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!).

To prove that it may not work if all members of T are required all we have to do is come up with one example where it doesn't work, so here is the example which shows the second part to be not possible:  T={1, 2, 3, 4, 5, 6, 7, 8, 9, 99}

Posted by Erik O. on 2004-06-29 16:00:01