Checkerboard - Wikipedia

Board with an alternating square pattern on which games are played For the pattern, see Checkerboard pattern.

A checkerboard (American English) or chequerboard (British English) 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 (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

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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

Gallery

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• 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

Mathematical description

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

f ( m , n ) = { black if   m ≡ n ( mod 2 ) , white if   m ≢ n ( mod 2 ) {\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,

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

Encoding

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In Unicode, checkerboard characters are encoded at various code points:

• U+2427 ␧ SYMBOL FOR DELETE SQUARE CHECKER BOARD FORM
• U+2428 ␨ SYMBOL FOR DELETE RECTANGULAR CHECKER BOARD FORM
• U+1F67E 🙾 CHECKER BOARD
• U+1F67F 🙿 REVERSE CHECKER BOARD
• U+1FB95 🮕 CHECKER BOARD FILL
• U+1FB96 🮖 INVERSE CHECKER BOARD FILL

See also

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• Chessboard
• Croatian checkerboard
• Hexmap

References

[edit] Look up checkerboard in Wiktionary, the free dictionary.

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