The Hardest One That I Have!

Question: Three cryptographers are sitting down to dinner at their favorite three-star restaurant. Their waiter informs them that arrangements have been made with the maitre d'hotel for the bill to be paid anonymously. One of the cryptographers might be paying for the dinner, or it might have been NSA (U.S. National Security Agency). The three cryptographers respect each other's right to make an anonymous payment, but they wonder if NSA is paying. They resolve their uncertainty fairly by carrying out the following protocol:

Answer: Each cryptographer flips an unbiased coin behind his menu, between him and the cryptographer on his right, so that only the two of them can see the outcome. Each cryptographer then states aloud whether the two coins he can see--the one he flipped and the one his left-hand neighbor flipped--fell on the same side or on different sides. If one of the
cryptographers is the payer, he states the opposite of what he sees. An odd number of differences uttered at the table indicates that a cryptographer is paying; an even number indicates that NSA is paying (assuming that the dinner was paid for only once). Yet if a cryptographer is paying, neither of the other two learns anything from the utterances about which cryptographer it is.

A situation one...

Question: There's a man in a corner who is afraid to go home because there are two masked men waiting for them there.  Who are the masked men (CLUE: there isn't ANY crime involved!)

Answer: The two masked men are the umpire and the catcher at a baseball game!  The person in the corner is on third base and he's afraid to come 'home'!

The Wise Man

Question: There is a city in the setting of around 500 BC that has a problem: their crime rate is very high.   One day, a wise man came in to the city and upon hearing about the problem, asked to speak to the ruler of the city.  He told the ruler of the city that he should pass out these magic sticks that he had with him, one to every person.  The wise man claimed that the sticks were magic; if someone stole something, the sticks would grow two inches that night.  Desperately, the ruler decided to give it a try.  The next day, something had been stolen, so everyone gathered at the temple (or whatever) and compared the length of their sticks to see who stole.  The wise man pointed out a man and said that he was the robber.  Nobody else suspected that he had done it; his stick wasn't longer than anyone else's.  How did the wise man know that he did it?

Answer: The sticks weren't really magic; the night the robbery took place, the robber cut off two inches of his stick so that his would be the same length as everyone else's, but his was really two inches shorter than everyone else's

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