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Interview prep / Brainteaser/Logic

Finding the heavy coin among nine in two weighings

Question

Nine coins look identical, and eight of them have the same weight while one is slightly heavier. Using a two-pan balance no more than twice, how can you identify the heavy coin?

Short answer

Split into three groups of three. Weigh group 1 against group 2: the heavier side holds the coin, or group 3 does if they balance. Then weigh two coins from the suspect group against each other: the heavier one is the coin, or the third if they balance. Each weighing has three outcomes, so it cuts the candidates by a factor of 33.

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