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?

(I might have missed some logical points here, so I'm not going to claim it's definitely the full solution)

Okay: First person:
Alonso would not ask this is he had eaten 5 or more apples. If he had, it would be impossible for Bertrand to have eaten more than him. So we know Alonso has eaten 1, 2, 3 or 4 apples.

Second person:
Betrand doesn't know. Based on the above, this means he cannot have eaten 1 apple. Also, similar to above, he cannot have eaten more than 4 as he would have obviously eaten more if that was the case. So Bertrand has eaten 2, 3 or 4 apples.

Third statement:
George doesn't know. So, George cannot have eaten 1 or 2. And, again, cannot have eaten more than 4. So, George has eaten 3 or 4 apples.

So, we have:
Alonso - 1, 2, 3 or 4
Bertrand: 2, 3 or 4
George - 3 or 4
Kurt - from the above, obviously no more than 5

Kurt then knows for certain. How is this so? He must have eaten 5 apples. This means Alonso would have had 1, Bertrand 2, and George 3. Any other number for Kurt would leave more than one possibility for distributing the remaining apples.

Is this right? I'm tired and I can't tell any more. :)

Posted by Nick Reed on 2002-09-24 12:32:23