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(Chessboard Problems)
My friend Captain Potham Hall, the renowned hunter of big game, says
there is nothing more exhilarating than a brush with a herd--a pack--a
team--a flock--a swarm (it has taken me a full quarter of an hour to
recall the right word, but I have it at last)--a _pride_ of lions. Why a
number of lions are called a "pride," a number of whales a "school," and
a number of foxes a "skulk" are mysteries of philology into which I will
not enter.
Well, the captain says that if a spirited lion crosses your path in the
desert it becomes lively, for the lion has generally been looking for
the man just as much as the man has sought the king of the forest. And
yet when they meet they always quarrel and fight it out. A little
contemplation of this unfortunate and long-standing feud between two
estimable families has led me to figure out a few calculations as to the
probability of the man and the lion crossing one another's path in the
jungle. In all these cases one has to start on certain more or less
arbitrary assumptions. That is why in the above illustration I have
thought it necessary to represent the paths in the desert with such
rigid regularity. Though the captain assures me that the tracks of the
lions usually run much in this way, I have doubts.
The puzzle is simply to find out in how many different ways the man and
the lion may be placed on two different spots that are not on the same
path. By "paths" it must be understood that I only refer to the ruled
lines. Thus, with the exception of the four corner spots, each combatant
is always on two paths and no more. It will be seen that there is a lot
of scope for evading one another in the desert, which is just what one
has always understood.

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