Homework Help: Using the method of mathematical induction

1. Feb 7, 2010

cocobaby

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1. The problem statement, all variables and given/known data
Let H be a ten- element set of potive integers ranged from 1 to 99. Prove that H has two disjoint subsets A and B so that the sum of the elements of A is equal to the sum of the elements of B.

2. Feb 7, 2010

Mandark

I think this is most naturally a pigeonhole problem. Pigeonhole hint: there are 2^10 - 2 = 1022 non-empty proper subsets of H, the sum of the elements of any such subset lies in 1..1000 so can take on at most 1000 different values (in fact it's quite less than this, but this is a strong enough statement) which is less than 1022.