math-ai/BlueMO
BlueMO 🚀 BlueMO: A Comprehensive Collection of Challenging Mathematical Olympiad Problems from the Little Blue Book Series BlueMO is a comprehensive and challenging dataset comprising mathematical olympiad problems paired with detailed solutions, meticulously curated from the esteemed "Little Blue Book" (小蓝书) series (Second Edition)—a vital resource for Chinese students training for national and international olympiad math competitions. Designed to… See the full description on the dataset page: https://huggingface.co/datasets/math-ai/BlueMO.
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1{2 "source_file": "./raw_volume-zh/volume1/exercise4.tex",3 "problem_type": "calculation",4 "problem": "问题7 $X=\\{1,2, \\cdots, n\\}, A 、 B 、 C$ 是 $X$ 的分划, 即 $A \\cup B \\cup C=X$, 并且 $A 、 B$ 、 $C$ 两两的交集都是空集.\n如果从 $A 、 B 、 C$ 中各取一个元素, 那么每两个的和都不等于第三个.\n求\n$$\n\\max \\{\\min (|A|,|B|,|C|)\\} .\n$$",5 "solution": "考虑奇偶性.\n如果 $A$ 由 $X$ 中的奇数组成, $B \\cup C$ 由 $X$ 中的偶数组成, 那么它们合乎题设要求.\n这时 $\\min (|A|,|B|,|C|)=\\left[\\frac{n}{4}\\right]$. 由此, 猜测 $\\max \\{\\min (|A|,|B|,|C|)\\}=\\left[\\frac{n}{4}\\right]$, 也就是恒有 $\\min (|A|,|B|$, $|C|) \\leqslant \\frac{n}{4}$.",6 "remark": "",7 "figures": []8}