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Amusements in Mathematics

Chessboard Problems
"You and I will goe to the chesse."
GREENE'S Groatsworth of Wit.
During a heavy gale a chimney-pot was hurled through the air, and crashed upon the
pavement just in front of a pedestrian. He quite calmly said, "I have no use for it: I do not
smoke." Some readers, when they happen to see a puzzle represented on a chessboard
with chess pieces, are apt to make the equally inconsequent remark, "I have no use for it:
I do not play chess." This is largely a result of the common, but erroneous, notion that the
ordinary chess puzzle with which we are familiar in the press (dignified, for some reason,
with the name "problem") has a vital connection with the game of chess itself. But there
is no condition in the game that you shall checkmate your opponent in two moves, in
three moves, or in four moves, while the majority of the positions given in these puzzles
are such that one player would have so great a superiority in pieces that the other would
have resigned before the situations were reached. And the solving of them helps you but
little, and that quite indirectly, in playing the game, it being well known that, as a rule,
the best "chess problemists" are indifferent players, and vice versa. Occasionally a man
will be found strong on both subjects, but he is the exception to the rule.
Yet the simple chequered board and the characteristic moves of the pieces lend
themselves in a very remarkable manner to the devising of the most entertaining puzzles.
There is room for such infinite variety that the true puzzle lover cannot afford to neglect
them. It was with a view to securing the interest of readers who are frightened off by the
mere presentation of a chessboard that so many puzzles of this class were originally
published by me in various fanciful dresses. Some of these posers I still retain in their
disguised form; others I have translated into terms of the chessboard. In the majority of
cases the reader will not need any knowledge whatever of chess, but I have thought it
best to assume throughout that he is acquainted with the terminology, the moves, and the
notation of the game.
I first deal with a few questions affecting the chessboard itself; then with certain statical
puzzles relating to the Rook, the Bishop, the Queen, and the Knight in turn; then
dynamical puzzles with the pieces in the same order; and, finally, with some
miscellaneous puzzles on the chessboard. It is hoped that the formulæ and tables given at
the end of the statical puzzles will be of interest, as they are, for the most part, published
for the first time.
"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