A labyrinth is a system of inter-connected passages in the earth with access points at the surface. (Others use different terminology.) It is therefore in mathematical terms the complement of a handle-body. The associated puzzle is, as with a maze, which is two-dimensional, to find a way to a defined goal and out again. Since the goal can be anyware to be sure of finding it we have to have a method which takes us to every point.
  As with a maze the possibility of path-repetition has to be excluded or the search could go on for ever. Close off every access except one with a set of points homeomorphic to a disc, that is, a door. This together with what follows corresponds to the method we adopted from Cauchy for mazes. Tremeaux's method of determing a path, formulated for a maze, can now be applied. We use it in a slightly adapted form. Take a tape-measure (which is better than a cord because of its orientation) into the labyrinth leaving the two ends at the entrance. Take a loop into every passage up to every dead-end or door. Stop also on coming to a passage where the tape has already been put and there is no other clear passage joining at that junction and free to use. Do this till all passages are covered. Then an explorer following the tape  round from the entrance and back to it will visit every point of the labyrinth.