I choose two different integers, both greater than 1, whose sum is less than 100. I whisper this sum to Sam, and whisper their product to Paula. They then have the following conversation:
Paula: I don’t know the numbers.
Sam: I knew you didn’t. I don’t either.
Paula: Ah, now I know them.
Sam: Now I know them too.
What is the LARGER number that I chose?
Credit for this problem goes to Hans Freudenthal in 1969 -- but do not Google it yet or you will have the solution spoiled!