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BOARDS WITH AN ODD NUMBER OF SQUARES.





(Chessboard Problems)
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]


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