[Illustration:  FIG. 19.—­Maze at Pimperne, Dorset.]

We will now pass to the interesting subject of how to thread any maze.  While being necessarily brief, I will try to make the matter clear to readers who have no knowledge of mathematics.  And first of all we will assume that we are trying to enter a maze (that is, get to the “centre”) of which we have no plan and about which we know nothing.  The first rule is this:  If a maze has no parts of its hedges detached from the rest, then if we always keep in touch with the hedge with the right hand (or always touch it with the left), going down to the stop in every blind alley and coming back on the other side, we shall pass through every part of the maze and make our exit where we went in.  Therefore we must at one time or another enter the centre, and every alley will be traversed twice.

[Illustration:  FIG. 20.—­M.  Tremaux’s Method of Solution.]

[Illustration:  FIG. 21.—­How to thread the Hatfield Maze.]

Now look at the Hampton Court plan.  Follow, say to the right, the path indicated by the dotted line, and what I have said is clearly correct if we obliterate the two detached parts, or “islands,” situated on each side of the star.  But as these islands are there, you cannot by this method traverse every part of the maze; and if it had been so planned that the “centre” was, like the star, between the two islands, you would never pass through the “centre” at all.  A glance at the Hatfield maze will show that there are three of these detached hedges or islands at the centre, so this method will never take you to the “centre” of that one.  But the rule will at least always bring you safely out again unless you blunder in the following way.  Suppose, when you were going in the direction of the arrow in the Hampton Court Maze, that you could not distinctly see the turning at the bottom, that you imagined you were in a blind alley and, to save time, crossed at once to the opposite hedge, then you would go round and round that U-shaped island with your right hand still always on the hedge—­for ever after!

[Illustration:  FIG. 22.  The Philadelphia Maze, and its Solution.]

This blunder happened to me a few years ago in a little maze on the isle of Caldy, South Wales.  I knew the maze was a small one, but after a very long walk I was amazed to find that I did not either reach the “centre” or get out again.  So I threw a piece of paper on the ground, and soon came round to it; from which I knew that I had blundered over a supposed blind alley and was going round and round an island.  Crossing to the opposite hedge and using more care, I was quickly at the centre and out again.  Now, if I had made a similar mistake at Hampton Court, and discovered the error when at the star, I should merely have passed from one island to another!  And if I had again discovered that I was on a detached part, I might with ill luck have recrossed to the first island again!  We thus see that this “touching the hedge” method should always bring us safely out of a maze that we have entered; it may happen to take us through the “centre,” and if we miss the centre we shall know there must be islands.  But it has to be done with a little care, and in no case can we be sure that we have traversed every alley or that there are no detached parts.