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## 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.

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