Ignat gives two tutors a problem. He’s thinking of two different positive integers greater than \(1\), whose sum is at most \(100\). Ignat tells Pier (\(P\)) the product of the two numbers, and Sasha (\(S\)) the sum of the two numbers. Both Pier and Sasha know all of this, and then have a little conversation:
Sasha says that Pier doesn’t know the two numbers.
Pier says that he knows the two numbers.
Finally Sasha says that he knows the two numbers.
What are the two numbers?