A friend of mine told me the following puzzle and I could not solve it.
Sam chooses a positive integer $x$, and Peter chooses another number $y$. They do this secretly, so that Peter does not know Sam's number and vice versa.
They then tell Sarah their numbers (secretly again). Sarah writes the sum $x+y$ on one paper and the product $xy$ on another. She then shows them one paper randomly. The value on the paper was $2002$. They know this is either the sum or the product, but they don't know which one!
After this, the following conversation take place:
Sam: I don't know your number.
Peter: I don't know your number either.
Sam: Now I know your number.
Peter: Now I know yours too.
How do I figure out what the two numbers are?
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