A man had no money but he had a gold chain
which contained 23 links.  His landlord agreed to
accept 1 link per day in payment for rent.  The
man, however, wanted to keep the chain as intact
as possible because he expected to receive a sum
of money with which he would by back what he
had given the landlord.  Of course, opened links
can be used in payment too and "change" can be
made with links already given to the landlord.

What is the smallest number of links which
must be opened in order for the man to be able to
pay his rent for 23 days?