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(3): Possible solution (spoiler)
After playing with triplets composed of small different integers it is possible to reach the conclusion that (1,2,3) , (2,2,4), (1,4,5) do not provide a solution, but (1,3,4) does.
Obiously so does (m.3m.4m) - for any positive integer m.
If 6m=144 than (18,54,72) is my candidate solution and following the reasoning of three logical guys/dolls/persons we establish the soundness of their thinking.
Edited on May 16, 2009, 12:06 pm