I A domestic partnership of two consenting adults has three children, Alice, Bob, and Charlie, and the difference between the adults' ages was the same as between Alice and Bob and between Bob and Charlie. The product of Alice and Bob’s ages equaled one parent's age. The product of Bob and Charlie’s ages equaled the other parent's age. The sum of the five ages amounted to ninety years. What was the age of each person?

II A woman has nine children(!), all born at regular intervals, and the sum of the squares of their ages (in years) was equal to the square of her own. What was the age of each child?

III Boadicea died one hundred and twenty-nine years after Cleopatra was born. Their combined life-span was one hundred years. Cleopatra died in 30 B.C.E. When was Boadicea born?

(In reply to re: solution by tomarken)

The sum of squares comes out to be 9x²+72xd+204d², and with x=2 and d=3 this evaluates to 48²=2304, of course. The sum can be written as (3x+12d)²+60d², so we want (3x+12d)²+60d²=y². At this point, I think Charlie needs to write a program!

Posted by Richard on 2006-03-24 13:53:10