A gardener wants to trisect his rectangular garden into three parts, with the proviso that he can neither enter on the left and leave on the right AND nor can he enter at the top and leave at the bottom.
But he can't seem to do it! Can you?
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that this is impossible.
Each of the four corners must belong to one of the three sections. By the pigeonhole principle, at least one section must own at least two corners, and since that section is a traversable region, there exists a path between those two corners. However, this is disallowed, since it will traverse either the entire horizontal length or vertical with (or both) of the field. The trisection is thus impossible.
If he trisects the garden like a flag of the Czech republic (depicted below) (by color), all conditions will be satisfied (note that white-blue and red-blue borders go exactly to the corners).