CH. IX] UNICURSAL PROBLEMS 183 



shall at some point arrive at the centre, and finally shall 

 emerge at the point from which we started. This description 

 will require us to go over every path in the maze twice, and 

 as a matter of fact the two passages along any path will be 

 always made in opposite directions. 



If a maze is traced on paper, the way to the centre is 

 generally obvious, but in an actual labyrinth it is not so easy 

 to find the correct route unless the plan is known. In order 

 to make sure of describing a maze without knowing its plan it 

 is necessary to have some means of marking the paths which 

 we traverse and the direction in which we have traversed them 

 — for example, by drawing an arrow at the entrance and end 

 of every path traversed, or better perhaps by marking the 

 wall on the right-hand side, in which case a path may not be 

 entered when there is a mark on each side of it. 



Of the various practical rules for threading a maze those 

 enunciated by M. Tr^maux seem to be the simplest*. These 

 I proceed to explain, For brevity I shall describe a path or a 

 node as old or new according as it has been traversed once 

 before or not at all. Then the rules are (i) whenever you come 

 to a new node, take any path you like ; (ii) whenever you come 

 by a new path to an old node or to the closed end of a blind 

 alley, turn back along the path by which you have just come ; 

 (iii) whenever you come by an old path to an old node, take a 

 new path, if there is one, but if not, an old path ; (iv) of course 

 a path traversed twice must not be entered. I should add that 

 on emerging at any node then, of the various routes which are 

 permitted by these rules, it will be convenient always to select 

 that which lies next to one's right hand, or always that which 

 lies next to one's left hand. 



Few if any mazes of the type I have been considering 

 (namely, a series of interlacing paths through which some 

 route can be obtained leading to a space or building at the 

 centre of the maze) existed in classical or medieval times. 

 One class of what the ancients called mazes or labyrinths seems 

 to have comprised any complicated building with numerous 

 * Lucas, vol. i, part iii, p. 47 et seq. 



