Warmup solution, Challenge 2, Spring '05


Most people adopt a strategy of halving the number of suspects with each weighing, and are therefore fooled into thinking that three weighings are required.

To determine the counterfeit in two weighings, put three coins on each tray. If they balance, there are two remaining "suspect" coins, and if they don't balance, the three coins in the tray that had the lesser weight are the only suspects. In any case, you've reduced the number of suspects to at most three. Put one suspect in one tray, one in the other, and if there is a third suspect, leave it off. If one tray is light, it contains the counterfeit; otherwise the counterfeit is the third coin.