AustMS Gazette Puzzle Corner 24

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

"Triangular trip 

Assume the Earth is perfectly spherical and you are standing somewhere on its surface.
You travel exactly 1 kilometre south, then 1 kilometre east, then 1 kilometre north.
Surprisingly, you find yourself back at the starting point.  If you are not at the north
pole, where can you possibly be?" 

You can find the Puzzle Corner, as well as the entire Gazette online at:
http://www.austms.org.au/Gazette+Volume+38+Number+4+September+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 November 2011.  The solutions will appear in the March
2012 issue of the Gazette.  

Thank you! 

Ivan Guo