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/volume12/chapter5.tex",3 "problem_type": "calculation",4 "problem": "例3. 如图(<FilePath:./images/volume12/figures/fig-c5i7.png>) 所示,在 $8 \\times 8$ 黑白方格的棋盘上跳动一只马, 不论跳动方向如何, 要使这只马跳遍棋盘的每一格且每格只经过一次, 问这是否可能? (一只马跳动一次是指从 $2 \\times 3$ 黑白方格组成的长方形的一个对角跳到另一个对角上)",5 "solution": "解:如图(<FilePath:./images/volume12/figures/fig-c5i8.png>) 中给出这个问题的一个解答.\n\\begin{tabular}{|l|l|l|l|l|l|l|l|}\n\\hline 56 & 41 & 58 & 35 & 50 & 39 & 60 & 33 \\\\\n\\hline 47 & 44 & 55 & 40 & 59 & 34 & 51 & 38 \\\\\n\\hline 42 & 57 & 46 & 49 & 36 & 53 & 32 & 61 \\\\\n\\hline 45 & 48 & 43 & 54 & 31 & 62 & 37 & 52 \\\\\n\\hline 20 & 5 & 30 & 63 & 22 & 11 & 16 & 13 \\\\\n\\hline 29 & 64 & 21 & 4 & 17 & 14 & 25 & 10 \\\\\n\\hline 6 & 19 & 2 & 27 & 8 & 23 & 12 & 15 \\\\\n\\hline 1 & 28 & 7 & 18 & 3 & 26 & 9 & 24 \\\\\n\\hline\n\\end{tabular}\n解决这类问题, 常常用以下 4 种方法尝试:\n1. 每次将马放到使它能走到的 (尚未走过的)方格为最少的位置, 即先走\"出路\"少的方格,后走\"出路\"多的方格.\n2. 将棋盘分为几个部分, 在每个部分中找一条哈密顿链 (见第六节), 然后把它们连接起来.\n3. 在棋盘上找几个圈,然后将这些圈连接起来.\n4. 将一个较小的棋盘镶上边, 产生一个大棋盘上的哈密顿链.",6 "remark": "",7 "figures": [8 "./images/volume12/figures/fig-c5i7.png",9 "./images/volume12/figures/fig-c5i8.png"10 ]11}