The Second Book of Mathematical Puzzles and Diversions

Henry Ernest Dudeney: England's Greatest Puzzlist 41
A remarkable variation of Dudeney's spider and fly prob-
lem will be found in Maurice Kraitchik's Mathematical
Recreations, 1953, page 17. Eight spiders start from a spot
80 inches above the center of one end wall of the rectangular
room. They take eight different paths to reach a fly that is
80 inches below the center of the opposite wall. Each spider
moves at a speed of .65 mile per hour, and at the end of
625/11 seconds they arrive simultaneously at the fly. What
are the room's dimensions?
ANSWERS
THE SHORTEST walking path of the spider to the fly is exactly
40 feet, as indicated on the unfolded room shown in Figure
17. The reader may be surprised that this geodesic carries
the spider across five of the room's six sides.
The fly reaches the honey along the five-inch path drawn
on the unrolled cylinder depicted in Figure 18. This is the
path that would be taken by an imaginary beam of light
moving across the rectangle from fly to honey and reflected
by the rectangle's upper boundary. Clearly it is the same
FIG. 17. FIG. 18.
Answer to spider and fly problem. Answer to fly and honey problem.