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Bosnia and Herzegovina TST 2003 Day 2 Problem 2

Source: Bosnia and Herzegovina Team Selection Test 2003

September 18, 2018
polygonquadrilateralcombinatorial geometrycombinatorics

Problem Statement

It is given regular polygon with 2n2n sides and center SS. Consider every quadrilateral with vertices as vertices of polygon. Let uu be number of such quadrilaterals which contain point SS inside and vv number of remaining quadrilaterals. Find uāˆ’vu-v