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# Moebius Chess

Menno Dekker from Haarlem, the Netherlands, invented Moebius Chess in 1992 or 1993. The rules of this game were sent to me by Rob Nierse. Moebius Chess has not been played often, as far as I know.

It is somewhat different from the Moebius Chess which is used sometimes in fairy chess problems: the board of the game described here has 128 squares, whereas the board of fairy chess problems Moebius chess has 64 squares.

## Moebius Rings

Take a strip of paper. Twist it once, and then glue the ends together. Now you have a Moebius Ring, called after the mathematician who invented this concept. Note that the Moebius ring has only one side: when you start to draw a line around the strip, you will first come to the other side of the paper of where you started to draw before you come back to the place where you started to draw.

## A Moebius Chess Board

The chess board of Moebius Chess is like a Moebius strip. The idea is: consider an 8 by 8 board, that is drawn at both sides of a piece of paper. (The paper should either be very elastic, or, better, the squares should be rectangles, e.g., with a size of 10 by 2 centimeters.) Make a Moebius ring of this board, as described above. Rob Nierse wrote me that he actually made a board this way (of paper, with pieces made of pieces of paper): it looks quite interesting, but is hard to use.

We have a chess board of 8 rows, and 16 columns. The first eight columns form a normal chess board; the second eight columns are a chess board `mirrored'. The squares of the second board have an accent (') in their notation.

 a8 b8 c8 d8 e8 f8 g8 h8 a1' b1' c1' d1' e1' f1' g1' h1' a7 b7 c7 d7 e7 f7 g7 h7 a2' b2' c2' d2' e2' f2' g2' h2' a6 b6 c6 d6 e6 f6 g6 h6 a3' b3' c3' d3' e3' f3' g3' h3' a5 b5 c5 d5 e5 f5 g5 h5 a4' b4' c4' d4' e4' f4' g4' h4' a4 b4 c4 d4 e4 f4 g4 h4 a5' b5' c5' d5' e5' f5' g5' h5' a3 b3 c3 d3 e3 f3 g3 h3 a6' b6' c6' d6' e6' f6' g6' h6' a2 b2 c2 d2 e2 f2 g2 h2 a7' b7' c7' d7' e7' f7' g7' h7' a1 b1 c1 d1 e1 f1 g1 h1 a8' b8' c8' d8' e8' f8' g8' h8'

The sides are supposed to be adjacent: so, h1' is adjacent to a8, etc.

Perhaps easiest it is to just put two chess boards side by side, perhaps marking the squares of the boards with their names.

Note that the board is `almost' like an 16 by 8 cylinder: the names of the squares and the phasing rule make the difference.

At the start of the game, the pieces stand on their normal squares, as in orthodox chess.

## Moves

Rules are the same as in orthodox chess, but there are a few additional rules.

Pieces can make two types of moves: normal moves (in which they can move over the entire 16 by 8 board, and wrap around), or phasing moves. When phasing, a piece moves from the square where it is on to the square at the other side of the board (when made as a Moebius strip, explained above): i.e., it goes from a square to a square with the same name but with or without an accent, e.g, a piece can phase from a5 to a5' or vice versa. Note that pieces can move over the entire 16 by 8 board, using all adjacencies of squares.

### Check and phasing

A problem of the game is that - without additional rules - 1. R a1-e8' is a legal first move for white: but this move also mates the black king. (Note that this is a legal move in the game: the rook continues to move leftwards until it reaches e8'. Black cannot take the rook, as it is guarded by whites rook on h1.) Thus, the inventor stated that it is illegal to give checkmate with phasing: i.e., one may not move a piece, such that the result of the move is checkmate, and the piece attacks the opponents king with a phasing move (for instance, this makes 1. R a1-e8' an illegal move, as this would be checkmate, and the moved piece attacks the black king by a phasing move: the piece is on e8' and the king on e8.)

Rob Nierse suggested a simpler rule (but states that this would take some possibilities out of the game): one may not give a check (hence also a checkmate) `by phasing', in the sense that if the opponents king is on a certain square, one may not move a piece to the opposing square. For instance, when playing this rule, when a black king is on e4, then no white piece may move to e4'.

Written by Hans Bodlaender, with help of Rob Nierse.
WWW page created: October 17, 1996. Last modified: March 29, 1999. ﻿