珍珠湾ART

标题: 天平平衡 [打印本页]

作者: ob 时间: 2006-11-14 09:56
标题: 天平平衡

抽屉里有重量是１到１００的砝码１００个。现在从里面随便取１０个出来。
试证明我们总可以从这十个砝码中挑出两组砝码来使得它们在天平上平衡。也就是
说这两组的重量和相等。注意，两组的个数不一定一样，也不一定要用到全部十个
砝码。

作者: xlxk 时间: 2006-11-14 23:36
标题: 回复：天平平衡

For a set with 10 elements, there are 2^10=1024 subsets (S_1, S_2, S_3, ..., S_1024).
Obviously, 0=

作者: xlxk 时间: 2006-11-14 23:55
标题: don't enter, the solution is wrong!回复：天平平衡

don't enter, the solution is wrong!回复：天平平衡

作者: xlxk 时间: 2006-11-15 00:01
标题: Solution here回复：回复：天平平衡

For a set with 10 elements, there are 2^10=1024 subsets (S_1, S_2, S_3, ..., S_1024).
Obviously, 0=Suppose sum(S_N)=sum(S_M).
If S_N and S_M are othogonal (no common elements), we proved the problem. If they are not, remove the common elements.

作者: ob 时间: 2006-11-16 23:29
标题: [:-Q][:-Q][@};-]

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