A puzzle by Princeton mathematician John Horton Conway:

Last night I sat behind two wizards on a bus, and overheard the following:

A: I have a positive integral number of children, whose ages are positive integers, the sum of which is the number of this bus, while the product is my own age.
B: How interesting! Perhaps if you told me your age and the number of your children, I could work out their individual ages?
A: No.
B: Aha! AT LAST I know how old you are!

Rem: Taking in account the fatherhood limitations, this is uniquely solvable.

I am curious as to what are the fatherhood limitations of wizards? There are various stories of wizards ages in years exceeding a thousand. There is implication in Scripture (though, in that source it may be simply to express some import of the patriarch) that children can be born at a father's age exceeding 100. In modern day, Charlie Chaplin fathered a child at the age of 73, which is evidence to an age that must be acceptable minimum upper limit for humans. Biologically, for humans (and assuming wizards belong to that set), the lower limit can be at least 8. As only one parent is mentioned, the number of children can be great. The King of Siam is given as having 82 children. A several-century old wizard, assuming he had a similar procreative life, could father many, many more.

Posted by Dej Mar on 2015-10-31 00:45:00