NS.

The young lady in the illustration is confronted with a little
cutting-out difficulty in which the reader may be glad to assist her.
She wishes, for some reason that she has not communicated to me, to cut
that square piece of valuable material into four parts, all of exactly
the same size and shape, but it is important that every piece shall
contain a lion and a crown. As she insists that the cuts can only be
made along the lines dividing the squares, she is considerably perplexed
to find out how it is to be done. Can you show her the way? There is
only one possible method of cutting the stuff.

[Illustration:

+-+-+-+-+-+-+
| | | | | | |
+-+-+-+-+-+-+
| |L|L|L| | |
+-+-+-+-+-+-+
| | |C|C| | |
+-+-+-+-+-+-+
| | |C|C| | |
+-+-+-+-+-+-+
|L| | | | | |
+-+-+-+-+-+-+
| | | | | | |
+-+-+-+-+-+-+

]

290.--BOARDS WITH AN ODD NUMBER OF SQUARES.

We will here consider the question of those boards that contain an odd
number of squares. We will suppose that the central square is first cut
out, so as to leave an even number of squares for division. Now, it is
obvious that a square three by three can only be divided in one way, as
shown in Fig. 1. It will be seen that the pieces A and B are of the same
size and shape, and that any other way of cutting would only produce the
same shaped pieces, so remember that these variations are not counted as
different ways. The puzzle I propose is to cut the board five by five
(Fig. 2) into two pieces of the same size and shape in as many different
ways as possible. I have shown in the illustration one way of doing it.
How many different ways are there altogether? A piece which when turned
over resembles another piece is not considered to be of a different
shape.

[Illustration:

+---*---+---+
| H | |
+---*===*---+
| HHHHH |
+---*===*---+
| | H |
+---+---*---+

Fig 1]

[Illustration:

+---+---+---+---+---+
| | | | | |
*===*===*===*---+---+
| | | H | |
+---+---*===*---+---+
| | HHHHH | |
+---+---*===*---+---+
| | H | | |
+---+---*===*===*===*
| H | | | |
+---*---+---+---+---+

Fig 2]

291.--THE GRAND LAMA'S PROBLEM.

Once upon a time there was a Grand Lama who had a chessboard made of
pure gold, magnificently engraved, and, of course, of great value. Every
year a