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/volume11/exercise12.tex",3 "problem_type": "calculation",4 "problem": "问题3. 能否将下列 $m \\times n$ 矩形完全剖分为若干个形如 $\\square$ 的\" $L$ 形\"?\n(1) $m \\times n=2003 \\times 2005$ ;(2) $m \\times n=2005 \\times 2007$.",5 "solution": "(1)因 $2003 \\times 2005$ 不被 3 整除,而每个 L 型含 3 个方格,故 $2003 \\times 2005$ 矩形不能完全剖分成若干个 L 形.\n(2) 因 L 形既可拼成 $2 \\times 3$ 的矩形又可拼成 $7 \\times 9$ 的矩形 (如图(<FilePath:./images/volume11/figures/fig-c12a3.png>)), 而 $2005 \\times 2007=1998 \\times 2007+ 7 \\times 2007=(2 \\times 3) \\times(999 \\times 669)+(7 \\times 9) \\times 223$. 故知 $2005 \\times 2007$ 的矩形可完全剖分为若干个 $\\mathrm{L}$ 形.",6 "remark": "",7 "figures": [8 "./images/volume11/figures/fig-c12a3.png"9 ]10}