Now, how many different routes are there from A to B in this maze if we must never in any route go along the same passage twice?  The four open spaces where four passages end are not reckoned as “passages.”  In the diagram (Fig. 22) it will be seen that I have again suppressed the blind alleys.  It will be found that, in any case, we must go from A to C, and also from F to B. But when we have arrived at C there are three ways, marked 1, 2, 3, of getting to D. Similarly, when we get to E there are three ways, marked 4, 5, 6, of getting to F. We have also the dotted route from C to E, the other dotted route from D to F, and the passage from D to E, indicated by stars.  We can, therefore, express the position of affairs by the little diagram annexed (Fig. 23).  Here every condition of route exactly corresponds to that in the circular maze, only it is much less confusing to the eye.  Now, the number of routes, under the conditions, from A to B on this simplified diagram is 640, and that is the required answer to the maze puzzle.

Finally, I will leave two easy maze puzzles (Figs. 24, 25) for my readers to solve for themselves.  The puzzle in each case is to find the shortest possible route to the centre.  Everybody knows the story of Fair Rosamund and the Woodstock maze.  What the maze was like or whether it ever existed except in imagination is not known, many writers believing that it was simply a badly-constructed house with a large number of confusing rooms and passages.  At any rate, my sketch lacks the authority of the other mazes in this article.  My “Rosamund’s Bower” is simply designed to show that where you have the plan before you it often happens that the easiest way to find a route into a maze is by working backwards and first finding a way out.

THE PARADOX PARTY.

    “Is not life itself a paradox?”
        C.L.  DODGSON, Pillow Problems.

“It is a wonderful age!” said Mr. Allgood, and everybody at the table turned towards him and assumed an attitude of expectancy.

This was an ordinary Christmas dinner of the Allgood family, with a sprinkling of local friends.  Nobody would have supposed that the above remark would lead, as it did, to a succession of curious puzzles and paradoxes, to which every member of the party contributed something of interest.  The little symposium was quite unpremeditated, so we must not be too critical respecting a few of the posers that were forthcoming.  The varied character of the contributions is just what we would expect on such an occasion, for it was a gathering not of expert mathematicians and logicians, but of quite ordinary folk.

“It is a wonderful age!” repeated Mr. Allgood.  “A man has just designed a square house in such a cunning manner that all the windows on the four sides have a south aspect.”

“That would appeal to me,” said Mrs. Allgood, “for I cannot endure a room with a north aspect.”