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 hypotenuse 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 |