AustMS Gazette Puzzle Corner 30

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

"Rolling roadblocks 

There are 10 cars on an infinitely long, single-lane, one-way road, all travelling at
different speeds.  When any car catches up to a slower car, it slows down and stays just
behind the slower car without overtaking.  Eventually, the cars form a number of
separate blocks.  On average, how many blocks do you expect to see?" 

You can find the Puzzle Corner, as well as the entire Gazette online at:
http://www.austms.org.au/Gazette+Volume+39+Number+5+November+2012 

Check it out when you feel like trying out random fun problems, and be sure to send your
solutions in.  A $50 book voucher is up for grabs for the best submission.  

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 28 February 2013.  The solutions will appear in the May
2013 issue of the Gazette.  

Thank you 

Ivan Guo