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3 polygons of area 3 inside square of area 6 (HOMC 2018 Ind. p9)

Source:

January 31, 2020
geometrycombinatorial geometrygeometric inequalityarea

Problem Statement

There are three polygons and the area of each one is 33. They are drawn inside a square of area 66. Find the greatest value of mm such that among those three polygons, we can always find two polygons so that the area of their overlap is not less than mm.
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