Checkerboard

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 ${\displaystyle m}$  rows and ${\displaystyle n}$  columns, a function ${\displaystyle f(m,n)}$ ,

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

or, alternatively,

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

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

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  An empty 8×8 checkerboard
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  An empty 8×8 checkerboard diagram
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  The opening setup of international draughts, which uses a 10×10 checkerboard
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  English draughts tournament standard

• Chessboard
• Croatian checkerboard
• Hexmap