Question: Let A be a set of six positive integers each of which is less than 13. Show that there must be two distinct subsets of A whose elements when added up give the same sum. (For example, if A = {5, 12, 10, 1, 3, 4}, then the elements of the subsets S1 = {1, 4, 10} and S2 = {5, 10} both add up to 15.)