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(4): Possible solution (spoiler)
by Dej Mar)
Dej Mar, again: how did C figure out that the sum is 144?
You are conducting your reasoning from the fact that, once the sum is 144, the numbers could only be 18, 54 and 72. I agree with this, with others triplets that sum 144, there´s no other possible solution.
But 144 is the consequence, not the cause!!! C figured out the numbers knowing only that one number is the sum of the two others, and this happened in the second run.
Posted by pcbouhid
on 2009-05-04 10:46:19