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 Nine kids (Posted on 2004-09-09)
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.)

 Submitted by e.g. Rating: 4.1250 (8 votes) Solution: (Hide) The basic solution, with all ages between 1 and 20, is 1, 2, 6, 7, 9, 14, 15, 18, 20. Replacing all ages with their difference to 21 also works (20, 19, 15, 14, 12, 7, 6, 3, 1) but is essentially the same solution.If you allow kids to be 0 years old (babies?) then there are many more solutions, as Penny showed.

 Subject Author Date Problem Solution K Sengupta 2007-04-20 15:21:27 No Subject nathan 2004-09-23 04:27:22 re: No Subject nathan 2004-09-15 04:17:51 No Subject nathan 2004-09-15 04:04:05 re(2): Nine Kids nathan 2004-09-14 11:19:13 No Subject nathan 2004-09-14 11:17:55 re: Nine Kids Juggler 2004-09-14 11:17:11 Nine Kids nathan 2004-09-14 11:10:01 Many different solutions Penny 2004-09-09 10:22:04 re: Brute force solutions (spoilers) Oskar 2004-09-09 10:14:51 Duplicate ages? Oskar 2004-09-09 10:13:35 re: maybe e.g. 2004-09-09 09:10:58 re(3): Solution...With a twist of Syzygy Juggler 2004-09-09 09:03:22 Brute force solutions (spoilers) Charlie 2004-09-09 09:01:05 maybe Martin 2004-09-09 08:46:40 re(2): Solution...With a twist of Syzygy e.g. 2004-09-09 08:43:46 re: Solution...With a twist of Syzygy Juggler 2004-09-09 08:25:22 re: (Not a) Solution Federico Kereki 2004-09-09 08:14:10 re: Valid Solution ? - I don't think so ! Federico Kereki 2004-09-09 08:13:19 re: Valid Solution ? - I think so ! Juggler 2004-09-09 08:10:17 Solution Juggler 2004-09-09 08:07:47 Valid Solution ? - I think so ! Syzygy 2004-09-09 07:53:06

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