"Good company's a chessboard."
BYRON'S _Don Juan_, xiii. 89.
A chessboard is essentially a square plane divided into sixty-four
smaller squares by straight lines at right angles. Originally it was not
chequered (that is, made with its rows and columns alternately black and
white, or of any other two colours), and this improvement was introduced
merely to help the eye in actual play. The utility of the chequers is
unquestionable. For example, it facilitates the operation of the
bishops, enabling us to see at the merest glance that our king or pawns
on black squares are not open to attack from an opponent's bishop
running on the white diagonals. Yet the chequering of the board is not
essential to the game of chess. Also, when we are propounding puzzles on
the chessboard, it is often well to remember that additional interest
may result from "generalizing" for boards containing any number of
squares, or from limiting ourselves to some particular chequered
arrangement, not necessarily a square. We will give a few puzzles
dealing with chequered boards in this general way.