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Finding one heavy bean among eight

Question

Among 88 beans that look the same, exactly one is a bit heavier than the rest. Using a two-pan balance, what is the fewest weighings that always suffices to identify it?

Short answer

22. Weigh 33 against 33. If they balance, compare the remaining two. If not, take the heavier group of three and weigh two of them against each other. One weighing has only 33 outcomes and cannot separate 88 cases, so 22 is optimal.

Adapted from QuantQuestions.io; question and answer rewritten by SelfMadeQuant.com.

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