[Illustration:  FIG. 23.—­Simplified Diagram of Fig. 22.]

If the maze has many islands, the traversing of the whole of it may be a matter of considerable difficulty.  Here is a method for solving any maze, due to M. Tremaux, but it necessitates carefully marking in some way your entrances and exits where the galleries fork.  I give a diagram of an imaginary maze of a very simple character that will serve our purpose just as well as something more complex (Fig. 20).  The circles at the regions where we have a choice of turnings we may call nodes.  A “new” path or node is one that has not been entered before on the route; an “old” path or node is one that has already been entered, 1.  No path may be traversed more than twice. 2.  When you come to a new node, take any path you like. 3.  When by a new path you come to an old node or to the stop of a blind alley, return by the path you came. 4.  When by an old path you come to an old node, take a new path if there is one; if not, an old path.  The route indicated by the dotted line in the diagram is taken in accordance with these simple rules, and it will be seen that it leads us to the centre, although the maze consists of four islands.

[Illustration:  FIG. 24.—­Can you find the Shortest Way to Centre?]

Neither of the methods I have given will disclose to us the shortest way to the centre, nor the number of the different routes.  But we can easily settle these points with a plan.  Let us take the Hatfield maze (Fig. 21).  It will be seen that I have suppressed all the blind alleys by the shading.  I begin at the stop and work backwards until the path forks.  These shaded parts, therefore, can never be entered without our having to retrace our steps.  Then it is very clearly seen that if we enter at A we must come out at B; if we enter at C we must come out at D. Then we have merely to determine whether A, B, E, or C, D, E, is the shorter route.  As a matter of fact, it will be found by rough measurement or calculation that the shortest route to the centre is by way of C, D, E, F.

[Illustration:  FIG. 25.—­Rosamund’s Bower.]

I will now give three mazes that are simply puzzles on paper, for, so far as I know, they have never been constructed in any other way.  The first I will call the Philadelphia maze (Fig. 22).  Fourteen years ago a travelling salesman, living in Philadelphia, U.S.A., developed a curiously unrestrained passion for puzzles.  He neglected his business, and soon his position was taken from him.  His days and nights were now passed with the subject that fascinated him, and this little maze seems to have driven him into insanity.  He had been puzzling over it for some time, and finally it sent him mad and caused him to fire a bullet through his brain.  Goodness knows what his difficulties could have been!  But there can be little doubt that he had a disordered mind, and that if this little puzzle had not caused him to lose his mental balance some other more or less trivial thing would in time have done so.  There is no moral in the story, unless it be that of the Irish maxim, which applies to every occupation of life as much as to the solving of puzzles:  “Take things aisy; if you can’t take them aisy, take them as aisy as you can.”  And it is a bad and empirical way of solving any puzzle—­by blowing your brains out.