I suppose you have to show that there aremoredisjoint subsets of than there are possible different sums of the elements of those subsets. So the first question to answer is how many different disjoint subsets of there are.

Next, if you are lucky and there are a sufficiently large number of disjoint subsets of , you might be able to use a very rough estimate of how many different sums there could possibly be (like, for example, ).