Finding the page number of the last page of a document, from within
the document, is somewhat tricky. The
zref-lastpage packages define a label
LastPage whose number is right (after sufficiently many
passes through LaTeX, of course). The
memoir class also
defines a “last page” label.
The documentation of the
fancyhdr package spells out exactly
how one might actually use this information to produce page numbering
as suggested in the question.