checkerboard
{{Short description|Board with an alternating square pattern on which games are played}}
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 web|url=https://mathworld.wolfram.com/Checkerboard.html|title=Checkerboard|first=Eric W.|last=Weisstein|website=mathworld.wolfram.com}} 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
File:The Childrens Museum of Indianapolis - Checkers.jpg]]
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.
Gallery
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
Mathematical description
Given a grid with rows and columns, a function ,
\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 is black and represents the lower left corner of the board.
Encoding
In Unicode, checkerboard characters are encoded at various code points:
- {{unichar|2427|Symbol for delete square checker board form}}
- {{unichar|2428|Symbol for delete rectangular checker board form}}
- {{unichar|1F67E|Checker board}}
- {{unichar|1F67F|Reverse checker board}}
- {{unichar|1FB95|Checker board fill}}
- {{unichar|1FB96|Inverse checker board fill}}