I never heard about "Cheryl's Birthday" puzzle until today, but back when I was at the university I heard about a different (and in my opinion, more elegant) ve

I never heard about "Cheryl's Birthday" puzzle until today, but back when I was at the university I heard about a different (and in my opinion, more elegant) version: Instead of day and month the two person involved must guess two natural numbers. One knows only the sum of the two numbers, the other only the product, but the dialog between them is exactly the same. It's been a number of years so I'm not sure about the details; I think the numbers were strictly positive, but I don't know if the first to talk was the one knowing the sum or the one knowing the product.