Ok, do not attempt this one unless you have a few days time to kill. This riddle took me over 3 days to solve. But you can solve it in pieces.
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?