The Smartest Prisoner
There were once three prisoners serving sentences in the same jail. The first prisoner could see out of both eyes, the second was blind in one eye, and the third was completely blind. One day the prison warden brought them out and told them that he would set them free, but on one condition. He brought out five cloths, two white and three black, and stuck one to the back of each of them, without letting them see the ones left over. None of them could see what colour they had on their back, but they were allowed to walk around and see what the others had on theirs. They were not allowed to talk. The king told them that they would be set free if they could guess the colour of the cloth on their back. There would be no penalty for guessing wrong or saying, "I don't know."
The warden then went to the first prisoner, who could see out of both eyes, and asked him whether he knew what colour he had on his back. He looked around at the other prisoners' cloths and said, "I don't know, sir." The warden went to the second prisoner, who was blind in one eye, and asked him the same question. The second prisoner looked around at the others' and said, "I don't know, sir." The warden then turned to the third prisoner, who was completely blind, and said, "I bet you don't know what colour you have." The third prisoner smiled and said, "Actually, sir, I do." What colour did the third prisoner have on his back?
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Since Prisoner #1 said "Don't know", Prisoner #2 and Prisoner #3 could not both have been wearing white, because then Prisoner #1 would have immediately concluded he was wearing black (there are only two white cloths available). This leaves us with Black-Black, Black-White and White-Black as the possible color combinations for Prisoner#2-Prisoner#3. If Prisoner#2 saw that #3 was wearing White he would know he himself was wearing Black because (Black-White) is the only combination that allows Prisoner#3 to be wearing White. But that didn't turn out to be the case and Prisoner#2 said "I don't know". This lets Prisoner#3 conclude that Black-Black or White-Black are the only combos left, and while he doesn't know what #2 is wearing, he knows he is definitely wearing Black.