Guess the numbers
Two mathematicians are placed in two rooms and one is given the sum of two
distinct numbers between 2 and 99 (2 and 99 excluded) and the other is given
the product of same two numbers. They both come out of the room and the
following conversation takes place.

Mathematician with product : "I don't know the two numbers".
Mathematician with sum : "I know, you won't know the two numbers".
Mathematician with product : "Now, I know the numbers".
Mathematician with Sum : "Now, I too know the numbers".

What are the numbers and how did they find it out ?

Hi there, I installed YACCS, so you can comment!

Mirror, Mirror...
I found this problem in "No Ordinary Genius" by Christopher Sykes. It's pretty easy. But I do not have an answer!
You look in a mirror, and let's say you part your hair on the right side. You look in the mirror, and your image has its hair parted on the left side, so the image is left-to-right mixed up. But it's not top-to-bottom mixed up, because the top of the head of the image is there at the top, and the feet are down at the bottom. The question is: how does the mirror know to get the left and right mixed up, but not the up and down?