Hi John. The problem does assume 2 things: Honesty and basic intelligence. That being said, Larry cannot answer for he does not have enough information to make a reasoned answer. Travis, on the other hand, can rightfully assume that Larry's silence can only mean that Larry not have enough information to make a reasoned answer, ie he looking at one black and one white hat. Using that given basic intelligence, Travis is able to ascertain with 100% certainty what is on his head. I'm actually just rearranging Mark's answer.