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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.)
    re: can't be solved | Comment 19 of 28 |
    (In reply to can't be solved by drew)

    Yes, but we are also told that this was enough information for Kurt to know the answer. That means that Kurt ate enough apples that only one possibility was left.

    In any scenario in which Kurt ate less than 5 apples, either Al or Bert could not ask the question -- they can't ask a question they already know the answer to--, or Kurt would have too many possibilities to be sure. But since he is sure, then he must have eaten 5.
      Posted by TomM on 2002-12-05 06:10:21

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