This was posted here before (spelling mistake and all, on page 22 if you give up).
Enjoy
There are two unknown whole numbers, x and y, both greater than 1, and less than 100. One mathematician, Mr. Product is given the product of these two numbers, while another mathematician, Mr. Sum is given the sum of these two numbers.
The following conversation takes place:
Mr. Product: I do not know the numbers.
Mr. Sum: I knew you didn’t knew the numbers.
Mr. Product: Now I know the numbers
Mr. Sum: Now I know the numbers, too.
What are the numbers?