7.0 KB · ⇊ 5 parts · ⤓ Micron 7.0 KB · ⤓ HTML 25.0 KB

top

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.cite-ref-1[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

• Gallery

• Mathematical description

• Encoding

• See also

• References

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

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.

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

• Chessboard

• Croatian checkerboard

• Hexmap

Look up

checkerboard

in Wiktionary, the free dictionary.

cite-note-11. ↑ citerefweissteinWeisstein, Eric W. "Checkerboard". mathworld.wolfram.com.