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Spider and Fly Problem


Spider and fly path

The spider and fly considers a rectangular room (a cuboid) with dimensions 30^'×12^'×12^' in which a spider is located in the middle of one 12^'×12^' wall one foot away from the ceiling. A fly is in the middle of the opposite wall one foot away from the floor. If the fly remains stationary, what is the shortest total distance (i.e., the geodesic) the spider must crawl along the walls, ceiling, and floor in order to capture the fly?

SpiderandFly

The answer, 40^', can be obtained by "flattening" the walls as illustrated above. Note that his distance is shorter than the 42^' the spider would have to travel if first crawling along the wall to the floor, then across the floor, then up one foot to get to the fly. The puzzle was originally posed in an English newspaper by Dudeney in 1903 (Gardner 1958).

A twist to the problem can be obtained by a spider that suspends himself from strand of cobweb and thus takes a shortcut by not being forced to remain glued to a surface of the room. If the spider attaches a strand of cobweb to the wall at his starting position and lowers himself down to the floor (thus not crawling a single inch), he can then cross the length of the room by foot (30^') and ascend a single foot, thus reaching his prey after a total crawl of 31^' (although the total distance traveled is of course 42^').

If the spider is not proficient with fastening strands to vertical walls, he can still get the fly crawling only 31^'. In particular, he can climb to the ceiling (1^'), then traverse the length of the ceiling (30^') and lowering himself 11^' (requiring no crawling), thus catching the fly.


See also

Geodesic

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References

Gardner, M. "Mathematical Games: About Henry Ernest Dudeney, A Brilliant Creator of Puzzles." Sci. Amer. 198, 108-112, Jun. 1958.Pappas, T. "The Spider & the Fly Problem." The Joy of Mathematics. San Carlos, CA: Wide World Publ./Tetra, pp. 218 and 233, 1989.Steinhaus, H. Mathematical Snapshots, 3rd ed. New York: Dover, pp. 173-175, 1999.

Referenced on Wolfram|Alpha

Spider and Fly Problem

Cite this as:

Weisstein, Eric W. "Spider and Fly Problem." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/SpiderandFlyProblem.html

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