Identify the two numbers from the following conversation?

Question

There is a one person who have two numbers, he tells sum to the person A and product of those numbers to B.

Now there is this conversion between A and B.

A: I don't know what are the numbers.

B: I also don't know what are the numbers.

A: Now i know what are the numbers.

B: Now i also know what are the numbers.

Assuming A and B to be very wise and good in mathematics, What are those two numbers?

Answer 1

Numbers are 2 and 2.
A would have got 4, which means 1+3 or 2+2. so that’s why he was not sure of the numbers.
B would have also got 4, possibilities 1*4 and 2*2.

Now, had the numbers be 1 and 3, B would have got 3 and he would have been sure of the numbers, but that was not the case, So A became sure that numbers are 2 and 2.

Now, B knows that numbers cant be 1 and 4, because there are two possibilities of getting the sum as 5, 1+4, 2+3, and in both these cases A cant guess the number depending on B’s earlier answer, as for both product 4 and 6 there are more than 1 possibilities.

Thus B also knows that the numbers are 2 and 2.

Answer 2

A: I don't know what are the numbers.