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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: equivalent | Comment 4 of 28 |
    (In reply to equivalent by Cheradenine)

    Not exactly. Unless you would also say that (5*2)+(5*3)=10+15=25 and 5(2+3)=5*5=25 are saying the same thing just because you know that there is a distributive propery for multiplication over addition.

    Nick determined both maximum and minimum amounts for the first three people. This gave him a limited number of possibilities going into Kurt's turn, only one of which allowed Kurt to be sure. The final element was the eliminaton of the other possibilities.

    In my case, I eliminated (accounted for) apples, and then noted that any left over after Kurt's were accounted for would not be able to be accounted for.

    The answer was the same (of course) and even most of the arithmetic, but the thought process was completely different
      Posted by TomM on 2002-09-25 05:13:34

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