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Intersection of polygons

Source: Romania TST 1995 Test 2 P2

February 22, 2014
geometrygeometry proposed

Problem Statement

Suppose that nn polygons of area s=(n−1)2s = (n - 1)^2 are placed on a polygon of area S=n(n−1)22S = \frac{n(n - 1)^2}{2}. Prove that there exist two of the nn smaller polygons whose intersection has the area at least 11.
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