Answer to Problem of the Week for 9/30/2002

Answer to September 30, 2002 Problem Adapted from a problem by Henry Dudeney

The Spider and the Fly Problem

There is a rectangular room whose dimensions are 30 feet long by 12 feet wide by 12 feet high. A spider is located on one of the 12' x 12' end walls, 1 foot down from the ceiling and 6 feet from each side wall. A fly is located on the opposite 12' x 12' wall, 1 foot up from the floor and 6 feet from each side wall. The spider desires to dine on the fly which is asleep. Determine the shortest route that the spider may follow to get to the fly (the spider must always be touching one of the four walls, the ceiling, or the floor). No web-spinning!
Solution to the Problem: The answer is 40 feet, *not* 42 feet! The shortest route is not down to the floor, across the room, and up. The spider actually travels over five of the six surfaces in the room. To solve this problem, "unfold" the room, making a drawing of the six surfaces in the room. Then connect the spider and the fly by a line segment, and solve for the length of the segment. I have shown two ways to make the drawing below. The drawing on the left results in 42 feet, but the drawing on the right yields the shortest route of 40 feet. Use the Pythagorean Theorem to solve for the distance between the spider and the fly. The lengths of the legs of the right triangle are 32' and 24'. therefore, the hyptoenuse would be 40 feet. See the picture below:

There is a rectangular room whose dimensions are 30 feet long by 12 feet wide by 12 feet high. A spider is located on one of the 12' x 12' end walls, 1 foot down from the ceiling and 6 feet from each side wall.
A fly is located on the opposite 12' x 12' wall, 1 foot up from the floor and 6 feet from each side wall.

The spider desires to dine on the fly which is asleep. Determine the shortest route that the spider may follow to get to the fly (the spider must always be touching one of the four walls, the ceiling, or the floor). No web-spinning!

Solution to the Problem:

The answer is 40 feet, not 42 feet!

The shortest route is not down to the floor, across the room, and up. The spider actually travels over five of the six surfaces in the room. To solve this problem, "unfold" the room, making a drawing of the six surfaces in the room. Then connect the spider and the fly by a line segment, and solve for the length of the segment.
I have shown two ways to make the drawing below. The drawing on the left results in 42 feet, but the drawing on the right yields the shortest route of 40 feet.

Use the Pythagorean Theorem to solve for the distance between the spider and the fly. The lengths of the legs of the right triangle are 32' and 24'. therefore, the hyptoenuse would be 40 feet. See the picture below:

Correctly solved by:

1. James Alarie	University of Michigan -- Flint Flint, Michigan
2. Kirstine Wynn	St. Olaf's College Northfield, Minnesota
3. ----------	United Kingdom
4. Keith Mealy	Cincinnati, Ohio
5. George Gaither	Winchester, Virginia
6. Richard K. Johnson	La Jolla, California
7. Jeff Gaither	Winchester, Virginia
8. Joe Jenkins	Winchester, Virginia
9. Kyle Martin	North Andover, Massachussetts
10. Daniel Wilberger	Winchester, Virginia
11. Matt Stillwagon	Winchester, Virginia
12. Rick Jones	Kennett Square, Pennsylvania
13. Kathleen Altemose	Winchester, Virginia
14. Laura Crotty	North Andover, Massachussetts
15. Katie Nickerson	North Andover, Massachussetts
16. Travis Riggs	Old Dominion University Norfolk, Virginia
17. Peggah Sadeghzadeh	Winchester, Virginia

Answer to September 30, 2002 Problem Adapted from a problem by Henry Dudeney

Correctly solved by:

Answer to September 30, 2002 Problem
Adapted from a problem by Henry Dudeney