Question: (a) [BB] Given an equal arm balance capable of determining only the relative weights of two quantities and eight coins, all of equal weight except possibly one which is lighter, explain how to determine if there is a light coin and how to identify it in just two weighings.
(b) Given an equal arm balance as in (a) and 3n - 1 coins, n ≥ 1, all of equal weight except possibly one which is lighter, show how to determine if there is a light coin and how to identify it in at most n weighings.