Two different integers from 1 to N are chosen. Sam is given the sum and Pat is given the product. Sam and Pat take turns stating whether they can determine the numbers

Sam: I don't know the numbers.
Pat: I don't know the numbers.
Sam: I don't know the numbers.
Pat: I don't know the numbers.
.
.
.
.
Sam and Pat continue like this until one of them realizes that it is impossible for either of them to determine the numbers. What is the smallest possible N for which this can happen?

Could someone please explain Charlie's solution to me? This sounds like a very interesting problem, but I can't for the life of me figure out how it works.

Thanks in advance.

Posted by George on 2007-03-18 11:44:30