ejb@think.ARPA (Erik Bailey) (10/26/85)
This is known (to me, my friends, teachers, and father) as the
infamous 'PIRATE PROBLEM'. It goes something like this...
A group of pirates in a ship land on an island (shape is irrelavent;
anything will work) with intent to bury their recently aquired booty.
They figure that they will use a method, instead of a map to bury their
treasure. This island is completely barren, except for two odd, distinct
landmarks: Devil's Rock, and the Dark Forest. One man holding some of
the treasure walks in a straight line to Devil's Rock, noting the distance
that he walks. Another man holding the rest of the treasure walks to the
Dark Forest, he also noting the distance that he walks. When each man
reaches his landmark, they each turn 90 degrees and proceed away from their
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.
... That was the easy part. Now the puzzle ...
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.
GOOD LUCK!! (It can be done! [Heh heh heh...])
BTW - A little side note: This problem appeared in chapter * ONE * of my
father's FRESHMAN (high school) geometry book! He finaly solved
it about 6 months ago...
--
Erik Bailey
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Erik Bailey -- 7 Oak Knoll (USENET courtesy of
ihnp4!godot!ejb Arlington, MA 02174 Thinking Machines Corp.
ejb@think.com.arpa (617) 643-0732 Cambridge, MA)
"What is the most enforced law in the world?"
"Murphy's."
** FREEWARE FOREVER **
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_- _- _- _- _- _- _- _- _- _- _- _- _- _- _- _- _- _- _- _- _- _- _- _-chuck@dartvax.UUCP (Chuck Simmons) (10/30/85)
> A group of pirates in a ship land on an island (shape is irrelavent; > anything will work) with intent to bury their recently aquired booty. > They figure that they will use a method, instead of a map to bury their > treasure. This island is completely barren, except for two odd, distinct > landmarks: Devil's Rock, and the Dark Forest. One man holding some of > the treasure walks in a straight line to Devil's Rock, noting the distance > that he walks. Another man holding the rest of the treasure walks to the > Dark Forest, he also noting the distance that he walks. When each man > reaches his landmark, they each turn 90 degrees and proceed away from their > 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. I love poorly defined puzzles. No matter where the pirates land on the island, there are about 4 places where they may end up burying the treasure. The first pirate can turn either 90 degrees to the left or right as can the second pirate. The shape of the island is not completely irrevelent in the context of the story unless the pirates can walk on water. Would you care to clarify? chuck@dartvax
vsh@pixel.UUCP (vsh) (10/31/85)
> ... When each man > reaches his landmark, they each turn 90 degrees and proceed away from their > landmark ... Does it matter which way each turns (left vs. right, in vs. out, the same vs the opposite)? It must but you do not specify. (Consider two cases that differ only in the direction the pirate at the forest turns; the mid-point of the line segments cannot be the same!) -- Steve Harris | {allegra|ihnp4|cbosgd|ima|genrad|amd|harvard}!\ Pixel Systems Inc. | wjh12!pixel!vsh 300 Wildwood Street | Woburn, MA 01801 | 617-933-7735 x2314
ejb@think.ARPA (Erik Bailey) (11/01/85)
In article <34@pixel.UUCP> vsh@pixel.UUCP (vsh) writes: >> ... When each man >> reaches his landmark, they each turn 90 degrees and proceed away from their >> landmark ... > >Does it matter which way each turns (left vs. right, in vs. out, >the same vs the opposite)? It must but you do not specify. >(Consider two cases that differ only in the direction the pirate at the >forest turns; the mid-point of the line segments cannot be the same!) > Ahhh... Given there are two choices, but we shall assume (for simplicity) that the pirates choose the one that works. If the treasure is on one side of the line determined by the two landmarks, relative to the boat's landing, they turn one way, but if they land on the same side as the treasure, they must turn the other way. Granted, this is the one confusing point about the problem. There is no real way to specify it, but if anyone can do a better job than me, feel free to speak up! Anyway, good luck and keep on tryin! I'll try to get some more interesting problems up here soon... --Erik -- Erik Bailey _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ -_ -_ -_ -_ -_ -_ -_ -_ -_ -_ -_ -_ -_ -_ -_ -_ -_ -_ -_ -_ -_ -_ -_ -_ Erik Bailey -- 7 Oak Knoll (USENET courtesy of ihnp4!godot!ejb Arlington, MA 02174 Thinking Machines Corp. ejb@think.com.arpa (617) 643-0732 Cambridge, MA) "I was walking in a forest one day and a tree fell in front of me, and I didn't hear it." _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _- _- _- _- _- _- _- _- _- _- _- _- _- _- _- _- _- _- _- _- _- _- _- _-
vsh@pixel.UUCP (Steve Harris) (11/05/85)
It is sufficient to say that the pirates must turn opposite directions
(if one turns right, the other must turn left), and that when they return,
each must turn the same direction as before (left at the rock, right at
the forest, or vice-versa).
-------------------- SPOILER / BIG HINT FOLLOWS --------------------
Draw a square such that the rock and the forest are opposite corners.
BEHOLD!
--
Steve Harris | {allegra|ihnp4|cbosgd|ima|genrad|amd|harvard}\
Pixel Systems Inc. | !wjh12!pixel!vsh
300 Wildwood Street |
Woburn, MA 01801 | 617-933-7735 x2314