X and Y are two different whole numbers greater than 1. Their sum is no greater than 100, and Y is greater than X. S and P are two mathematicians (and consequently perfect logicians); S knows the sum X + Y and P knows the product X * Y. Both S and P know all the information in this paragraph.
The following conversation occurs:
S says "P does not know X and Y." P says "Now I know X and Y." S says "Now I also know X and Y." What are X and Y?