AustMS Gazette Puzzle Corner 23

The Australian Mathematical Society Gazette’s Puzzle Corner is a regular column with
entertaining mathematical puzzles, here’s an example: 

"Garden gnomes 

Jack positions nine garden gnomes in such a way that ten distinct straight lines are
formed, each containing three gnomes.  Jill thinks the arrangement is taking up too much
space and moves two gnomes to new locations.  Jack notices that even though the new
configuration is more compact, it still contains ten distinct lines of three.  How is
this possible?" 

You can find the Puzzle Corner, as well as the entire Gazette online at:
http://www.austms.org.au/Gazette+Volume+38+Number+3+July+2011 

Please check it out when you feel like trying out random fun problems, and be sure to
send your solutions to us.  A $50 book voucher is up for grabs for the best submission,
not to mention fame, glory and eternal bragging rights! Entries are judged on the
following criteria, in decreasing order of importance: accuracy, elegance, difficulty,
and the number of correct solutions submitted.  

Please e-mail solutions to ivanguo1986@gmail.com or send paper entries to: Kevin White,
School of Mathematics and Statistics, University of South Australia, Mawson Lakes SA
5095 

The deadline for submission is 1 September 2011.  The solutions will appear in the
November 2011 issue of the Gazette.  

Thank you! 

Ivan Guo