions": ["\\boxed{6}"]}
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{"prompt": "<\uff5cUser\uff5c>The square of a natural number has 202 digits. The first 100 digits are 1, followed by 101 digits of 2. Determine the last digit and the number.\nPlease reason step by step, and put your final answer within \\boxed{}.<\uff5cAssistant\uff5c><think>", "task": "math", "query_id": "0041f14cc37aee13", "solutions": ["\\boxed{5}"]}
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{"prompt": "<\uff5cUser\uff5c>The descriptors 'even', 'factors of 240', 'multiple of 3', 'odd', 'prime' and 'square' are to be placed in some order as row and column headings around a grid in positions \\(a, b, c, d, e,\\) and \\(f\\). The digits 1 through 9 are to be placed in the empty cells inside the grid so that each digit satisfies both the relevant row and column headings.\n(i) Show that it is possible to complete the grid.\n(ii) In how many different ways can the grid be completed?\nPlease reason step by step, and put your final answer within \\boxed{}.<\uff5cAssistant\uff5c><think>", "task": "math", "query_id": "00514ff45cc98a48", "solutions": ["\\boxed{72}"]}
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