# Checkerboard

A checkerboard (American English) or chequerboard (British English; see spelling differences) is a board of checkered pattern on which checkers (also known as English draughts) 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:

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

## Mathematical description

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

${\displaystyle \displaystyle {f(m,n)}={\begin{cases}{\text{black}}&{\text{if}}\ m\equiv n{\pmod {2}}\,,\\{\text{white}}&{\text{if}}\ m\not \equiv n{\pmod {2}}\\\end{cases}}}$

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.