My neighbor has nine kids (all under 21), and their ages are such that you can never pick three kids so that the middle one is the average of the ages of the extreme ones. What are their ages?
(Note that you could also say that you can never find three kids whose ages are in arithmetic progression.)
I don't think duplicate ages should be allowed -- if so, out of solutions like Charlie's, we could produce 18-ages solutions, just duplicating every age.
Duplicate ages?
