Three logical people, A, B, and C, are wearing hats with positive integers painted on them. Each person sees the other two numbers, but not her own, and each person knows that the numbers are positive integers and that one of them is the sum of the other two.

They take turns (A, then B, then C, then A, etc.) in a contest to see who can be the first to determine her number.

During round one, A, B, and C pass. In round two, A and B again pass, at which point C states that she now knows all three numbers and that their sum is 144.

How did C figure this out?

(In reply to re(5): Possible solution (spoiler) by pcbouhid)

Finding out the sum is finding his own number. For his number, there

are two possibilities from which he eliminated one of the possibilities 

using other's conclusions. This is a special case, only where C can 

find the solution on his 2nd turn.

Posted by Praneeth on 2009-05-04 11:11:15