Sam and Pete, two perfectly intelligent logicians, are sitting facing each other, each with a hat on. The number on Pete's hat, they are told, is the sum of two integers larger than 1; the number on Sam's hat is the product of these two integers. The following conversation ensues:

Sam: I don't know the number on my hat.
Pete: I don't know the number on my hat.
Sam: I don't know the number on my hat.
Pete: I don't know the number on my hat.
Sam: I don't know the number on my hat.
Pete: I don't know the number on my hat.
Sam: OK, now I know the number on my hat.
Pete: And I know the number on mine.

What are the numbers on Pete's and Sam's hats?

(In reply to Solution by nikki)

Nice work nikki :) I solved this in exactly same way this morning. This one seemed pretty much easier than the original Logicians, hats, and numbers problem althought I never quite solved it in a satisfying way.

Posted by atheron on 2006-11-08 03:01:51