X and Y are two whole numbers greater than 1, and Y > X. Their sum is not greater than 100. 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.
In the following conversation, both participants are always telling the truth:
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?
