point of your compasses at D and with the
distance D E describe the arc cutting the circumference at F. Now, D F
is one of the sides of your pentagon, and you have simply to mark off
the other sides round the circle. Quite simple when you know how, but
otherwise somewhat of a poser.

[Illustration]

Having formed your pentagon, the puzzle is to cut it into the fewest
possible pieces that will fit together and form a perfect square.

[Illustration]

156.--THE DISSECTED TRIANGLE.

A good puzzle is that which the gentleman in the illustration is showing
to his friends. He has simply cut out of paper an equilateral
triangle--that is, a triangle with all its three sides of the same
length. He proposes that it shall be cut into five pieces in such a way
that they will fit together and form either two or three smaller
equilateral triangles, using all the material in each case. Can you
discover how the cuts should be made?

Remember that when you have made your five pieces, you must be able, as
desired, to put them together to form either the single original
triangle or to form two triangles or to form three triangles--all
equilateral.

157.--THE TABLE-TOP AND STOOLS.

I have frequently had occasion to show that the published answers to a
great many of the oldest and most widely known puzzles are either quite
incorrect or capable of improvement. I propose to consider the old poser
of the table-top and stools that most of my readers have probably seen
in some form or another in books compiled for the recreation of
childhood.

The story is told that an economical and ingenious schoolmaster once
wished to convert a circular table-top, for which he had no use, into
seats for two oval stools, each with a hand-hole in the centre. He
instructed the carpenter to make the cuts as in the illustration and
then join the eight pieces together in the manner shown. So impressed
was he with the ingenuity of his performance that he set the puzzle to
his geometry class as a little study in dissection. But the remainder of
the story has never been published, because, so it is said, it was a
characteristic of the principals of academies that they would never
admit that they could err. I get my information from a descendant of the
original boy who had most reason to be interested in the matter.

The clever youth suggested modestly to the master that the hand-holes
were too big, and that a small boy might perhaps fall through them.