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?

Twenty-four hours later, I am still humming the tune for Jeopardy. Hmmm-hmm-hmm-hmm . . .

Working on it.

Posted by Leming on 2007-03-14 07:25:20