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The Royal Gardens

It was now daylight, and still had I to pass through the royal gardens outside of the castle walls.
These gardens had once been laid out by an old king's gardener, who had become bereft of his senses, but was allowed to amuse himself therein.
They were square, and divided into 16 parts by high walls, as shown in the plan thereof, so that there were openings from one garden to another, but only two different ways of entrance.
Now, it was needful that I enter at the gate A and leave by the other gate B; but as there were gardeners going and coming about their work, I had to slip with agility from one garden to another, so that I might not be seen, but escape unobserved.
I did succeed in so doing, but afterwards remembered that I had of a truth entered every one of the 16 gardens once, and never more than once.
This was, indeed, a curious thing.

How might it have been done?

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