Ade, Binky, and Carl are honest perfect logicians. A hat is placed on each of their heads. Each hat has a whole number larger than zero written on it, which the other two logicians can see but which the wearer cannot. One of these numbers is the sum of the other two (so for example, the three numbers could be 3, 7, 4, or another possibility is 6, 6, 12). All of this is public knowledge.