Amusements in Mathematics HTML version

(See No. 318, "Lion Hunting.")
"Push on—keep moving."
THOS. MORTON: Cure for the Heartache.
The puzzle is to move the single rook over the whole board, so that it shall visit every
square of the board once, and only once, and end its tour on the square from which it
starts. You have to do this in as few moves as possible, and unless you are very careful
you will take just one move too many. Of course, a square is regarded equally as "visited"
whether you merely pass over it or make it a stopping-place, and we will not quibble over
the point whether the original square is actually visited twice. We will assume that it is
This puzzle I call "The Rook's Journey," because the word "tour" (derived from a turner's
wheel) implies that we return to the point from which we set out, and we do not do this in
the present case. We should not be satisfied with a personally conducted holiday tour that
ended by leaving us, say, in the middle of the Sahara. The rook here makes twenty-one
moves, in the course of which journey it visits every square of the board once and only
once, stopping at the square marked 10 at the end of its tenth move, and ending at the
square marked 21. Two consecutive moves cannot be made in the same direction—that is
to say, you must make a turn after every move.
A wicked baron in the good old days imprisoned an innocent maiden in one of the
deepest dungeons beneath the castle moat. It will be seen from our illustration that there
were sixty-three cells in the dungeon, all connected by open doors, and the maiden was
chained in the cell in which she is shown. Now, a valiant knight, who loved the damsel,
succeeded in rescuing her from the enemy. Having gained an entrance to the dungeon at
the point where he is seen, he succeeded in reaching the maiden after entering every cell
once and only once. Take your pencil and try to trace out such a route. When you have
succeeded, then try to discover a route in twenty-two straight paths through the cells. It
can be done in this number without entering any cell a second time.
A French prisoner, for his sins (or other people's), was confined in an underground
dungeon containing sixty-four cells, all communicating with open doorways, as shown in
our illustration. In order to reduce the tedium of his restricted life, he set himself various
puzzles, and this is one of them. Starting from the cell in which he is shown, how could
he visit every cell once, and only once, and make as many turnings as possible? His first
attempt is shown by the dotted track. It will be found that there are as many as fifty-five