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.)

(In reply to re(2): Solution...With a twist of Syzygy by e.g.)

Ok, How about

0, 1, 3, 4, 4, 15, 17,18, 19.

or

0, 2, 3, 5, 9, 11, 12, 14, 14

or

1, 2, 4, 5, 10, 11, 13, 14, 14

of course the twins can be anywhere in the set.

Posted by Juggler on 2004-09-09 09:03:22