Checkerboard

A checkerboard (American English) or chequerboard (British English; see spelling differences) is a board of chequered pattern on which draughts (checkers) is played.[1] Most commonly, it consists of 64 squares (8×8) of alternating dark and light color, typically green and buff (official tournaments), black and red (consumer commercial), or black and white (printed diagrams). An 8×8 checkerboard is used to play many other games, including chess, whereby it is known as a chessboard. Other rectangular square-tiled boards are also often called checkerboards.

A checkerboard

Games and puzzles using checkerboards

A game of checkers within the permanent collection of The Children's Museum of Indianapolis

Martin Gardner featured puzzles based on checkerboards in his November 1962 Mathematical Games column in Scientific American. A square checkerboard with an alternating pattern is used for games including:

Amazons
Chapayev
Chess and some of its variants (see chessboard)
Czech draughts
Draughts, also known as checkers
Frisian draughts
Gounki
International draughts
Italian draughts
Lines of Action
Pool checkers
Russian checkers

The following games require an 8×8 board and are sometimes played on a chessboard.

Mathematical description

Given a matrix with $m$ rows and $n$ columns, a function $f(m,n)$ ,

$\displaystyle {f(m,n)}={\begin{cases}{\text{black}}&{\text{if}}\ m\wedge 1=n\wedge 1\,,\\{\text{white}}&{\text{if}}\ m\wedge 1\neq n\wedge 1\\\end{cases}}$

or, alternatively,

$\displaystyle {f(m,n)}={\begin{cases}{\text{black}}&{\text{if}}\ m+n{\text{ is even}},\\{\text{white}}&{\text{if}}\ m+n{\text{ is odd}}\\\end{cases}}$

The element $(m,n)=(0,0)$ is black and represents the lower left corner of the board.

Gallery

An empty 8×8 checkerboard
An empty 8×8 checkerboard diagram
The opening setup of international draughts, which uses a 10×10 checkerboard
English draughts tournament standard

gollark: Move stuff so it's BABA IS MELT AND YOU at the bottom, and you should be left with BABA IS, and push the IS to beside the HOT then put the BABA beside that.

gollark: Or probably "WATER IS YOU".

gollark: You could move stuff so "BABA IS HOT", I guess.

gollark: I see.

gollark: If something is right beside the edge of the gamefield, you can't push it, right?

References

Weisstein, Eric W. "Checkerboard". mathworld.wolfram.com.

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[1] Weisstein, Eric W. "Checkerboard". mathworld.wolfram.com.