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partition a square into n^2+1 disjointed rectangles with // sides to square

Source: Mathematics Regional Olympiad of Mexico West 2021 P6

September 9, 2022

geometrycombinatoricscombinatorial geometryRectanglestiles

Problem Statement

Let

n

be an integer greater than

3

. Show that it is possible to divide a square into

n^2 + 1

or more disjointed rectangles and with sides parallel to those of the square so that any line parallel to one of the sides intersects at most the interior of

n

rectangles.
Note: We say that two rectangles are disjointed if they do not intersect or only intersect at their perimeters.

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