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Hat #11 (Posted on 2016-07-27) Difficulty: 3 of 5
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?

See The Solution Submitted by Ady TZIDON    
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Solution? | Comment 1 of 3
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 2016-07-27 14:37:43

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