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MathNet 2019-part-05 — 184 problems (EN–VI) Question 157

Math Olympiad Vault · MathNet 2019-part-05 — 184 problems (EN–VI)

Question 157

Several cardboard rectangles, possibly of different sizes, are put onto a rectangular table; the sides of rectangles are parallel to those of the table. The rectangles may overlap, but there are no two rectangles with four common vertices. May it happen that each point which is a vertex of some rectangle is in fact a vertex of exactly three rectangles?
(I. Bogdanov)