Toroidal chess

Toroidal chessboard

Toroidal chess or torus chess is a variant of chess in which the board is connected on the a- and h-lines as well as on the first and last row. This cannot be achieved with a normal chessboard; the board can be thought of as a torus with a checkerboard pattern.

In contrast to cylinder chess, toroidal chess is difficult to play as a game: the usual starting position is e.g. B. not possible because the two kings stand next to each other and would threaten each other.

One possible starting position is suggested by Jeffrey Weeks:

	a	b	c	d	e	f	G	H
8th									8th
7th									7th
6th									6th
5									5
4th									4th
3									3
2									2
1									1
	a	b	c	d	e	f	G	H

Above all, however, toroidal chess is used in chess composition . There it allows demanding mating leads, because the king cannot easily be mated in the absence of a board edge. So the king and queen can no longer fulfill this task alone. Reinforced by a jumper, however, it succeeds:

	a	b	c	d	e	f	G	H
8th									8th
7th									7th
6th									6th
5									5
4th									4th
3									3
2									2
1									1
	a	b	c	d	e	f	G	H

Here White can checkmate on the torus in four moves: 1. Qf5 – h7! with the two variants:

a) 1. Ke8 – f8 2. Qh7 – g6 Kf8 – e7 3. Ke2 – e1 Ke7 – d7 (the squares d8 and f8 are controlled by the white king on e1) 4. Qg6 – e8 #.

b) 1. Ke8 – d8 2. Qh7 – c7 + Kd8 – e8 3. Nb5 – h6! 3. Ke8 – f8 4. Qc7 – e1 #

In toroidal chess, just like in cylinder chess, there is no solution to the queens problem .

See also : Chess Mathematics

Individual evidence

1. ^ John J. Watkins: Across the board: The mathematics of chessboard problems . Princeton University Press, Princeton 2004, ISBN 978-0-691-15498-5 , pp. 65 .
2. ↑ Jeffrey R. Weeks: The shape of space . 2nd ed.CRC Press, New York 2010, ISBN 978-0-8247-4837-1 , pp. 13 .

Web links

• Torus Games - Freeware that allows you to play toroidal chess, created by Jeffrey Weeks