Response to the following problem:
Coin weighing.
Suppose that one has n coins, among which there may or may not be one counterfeit coin. If there is a counterfeit coin, it may be either heavier or lighter than the other coins. The coins are to be weighed by a balance.
(a) Find an upper bound on the number of coins n so that k weighings will find the counterfeit coin (if any) and correctly declare it to be heavier or lighter.
(b) (Difficult) What is the coin- weighing strategy for k = 3 weighings and 12 coins?