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 tournament was held at Lhassa among the priests, and whenever any one beat the Grand Lama it was considered a great honour, and his name was inscribed on the back of the board, and a costly jewel set in the particular square on which the checkmate had been given. After this sovereign pontiff had been defeated on four occasions he died--possibly of chagrin. [Illustration: +---+---+---+---+---+---+---+---+ | * | | | | | | | | +---+---+---+---+---+---+---+---+ | | * | | | | | | | +---+---+---+---+---+---+---+---+ | | | * | | | | | | +---+---+---+---+---+---+---+---+ | | | | * | | | | | +---+---+---+---+---+---+---+---+ | | | | | | | | | +---+---+---+---+---+---+---+---+ | | | | | | | | | +---+---+---+---+---+---+---+---+ | | | | | | | | | +---+---+---+---+---+---+---+---+ | | | | | | | | | +---+---+---+---+---+---+---+---+ ]