ccc@bu-cs.UUCP (02/10/86)
> Three men are in a room. The room has no mirrors and the three men >are in a straight line such that the person in the back of the line >can see the two people in front of him, the middle person can see >only the person in front of him, and the person in front can't see >anyone. Another person walks in with a bag containing 3 black hats >and two red hats. The man pulls three hats at random out of the bag >and places them randomly on the three men. He walks out of the room. >The man in the back says,"I don't know what color hat I'm wearing." >The man in the middle says,"I don't know what color hat I'm wearing, either." >Now tell me what color hat the man in the front of the line is wearing >and why. There are four cases for the permutations of hats among the man in the front (F) and the man in the middle (M): 1) F - red, M - red; 2) F - red, M - black; 3) F - black, M - black 4) F - black, M - red. 1) If both were wearing red, then the Man in the Back would know he was wearing a black hat. No good. 2) M now knows that he and F share at most one red hat between them; if F has it, then he knows he has black; but he doesn't know. This leaves cases 3 or 4 in which F must be wearing a black hat. -- Cameron C. Carson Distributed Systems Group Boston University ACC UUCP: ...!harvard!bu-cs!ccc ARPA: ccc%bu-cs@csnet-relay.arpa