As a final poser for those who like to puzzle their brains, I give the following as a problem. Place the men in due order on the draught-board, and then by a series of legal moves reverse the position of the men, that is, the Black men must stand where the White men came from, and vice versa.
Quaternions.—Quaternions is the name of a somewhat easy yet interesting game played on a checkered board (similar to a draughts board) with thirty-two counters or draughtsmen (sixteen white and sixteen black). The players move alternately by placing one of their men on a white square of the board, and the object of the game is to get four men of the same colour in a line, either perpendicular, horizontal, or diagonally, and the player who first succeeds in doing this wins the game. Of course, each player also does his best to stop his opponent from forming his quaternion or file of four. Should neither player be able to form a quaternion, then the game is drawn.
To show clearly what a quaternion is, I give the following diagram:—
Fig. 26.
The four men on squares 1, 2, 3, and 4, form a quaternion, and similarly do those on 5, 13, 21, and 29, and those on 10, 15, 19, and 24. The numbers here given to the squares are the same as in draughts. The point to be borne in mind in playing the game is to try to unite a perpendicular with a horizontal line of squares, or with a diagonal line. By careful play three men can be got on one of these lines, and three on a communicating line, each having a vacant square. The player of the opposite colour can fill only one of these squares, and consequently cannot prevent the formation of the quaternion on the other line.
The most careful play on both sides is required from the very first move, or the game can be forced right off. I give a diagram of an opening:—
Fig. 27.