Jezebel is at lease several orders of magnitude better qualified to
answer but I will give it a stab.

When he says that there is no easy way...I would say if there is a way
it would likely be incredibly complex.

There are several factors.  First what you call a page (on your machine
or as the output of your printer) is likely different if I opened your
document on my machine or printed it with my printer.  A Word document
only becomes organized as pages at the output of the printerdriver
(which also drives the screen display). Different drivers = different
pages.

Secondly, creating different header text based on the content of a page
(whether that be some text or some count) is complex in itself.  See:

http://gregmaxey.mvps.org/Conditional_Headers_Footers.htm for an
example.

So if you abandon the header idea then it is back to somewhere on the
page.  Well that will add complexity as you will then have to figure
out how to exclude the text of the count itself.

There is a relatively simple way but it requires that you divide each
page of your document into a section (i.e., at the end of each page
insert a section break).  Then you could use the following:

Sub ScratchMacro()
Dim oDoc As Document
Dim oSec As Section
Dim oRng As Range
Set oDoc = ActiveDocument
For Each oSec In oDoc.Sections
  With oSec.Headers(wdHeaderFooterPrimary)
    .LinkToPrevious = False
    Set oRng = .Range
    With oRng
      .ParagraphFormat.Alignment = wdAlignParagraphRight
      .Text = oSec.Range.ComputeStatistics(wdStatisticWords)
    End With
 End With
Next
End Sub