Page:Amusements in mathematics.djvu/236

224 321.—THE ROOK'S JOURNEY.

the route in the diagram. It will be seen that the tenth move lands us at the square marked "10," and that the last move, the twenty-first, brings us to a halt on square " 21."

322.—THE LANGUISHING MAIDEN. The dotted line shows the route in twenty-two straight paths by which the knight may rescue the maiden. It is necessary, after entering the first cell, immediately to return before entering another. Otherwise a solution would not be possible. (See "The Grand Tour," p. 200.)

323.—A DUNGEON PUZZLE. If the prisoner takes the route shown in the diagram — where for clearness the doorways are omitted — he will succeed in visiting every cell once, and only once, in as many as fifty-seven straight lines. No rook's path over the chess- board can exceed this number of moves.

324.—THE LION AND THE MAN. of all, the fewest possible straight lines in each case are twenty-two, and in order that no cell may be visited twice it is absolutely necessary that each should pass into one cell and then immediately "visit" the one from which he started, afterwards proceeding by way of the second available cell. In the following diagram the man's route is indicated by the unbroken lines, and the lion's by the dotted lines. It will be found, if the two routes are followed cell by cell with two pencil points, that the lion and the man never meet. But there was one little point that ought not to be overlooked—"they occasionally got glimpses of one another." Now, if we take one route for the