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[pbmserv] New game: Projex

Hello,

A new connection game Projex has been added to the server. This is an elegant game for those who like a bit of topological stimulation.

Although invented 10 years ago, Projex has only recently surfaced. Please challenge me if you're interested in trying it out:

  projex challenge yourname camb
  projex challenge camb yourname

help projex (rules appended below)

camb

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Help For the Game Of Projex

Introduction

   Welcome to the network Projex server. The Projex challenge command
   starts a new game between userid1 and userid2 as follows:

projex challenge [-size=number] userid1 userid2

   The -size parameter sets the board size in the range 3..11 (default =
   6). This number describes the number of cells along each of the
   board's three longest sides.

Other commands are the same as for all pbmserv games.

Board Layout

   Projex is played on a hexagonal grid within a six-sided board. The
   number of cells per side alternate between n and n-1 around the board.
   For instance, a board of size 6 consists of 6, 5, 6, 5, 6, 5 cells
   along each edge, as shown below:


           1-   . . . . .
          2-   . . . . . .
         3-   . . . . . . .
        4-   . . . . . . . .
       5-   . . . . . . . . .
      6-   . . . . . . . . . .
       7-   . . . . . . . . .
        8-   . . . . . . . .   \
         9-   . . . . . . .   \ J
         10-   . . . . . .   \ I
                            \ H
                 \ \ \ \ \ \ G
                  A B C D E F

   Each cell is adjacent to its hexagonal neighbours. In addition, each
   edge cell is adjacent to the two edge cells directly across from it.
   This means that the game is played on a projective plane on which
   chains may leave the board from one side and reenter from the opposite
   side.

   For instance, edge cell 'X' is adjacent to cells 'J' and 'K' as shown
   below. The figure on the right shows each cell's projection (denoted
   by lower case) on the far side of the board.


                                           o o p q r s
          . . . . .                       n A B C D E s
         . . . . . .                     m # . . . . F t
        . . . . . . .                   l Z . . . . . G u
       . . . . . . . .                 k Y . . . . . . H v
      X . . . . . . . .               j X . . . . . . . I w
     . . . . . . . . . J             j W . . . . . . . . J x
      . . . . . . . . K               i V . . . . . . . K x
       . . . . . . . .                 h U . . . . . . L y
        . . . . . . .                   g T . . . . . M z
         . . . . . .                     f S R Q P O N #
                                          f e d c b a a

Rules

   The board is initially empty. Players take turns placing one of their
   pieces at an empty point. The first player to complete a global loop
   wins. A global loop is a cycle of pieces that crosses the board edge
   an odd number of times.

   The following games have been won by X who has completed a global
   loop:


          . . x . .                          . . x . .
         . . x . . .                        . . . x . .
        . . . x . . .                      . . . . x . .
       . . . x . . . .                    x . . . . x x x
      . . . . x . . . .                  . x . . . . . . .
     . . . . x . . . . .                . . x . . . . . . .
      . . . . x . . . .                  . x . . . . . . .
       . . . x . . . .                    x . . . . x x x
        . . . x . . .                      . . . . x . .
         . . x . . .                        . . . x . .

One edge crossing Three edge crossings

   The following games have an even number of edge crossings and
   therefore have not been won by either player (yet):


          . . x . .                          . . x . .
         . . x . . .                        x . . x . .
        x x x . . . .                      . x . . x x x
       . . . . . . . .                    . . x . . . . .
      . . . . . . . . .                  x . . x . . . . .
     . . . . . . . . . .                . x . . x . . . . .
      . . . . . . . . .                  . x . . x x x x x
       . . . . x x x x                    x . . . . . . .
        . . . x . . .                      . . . . x x x
         . . X . . .                        . . . x . .

Two edge crossings Four edge crossings

   Ties are not possible. A filled board must contain a global loop, and
   a global loop cuts all possible opponent's global loops.

   We can also describe global loops in the following way: a player has a
   global loop if the opponent cannot possibly connect any two opposed
   edge points directly across the board. For instance, it is still
   possible for O to connect two opposed edge points directly across the
   board in the "Two edge crossings" and "Four edge crossings" examples
   above, hence X has not yet completed a global loop in either of the
   these games.

Move Syntax

X moves first. The move syntax is:

projex move board# userid password coord

   Where "coord" is an empty board point in the form 'F6'. The following
   command swaps the opening move (second move only):

projex move board# userid password swap

Other commands are the same as for all pbmserv games.

History

Projex was invented by Bill Taylor in 1994.

   Bill would like to point out that a global loop leaves the rest of the
   board connected, whereas a local loop doesn't - it has two sides.

Implementation and help file by Cameron Browne, November 2003.