Relay-Version: version B 2.10 5/3/83; site utzoo.UUCP Posting-Version: version B 2.10.2 9/12/84; site nbs-amrf.UUCP Path: utzoo!linus!philabs!cmcl2!seismo!lll-crg!gymble!umcp-cs!nbs-amrf!hopp From: hopp@nbs-amrf.UUCP (Ted Hopp) Newsgroups: net.puzzle,net.math Subject: Re: Polar Bear Problem Sequel **SPOILER** Message-ID: <41@nbs-amrf.UUCP> Date: Mon, 28-Oct-85 20:17:48 EST Article-I.D.: nbs-amrf.41 Posted: Mon Oct 28 20:17:48 1985 Date-Received: Fri, 1-Nov-85 00:45:46 EST References: <361@proper.UUCP> <606@ecsvax.UUCP> Distribution: net Organization: National Bureau of Standards Lines: 19 Xref: linus net.puzzle:1026 net.math:2083 > > The old Polar Bear Problem: > > 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. > > There is an infinite number of them, all close to the S pole. Take any > circle around the S pole which has a circumfrence (1 mile)/n for n=1,2,... > and draw another concentric circle 1 mile further away (N) from the pole. > Then any point on this latter circle fits the description. Partial credit. You forgot one other point: the N pole. -- Ted Hopp {seismo,umcp-cs}!nbs-amrf!hopp