Seven knights can be placed on the board on white squares so as to attack every black square in two ways only. These are shown in Diagrams 1 and 2. Note that three knights occupy the same position in both arrangements. It is therefore clear that if we turn the board so that a black square shall be in the top left-hand corner instead of a white, and place the knights in exactly the same positions, we shall have two similar ways of attacking all the white squares. I will assume the reader has made the two last described diagrams on transparent paper, and marked them _1a_ and _2a_. Now, by placing the transparent Diagram _1a_ over 1 you will be able to obtain the solution in Diagram 3, by placing _2a_ over 2 you will get Diagram 4, and by placing _2a_ over 1 you will get Diagram 5. You may now try all possible combinations of those two pairs of diagrams, but you will only get the three arrangements I have given, or their reversals and reflections. Therefore these three solutions are all that exist. 320.--THE ROOK'S TOUR. [Illustration] The only possible minimum solutions are shown in the two diagrams, where it will be seen that only sixteen moves are required to perform the feat. Most people find it difficult to reduce the number of moves below seventeen*. [Illustration: THE ROOK'S TOUR.] 321.--THE ROOK'S JOURNEY. [Illustration] I show 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 chessboard can exceed this number of moves. [Illustration: THE LANGUISHING MAIDEN] [Illustration: A DUNGEON PUZZLE.] 324.--THE LION AND THE MAN.