Three Hats

Donald Aucamp offered this problem in the Puzzle Corner department of MIT Technology Review in October 2003. Three logicians, A, B, and C, are wearing hats. Each of them knows that a positive integer has been painted on each of the hats, and each of them can see her companions’ integers but not her own. They also know that one of the integers is the sum of the other two. Now they engage in a contest to see which can be the first to determine her own number. A goes first, then B, then C, and so on in a circle until someone correctly names her number. In the first round, all three of them pass, but in the second round A correctly announces that her number is 50. How did she know this, and what were the other numbers?

Click for Answer