The Impossible Puzzle

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!


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