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 re(2): Second part by Charlie)

Of course!  (Slaps forehead.)

Posted by Nick Hobson on 2004-06-29 14:44:03