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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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 Puzzle Solution Comment 28 of 28 |

Let the respective number of apples eaten by Alonso, Betrand, george and Kurt be p, q, r and s.

By conditions of the problem, min(p) =1. if in this situation, g=q=1, then bertrand would know the answer to Alonso's question. this is a contradiction. Accordingly, min(q) =2.

Assume that r<3. If so, then George would know for sure that he did not eat more apples than Bertrand. Accordingly, min(r) = 3.

Since, by the problem: p+q+r+s = 11, we must have:

s <= 11-(1+2+3) = 5
-> max(s) = 5

If s<=4, then the difference (5-s) would be added to one or more of p, q and r. However, in that situation Kurt would not be able to deduce the precise number of apples eaten by each person.

Since, Kurt know the number of of apples he consumed, the only way he can be certain is for s to equal 5, giving:(p, q, r) = (1,2,3)

Consequently, the respective number of apples consumed by Alonso, bertrand, George and kurt are 1,2,3 and 6.

 Posted by K Sengupta on 2008-12-17 06:07:25

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