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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)