VARIOUS DISSECTION PUZZLES.

We will now consider a small miscellaneous selection of cutting-out puzzles, varying in degrees of difficulty.

146.—­AN EASY DISSECTION PUZZLE.

First, cut out a piece of paper or cardboard of the shape shown in the illustration.  It will be seen at once that the proportions are simply those of a square attached to half of another similar square, divided diagonally.  The puzzle is to cut it into four pieces all of precisely the same size and shape.

147.—­AN EASY SQUARE PUZZLE.

If you take a rectangular piece of cardboard, twice as long as it is broad, and cut it in half diagonally, you will get two of the pieces shown in the illustration.  The puzzle is with five such pieces of equal size to form a square.  One of the pieces may be cut in two, but the others must be used intact.

148.—­THE BUN PUZZLE.

THE three circles represent three buns, and it is simply required to show how these may be equally divided among four boys.  The buns must be regarded as of equal thickness throughout and of equal thickness to each other.  Of course, they must be cut into as few pieces as possible.  To simplify it I will state the rather surprising fact that only five pieces are necessary, from which it will be seen that one boy gets his share in two pieces and the other three receive theirs in a single piece.  I am aware that this statement “gives 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