Can You Solve This Math Riddle About Sum and Product of Two Numbers?

[rkastner]

Just for fun and for community participation, I offer the following riddle. The person who answers first (with complete explanation of how the answer is deduced) wins a free copy of Understanding Our Unseen Reality: Solving Quantum Riddles.

Question: Susie and Paula's teacher gives Susie the sum of two numbers. The teacher gives Paula the product of the same two numbers. Both numbers are greater than or equal to 2. While trying to determine the two numbers, Susie and Paula have the following conversation:

Susie: Paula, I don't know what the numbers are.
Paula: I knew you didn't know, but neither do I.
Susie: In that case, I know the numbers!

What are the numbers?

 

[jackwhirl]

Spoiler

The numbers are 3 and 4.
Susie's sum is 7, which she knows could be the sum of (2 and 5) or (3 and 4), but not which.
Paula's product is 12, which she knows could be the product of (2 and 6) or (3 and 4), but not which.
When Paula admits ignorance, Susie knows the answer because if the numbers were 2 and 5, Paula's product would be 10 with only one solution, 2 and 5.

This is a solution. Is it the only one?

 

[rkastner]

Thanks! That is the intended answer to the riddle (which was not my own invention). But on further reflection, I believe there is at least one counterexample to the premise of the riddle. That is, it seems to me that (without further restriction on the range of numbers), there are pairs of numbers whose sum and product do not permit Susie to infer with certainty what the numbers are based only on Paula's statement. I leave that out there in case anyone wants to check for themselves.
Meanwhile, Jackwhirl, please contact me privately to let me know where you'd like the book to be sent!