Daughters' ages Quiz Puzzle

A door-to-door salesman is trying to persuade a woman to buy his product. Eventually she says "I will buy one if you can answer this question. I have three daughters and you have not seen any of them. The product of their ages is 36 and the sum of their ages in the same as my house number. How old are they?"

The salesman immediately goes outside to find out the house number, and returns saying "It is not possible to find their ages from the information you have given me - I need something more."

She replies "You are correct, you do need more information - my eldest daughter plays the piano".

The salesman then tells her the daughters' ages and makes the sale.

What are their ages, and incidentally what is the house number?

We'll give the answer and explanation on Monday.

• Josh

Their ages are 2, 2 and 9. The house number is of course 13.

When the salesman sees that the house number is 13, he finds there are 2 options for the ages that will give a sum of 13 and a product of 36: [2, 2, 9] and [1, 6, 6]. Upon hearing that there is an eldest daughter, it must be the first set, otherwise there would be two eldest daughters.

• Dank Naj

Hi,

I would like the answer to this riddle please and thank you.

• Caitlin Minor