# Checkerboard

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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 (8Ã—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 8Ã—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.

## Mathematical description

Given a matrix with ${\displaystyle m}$Â  rows and ${\displaystyle n}$Â  columns, a function ${\displaystyle f(m,n)}$Â ,

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

or, alternatively,

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

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

## Games and puzzles using checkerboards

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:

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