Answer
:
Though this problem was much discussed in the Daily
Mail from 18th
January to 7th February 1905, when it appeared to create great public
interest, it was actually first propounded by me in the Weekly
Dispatch
of 14th June 1903.
Imagine the room to be a cardboard box.
Then the box may be
cut in
various different ways, so that the cardboard may be laid flat on the
table.
I show four of these ways, and indicate in every case the
relative
positions of the spider and the fly, and the straightened course which
the spider must take without going off the cardboard.
These are the
four
most favourable cases, and it will be found that the shortest route is
in
No. 4, for it is only 40 feet in length (add the square of 32 to the
square of 24 and extract the square root).
It will be seen that the
spider actually passes along five of the six sides of the
room!
Having
marked the route, fold the box up (removing the side the spider does
not
use), and the appearance of the shortest course is rather
surprising.
If
the spider had
taken what most persons will consider obviously the
shortest route (that shown in No. 1), he would have gone 42 feet! Route
No. 2 is 43.174 feet in length, and Route No. 3 is 40.718 feet.
I will leave the reader to discover which are the
shortest
routes when
the spider and the fly are 2, 3, 4, 5, and 6 feet from the ceiling and
the floor respectively.
