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?
(In reply to
re: Solution? by Ady TZIDON)
AFAIK, and supposing that the logician must speak in order A,B,C to say if they know their number:
If numbers has the pattern:
(n, n, 2n): there are two hats with the same number and one hat with the douuble of the number, the logician who is wearing that hat will always know his number.
(n, 2n ,3n) the hats are numbered in arithmetic progression, the logician wearing the 3n hat will be also able to know his number, in first or in second round of speeches.
Otherwise I don't see how they will know.

Posted by armando
on 20160728 04:22:30 