away" the puzzle, but it
should not destroy its interest to those who like to discover the
"reason why."

149.--THE CHOCOLATE SQUARES.

Here is a slab of chocolate, indented at the dotted lines so that the
twenty squares can be easily separated. Make a copy of the slab in paper
or cardboard and then try to cut it into nine pieces so that they will
form four perfect squares all of exactly the same size.

150.--DISSECTING A MITRE.

The figure that is perplexing the carpenter in the illustration
represents a mitre. It will be seen that its proportions are those of a
square with one quarter removed. The puzzle is to cut it into five
pieces that will fit together and form a perfect square. I show an
attempt, published in America, to perform the feat in four pieces, based
on what is known as the "step principle," but it is a fallacy.

[Illustration]

We are told first to cut oft the pieces 1 and 2 and pack them into the
triangular space marked off by the dotted line, and so form a rectangle.

So far, so good. Now, we are directed to apply the old step principle,
as shown, and, by moving down the piece 4 one step, form the required
square. But, unfortunately, it does _not_ produce a square: only an
oblong. Call the three long sides of the mitre 84 in. each. Then, before
cutting the steps, our rectangle in three pieces will be 84 x 63. The
steps must be 101/2 in. in height and 12 in. in breadth. Therefore, by
moving down a step we reduce by 12 in. the side 84 in. and increase by
101/2 in. the side 63 in. Hence our final rectangle must be 72 in. x 731/2
in., which certainly is not a square! The fact is, the step principle
can only be applied to rectangles with sides of particular relative
lengths. For example, if the shorter side in this case were 61+5/7
(instead of 63), then the step method would apply. For the steps would
then be 10+2/7 in. in height and 12 in. in breadth. Note that 61+5/7 x
84 = the square of 72. At present no solution has been found in four
pieces, and I do not believe one possible.

151.--THE JOINER'S PROBLEM.

I have often had occasion to remark on the practical utility of puzzles,
arising out of an application to the ordinary affairs of life of the
little tricks and "wrinkles" that we learn while solving recreation
problems.

[Illustration]

The joiner, in the illustration, wants to cut the piece of wood into as
few pieces as possible to form a square table-top, without any waste of
m