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?

I just realized that this can be solved by making a table where you place numbers greater than 4 and determine which numbers satisfy  x+y=4,5,6... and what their product is. From this table you can eliminate most of the possibilities and with little time one could show that rest of them don't work. Perhaps if I have more time tomorrow I might post a better solution with clearer explanation.

Posted by atheron on 2006-11-07 12:47:47