THE FOUR KANGAROOS.
(
The Guarded Chessboard)
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.
Answer:
A pretty symmetrical solution to this puzzle is shown in the diagram.
Each of the four kangaroos makes his little excursion and returns to his
corner, without ever entering a square that has been visited by another
kangaroo and without crossing the central line. It will at once occur to
the reader, as a possible improvement of the puzzle, to divide the board
by a central vertical line and make the condition that this also shall
not be crossed. This would mean that each kangaroo had to confine
himself to a square 4 by 4, but it would be quite impossible, as I shall
explain in the next two puzzles.
