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/volume1/exercise5.tex",3 "problem_type": "calculation",4 "problem": "问题3 对于 $\\{1,2, \\cdots, n\\}$ 和它的每个非空子集, 我们定义“交替和”如下：把子集中的数按从大到小的顺序排列, 然后从最大的数开始交替地加减各数 (例如, $\\{1,2,4,6,9\\}$ 的交替和是 $9-6+4-2+1=6$, 而 $\\{5\\}$ 的交替和就是 5). 对于 $n=7$; 求所有这些交替和的总和.",5 "solution": "集合 $\\{1,2,3,4,5,6,7\\}$ 中每个元素在子集中均出现 $2^6=64$ 次.\n可计算 $1,2,3,4,5,6$ 在子集中按从大到小的顺序排列时各有 32 次在奇数位, 32 次在偶数位,因此子集中这些数的交替和的总和为 0 ; 而 7 也出现 64 次, 且均取正值, 所以所有子集的交替和的总和为 $7 \\times 64=448$.",6 "remark": "",7 "figures": []8}