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UNICURSAL AND ROUTE PROBLEMS.

“I see them on their winding way.” 
REGINALD HEBER.

It is reasonable to suppose that from the earliest ages one man has asked another such questions as these:  “Which is the nearest way home?” “Which is the easiest or pleasantest way?” “How can we find a way that will enable us to dodge the mastodon and the plesiosaurus?” “How can we get there without ever crossing the track of the enemy?” All these are elementary route problems, and they can be turned into good puzzles by the introduction of some conditions that complicate matters.  A variety of such complications will be found in the following examples.  I have also included some enumerations of more or less difficulty.  These afford excellent practice for the reasoning faculties, and enable one to generalize in the case of symmetrical forms in a manner that is most instructive.

239.—­A JUVENILE PUZZLE.

For years I have been perpetually consulted by my juvenile friends about this little puzzle.  Most children seem to know it, and yet, curiously enough, they are invariably unacquainted with the answer.  The question they always ask is, “Do, please, tell me whether it is really possible.”  I believe Houdin the conjurer used to be very fond of giving it to his child friends, but I cannot say whether he invented the little puzzle or not.  No doubt a large number of my readers will be glad to have the mystery of the solution cleared up, so I make no apology for introducing this old “teaser.”

The puzzle is to draw with three strokes of the pencil the diagram that the little girl is exhibiting in the illustration.  Of course, you must not remove your pencil from the paper during a stroke or go over the same line a second time.  You will find that you can get in a good deal of the figure with one continuous stroke, but it will always appear as if four strokes are necessary.

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Another form of the puzzle is to draw the diagram on a slate and then rub it out in three rubs.

240.—­THE UNION JACK.

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The illustration is a rough sketch somewhat resembling the British flag, the Union Jack.  It is not possible to draw the whole of it without lifting the pencil from the paper or going over the same line twice.  The puzzle is to find out just how much of the drawing it is possible to make without lifting your pencil or going twice over the same line.  Take your pencil and see what is the best you can do.

241.—­THE DISSECTED CIRCLE.

How many continuous strokes, without lifting your pencil from the paper, do you require to draw the design shown in our illustration?  Directly you change the direction of your pencil it begins a new stroke.  You may go over the same line more than once if you like.  It requires just a little care, or you may find yourself beaten by one stroke.