Three sheep facing right and three facing left meet on a narrow mountain pass with one empty space between...

Problem

Three sheep facing right and three facing left meet on a narrow
mountain pass with one empty space between them; how can they get past
each other?

       |                                         |
       |----> ----> ---->       <---- <---- <----|
       |                                         |

Okay these are six sheep on a mountain pass (aerial view).  They need
to get past each other so that those facing right (---->) can continue
on their way, likewise those facing left.  The sheep (matches) can jump
over each other and all the moves have to be done within the confined
space (|).  There is only the space of one sheep between the two groups
of sheep.  The sheep can only jump over one sheep maximum and need to
land in a space (they can't stand on each other's backs).  Also since
the pass is so thin the sheep cannot stand alongside one another, ie.

     ---->
     <----

The end result should look as follows:

       |                                         |
       |<---- <---- <----       ----> ----> ---->|
       |                                         |

(Matches are necessary.)  It is a great party trick in that you bet
someone 5 bucks that in three attempts they will not get it, and that
you will show them once how it is done.

-- Lisa D'Oger de Speville <108dol@cosmos.wits.ac.za>

[ Editor: the first paragraph is the editor's summary. ]