THE LION AND THE MAN.
(
The Guarded Chessboard)
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.
[Illustration:
+-----+-----+-----+-----+-----+-----+-----+-----+
| | | | | | | | |
| L |
| | | | | | | | |
+-- --+-- --+-- --+-- --+-- --+-- --+-- --+-- --+
| | | | | | | | |
| |
| | | | | | | | |
+-- --+-- --+-- --+-- --+-- --+-- --+-- --+-- --+
| | | | | | | | |
| |
| | | | | | | | |
+-- --+-- --+-- --+-- --+-- --+-- --+-- --+-- --+
| | | | | | | | |
| |
| | | | | | | | |
+-- --+-- --+-- --+-- --+-- --+-- --+-- --+-- --+
| | | | | | | | |
| |
| | | | | | | | |
+-- --+-- --+-- --+-- --+-- --+-- --+-- --+-- --+
| | | | | | | | |
| |
| | | | | | | | |
+-- --+-- --+-- --+-- --+-- --+-- --+-- --+-- --+
| | | | | | | | |
| |
| | | | | | | | |
+-- --+-- --+-- --+-- --+-- --+-- --+-- --+-- --+
| | | | | | | | |
| C |
| | | | | | | | |
+-- --+-- --+-- --+-- --+-- --+-- --+-- --+-- --+
]
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.
Answer:
First of all, the fewest possible straight lines in each case are
twenty-two, and in order that no cell may be visited twice it is
absolutely necessary that each should pass into one cell and then
immediately "visit" the one from which he started, afterwards proceeding
by way of the second available cell. In the following diagram the man's
route is indicated by the unbroken lines, and the lion's by the dotted
lines. It will be found, if the two routes are followed cell by cell
with two pencil points, that the lion and the man never meet. But there
was one little point that ought not to be overlooked--"they occasionally
got glimpses of one another." Now, if we take one route for the man and
merely reverse it for the lion, we invariably find that, going at the
same speed, they never get a glimpse of one another. But in our diagram
it will be found that the man and the lion are in the cells marked A at
the same moment, and may see one another through the open doorways;
while the same happens when they are in the two cells marked B, the
upper letters indicating the man and the lower the lion. In the first
case the lion goes straight for the man, while the man appears to
attempt to get in the rear of the lion; in the second case it looks
suspiciously like running away from one another!
