Updated: Mar 6
One day I run into two of my friends from university, Rosalind and Max. We immediately started to talk about science and math as we used to do in the past. I told them "Let's play a game together." They were both excited. I wrote the sum of two integer numbers on a piece of paper and handed out the paper to Rosalind. I made sure that Max did not see it. And, on a separate paper, I wrote the product of these two numbers and gave this paper to Max, making sure that Rosalind did not see it. I stated that the two numbers that I initially picked are both positive integers. Then, here is how the conversation continued ...
"Rosalind, you know the sum of these two numbers and Max, you know the product of these two numbers." I said.
Rosalind: "I can not tell what these two numbers are by just knowing their sum."
Max: "I can't tell what these two numbers are by just knowing their product either."
Rosalind: "I know which numbers you picked." Then, she told me the numbers.
WHAT ARE THESE TWO NUMBERS? Write your answer under comments below.