Checkerboard

For the pattern, see Checkerboard pattern.

A checkerboard

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. 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

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
• Checkers, also known as draughts
• 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

• 
  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

Given a grid with $m$ rows and $n$ columns, a function $f(m,n)$,

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

or, alternatively,

$\displaystyle {f(m,n)}={\begin{cases}{\text{black}}&{\text{if}}\ m+n{\text{ is even}},\\{\text{white}}&{\text{if}}\ m+n{\text{ is odd}}\\\end{cases}}$

The element $(m,n)=(0,0)$ is black and represents the lower left corner of the board.

Encoding

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

• Chessboard
• Croatian checkerboard
• Hexmap