Sum Sam and Product Pete are in class when their teacher gives Sam the Sum of two numbers..........What are the numbers?

Question

Sum Sam and Product Pete are in class when their teacher gives Sam the Sum of two numbers and Pete the product of the same two numbers (these numbers are greater than or equal to 2). They must figure out the two numbers.

Sam: I don't know what the numbers are Pete.
Pete: I knew you didn't know the numbers... But neither do I.
Sam: In that case, I do know the numbers.

What are the numbers?

Answer 1

For Sam to not know the numbers there must be multiple ways to get that sum. And for Pete to know that Sam didn't know the answer and not to know the answer himself the product of the 2 numbers must have multiple solutions.

Both of this happens if we take the numbers as 3 & 4.
Sum = 7
Possibilities => (2 + 5), (3 + 4).
Product = 12
Possibilities ========>(2 * 6), (3 * 4)
Corresponding sums.........II..........II
............................................8..........7.

Now Sam can eliminate (2 + 5) option because the corresponding product 10 has only this possibility so Pete would have known the answer in that case.

So he can declare the numbers as 3 and 4.

Answer 2

both are given number 4 which is product of 2 and 2 and sum of 2 and 2

Comments

If that's the case then Sam would have known the answer. He would not have needed Pete's help. Neither would Pete need Sam's help. Both can answer simultaneously.