Tuesday, July 8, 2008
3 Prisoners and Hats
A king has three prisoners. He decides to give them a chance to earn their freedom. He has a total of three white hats and two black hats. The prisoners know that the king has these five hats total. The next day, the king says he will blindfold all three prisoners and place a colored hat on each of their heads. He will then remove the blindfold from the first prisoner and let him look around at the other two hats. If the prisoner can guess his hat color with 100% certainty, the king will let them all go free. If not, the king will put the blindfold back on the first prisoner and remove the blindfold from the second prisoner. The second prisoner now has a chance to see the other two hats and if he guesses his own hat color with 100% certainty, the king will let them all go free. If not, the king puts the blindfold back on the second person and allows the third person to guess his own hat color (without ever removing the blindfold). When the game is played, the first prisoner does not make a guess. The second prisoner, knowing the first did not guess, does not make a guess. When it gets to the third prisoner, who knows the first two did not guess, he is 100% sure what his hat color is and guesses it correctly, setting all the prisoners free. What is the third prisoner's hat color and how did he know it for sure?
ANSWER:
ReplyDeleteHere are the possibilities:
WWW
WBW
WWB
WBB
BWW
BWB
BBW
Notice there are only 3 situations where the third person could be wearing a black hat. If the split was WBB, then the first person would be able to guess that his was white. If the split was BWB, then the second person (who knows that both he and the third person are not wearing black hats because the first person did not guess) would be able to guess white for himself. Since he did not, it is one of the remaining scenarios, all of which have the last hat as white