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One-dimensional Chess Variants

Three dimensional chess variants are popular; two dimensional chess variants are even more popular, but it cannot be said that one dimensional chess variants are most popular. However, these may be amusing or interesting, or perhaps even analysable.

In all variants below, the object is to mate the opponents king.

Gardner's variants

In his column in the July 1980 issue of Scientific American, Martin Gardner (well known for this writings on mathematical recreations), gives the following one dimensional chess variants;

From left to right:
White King, Knight, Rook, two empty squares, Black Rook, Knight, King.

From left to right:
White King, Knight, Rook, three empty squares, Black Rook, Knight, King.


Here, the King and Rook move as usual, and the knight moves exactly two squares, and may jump over a piece doing that. Gardner asks his readers whether white can win. (White can make a draw by taking the opponents rook and thus giving stalemate.)

Sackson's variant

Sid Sackson, a well known game inventor, proposed the following enlarged version of Gardners variants. The opening setup is:

Pieces move as in Gardners variants, but also each player may once during the game have its king change places with the rook at the outer-side of the board. (This is a kind of castling, but may also be done when king or rook has moved, or when the king is in check, etc.) When this is the only available move, the player may select not to make it, and claim a draw by stalemate. (This, for instance would happen, when white takes in his first move blacks rook.)

Glimne's variant

In 1977, Dam Glimne proposed this variant. The opening setup is:

The King moves one or two squares, but moving two it may not jump over a piece. A Rook moves as usual. A Bishop moves an even number of squares (i.e., only on squares of his own color), and jumps over squares of the other color, e.g., when white starts the game with moving his pawn, he can move the next turn the bishop that is most towards the black pieces. The Queen has the combined moves of bishop and rook. A kNight moves two or three squares, and may jump over other pieces. A pawn moves one square, but may move two on its first move. Pawns (and all other pieces) take as they move.

Castling is allowed under the same restrictions as castling in usual chess.

The inventor thinks that white can force a win.

Parton's Linear Chess

V. R. Parton (a well known inventor of many chess variants) also invented an one-dimensional chess variant, called Linear Chess. This game is played on a row of 21 squares. Every player has one king, one jumper, one runner, two hoppers, and two steppers.

The opening setup is as follows:

All pieces can only move in the direction of the opponents side of the board, and take as they move. The steppers (pawns in the diagram) move one square. The hoppers (grasshoppers in the diagram) move two squares, and may jump over a piece when moving. The runners (rooks in the diagram) move as rooks. The jumpers (knights in the diagram) move by going first over a number (or zero) of unoccupied squares, then jumping over a piece, and then landing in the square directly after that piece (thus taking an opposing piece if it occupies that square).

Pritchard does not mention whether the king can move. One could either play that the king doesn't move, or that the king moves as a stepper; this seems not to make a large impact on the game.

Parton has also suggested two somewhat larger variants, by taking board with 25 or 27 squares, and taking as opening setup:

Source: The Encyclopedia of Chess Variants by D. B. Pritchard.
Written by Hans Bodlaender.
Last modified: October 10, 2002.