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From: john@hp-pcd.UUCP
Newsgroups: net.math
Subject: Spider Gets Fly - (nf)
Message-ID: <1863@hp-pcd.UUCP>
Date: Sat, 17-Sep-83 03:28:26 EDT
Article-I.D.: hp-pcd.1863
Posted: Sat Sep 17 03:28:26 1983
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#N:hp-pcd:6100004:000:2439
hp-pcd!john    Sep 15 08:40:00 1983



     A spider and a fly are both in a rectangular room with 30 foot long side
walls,12 foot wide end walls and a 12 foot high ceiling. The spider is on a 
end wall exactly 6 feet from either side wall and 1 foot down from the ceiling.
The fly is on the other end wall exactly 6 feet from either side wall and 1 
foot up from the floor. The spider can travel over floor,wall or ceiling with 
equal ease and the fly does not move irregardless of the consequences. What
is the shortest distance that the spider has to travel to catch the fly?

 -------------------------------------------------------------------------

     This is a interesting problem since it involves a two dimensional 
solution to what appears to be a three dimensional problem. Most people
tend to think that 42 is the answer because that is the simplest line
that can be drawn between them. I have received answers that ranged from
40 to 43 thru an interesting variety of paths. The correct answer is
40 and only one person(Larry Bickford ihnp4!decwrl!qubix!lab) managed to 
get that.

     Getting the right answer involves unwrapping the room into a two
dimensional shape that shows the actual positions of the bugs. The best way
is:





   -----------------------------------------------------------
   |         |                                  Ceiling      |
   |       S |                                               |
   |       : |                                               |
   -----------------------------------------------------------
           : |                                  Side Wall    |
       24' : |                                               |
           : |                                               |
           : ----------------------------------------------------------
           : |               32'                             |        |
           L.|...............................................|.F      |
             |  Floor                                        |        |
             ----------------------------------------------------------
             |                                               |
             |  Side Wall                                    |
             |_______________________________________________|

 A straight line between them will be 40 ' long. This puzzle was originally
published in Link-Belt News in Aug 35 and again in Jan 62.


John Eaton

hplabs!hp-pcd!john