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(2): Possible solution (spoiler) by Dej Mar)

I think IŽm not making myself clear. My question still remains: how did C figured out that the sum was 144? Why not 100? or 200?

You all are assuming that if C are looking at 18 and 54, heŽll figure out his number (72) in round two and the sum 144.

What if C is looking at, for example, 16 and 24? Obviously his conclusion for the sum would not have been 144.

What if C is looking at 24 and 36?

etc... etc... etc...

Posted by pcbouhid on 2009-05-03 23:58:19