Out of the set {1,2,3...100} take any subset of ten numbers and call it T. Prove you can find two disjoint subsets of T such as the sum of the numbers in each subset is the same.

Note: the subsets need not include every number in T; in fact, if you asked for this condition, the problem might be impossible (prove it!).

(In reply to Second part by Old Original Oskar!)

That doesn't follow, as the union of the two subsets need not equal T.

In fact, T = any subset of nine numbers also suffices!

Posted by Nick Hobson on 2004-06-29 14:11:34