PUZZLE #1: TWO MAGICIANS ON A BUS


Two magicians are riding on a bus. To while away the time, they engage in the following short conversation:

Magician 1: "The sum of the ages of my children is the number on the front of this bus, and the product of their ages is twice my age."

Magician 2: "Well, that's not very informative. Aside from the number on the front of this bus, I know practically nothing. If you were to tell me your age and the number of children you have, could I then work out their ages?"

Magician 1: "No, you couldn't."

Magician 2: "Maybe not, but at least I now know your age."

The problem is to determine the number on the front of the bus. (solution)