f course a half-square rectangle is the same as a double square, or two
equal squares joined together. Therefore, if you want to solve the
puzzle of cutting a Greek cross into four pieces to form two separate
squares of the same size, all you have to do is to continue the short
cut in Fig. 38 right across the cross, and you will have four pieces of
the same size and shape. Now divide Fig. 37 into two equal squares by a
horizontal cut midway and you will see the four pieces forming the two
squares.

[Illustration: FIG. 41]

Cut a Greek cross into five pieces that will form two separate squares,
one of which shall contain half the area of one of the arms of the
cross. In further illustration of what I have already written, if the
two squares of the same size A B C D and B C F E, in Fig. 41, are cut in
the manner indicated by the dotted lines, the four pieces will form the
large square A G E C. We thus see that the diagonal A C is the side of a
square twice the size of A B C D. It is also clear that half the
diagonal of any square is equal to the side of a square of half the
area. Therefore, if the large square in the diagram is one of the arms
of your cross, the small square is the size of one of the squares
required in the puzzle.

The solution is shown in Figs. 42 and 43. It will be seen that the small
square is cut out whole and the large square composed of the four pieces
B, C, D, and E. After what I have written, the reader will have no
difficulty in seeing that the square A is half the size of one of the
arms of the cross, because the length of the diagonal of the former is
clearly the same as the side of the latter. The thing is now
self-evident. I have thus tried to show that some of these puzzles that
many people are apt to regard as quite wonderful and bewildering, are
really not difficult if only we use a little thought and judgment. In
conclusion of this particular subject I will give four Greek cross
puzzles, with detached solutions.

142.--THE SILK PATCHWORK.

The lady members of the Wilkinson family had made a simple patchwork
quilt, as a small Christmas present, all composed of square pieces of
the same size, as shown in the illustration. It only lacked the four
corner pieces to make it complete. Somebody pointed out to them that if
you unpicked the Greek cross in the middle and then cut the stitches
along the dark joins, the four pieces all of the same size and shape
would fit together and form a