Posted by Sarah on Tuesday, September 28, 2010 at 12:28pm.
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:
2,3,3(twins),5
3,5,6
2,5,9
3,3(twins),10
2,3,15
6,15
5,18
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:
2,3,3(twins),5
3,5,6
2,5,9
2,3,15
Some cities do not put 13 as a house number, so we eliminate the first case, to leave us with:
3,5,6 (sum=14)
2,5,9 (sum=16)
2,3,15 (sum=20)
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.