5

Part of 2003 Bosnia and Herzegovina Team Selection Test

Problems(1)

Bosnia and Herzegovina TST 2003 Day 2 Problem 2

Source: Bosnia and Herzegovina Team Selection Test 2003

It is given regular polygon with

2n

sides and center

S

. Consider every quadrilateral with vertices as vertices of polygon. Let

u

be number of such quadrilaterals which contain point

S

v

number of remaining quadrilaterals. Find

u-v

polygonquadrilateralcombinatorial geometrycombinatorics