Let A be a k-element subset of { 1,2,3,......,16}. It is known that every two subsets of A have distinct sum of their elements and for any (k + 1) element subset B of { 1,2,3,......16}, containing A, there exist subsets of B with equal sums.
a) Prove that k \le 5
b) For different subsets A with the given property find the maximum and minimum possible values of the sum of the elements of A.