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From: wpt@princeton.UUCP (William Thurston)
Newsgroups: sci.math
Subject: Re: angels and devils
Message-ID: <2108@princeton.UUCP>
Date: Tue, 21-Oct-86 09:30:25 EDT
Article-I.D.: princeto.2108
Posted: Tue Oct 21 09:30:25 1986
Date-Received: Wed, 22-Oct-86 04:28:24 EDT
Distribution: net
Organization: CS Department, Princeton University
Lines: 30
Keywords: game

Since there hasn't been much response yet to the angels and devils question
I posted a few days ago, I'll add a little more.  The original question
is probably very difficult:

	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?

``Fools rush in where angels fear to tread''

There is a variation of the angel, called a fool, who, at the advice of the
hobgoblin of small minds, only travels forward through the stars:
the fool only travels in directions between north-east and north-west.
[Any resemblance to well-known people alive or dead is purely accidental.]

Find a strategy for the devil to trap the fool.  Hint: for maximum jump-size

                                   4*100*100
100, the devil needs no more than 2            rounds to trap the fool.

	Bill Thurston    ...!princeton!wpt
	Mathematics Department
	Princeton University
	Princeton NJ 08544