# 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.

## Mathematical description

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

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

or, alternatively,

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

The element ${\displaystyle (m,n)=(0,0)}$ 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 8×8 board and are sometimes played on a chessboard.