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From: stevev@tekchips.UUCP (Steve Vegdahl)
Newsgroups: net.puzzle
Subject: Re: Solution to Avoiding the Axe Murderer (Gary Levin)
Message-ID: <576@tekchips.UUCP>
Date: Mon, 20-Feb-84 15:54:22 EST
Article-I.D.: tekchips.576
Posted: Mon Feb 20 15:54:22 1984
Date-Received: Wed, 22-Feb-84 02:31:19 EST
Organization: Tektronix, Beaverton OR
Lines: 23

>   Consider the vector from the AxeWielder to the center of the lake.
>   Paddle in the direction of the vector.  This will get you further from
>   the center; this guarantees that you will eventually reach the shore.
>   It also keeps the center of the lake between you and the AxeWielder;
>   this guarantees safety.

>   Step 2 is a loop with the invariant ``The center is between me and the
>   AxeWielder''.  The termination function is the distance to the shore.
>   Step 1 is initialization.  

I believe that the Gary gives is incorrect, as it makes no use of the
ratio of the speeds of the Axe-man and woman.  His argument would be
equally (in)correct if the Axe-man could paddle 1,000,000,000 times as
fast as the woman could row.  The woman would end up going approximately
in a circle around the middle of the lake.  The invariant will certainly
not hold in this case.

I hacked up a computer simulation that suggests that the woman would indeed
fail to reach the shore using Gary's method.  I still believe that my
previously-posted solution (moving away from the Axe-man 0.25 across the
lake and then bolting) works.

		Steve