Getting tipsy helps you see through the problem. :) If A was wearing a black cap, then B and C both would see only ONE red hat each. Since all of them would be raising their hands, B then should know that he should have a red hat since C raised his hand. Same with C too. But if A REALLY has a red hat, then B and C would not know the color of their hats just by observing the raised hands. So, then A knows that he must have a red hat since B and C (both) do not know the color of their hats. Hence, A claims that he has a red hat.