Given 12 coins, with possibly (but not necessarily) one coin being counterfeit (heavy or light). You...

Given 12 coins, with possibly (but not necessarily) one coin being counterfeit (heavy or light). You have a comparison scale and you want to determine the fairness of all with a minimum number of comparisons.

(a) What is the smallest number of comparisons required? Give a theoretical reason. (Hint: each comparison has three possible outcomes)

(b) Give the procedure to identify the false coin or to show all are fair.

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