Moving The Knight Over All The Squares Alternately. The problem respecting the placing the knight on any given square, and moving him from that square to any house on the board, has not been thought unworthy the attention of the first mathematicians. Euler, Ozanam, De Montmart. De Moivre, De Majron, and others, have all given methods by which this feat might be accomplished. It was reserved, however, for the present century to lay this down on a general plan ; and the only English writer who has noticed this is Mr. George Walker, in his " Treatise on Chess." The plan is this : Let the knight be placed on any square, and move him from square to square, on the principle of always playing him to that point, from which, in actual play, he would command the fewest other squares; observing, that in reckoning the squares commanded by him you must omit such as he has already covered. If, too, there are two squares, on both of which his powers would be equal, you may move him to either. Try this on the board, with some counters or wafers, placing one on every square ; and, when you clearly understand it, you may astonish your friends by inviting them to station the knight on any square they like, and engaging to play him, from that square over the remaining sixty-three in sixty-three moves. When the automaton chess-player was last exhibited in England, this was made part of the wonders he accomplished, though an the above plan was not then known here, he could not adopt it, but used something like the method laid down by Euler, and which we subjoin.

Our young chess-players must remember that it does not matter on which square the knight is placed at starting ; as, by acquiring the plan by heart, which is soon done, he can play him over all the squares from any given point, his last square being at the distance of a knight's move from his first. It is obvious that this route may be varied many ways, and we have often amused ourselves by trying to work it on a slate.

Moving The Knight Over All The Squares Alternately 91

Euler's Method.