Let S be a set of 6 random positive integers whose sum is not bigger than 60.
Show that in any such set S there exists two non-empty , disjoint subsets whose elements have the same sum.
I've tried to somehow use the pigeon hole principle but I'm STUCK.
I know there are 2^6 possible subsets...though the empty set and the set with all six elements should be thrown away....which leaves us with 62 subsets.
Can anyone help me or "nudge" me in the right direction ?