# A logical problem

I heard this one many years ago. I have rewritten it, to make it harder and to avoid that my dear readers search the Internet for the answer instead of thinking themselves.

A mathematician, Professor Anderson, visited her colleague Dr. Smith. During the visit Anderson asked: “How old are your three kids actually?”

Dr. Smith thought for a moment, and then he answered: “None of them have the same age, the sum of their ages is less than eleven and the product of their ages is a number you know well, namely the street number of my house”.

This made Professor Anderson think, but after a short moment she said: “It can’t be solved, since we are missing…”

Dr. Smith interrupted, almost laughing: “Sure, we are…” and then he gave Professor Anderson an extra piece of information.

Now they *both* knew the exact ages of Dr. Smith’s children.

What is the street number of Dr. Smith’s house?

I think the street number is 12.

That is because there are two possible age combinations where the product of the ages is 12, namely 1, 3, and 4 years, or 1, 2, and 6 years. So, just by knowing the product the person wouldn’t be able to tell their ages but needs another piece of information.