THE CUBIC KNIGHT'S TOUR.
(
The Guarded Chessboard)
Some few years ago I happened to read somewhere that Abnit Vandermonde,
a clever mathematician, who was born in 1736 and died in 1793, had
devoted a good deal of study to the question of knight's tours. Beyond
what may be gathered from a few fragmentary references, I am not aware
of the exact nature or results of his investigations, but one thing
attracted my attention, and that was the statement that he had proposed
the question of a tour of the knight over the six surfaces of a cube,
each surface being a chessboard. Whether he obtained a solution or not I
do not know, but I have never seen one published. So I at once set to
work to master this interesting problem. Perhaps the reader may like to
attempt it.
Answer:
If the reader should cut out the above diagram, fold it in the form of a
cube, and stick it together by the strips left for that purpose at the
edges, he would have an interesting little curiosity. Or he can make one
on a larger scale for himself. It will be found that if we imagine the
cube to have a complete chessboard on each of its sides, we may start
with the knight on any one of the 384 squares, and make a complete tour
of the cube, always returning to the starting-point. The method of
passing from one side of the cube to another is easily understood, but,
of course, the difficulty consisted in finding the proper points of
entry and exit on each board, the order in which the different boards
should be taken, and in getting arrangements that would comply with the
required conditions.
Informational
