Originally Posted by Choux
I guess I should explain! lol
The third genius doesn't know what color hat he has on...that means he is not looking at two white hats, he is looking at either two red hats or a red and white hat.
The second genius knows that the first genius didnt see two white hats, so if he looks and sees the first genius has on a white hat, he will know he has on a red hat. But, he doesn't know what color hat he has on.
So, the first genius figured all of this out, and he knows the first genius saw a red and a white hat, he knows that the second genius didn't see a white hat, or he could have solved the puzzle, so the first genius has on a red hat.