Re: DIS: The Maze Craze

Normand Veilleux (nve...@emr1.emr.ca) writes:
>One thing that has always amazed me about mazes is that a lot of
>people believe that they are always easier if you start from FINISH
>and move towards START.  I have never seen any facts or arguments
>proving or disproving this belief.  So, is this fact or fiction?

Basically this belief comes down to the psychology of the maze creator
and that of the maze solver.  Your logic in showing that a maze can be
equally difficult from both ends or harder from either one or the other
is infallible (if somewhat loosely reasoned), but the common belief is
still often true because those who craft mazes tend to put in branches
meant to confuse those who start at the beginning.  Witness your attempt
to show a maze offering 3 long choices:

>So, let's create a maze that offers, at the very beginning of the
>START path, a choice between 3 paths.  Let's make those three paths
>as long as possible and connect only one of them with the FINISH. 
>Here is such an example (the START is at the bottom):

aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa  a
8               8       8           8                   8   8       8   8
8   aaaaaaaaa   8   a   8   aaaaa   8   aaaaa   aaaaa   8   8   a   8   8
8   8       8   8   8   8       8   8   8       8           8   8   8   8
8   8   a   8   8aaa8   8aaaa   8   8aaa8   aaaa8aaaaaaaa   8   8   8   8
8   8   8   8                   8       8               8       8   8   8
8   8   8   8aaaaaaaaaaaaaaaaaaa8aaaa   8aaaaaaaaaaaa   8aaaaaaa8aaa8   8
8   8   8       8                   8               8       8           8
8   8aaa8   a   8   aaaaaaaaaaaaa   8aaaaaaaaaaaa   8   a   8   aaaaaaaa8
8           8   8           8   8               8   8   8   8           8
8   aaaaa   8   8aaaaaaaa   8   8aaaaaaaaaaaa   8   8aaa8   8aaaaaaaa   8
8       8   8           8   8               8   8                   8   8
8aaaaaaa8aaa8aaaaaaaa   8   8   a   aaaaa   8   8aaaaaaaaaaaaaaaa   8   8
8                       8   8   8       8   8               8   8   8   8
8   a   aaaaaaaaaaaaaaaa8   8   8aaaa   8   8aaaaaaaaaaaa   8   8   8   8
8   8   8                   8   8       8           8   8   8       8   8
8   8   8   aaaaaaaaaaaaaaaa8   8   aaaa8aaaaaaaa   8   8   8   aaaa8   8
8   8   8       8       8       8       8           8   8   8   8       8
8aaa8   8aaaa   8   a   8   aaaa8aaaa   8   aaaaaaaa8   8   8aaa8   aaaa8
8               8   8   8           8   8       8       8       8       8
8   a   aaaaaaaa8   8   8aaaaaaaa   8   8aaaa   8   a   8aaaa   8aaaa   8
8   8               8               8       8       8       8           8
8   8aaaaaaaaaaaaaaa8aaaaaaaaaaaaaaa8aaaaaaa8aaaaaaa8aaaaaaa8aaaaaaaaaaa8

Most maze creators tend to think along these lines: "How can I put in
more tricks?  Branch off at the start!"  The very best mazes, though, do
exactly what you did later on; they make many long branches from both
ends so that there is no easy starting place.  Of course, they often
fail to put extra branches in the middle, so it can be useful in a tough
maze to pick a point in the middle and try to connect it to both ends .
. . Anyway, good discussion!  (Not exactly sure that ascii-art is the
place for it, though.  Rec.puzzles??)
--
       
_____
|\ /|  G. Sumner Hayes     | A man, a plan, a
| O |  gh2...@andrew.cmu.edu| canoe, pasta, hero's
|/_\|  rajahs, a coloratura, maps, snipe, percale, 
macaroni, a gag, a banana bag, a tan, a tag, a 
banana bag again (or a camel), a crepe, pins, spam,
a rut, a Rolo, cash, a jar, sore hats, a peon, a canal,  
 - Panama!

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