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248:. Depending on the dimensions of the cuboid, and on the initial positions of the spider and fly, one or another of these paths, or of four other paths, may be the optimal solution. However, there is no rectangular cuboid, and two points on the cuboid, for which the shortest path passes through all six faces of the cuboid.
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A naive solution is for the spider to remain horizontally centred, and crawl up to the ceiling, across it and down to the fly, giving a distance of 42 feet. Instead, the shortest path, 40 feet long, spirals around five of the six faces of the cuboid. Alternatively, it can be described by unfolding
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room 30 feet long, 12 feet wide and 12 feet high contains a spider and a fly. The spider is 1 foot below the ceiling and horizontally centred on one 12′×12′ wall. The fly is 1 foot above the floor and horizontally centred on the opposite wall. The problem is to find the minimum
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and finding a shortest path (a line segment) on the resulting unfolded system of six rectangles in the plane. Different nets produce different segments with different lengths, and the question becomes one of finding a net whose segment length is minimum. Another path, of intermediate length
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to the wall to lower itself to the floor, and crawling 30 feet across it and 1 foot up the opposite wall, giving a crawl distance of 31 feet. Similarly, it can climb to the ceiling, cross it, then attach the silk to lower itself 11 feet, also a 31-foot crawl.
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Miller, S. Michael; Schaefer, Edward F. (Spring 2015). "The distance from a point to its opposite along the surface of a box".
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461:; Ito, Hiro; Katayama, Yuta; Murayama, Wataru; Uno, Yushi (2022). "Geodesic paths passing through all faces on a polyhedron".
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distance the spider must crawl along the walls, ceiling and/or floor to reach the fly, which remains stationary.
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Isometric projection and net of naive (1) and optimal (2) solutions of the spider and the fly problem
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509:(June 1958). "About Henry Ernest Dudeney, a brilliant creator of puzzles". Mathematical Games.
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390:. Classroom Resource Materials. Vol. 28. American Mathematical Society. pp. 45–46.
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Conference on Discrete and Computational Geometry, Graphs, and Games (JCDCG 2022)
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Complex Continued Fractions: A Historical Approach and Modern Perspectives
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552:(Doctoral dissertation). Julius-Maximilians-Universität Würzburg. pp. 36–41.
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Mellinger, Keith E.; Viglione, Raymond (March 2012). "The spider and the fly".
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solution, beyond the stated rules of the puzzle, involves the spider attaching
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problem with an unintuitive solution, asking for a shortest path or
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359:; Chinn, William G. (1985). "Chapter 16: The Spider and the Fly".
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in his diary in 1908. Hurwitz stated that he heard it from
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In the typical version of the puzzle, an otherwise empty
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193:{\displaystyle {\sqrt {(w+h)^{2}+(b+l+a)^{2}}}}
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546:Oswald, Nicola (2014). "Spider meets Fly?".
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96:{\displaystyle {\sqrt {1658}}\approx 40.7}
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241:{\displaystyle l+h-|b-a|}
570:Recreational mathematics
486:"Spider and Fly Problem"
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