The Knight’s move over the chess board has engaged the attention of so
many scientific men, that I cannot doubt that a collection of different
solutions of the problem will prove acceptable to all admirers of chess.
The Knight’s path is of two kinds—terminable and interminable—it is
interminable, whenever the last, or concluding, move of a series be
made on a square, which lies within the Knight’s reach of that from
which he originally set out—and terminable in every other instance.
Euler published a paper in the Memoirs of the Academy of Berlin, 1759,
which contains a method of filling up all the squares, setting out from
one of the corners. It also contains an endless or interminable route;
and explains a principle by which these routes may be varied so as to
end upon any square. Montmort, Demoivre, and Mairan, have severally
given solutions of the same problem. These solutions will be found in
the following collection.
Observing that the Automaton, under the direction of Mr. Maelzel,
occasionally traversed half the board, I was induced to pursue
the subject, and I found that the move might be performed on any
_parallelogram_ consisting of _twelve_ squares and upwards, with the
exception of _fifteen_ and _eighteen_ squares. The whole board admits
of a great variety both in the terminable and interminable routes.
In describing the Knight’s path, I have preferred lines to figures;
the former giving a clearer idea of the plan pursued, and affording a
greater facility of comparing one route with another, than the latter.