One year he had a large square field divided into forty-nine square plots, as shown in the illustration.  The white squares were sown with wheat and the black squares with barley.  When the harvest time came round he gave orders that his men were first to cut the corn in the patch marked 1, and that each successive cutting should be exactly a knight’s move from the last one, the thirteenth cutting being in the patch marked 13, the twenty-fifth in the patch marked 25, the thirty-seventh in the one marked 37, and the last, or forty-ninth cutting, in the patch marked 49.  This was too much for poor Hodge, and each day Farmer Lawrence had to go down to the field and show which piece had to be operated upon.  But the problem will perhaps present no difficulty to my readers.

[Illustration]

336.—­THE GREYHOUND PUZZLE.

In this puzzle the twenty kennels do not communicate with one another by doors, but are divided off by a low wall.  The solitary occupant is the greyhound which lives in the kennel in the top left-hand corner.  When he is allowed his liberty he has to obtain it by visiting every kennel once and only once in a series of knight’s moves, ending at the bottom right-hand corner, which is open to the world.  The lines in the above diagram show one solution.  The puzzle is to discover in how many different ways the greyhound may thus make his exit from his corner kennel.

[Illustration]

337.—­THE FOUR KANGAROOS.

[Illustration]

In introducing a little Commonwealth problem, I must first explain that the diagram represents the sixty-four fields, all properly fenced off from one another, of an Australian settlement, though I need hardly say that our kith and kin “down under” always do set out their land in this methodical and exact manner.  It will be seen that in every one of the four corners is a kangaroo.  Why kangaroos have a marked preference for corner plots has never been satisfactorily explained, and it would be out of place to discuss the point here.  I should also add that kangaroos, as is well known, always leap in what we call “knight’s moves.”  In fact, chess players would probably have adopted the better term “kangaroo’s move” had not chess been invented before kangaroos.

The puzzle is simply this.  One morning each kangaroo went for his morning hop, and in sixteen consecutive knight’s leaps visited just fifteen different fields and jumped back to his corner.  No field was visited by more than one of the kangaroos.  The diagram shows how they arranged matters.  What you are asked to do is to show how they might have performed the feat without any kangaroo ever crossing the horizontal line in the middle of the square that divides the board into two equal parts.

338.—­THE BOARD IN COMPARTMENTS.

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