Ndtyjky

An empty 8×8 checkerboard

A checkerboard (American English) or chequerboard (British English; see spelling differences) is a board of chequered pattern on which draughts (checkers) is played.^[1] Most commonly, it consists of 64 squares (8×8) of alternating dark and light color, often black and white. 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.

Mathematical description

An empty 8×8 checkerboard diagram

Given a matrix with m{displaystyle m} rows and n{displaystyle n} columns, a function f(m,n){displaystyle f(m,n)},

f(m,n)={trueif m∧1=1 and n∧1=1,falseif m∧1=1 and n∧1=0,falseif m∧1=0 and n∧1=0,trueif m∧1=0 and n∧1=1,{displaystyle displaystyle {f(m,n)}={begin{cases}{text{true}}&{text{if}} mwedge 1=1 {text{and}} nwedge 1=1,,\{text{false}}&{text{if}} mwedge 1=1 {text{and}} nwedge 1=0,,\{text{false}}&{text{if}} mwedge 1=0 {text{and}} nwedge 1=0,,\{text{true}}&{text{if}} mwedge 1=0 {text{and}} nwedge 1=1,,\end{cases}}}

returns true if the cell is white and false if the cell is black. The element (m,n)=(0,0){displaystyle (m,n)=(0,0)} is black.

Games and puzzles using checkerboards

The opening setup of international draughts, which uses a 10×10 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


• Frisian draughts


• Gounki


• International draughts


• Italian draughts


• Lines of Action


• Pool checkers


• Russian checkers


• Turkish draughts

The following games require an 8×8 board and are sometimes played on a chessboard.

• Arimaa


• Breakthrough


• Crossings


• Mak-yek


• Makruk


• Martian Chess

References

Look up checkerboard in Wiktionary, the free dictionary.