A vacuum salesman rings on the door of a woman, trying to sell her a vacuum. The woman declines the continous offers and gets annoyed by the persistent salesman. She eventually offers to buy a vacuum from him if he can name the ages of her three daughters based on the following information:
The product of the ages of my daughters is 36 and their sum is our house number.
The salesman takes a walk around the block, of course seeing the house number. He eventually ends up back at the woman's doorstep, complaining that there still is a missing piece of information. The woman agrees and tells him:
My youngest daughter plays piano.
He immediately knows the ages of the three daughters, successfully selling the woman a vacuum.
What are the ages of the three daughters?
PS: There are no tricks involved, all necessary information is contained in what the woman says.