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Path: utzoo!watmath!clyde!burl!ulysses!mhuxl!ihnp4!ihuxe!rainbow
From: rainbow@ihuxe.UUCP
Newsgroups: net.puzzle
Subject: starting places for bear hunt
Message-ID: <807@ihuxe.UUCP>
Date: Tue, 21-Aug-84 12:36:53 EDT
Article-I.D.: ihuxe.807
Posted: Tue Aug 21 12:36:53 1984
Date-Received: Wed, 22-Aug-84 01:40:29 EDT
Sender: rainbow@ihuxe.UUCP
Organization: AT&T Bell Labs, Naperville, IL
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> How many places can one walk X miles south, then X miles west, and return
> to your starting point by walking X miles north.

The obvious place is the north pole. But there are an infinite number of more 
places where this can be done. Consider the ring near the south pole where
the circumference of the earth is X miles. In other words walking in a west-
word direction will take you completely around once(the solution can be 
expanded to include rings which make any number of exact loops in X miles).
Now consider the infinite points which are X miles north of the ring in
consideration. Start your journey here.