A logician has a favorite game to play at parties. He shows a set of solidly colored stickers to all his logician friends. Each logician, without looking, puts a random sticker on his/her own back. Each logician can only see the stickers on other people's backs, and no one can look at the unused stickers. The logicians take turns announcing whether they can deduce their own color. The game ends when someone announces he/she can deduce his/her own color.

One time while playing this game, no one had yet ended the game even though everyone had a turn. Should they continue to take second turns, or should they just give up and start a new game? Prove that it is impossible for a game that hasn't ended after everyone's first turn to ever end, or provide a counterexample.

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HERE IS AN EXAMPLE PROBLEM

Three intelligent women were applying for a computer job for which they were equally qualified. The interviewer, who was also pretty smart and liked games of logic (she was a retired math teacher), decided that the job would go to the applicant who could first solve this problem:

The interviewer said: "I will blindfold you and place a mark on each of your foreheads. Each of you will either have a black or a white mark. When I tell you to take your blindfolds off, you are to raise your hand if you see a black mark on the foreheads of either of the other applicants. The first one that correctly tells the color of your own mark will get the job."

All three women raised their hands at the same time. One of them, however, came up with the correct color of her own mark. What color is her mark, and how did she figure it out?

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Posted by Brandon on 2005-04-08 20:01:49