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/volume14/exercise14.tex",3 "problem_type": "calculation",4 "problem": "问题2. 如图(<FilePath:./images/volume14/figures/fig-c14p2.png>),把正方体形的房子分割成 27 个相等的小房间,每相邻两个房间 (即有公共面的两个小正方体) 都有门相通, 在中心的那个小正方体中有一只甲虫, 甲虫能从每个小房间走到与它相邻的任何一个小房间去.\n如果要求甲虫只能走到每个小房间一次,那么甲虫能走遍所有的小房间吗?",5 "solution": "甲虫不能走遍所有的小房间.\n我们如图(<FilePath:./images/volume14/figures/fig-c14a2.png>), 将正方体分割成 27 个小正方体 (每个小正方体表示一间房间), 涂上黑白相间的两种颜色, 使得中心的小正方体染成白色,再使两个相邻的小正方体染上不同的颜色.\n显然, 在 27 个小正方体中, 14 个是黑的, 13 个是白的.\n甲虫从中间的白色小正方体出发, 每走一步, 方格就改变一种颜色.\n故它走 27 步, 应该经过 14 个白色的小正方体、13 个黑色的小正方体.\n因此在 27 步中至少有一个小正方体, 甲虫进去过两次.\n由此可见, 如果要求甲虫到每一个小房间只去一次, 那么甲虫不能走遍所有的小房间.",6 "remark": "",7 "figures": [8 "./images/volume14/figures/fig-c14p2.png",9 "./images/volume14/figures/fig-c14a2.png"10 ]11}