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Brainteasers

Eight coins, and maybe none of them is fake

weighingbalance-scaleternaryedge-cases

You have eight coins. At most one of them is counterfeit, and a counterfeit coin is heavier than a genuine one. It is entirely possible that all eight are genuine.

Using a two-pan balance, you must either point to the heavy coin or declare with certainty that there is no heavy coin.

Can you always do this in two weighings? If so, how?

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Count the possible states: eight "coin k is heavy" states plus one "nobody is heavy" state. Compare that with the number of outcomes two weighings can produce. Then make sure your last weighing can end in a balance that means "all clear".

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