Philosophy Critical Thinking- Three Prisoners?

If man C could see two black hats, he would know that he was wearing a white hat. Since he doesn't say anything, man B knows that man C sees at least one white hat, but possibly two white hats. If man B could see that man A is wearing a black hat, then he would know that he's wearing a white hat, hence man C's silence. Since man B doesn't say anything, man A correctly concludes that man B is looking at a white hat on man A's head.