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Checkerboard

Board with an alternating square pattern on which games are played

Acheckerboard (American English) or chequerboard (British English; see spelling differences) is a game boardofcheckered 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.

Games and puzzles using checkerboards[edit]

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[edit]

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.

Gallery[edit]

• 
  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

See also[edit]

• Chessboard
• Croatian checkerboard
• Hexmap

References[edit]

Look up checkerboard in Wiktionary, the free dictionary.