Two perfect logicians, S and P, are told that integers x and y have been chosen such that 1 < x < y and x+y < 100. S is given the value x+y and P is given the value xy. They then have the following conversation.

P: I cannot determine the two numbers.Given that the above statements are true, what are the two numbers? (computer assistance is allowed.)

S: I knew that.

P: Now I can determine them.

S: So can I.

Moderator edit:Apporved Challenge question.