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From: vnend@ukecc.UUCP (D. W. James)
Newsgroups: sci.math
Subject: Re: angels and devils
Message-ID: <742@ukecc.UUCP>
Date: Fri, 7-Nov-86 00:53:15 EST
Article-I.D.: ukecc.742
Posted: Fri Nov  7 00:53:15 1986
Date-Received: Sun, 9-Nov-86 03:35:58 EST
References: <2056@princeton.UUCP> <514@aurora.UUCP> <126@fortune.UUCP> <188@mck-csc.UUCP> <255@BMS-AT.UUCP>
Reply-To: vnend@ukecc.UUCP (So many Davids here we went through numbers and...
Organization: Univ. of KY, Engineering Computing Center
Lines: 27
Summary: The angel gets away, (rats!)

Distribution:net


Keywords:Lets keep it simple....
 


Ok, lets look at the simplest case. As stated we gave the angel a movement
of at most 100 per day, while only letting the devil destroy 1 planet in
the same time frame. Lets 'handicap' the angel. Lets say that now he can only
move 1 planet per day. If we assume that the devil and angel know nothing about each others actions (except we will let the devil know the angels starting
position) then the question boils down to this: at what distance must the
devil begin destroying planets so that the angel will be unable to get around
the devils barrier?
	The formula for the number of planets that the devil must destroy to
successfully trap the angel is simply the equation for the circumference of
a circle. This follows from the principle that the devil wants to destroy the 
minimum number of planets to achieve his task ( to big an assumption? ). If
this is true then we have 2piR planets to be destroyed before the angel
is trapped with a finite number of planets to live on. R is dependant on the 
speed of the angel. Our devil need only pick an R that will enable him to
complete the encirclement of the angel to win. So what is that number? It is
obviously dependant on the speed of the angel. And in fact it is not definable.
The poor devil must destroy 2pi times the distance the angel can travel in
the same interval, and he just can't do it. Give them each total knowledge 
of each others actions and the answer remains the same. The devil can trap
a DUMB angel (random movement or some such garbage, remember the drunkards
walk?) but he can't be guarenteed of trapping the angel unless he has the
ability to destroy 2pi the angels movement. 

-- 
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Later y'all,             Vnend            Ignorance is the Mother of Adventure.
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