by biblioman » Fri Aug 15, 2014 5:17 pm
A doesn't know whether he has a black hat or a red hat, and he can't see those of the other two.
B can see A's hat, but he doesn't know which hat he wears. As knowing the color of one hat is insufficient to conclude a hat color, he can't say anything.
C can see both of their hats, and knows the distribution of the colors. Since he knows what hat he's wearing, the only conclusion to draw is that A and B are wearing hats that led him to figure out the color of his own.
If A and B were wearing red hats, C would not know whether he was wearing a red hat (from 1 left over) or a black hat (from 2 left over).
If A and B were wearing 1 red and 1 black hat, C would not know whether he was wearing a red hat or a black hat, using similarly logic.
If A and B were wearing black hats, C's only option is that he is wearing one of the 3 red hats instead of any of the black ones.
So, A is wearing a black hat, B is wearing a black hat, C is wearing a red hat.