Let n and b be positive integers. We say n is b-discerning if there exists a set consisting of n different positive integers less than b that has no two different subsets U and V such that the sum of all elements in U equals the sum of all elements in V.(a) Prove that 8 is 100-discerning.
(b) Prove that 9 is not 100-discerning.Senior Problems Committee of the Australian Mathematical Olympiad Committee pigeonhole principlefloor functionnumber theoryalgebracombinatorics