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MMO 340 Moscow MO 1956 rectangles inside rectange, area overlap

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August 19, 2019
combinatoricscombinatorial geometryareasRectanglesgeometryrectangle

Problem Statement

a) * In a rectangle of area 55 sq. units, 99 rectangles of area 11 are arranged. Prove that the area of the overlap of some two of these rectangles is ≥1/9\ge 1/9
b) In a rectangle of area 55 sq. units, lie 99 arbitrary polygons each of area 11. Prove that the area of the overlap of some two of these rectangles is ≥1/9\ge 1/9
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