thumb|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

thumb|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 mode="nolines" widths="200px">

File:Empty wooden chessboard.jpg|An empty 8×8 checkerboard

File:Font Awesome 5 solid chess-board.svg|An empty 8×8 checkerboard diagram

File:International draughts.jpg|The opening setup of international draughts, which uses a 10×10 checkerboard

File:CheckersStandard.jpg|English draughts tournament standard

</gallery>

Mathematical description

Given a grid with <math>m</math> rows and <math>n</math> columns, a function <math>f(m,n)</math>,

<math>

\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}

</math>

or, alternatively,

<math>

\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}

</math>

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

Encoding

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

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See also

  • Chessboard
  • Croatian checkerboard
  • Hexmap

References