Lee WNine coins, one of them heavy, and a balance that can only compare.
You have nine coins that look the same, but one is slightly heavier than the rest. With a balance scale, what is the smallest number of weighings that is sure to find the heavy one?
Split them into three piles.
Put three against three. If one side drops, the heavy coin is in it; if they balance, it’s in the three you left off. Then weigh one of those three against another, and either the scale tips or the heavy coin is the one you kept back.
A balance has three outcomes, not two, which is why thirds beat halves. Halving takes three weighings.
Source: Traditional; analysed by C. A. B. Smith, The Counterfeit Coin Problem, 1947