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: Second part by Nick Hobson)
Oskar's comment was for the second part, which does require that the union of the two subsets must be T. The first part doesn't require that, but the second part does.

Posted by Charlie
on 20040629 14:19:40 