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 Four Perfect Logicians (Posted on 2002-09-24)
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)

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 A different approach | Comment 2 of 28 |
Bert knows that Alonso has had at least one apple. If he had only one, he would know that he did not have more than Alonso, so he must have had at least 2.

Similarly, George Knows that Bert had at least two, so he must have had at least three.

On Kurt's turn, the previous questions account for at least six plus whatever Kurt ate. Since any apples unaccounted for could have been eaten by any of the first three, if Kurt knows, there were no unaccounted for apples, so Kurt ate 5, Alonso ate 1, Bert ate 2 and George ate 3.
 Posted by TomM on 2002-09-24 19:08:30

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