Checkerboard Explained

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

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

Given a grid with

m rows and n columns, a function f(m,n) ,\displaystyle {f(m,n)} = \begin{cases} black & if m \equiv n \pmod 2 , \\ white & if m \not\equiv n \pmod 2 \\ \end{cases}

or, alternatively,

\displaystyle {f(m,n)} = \begin{cases} black & if m + n iseven , \\ white & if m + n isodd \\ \end{cases}

The element

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

See also

• Chessboard
• Croatian checkerboard
• Hexmap

References

Notes and References

1. Web site: Checkerboard. Eric W.. Weisstein. mathworld.wolfram.com.