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 More hats! (Posted on 2002-07-15)
Three logicians, Albert, Bill and Carl, are wearing hats, which they know are either black or white but not all white. Albert and Bill can each see the other two logicians, but not Carl, who is facing away and cannot see them.

Each is asked in turn if they know the color of their own hat. The answers are:

• Albert: "No."
• Bill: "No."
• Carl: "Yes."

What color is Carl's hat and how does he know?

•  Submitted by levik Rating: 3.4615 (13 votes) Solution: (Hide) The hats are not all white. This means that if Albert did not know his hat color, he saw at least one black hat among Bill and Carl. Otherwise he would have known his own hat to be black. Bill must have realised this. He saw Albert's hat color, and also saw Carl's. He knew that Albert's statement meant that either he or Carl (or both) is wearing a black hat. Had he seen Carl in a white hat, he would immediately know his hat to be black. The fact that he did not make this guess let Carl know that his hat color was black.

 Subject Author Date Solution Dej Mar 2008-01-11 10:45:11 partial answer K Sengupta 2008-01-10 11:23:14 answer Praneeth 2007-09-14 06:31:12 Solution Kevin 2006-04-13 19:28:03 My answer fractaloon 2005-09-27 13:34:24 Good one! Linda Malone 2003-12-17 20:27:04 solution Talon5000 2003-07-31 11:00:56 simple zineera 2003-05-26 14:21:14 EASY!! zineera 2003-05-26 14:20:51 Solution Henry 2002-07-15 09:09:07

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