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把1-8按要求平分成两个集合

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isee posted 2014-9-17 14:46 |Read mode
若$a,b,c,d$为两两相异的4个数,那么每次取两个数相加,能形成6种各和式:\[a+b,a+c.a+d,b+c,b+d,c+d.\]将整数1,2,3,4,5,6,7,8平分成两个集合,使得一个集合中的4个数以上述方法所得的6个和,恰好与另一个集合所得的各个和一样(顺序不必相同)。试列出所有可能的分拆法。

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