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More hats! (Posted on 2002-07-15) Difficulty: 2 of 5
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?

    (Taken from

  •   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.

    Comments: ( You must be logged in to post comments.)
      Subject Author Date
    SolutionSolutionDej Mar2008-01-11 10:45:11
    partial answerK Sengupta2008-01-10 11:23:14
    answerPraneeth2007-09-14 06:31:12
    SolutionSolutionKevin2006-04-13 19:28:03
    SolutionMy answerfractaloon2005-09-27 13:34:24
    Good one!Linda Malone2003-12-17 20:27:04
    SolutionsolutionTalon50002003-07-31 11:00:56
    Solutionsimplezineera2003-05-26 14:21:14
    EASY!!zineera2003-05-26 14:20:51
    SolutionSolutionHenry2002-07-15 09:09:07
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