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!
[Illustration]