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.)
There are many solutions to this problem. One of these is:
(1, 3, 6, 7, 12, 14, 15, 19, 20)