MathDB

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

Problem Statement