The Second Book of Mathematical Puzzles and Diversions

Henry Ernest Lludeney: England's Greatest Puzzlist 37
is at the middle of an end wall, one foot from the ceiling.
The fly is at the middle of the opposite end wall, one foot
above the floor, and too paralyzed with fear to move. What
is the shortest distance the spider must crawl in order to
reach the fly?
The problem is solved by cutting the room so t~ a+ walls
and ceiling can be folded flat, then drawing a straight line
from spider to fly. However, there are many ways in which
the room can be folded flat, so it is not as easy as it first ap-
pears to determine the shortest path.
A less well-known but similar geodesic problem, which
appears in Dudeney's Modern Puzzles (published in 1926),
involves the cylindrical glass shown in Figure 15. It is four
inches high and six inches in circumference. On the inside,
one inch from the top, is a drop of honey. On the outside,
one inch from the bottom and directly opposite, is a fly.
What is the shortest path by which the fly can walk to the
honey, and exactly how far does the fly walk?
FIG. IS.
The fly and the honey.