AustMS Gazette Puzzle Corner 31

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

"Picky padlocks 

An ancient scroll is kept in a chest, which is locked by a number of padlocks.  All
padlocks must be unlocked in order to open the chest.  Copies of the keys to the
padlocks are distributed amongst 12 knights, such that any group of 7 or more knights
can open the chest should they choose to do so, but any group of less than 7 cannot.
What is the minimal number of padlocks required to achieve this?" 

You can find the Puzzle Corner 31 online at:
http://www.austms.org.au/Publ/Gazette/2013/Mar13/Puzzle.pdf 

Check it out when you feel like trying out some fun problems, and be sure to email your
solutions to [email protected].  A $50 book voucher is up for grabs for the best
submission.  The deadline for submissions is 1 May 2013.  The solutions will appear in
the July 2013 issue of the Gazette.  

Thank you 

Ivan Guo