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/volume13/exercise2.tex",3 "problem_type": "calculation",4 "problem": "问题2. 求一个十进制 3 位数, 使它与其各位数字之和的比最小.",5 "solution": "设所求的三位数为 $100 x+20 y+z$, 考察 $F=\\frac{100 x+10 y+z}{x+y+z}=1+ \\frac{99 x+9 y}{x+y+a}$, 注意到上式右边, $z$ 仅在分母中出现, 从而 $F$ 是关于 $z$ 的单调函数.\n固定 $x 、 y$, 则由 $z \\leqslant 9$, 得 $F \\geqslant 1+\\frac{99 x+9 y}{x+y+9}=10+\\frac{90 x-81}{x+y+9}$. 注意到上式右边, $y$ 仅在分母中出现, 从而右边是关于 $y$ 的单调函数.\n再固定 $x$, 则由 $y \\leqslant 9$, 得 $F \\geqslant 10+\\frac{90 x-81}{x+9+9}=100-\\frac{1701}{18+x} \\geqslant 100-\\frac{1701}{19}=\\frac{199}{99}$. 其中等式在 $x=1 、 y=z=9$ 时成立.\n故所求的三位数为 199 .",6 "remark": "",7 "figures": []8}