The following question goes back to Henry Ernest Dudeney (1857 - 1930).[br][br]In a room that is 6 m long, 2.40 m wide and 2.40 m high there is a spider and a fly. The spider is in the middle of the front side surface 20 cm above the floor and the fly on the opposite wall is also in the middle but 20 cm below the ceiling.[br]Which path does the spider have to take along the walls so that it can reach the spider by the shortest possible route?

There are two paths, each 8 m long.[br][br][b]Task[/b][br]Change the position of the [b][color=#ff0000]spider [/color][/b]on the front side wall of the room and the position of the [b][color=#f6b26b]fly [/color][/b]on the back wall and observe the shortest paths in each case.

The shortest path can be found by looking at the net of the cuboid space. Here the shortest path can be drawn as a straight line connection between spider and fly. However, there are several options - depending on how the net is designed.[br]The [b][color=#ff0000]shortest path[/color][/b] is shown in [b][color=#ff0000]red [/color][/b]in the applet.[br][br][i]Notice[br]In addition to the routes drawn in black, there are other paths (drawn here in yellow) that the spider could take, but for reasons of symmetry they are the same length as other paths.[/i]

A very good article on this topic can be found in the online edition of the magazine Spektrum der Wissenschaft [url=https://www.spektrum.de/raetsel/fliege-und-spinne/1797209]https://www.spektrum.de/raetsel/fliege-und-spinne/1797209[/url]