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Four Perfect Logicians (Posted on 2002-09-24) Difficulty: 4 of 5
Four perfect logicians, who all knew each other from being members of the Perfect Logician's Club, sat around a table that had a dish with 11 apples in it. The chat was intense, and they ended up eating all of the apples. Everybody had at least one apple, and everyone knew that fact, and each logician knew the number of apples that he ate. They didn't know how many apples each of the other ate, though.

They agreed to ask only questions that they didn't know the answers to.

  • Alonso: Did you eat more apples that I did, Bertrand?
  • Bertrand: I don't know. Did you, George, eat more apples than I did?
  • George: I don't know.
  • Kurt: Aha!!

    Kurt figured out how many apples each person ate. Can you do the same?

  • See The Solution Submitted by Chris Middlemiss    
    Rating: 3.6154 (13 votes)

    Comments: ( Back to comment list | You must be logged in to post comments.)
    Possible solution... but still sketchy | Comment 23 of 28 |

    Bertrand answers "I don't know" because he probably ate more than one, therefore since they all had at least one, his options were: Alonso ate 1, 3, 4, 5, 6, or 7 apples (supposing Kurt and George only ate one, and Bertrand knows he ate two).  He asks George because his options are many.

    George, being a perfect logician and knowing very well why Bertrand doesn't know, realizes that Betrand ate more than one apple.  If Bertrand had eaten only one apple, his answer would've been NO because it would be equal or less than what Alonso ate.  However, George still had many possibilities:

    Alonso 1 Bertrand 2 Kurt 5 (knowing George ate 3)

    Alonso 2 Bertrand 2 Kurt 4

    Alonso 2 Bertrand 3 Kurt 3

    and so on and so forth...

    Kurt, knowing he ate 5 apples, knows exactly what George was thinking.  Therefore, the answer is Alonso ate 1, Bertrand ate 2, George ate 3 and Kurt ate 5.

    I still believe there are many solutions.  If Kurt ate four apples, then anyone could've eaten them.  As complex as the problem seems, it just has many solutions.  The only way for Kurt to know the solution is to know how many apples he ate (which he does) BUT there's no way for us to know the solution without knowing at LEAST how many apples Kurt ate beforehand.  The only way I knew how many apples Kurt ate is by watching the solution...

    If Kurt had eaten one apple, for example, the puzzle wouldn't be so simple.  YES, he knew how many apples he ate, but how in the heck can I?

      Posted by Alexis on 2005-10-30 10:47:35
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