Cheryls_nan

If you like Cheryl's Birthday, try this

When I saw the now famous Cheryl's Birthday problem, it reminded me of this one.  It's a few years old (the woman might have been Cheryl's grandmother), but has stood the test of time:

 

A travelling salesman rings a doorbell; woman answers.

 

Salesman: Good morning, madam. I'm selling children's books. Do you have any children and what ages are they?

 

Woman: I have three.  The product of their ages is 36.

 

Salesman: I can't work out their ages from that; tell me more.

 

Woman: The sum of their ages equals the number of the house next door.

 

Salesman [who can see whether the houses go up in odds/evens or up one side and down the other, but doesn't know which side next door she means]:  I still can't work out the ages.

 

Woman: The eldest plays the piano.

 

Salesman: Now I can work out their ages.

 

So what are the ages of the three children?