s 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 t