Checkerboard

File:Chess.board.fabric.png

A checkerboard

A checkerboard (North American English) or chequerboard (Commonwealth English except Canada; see spelling differences) is a game board of checkered pattern on which checkers (also known as English draughts) is played. 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. In The Netherlands, however, a dambord (checker board) has 10 rows and 10 columns for 100 squares in total (see article International draughts).

Games and puzzles using checkerboards

File:The Childrens Museum of Indianapolis - Checkers.jpg

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
• Fox games
• 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 grid with $m$ rows and $n$ columns, a function $f(m,n)$, $$\begin{gathered} f(m,n)=\{\begin{array}{ll}\text{black}& \text{if} \\ m\equiv n(\mathrm{mod}2),\\ \text{white}& \text{if} \\ m\equiv ̸n(\mathrm{mod}2)\\ \end{array} \end{gathered}$$ or, alternatively, $$\begin{gathered} f(m,n)=\{\begin{array}{ll}\text{black}& \text{if} \\ m+n\text{ is even},\\ \text{white}& \text{if} \\ m+n\text{ is odd}\\ \end{array} \end{gathered}$$ 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
• An empty 8×8 checkerboard diagram
  An empty 8×8 checkerboard diagram
• The opening setup of international draughts, which uses a 10×10 checkerboard
  The opening setup of international draughts, which uses a 10×10 checkerboard
• English draughts tournament standard
  English draughts tournament standard

See also

• Chessboard
• Croatian checkerboard
• Hexmap