197.—­THE COMPASSES PUZZLE.

It is curious how an added condition or restriction will sometimes convert an absurdly easy puzzle into an interesting and perhaps difficult one.  I remember buying in the street many years ago a little mechanical puzzle that had a tremendous sale at the time.  It consisted of a medal with holes in it, and the puzzle was to work a ring with a gap in it from hole to hole until it was finally detached.  As I was walking along the street I very soon acquired the trick of taking off the ring with one hand while holding the puzzle in my pocket.  A friend to whom I showed the little feat set about accomplishing it himself, and when I met him some days afterwards he exhibited his proficiency in the art.  But he was a little taken aback when I then took the puzzle from him and, while simply holding the medal between the finger and thumb of one hand, by a series of little shakes and jerks caused the ring, without my even touching it, to fall off upon the floor.  The following little poser will probably prove a rather tough nut for a great many readers, simply on account of the restricted conditions:—­

Show how to find exactly the middle of any straight line by means of the compasses only.  You are not allowed to use any ruler, pencil, or other article—­only the compasses; and no trick or dodge, such as folding the paper, will be permitted.  You must simply use the compasses in the ordinary legitimate way.

198.—­THE EIGHT STICKS.

I have eight sticks, four of them being exactly half the length of the others.  I lay every one of these on the table, so that they enclose three squares, all of the same size.  How do I do it?  There must be no loose ends hanging over.

199.—­PAPA’S PUZZLE.

Here is a puzzle by Pappus, who lived at Alexandria about the end of the third century.  It is the fifth proposition in the eighth book of his Mathematical Collections.  I give it in the form that I presented it some years ago under the title “Papa’s Puzzle,” just to see how many readers would discover that it was by Pappus himself.  “The little maid’s papa has taken two different-sized rectangular pieces of cardboard, and has clipped off a triangular piece from one of them, so that when it is suspended by a thread from the point A it hangs with the long side perfectly horizontal, as shown in the illustration.  He has perplexed the child by asking her to find the point A on the other card, so as to produce a similar result when cut and suspended by a thread.”  Of course, the point must not be found by trial clippings.  A curious and pretty point is involved in this setting of the puzzle.  Can the reader discover it?

[Illustration]

200.—­A KITE-FLYING PUZZLE.

While accompanying my friend Professor Highflite during a scientific kite-flying competition on the South Downs of Sussex I was led into a little calculation that ought to interest my readers.  The Professor was paying out the wire to which his kite was attached from a winch on which it had been rolled into a perfectly spherical form.  This ball of wire was just two feet in diameter, and the wire had a diameter of one-hundredth of an inch.  What was the length of the wire?