A woman, under sixty, told me, that the square of her age equals the sum of the squares of her children's ages.

How old is she , given that the children's ages form an arithmetic series of nine integers?

It seems reasonable to assume that the square of Mum's age is somewhere in the region 1000 to 10000.       
Then the average age of the children is somewhere between 10 and around 30.       
It's doubtful whether the mother would have more than 30 childbearing years.       
Since there are 9 children and their ages are in arithmetic progression, we are looking at sequences like a,a+n, a+2n,... where n={1,2,3}, etc.       
An ideal task for Excel, which quickly produces a=2, n=3, giving Mum the age of 48.

In fact any multiple of 3 will do, but the next one, n=6, makes Mum an aged crone with an infant in arms, which doesn't seem likely.

Posted by broll on 2010-12-04 00:38:53