Copyright (c) 2004 Bill Taylor

ZeN is a two player strategy game played on any square board. The author suggests 15x15 (as usual, smaller is more tactical, larger more strategic). 

  • BOARD - The board is a Torus, i.e., the first and last row are adjacent and the left and right column are adjacent.
  • MOVE - On each turn, each player must do one of the following actions:
    • Drop a stone into an empty cell.
    • Connect two friendly stones which are diagonally adjacent, if it does not cross another such connection.
  • GOAL
    • The Z player (in the diagrams, the black stones) wins by forming a horizontal loop around the Torus or make a SW-NE (/) spiral loop.
    • The N second player (the red stones) wins by forming a vertical loop around the Torus or make a SE-NW (\) spiral loop.
A connecting example

The black stones are connected. The red stones cannot be connected directly.

A completed game

Black (the Z player) made a horizontal loop. Notice the link between a7 and k6.

Spiral loops

The spiral loops are required, because it is possible that neither player can now get a loop in their primary direction (horizontal for Z, vertical for N), though both have a spiral loop.

In this case, Z has won the game.

This game is similar to Quax but on a different board topology (there are no edges on a Torus). The game will be available on Richard Rognlie's email server (at June or July).

A sample game

This is a board position of a real game when N resigned (the red stones).

The player cannot stop the horizontal loop for Z. If Red tries to block off black's c9 end, say by playing b10, then black can play d8 and threat to occupy the green dot connection path.

If Red plays at one of the green points, then Black extends his c9 end with b10, easily reaching the other black stones across the edge of the board.

The remaining chains are already too strong.

Some words from the author: This game was invented specifically as a companion to the popular game "Projex" (by the same author), for two purposes. One is that the projective planar topology of the latter is difficult for the non-mathematical learner to follow at first; whereas the Toroidal topology is to some extent much simpler, and may be already familiar from various computer war games. The other is to produce such a game with local *rectangular* geometry, which is more familiar and convenient for the casual gamer, rather than the "purer" local hexagonal geometry so beloved of true abstract gamers.

Note that the "N" and "Z" names of the stones exactly reflect the directions of the connections required by each side! Horizontal or "positive" sloped diagonals for "Z", and vertical or negative slopes for "N". Very neat. Even better, it allows the game to reflect the origin of the author, New Zealand, and also to make up the main part of the name, ZeN, which may also reflect the mind-boggling nature of the opposing connections!