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> How, exactly, did they compute the number of possible combinations,
> and what did the number turn out to be? You keep assuring me it was
> "gazillions," which I don't find very clear. I'm actually more
> interested in how it was computed than what it turned out to be.

This Google search will bring up a number of pages that have references to
Appel's papers:

http://www.google.com/search?hl=en&lr=&safe=off&q=Appel+Haken+%22Every+planar+map+is+four+colorable%22&btnG=Google+Search

Regards,
   Rick Parker