No, (2,2) is wrong. In that case, this would have been the situation:
First mathematician: "Because I got 4 as the product, it's either 1*4 or 2*2, I can't decide. I DON'T KNOW."
First mathematician: "Because I got 4 as the product, it's either 1*4 or 2*2, I can't decide. I DON'T KNOW."
The second child is 2 years old
The product of 2×2 and the sum of 2+2 are the same
But them saying oh I get it fools me. Just because they have no clue then they know immediately because the other one does not know is crazy