A Logic Problem

A Census-taker stopped at a lady's house and wanted to find out how many children she had. The lady, a math teacher, wanted to see if the Census-taker still knew his math.

Census-taker to lady: How many children do you have?
Lady: Three.
Census-taker: How old are they?
Lady: the product of their ages is 36.
Census-taker: Well, that's just not enough information.
Lady: The sum of their ages is our house number.
Census-taker looks at the house number thinking this would give it away, but says: Still not enough information!.
Lady: My oldest child plays the piano.
Census-taker: AHA! I know now. Thank you!

Questions to Contemplate

1. Can you solve the problem?
2. What knowledge does a computer need to solve the problem?
3. How could this knowledge be represented for the computer?
4. How could the computer find the solution?