Census Puzzle Solution

The Puzzle:

A census taker approaches a house and asks the woman who answers the door "How many children do you have, and what are their ages?"

The woman replies "I have three children, the product of their ages is 36, the sum of their ages is equal to the address of the house next door."

The census taker walks next door, comes back and says "I need more information."

The woman replies "I have to go, my oldest child is sleeping upstairs."

Census taker then says "Thank you, I now have everything I need."

The Solution:

The reason the census taker could not figure out the children's ages is because, even with knowing the number on the house next door, there were still two possibilities.

The only way that the product could be 36 and still leave two possibilities is when the sum equals 13. These possibilities being 9, 2 and 2 and 6, 6 and 1.

When the home owner stated that her "oldest" child is sleeping she was giving ths census taker the fact that there is an "oldest".

So the children's ages are 9, 2 and 2.