THE FOUR KNIGHTS' TOURS.
(
The Guarded Chessboard)
I will repeat that if a chessboard be cut into four equal parts, as
indicated by the dark lines in the illustration, it is not possible to
perform a knight's tour, either re-entrant or not, on one of the parts.
The best re-entrant attempt is shown, in which each knight has to
trespass twice on other parts. The puzzle is to cut the board
differently into four parts, each of the same size and shape, so that a
re-entrant knight's tour may be made on each part. Cuts along the dotted
lines will not do, as the four central squares of the board would be
either detached or hanging on by a mere thread.
Answer:
It will be seen in the illustration how a chessboard may be divided into
four parts, each of the same size and shape, so that a complete
re-entrant knight's tour may be made on each portion. There is only one
possible route for each knight and its reversal.
