MathDB

Convex polygons

Source: Balkan MO 2007

April 28, 2007

floor functiongeometrygeometric transformationrotationcombinatorial geometrycombinatorics unsolvedcombinatorics

Problem Statement

For a given positive integer

n >2

, let

C_{1},C_{2},C_{3}

be the boundaries of three convex

n-

gons in the plane , such that

C_{1}\cap C_{2}, C_{2}\cap C_{3},C_{1}\cap C_{3}

are finite. Find the maximum number of points of the sets

C_{1}\cap C_{2}\cap C_{3}