Mathematical_Recreations-Kraitchik-2e

Mathematic8 without Numbers 17
word they would have been in a pretty quandary. But needless
to say they shot him anyway.
Problems such as these, that can be solved without numerical
calculation, are really far more numerous than one might
suppose. To this group belong the problem of the eight
queens on the chessboard and the problem of the knight, both
of which we shall examine later. Also magic squares, which
are so fascinating and which appear to belong exclusively to
the domain of numerical calculations, may be studi~d without
any computations.
On the other hand, certain problems appear from their
statements to be relatively innocent of extensive calculations,
but it turns out that their solution involves rather complicated
number work. The following is a good illustration of
this type of problem.
7. An honorable family of spiders, consisting of a wise
mother and eight husky youngsters, were perched on the wall
at one end of a rectangular room. Food being scarce, owing
to the second World War, they were grumbling, when an
enormous fly landed unnoticed on the opposite wall. If Euclid
could have been summoned from his grave (location, alas,
unknown), he would have been able to show that both the
hunters and the prey were in the vertical plane bisecting the
two opposite walls, the spiders eighty inches above the center
and the fly eighty inches below.
Suddenly one young spider shouted with glee. "Mamma!
Look! There's a fly! Let's catch him and eat him!"
"There are four ways to reach the fly. Which shall we
take?" came the eager query from another.
"You have forgotten your Euclid, my darling. There are
eight ways to reach the fly. Each of you take a different path,
without using any other means of conveyance than your God-