This is a very challenging question. Anyone good at logic and calculation can try it.
X, Y are two natural numbers. 1<X<Y<99. A knows the sum of X+Y, B knows the product of X*Y.A says: I do not know the values of X and Y, and I am sure you do not know either. B says: I did not know the values of X and Y, but now I know.A says: Now I know also.
So what are the values of X and Y?