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.

• Arimaa
• Breakthrough
• Crossings
• Mak-yek
• Makruk
• Martian Chess

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.

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

References

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