Comparing Routes with a Net

To solve this puzzle, it helps to cut out pieces of graph paper representing the walls, ceiling, and floor and lay them flat to create a net of the room. (A net is a 2D shape that can be folded into a 3D shape.)

You can then use the Pythagorean theorem to compare the lengths of different routes, or, if you build the net with accurate proportions, use a ruler to do so.

See a more detailed explanation here: The Spider and the Fly Puzzle.