posted by Sarah on .
The census taker says, "I need to know the ages of your children."
The mother replies, "I have no one-year-olds. The product of my
children's ages is 90, and the sum of their ages is the same as my
The census taker replies. "I can see the house number but I still need
The mother says, "You're right. You also need to know that the boy
across the street is older than my oldest child."
The census taker says, "Thank you, I now know the ages of your
What are the ages of the children?
What is the house number?
What is the age of the boy across the street?
I made a list of factors, but don't know where to go from there. Thank you for your help!
Can you post the list of factors that you have made?
I feel like I'm missing information, but here's the best I can do.
Product of ages = 90
Prime factors of 90: 2,3,3,5
So the possible number and age of children are:
Since the mother said "...older than my oldest child.", there must be three or more children, or even three different ages. That leaves us with:
Some cities do not put 13 as a house number, so we eliminate the first case, to leave us with:
If we eliminate ages that are too close, one year apart (but logically & physically feasible), that leaves us only with 2,5,9 (sum=16).
Also, the boy across the street can be one or more years older than the oldest child.
If you have other hints/conclusions, please post.