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.^[1] Most commonly, it consists of 64 squares (×ばつ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 ×ばつ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).

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 ×ばつ8 board and are sometimes played on a chessboard.

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

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

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

or, alternatively,

${\displaystyle \displaystyle {f(m,n)}={\begin{cases}{\text{black}}&{\text{if}}\ m+n{\text{ is even}},\\{\text{white}}&{\text{if}}\ m+n{\text{ is odd}}\\\end{cases}}}${\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 ${\displaystyle (m,n)=(0,0)}${\displaystyle (m,n)=(0,0)} is black and represents the lower left corner of the board.

• ×ばつ8 checkerboard">An empty ×ばつ8 checkerboard
  An empty ×ばつ8 checkerboard
• ×ばつ8 checkerboard diagram">An empty ×ばつ8 checkerboard diagram
  An empty ×ばつ8 checkerboard diagram
• ×ばつ10 checkerboard">The opening setup of international draughts, which uses a ×ばつ10 checkerboard
  The opening setup of international draughts, which uses a ×ばつ10 checkerboard
• English draughts tournament standard
  English draughts tournament standard

• Chessboard
• Croatian checkerboard
• Hexmap

• Draughts
• Game equipment

• Articles with short description
• Short description is different from Wikidata