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?

These are the possible apple distributions :

8,1,1,1
7,2,1,1
6,2,2,1
6,3,1,1
5,4,1,1
5,3,2,1
5,2,2,2
4,4,2,1
4,3,2,2
4,3,3,1
3,3,3,2

Alonso must have eaten 3 or less apples because otherwise he would know that Bertrand could not have eaten more.
Similarly Bertrand must have eaten 3 or less and George also.
Bertrand could not have eaten 1 apple because he would know that he had not eaten more than Alonso.
Similarly George could not have eaten 1 apple
Alonso + Bertrand + George must eat 9 apples or less so Kurt cannot eat 1 apple

this leaves

5,3,2,1
4,3,2,2
4,3,3,1
3,3,3,2

as he has deduced what everyone ate the only way he could tell this is if the answer is

A = 3
B = 3
G = 3
K = 2

Posted by John on 2002-10-18 01:07:41