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From: waf0116@ritcv.UUCP (William A. Fuss)
Newsgroups: net.puzzle
Subject: pirate solution (where did you go to school?)
Message-ID: <9001@ritcv.UUCP>
Date: Wed, 6-Nov-85 03:13:40 EST
Article-I.D.: ritcv.9001
Posted: Wed Nov  6 03:13:40 1985
Date-Received: Fri, 8-Nov-85 08:21:52 EST
Reply-To: waf0116@ritcv.UUCP (William A. Fuss)
Organization: Rochester Institute of Technology, Rochester, NY
Lines: 50
Keywords: definition of midpoint


 
>This is known (to me, my friends, teachers, and father) as the
>infamous 'PIRATE PROBLEM'. It goes something like this...
>blah, blah, blah...

>A group of pirates in a ship land on an island (shape is irrelavent;
>landmark the same distance that they each walked from the boat. When they
>reach these new positions, they decide that they will bury the treasure
>on the midpoint of the line segment that their positions now represent.
	^^^^^^^^^^^^^^^^^^^^^^^^^^^^
KEY PHRASE: MIDPOINT OF THE LINE SEGMENT (OF THEIR CURRENT POSITIONS!)

>PROVE (ie formal geometric proof) that regardless of where they land on
>the island, provided that there is no earthquake (causing the landmarks
>to move...), they will bury the treasure in EXACTLY the same place.
>Erik Bailey


>First off, we must note that a rotation by 90 degress takes a vector (p1,p2) to
>(-/+p2, +/-p1).  note that the first is minus-plus, and the second is
>plus-minus.  You take the top or bottom signs depending on whether you turn to
>the left or the right.
> etc...

and (MAGICALLY) the answer is...
>	((+/- y + a +/- (b-y)) / 2, (-/+ x + b -/+ (a-x)) / 2)
>	 =  ((+/- y + a +/- b -/+ y) / 2, (-/+ x + b -/+ a +/- x) / 2)
>
>    ((a +/- b) / 2, (b -/+ a) / 2)
>/Bernie


where i went to school, there was only one midpoint given one
segment.  Of course they will bury the treasure at at the same point if
>bury the treasure
>on the midpoint of the line segment that their positions now represent.
	^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

If you have any questions, look up the definition of MIDPOINT in
any High School Geometry book :-)


dr. billfuss

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