Wednesday, December 15, 2010

A Small Challenge

Pick any 10 numbers between 1 and 100.
There will always be two subsets of these 10 numbers whose sums are equal.
Thus, for example, if you were to choose 51, 11, 81, 68, 73, 87, 23, 29, 25, 94,
you would soon observe that

25 + 51 + 29 = 94 + 11.

The claim is that this works for every 10 numbers you choose.


Prove it!

Likewise, if you were to pick 20 whole numbers between 1 and 50,000,
you would always find two subsets of these 20 numbers whose sums were equal.

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