Three logicians, A, B, and C were each wearing a hat displaying a positive integer,  the number visible only to the participants not wearing the corresponding hat.
They were told the number on one of the hats is the sum of the other two.
After a statement by A that he does not know his number, B declared that he is wearing a hat with number 15  and indeed he was right.
a. What were the other 2 numbers and what reasoning was applied?
b. What triplets of numbers make such discovery possible?
The other numbers were 5 in C and 10 in A.
Logician B is seeing those numbers, so he knows that his own number is a 5 or a 15. But in the first case logician A would have inmediately guess her own number (seeing 5, 5).
This is going to happen always if two hats have the same number.
Edited on July 27, 2016, 2:40 pm

Posted by armando
on 20160727 14:37:43 