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From: td@alice.UucP (Tom Duff)
Newsgroups: sci.math
Subject: Re: angels and devils
Message-ID: <6200@alice.uUCp>
Date: Thu, 23-Oct-86 13:02:18 EDT
Article-I.D.: alice.6200
Posted: Thu Oct 23 13:02:18 1986
Date-Received: Fri, 24-Oct-86 00:39:55 EDT
References: <2056@princeton.UUCP>, <1596@ncoast.UUCP>
Organization: Bell Labs, Murray Hill
Lines: 20
Keywords: game

>Of course the angel can always avoid being trapped... it is sort of like
>that game where you chase each other around a computer screen trying to
>cut each other off... (see also, Tron motorcycle races (?))... perhaps a
>(an) intuitive stategy would be to just continue moving away from the center
>of mass (nonmass) of the destroyed planets... what can a devil possibly do?

No such simple strategy can possibly solve this problem.  The devil has
too much mobility.  This particular strategy is easy to break:
The devil can maintain a configuration that's as close as possible
to symmetric about the angel's starting point.  On those moves where the devil
is forced to off-balance the configuration, he can force the angel following
this strategy to go any direction he wants -- in particular, he can keep him
running around in small circles around the origin forever.  Eventually, the
devil will fill in a donut too wide for the angel to jump.

The angel must come up with much more subtle strategy than this to win.
If you think this problem is easy enough to rattle of a solution while
following up netnews without thinking about it for a week or so, you're
foolishly mistaken.  If JH Conway doesn't know the answer, years after
publishing the question, then it is surely an extremely difficult problem.