## Wednesday, September 17, 2008

### Labyrinth-Generating Game

(This game seems like it might actually be somewhat fun. And, at
least,
if the game is not fun to play, its output, a maze, might be fun to
solve, anyway.)
Begin with an n-by-n grid drawn with pencil. (The game would be more
interesting with a larger n.)
2 players take turns erasing single segments (connecting adjacent
vertexes of the grid) so as to form doors, one door per move, under
certain rules:
1) There is never more than one path leading from any grid-square
(though
the doors) to any other square. (ie. there is only one sequence, at
most,
of particular squares that one can pass through {not passing through
any
solid "walls"} to get from any square to any other accessible square.)
2) No player can make a door connected to the square that his/her last
door was connected to.
3) The outside wall is to not have any doors, with the exception of
off
the upper-left {entrance} square and the lower-right square {exit}.
4) At the game's end, there is exactly one path from each square in
the
grid to any other particular grid-square.
Each player tries to get the other player, either by accident or by
force, to violate a rule before the maze is completed. The player
violating a rule loses.
Regarding rule 1: One goal of play is to confuse your opponent by
creating convoluted passageways in the maze-under-construction, so
that
she/he might violate this rule by accident.
It is up to each player to watch out for her/his opponent's mistakes,
however...
Regarding rule 4: Any player can claim that they cannot make a move
because the maze is complete.
But if his/her challenger proves that a player's claim of
game-completion
is erroneous (by finding counter-example to rule-4), then the
challenger
wins the game.
What is unusual about this game is that it is advantageous, in a way,
to
end in a draw. For then we have a completed maze that, ideally, is
relatively difficult to solve.
(Players can still break the tie by trying to each solve a different
copy
of this maze faster than their opponent....if you have a photocopy
machine handy, or if this all was done on a computer, or you do not
mind
copying the maze over by hand, or each player solves the maze
separately
using a transparency overlaying the maze and times how long it
takes,...)
Also, it might be easier (because players would DRAW segments and not
erase them)
to use an n-by-n lattice, then connect the vertexes with segments, so
as
to form a maze where you move ALONG the lines, not between them.
This is an unfinished idea. Feel free to submit suggestions.
(It is also in the public-domain. How would I copyright it anyway?...)
Thanks,
Leroy
Quet
A sample game in progress:
V______________________
! !____! !_!_!_!_!_!_!_!
! !__!_! !_!_!_! !_!_!
!__!_!_______!___!____ !
!____!_!___!____ !_! _!
!_!__!_____!_!_!_!_ _!_!
! !____! !_!_ _!_ _!_!_!
!_!__!_! !_!_!_!_ !_!_!
!__!_!____!__!___!_!_ !
!____!_!___!_! _ !_!_!_!
!_!__!_____!_!_!_!_!_! !
......................V

Thanks,
Leroy Quet