Relay-Version: version B 2.10 5/3/83; site utzoo.UUCP Posting-Version: version B 2.10.1 6/24/83; site mmintl.UUCP Path: utzoo!watmath!clyde!burl!ulysses!unc!mcnc!philabs!pwa-b!mmintl!franka From: franka@mmintl.UUCP (Frank Adams) Newsgroups: net.puzzle,net.math Subject: Re: Polar Bear Problem Sequel (SPOILER) Message-ID: <728@mmintl.UUCP> Date: Thu, 24-Oct-85 13:29:44 EST Article-I.D.: mmintl.728 Posted: Thu Oct 24 13:29:44 1985 Date-Received: Mon, 28-Oct-85 03:23:51 EST References: <361@proper.UUCP> <749@inset.UUCP> Reply-To: franka@mmintl.UUCP (Frank Adams) Distribution: net Organization: Multimate International, E. Hartford, CT Lines: 26 Keywords: easy, easy Xref: watmath net.puzzle:1087 net.math:2434 Summary: In article <749@inset.UUCP> dave@inset.UUCP (Dave Lukes) writes: >In article <361@proper.UUCP> judith@proper.UUCP (judith) writes: >>The old Polar Bear Problem: You go somewhere, set up a tent, walk a mile >>south, walk a mile due west, shoot a bear. Then you drag the bear a mile north >>to your tent & have him for dinner. What color is the bear? >> >>The sequel: (1) From how many points on Earth (assuming it's spherical, etc.) >> can you make exactly these moves, i.e., walk 1 mile south, 1 >> mile west, 1 mile north, and be back where you started? >> >> (2) Describe all of them. >> >I dunno about anyone else, but I though this was junior school >(?? ``3rd. grade'' is what you colonials say, I think) stuff: > >1) a) The North Pole > b) anywhere 1 + 1/(2pi) miles from the south pole >i.e. an arbitrarily large number of places. Actually, this isn't yet a complete list. Change (b) to "anywhere 1 + 1/(2n*pi) miles from the south pole, where n is a positive integer". This isn't exactly right, either; it assumes the Earth is flat in the neighborhood of the South Pole. The exact distances are a little larger. Frank Adams ihpn4!philabs!pwa-b!mmintl!franka Multimate International 52 Oakland Ave North E. Hartford, CT 06108