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From: hes@ecsvax.UUCP (Henry Schaffer)
Newsgroups: net.puzzle,net.math
Subject: Re: Polar Bear Problem Sequel(s) **SPOILER**
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Date: Wed, 23-Oct-85 22:03:54 EDT
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Posted: Wed Oct 23 22:03:54 1985
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> > The old Polar Bear Problem:  You go somewhere, set up a tent, walk a mile
> 
> How about a more difficult sequel like the following:
> 
> 	Where on the earth can one walk 1 mile south, 1 mile west, 1 mile
> 	north, AND 1 mile east, and end up at the starting point?
> 
> If you think you have a solution, there should be more...  It would be nice
> if some mathematically inclined readers could contribute exact and complete
> solutions (to both sequels).

   One set of solutions is a set of small circles close to the North Pole.
They are of a size so that the 1 mile east takes one around the pole n times
(1, 2, ...) and enough extra to end up at the starting point.  (Sorry, I
don't feel like doing the math tonight.)
  Another set of solutions is the circle 1/2 mile north of the equator.
--henry schaffer