Amusements in Mathematics HTML version

straight lines in his path, but after many attempts he improved upon this. Can you get
more than fifty-five? You may end your path in any cell you like. Try the puzzle with a
pencil on chessboard diagrams, or you may regard them as rooks' moves on a board.
In a public place in Rome there once stood a prison divided into sixty-four cells, all open
to the sky and all communicating with one another, as shown in the illustration. The
sports that here took place were watched from a high tower. The favourite game was to
place a Christian in one corner cell and a lion in the diagonally opposite corner and then
leave them with all the inner doors open. The consequent effect was sometimes most
laughable. On one occasion the man was given a sword. He was no coward, and was as
anxious to find the lion as the lion undoubtedly was to find him.
The man visited every cell once and only once in the fewest possible straight lines until
he reached the lion's cell. The lion, curiously enough, also visited every cell once and
only once in the fewest possible straight lines until he finally reached the man's cell. They
started together and went at the same speed; yet, although they occasionally got glimpses
of one another, they never once met. The puzzle is to show the route that each happened
to take.
The white squares on the chessboard represent the parishes of a diocese. Place the bishop
on any square you like, and so contrive that (using the ordinary bishop's move of chess)
he shall visit every one of his parishes in the fewest possible moves. Of course, all the
parishes passed through on any move are regarded as "visited." You can visit any squares
more than once, but you are not allowed to move twice between the same two adjoining
squares. What are the fewest possible moves? The bishop need not end his visitation at
the parish from which he first set out.
Here is a new puzzle with moving counters, or coins, that at first glance looks as if it
must be absurdly simple. But it will be found quite a little perplexity. I give it in this
place for a reason that I will explain when we come to the next puzzle. Copy the simple
diagram, enlarged, on a sheet of paper; then place two white counters on the points 1 and
2, and two red counters on 9 and 10, The puzzle is to make the red and white change
places. You may move the counters one at a time in any order you like, along the lines
from point to point, with the only restriction that a red and a white counter may never
stand at once on the same straight line. Thus the first move can only be from 1 or 2 to 3,
or from 9 or 10 to 7.
This is quite a fascinating little puzzle. Place eight bishops (four black and four white) on
the reduced chessboard, as shown in the illustration. The problem is to make the black
bishops change places with the white ones, no bishop ever attacking another of the