that contains 10 elements. Use the Pigeonhole Principle to prove that there exists two disjoint subsets of S whose elements have the same sum.
Don't know what to do.
I suppose you have to show that there are more disjoint 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, ).