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?

The numbers on Sam's hat is 24, the number on Pete's hat is 10, i.e. the number pair from which sum and product are built is (4,6).

Posted by K Sengupta on 2024-06-17 00:44:52