6

Part of 2009 Chile National Olympiad

Problems(1)

n green points in plane

Source: Chile Finals 2009 L2 p6

n \ge 6

green points in the plane, such that no

3

of them are collinear. Suppose further that

6

of these points are the vertices of a convex hexagon. Prove that there are

5

green points that form a pentagon that does not contain any other green point inside.

pointsgeometrycombinatoricscombinatorial geometry