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?

Nice question,and quite original.

Prior to posting my solution I've read all the posts and  so have nothing to add.

However - I wonder about  the gender of the persons with the numbered hats:  you call them  "guys" and refer to them as "her own", '" she now knows "...

Please advise.

Posted by Ady TZIDON on 2009-05-04 08:02:02