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,