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/exercise4.tex",3 "problem_type": "calculation",4 "problem": "问题4. 已知一棵树 $T$ 有3个3度顶点,一个2度定点, 其余的都是悬挂点.\n1) $T$中有几个悬挂点? (2)试画出两棵满足上述度数要求的不同构的树.",5 "solution": "(1) 设 $T$ 中有 $x$ 个悬挂点, 则 $T$ 的顶点数 $n=3+1+x$, 边数 $e=n- 1=x+3$. $\\sum_{i=1}^n d\\left(v_i\\right)=3 \\times 3+2 \\times 1+1 \\times x=11+x$, 故 $11+x=2(x+3)$, $x=5$.\n(2) 如图(<FilePath:./images/volume12/figures/fig-c4a4.png>)所示的两棵树均满足要求,但它们不同构.",6 "remark": "",7 "figures": [8 "./images/volume12/figures/fig-c4a4.png"9 ]10}