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The Counterfeit Dozen

brainteaser
Twelve coins are visually indistinguishable. Eleven have exactly the same weight; the remaining coin is either heavier or lighter, but you do not know which. You have a two-pan balance scale that reports only whether the left pan falls, the right pan falls, or the pans balance. No reference weights or additional coins are available. You may choose later weighings after seeing earlier results. Your method must always identify the unusual coin and determine whether it is heavier or lighter. What is the smallest number of balance-scale weighings that guarantees success?

Hints

Hint 1
Hint 2
Hint 3

Solution

Commit an attempt to unseal the proof. Write your answer — right or wrong, thinking it through is the point.

What is the minimum number of weighings required?

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