Finding one heavy bean among eight
Question
Among 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
. Weigh against . 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 outcomes and cannot separate cases, so is optimal.
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