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Finding the page number of the last page of a document, from within the document, is somewhat tricky. The lastpage and 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.