Three families make a remarkable discovery. The sum of the ages of their members are all the same, the sum of the squares of the ages of their members are all the same, and the sum of the cubes of the ages of their members are all the same. Everyone in all 3 families has a different age, and nobody is more than 100 years old.
What is the smallest possible sum of their ages? Can this be done with 4 families?
May I assume:
1) A family is comprised of only parents and their children.
2) A family includes two parents and at least one child.
3) Parents are age 14 or over (in parts of the US, for example, under exceptions, 14 is a legal age for marriage).
4) All children are younger than their parents.
5) The phrase here: Everyone in all 3 families has "a different age"
means "a different age than any member of any family"
6) That families have a reasonable number of children, say, less than 7.
?
Thank you.
Edited on April 17, 2019, 8:48 am
clarifications asked
