Adacore wrote:A better non-logical answer would be that the guy at the front can see the unused hats the warden is still holding and they're both black. The 'proper' answer is far more elegant, though, obviously.
That doesn't work, because the problem explicitly states that the guy in front "can see no hats", which must include the remaining unused hats.
The only other possible explanation is that the front prisoner, being the ne'er-do-well brother-in-law of the warden, was slipped a note by the warden when everyone was still blindfolded. The warden knew his brother-in-law couldn't logic his way out of a wet paper bag, so he slipped him the note so he would have an excuse to release his wife's brother and therefore get some thank-you nooky from his wife that night. The only worry the warden had is whether his brother-in-law could get that second brain cell to fire and be able to read the note and figure out that it was the answer to be given.
Really, that's the only other possibility I can come up with!
[ Edit: Dang, I just came up with another possibility. ]
Since there is no down-side given to providing a wrong answer, the third prisoner thinks about the fact that there are a total of three white hats and two black hats, reasons that this means that there is a 3/5 (60%) chance of his hat being white (given a random distribution) and decides to go for it. After all, a 60% chance of freedom by guessing based on probabilities is better than a 100% chance of failure by not answering.