Find an upper bound on the number of coins, Other Subject

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Find an upper bound on the number of coins

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?

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