Relay-Version: version B 2.10 5/3/83; site utzoo.UUCP Posting-Version: version B 2.10.2 9/18/84; site ritcv.UUCP Path: utzoo!linus!philabs!cmcl2!seismo!rochester!ritcv!waf0116 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 -------------------------------------------- "Smile, the world may never know!" . . \_/