Question 7
Among some banknotes with pairwise distinct positive-integer denominations, exactly $N$ are counterfeit. In one test a detector reports the sum of the denominations of the genuine notes in any chosen subset. Prove that all counterfeit notes can be identified in $N$ tests if (a) $N=2$; (b) $N=3$. Original weights: (a) 3 points, (b) 8 points.
