Relay-Version: version B 2.10 5/3/83; site utzoo.UUCP Path: utzoo!watmath!clyde!caip!rutgers!ll-xn!mit-eddie!genrad!decvax!dartvax!kevins From: kevins@dartvax.UUCP (Kevin M. Schofield) Newsgroups: sci.math Subject: Re: angels and devils Message-ID: <5283@dartvax.UUCP> Date: Tue, 21-Oct-86 12:47:26 EDT Article-I.D.: dartvax.5283 Posted: Tue Oct 21 12:47:26 1986 Date-Received: Wed, 22-Oct-86 05:53:01 EDT References: <2056@princeton.UUCP> Reply-To: kevins@dartvax.UUCP (Kevin M. Schofield) Distribution: net Organization: Dartmouth College, Hanover, NH Lines: 48 Keywords: game In article <2056@princeton.UUCP> wpt@princeton.UUCP writes: >Imagine a universe consisting of planets arrayed at the grid points >of an infinite plane. On one of the planets, an angel is sitting. >Every day, the angel can fly off to another planet, but the angel's >range is limited to a distance of (say) 100. > >Unfortunately, there is a devil in the universe. Every day, the devil >can destroy a planet, anywhere in the universe. > >Can the angel forever avoid being trapped? After spending some time pondering this wonderful question, I concluded that the angel can indeed forever avoid being trapped. There are 2 ways that the angel could be trapped: 1. by walking into a "trap", i.e. a region completely enclosed except for 1 opening which the devil could remove in 1 turn. 2. by being completely enclosed by a wall on all four sides. Assuming the angel is intelligent, it will not "walk" on its own volition into a trap. Also, it is impossible for the devil to "force" the angel to move in any particular direction; thus we can forget about traps. Now still assuming the angel is intelligent, when it sees that a box is being constructed around it, it heads at full speed towards the perimiter of the box and then moves around it, it is not too difficult to prove that the angel can get to the perimiter and find an opening before the devil can complete the box. What seems like a much more interesting question is when the angel is limited to moves to adjacent grid points. I'm still working on this one, and any comments or suggestions would be appreciated... -Kevin -- ------------------------------------------------------------------------------- "There may be no heaven, but somewhere there is a San Francisco." Kevin M. Schofield '88 email: {decvax,ihnp4} !dartvax!kevins kevins@dartmouth.EDU U.S. Mail: College: H.B. 2908, Dartmouth College, Hanover, NH 03755 Real World: 1851 Vallejo Street, St.Helena, CA 94574 --------------------------------------------------------------------------------