It is known that among several banknotes of pairwise distinct face values (which are positive integers) there are exactly N fakes. In a single test, a detector determines the sum of the face values of all real banknotes in an arbitrary set we have selected. Prove that by using the detector N times, all fake banknotes can be identified, if a) N=2 and b) N=3.Proposed by S. Tokarev combinatoricsTournament of TownsKvant