MathDB

Let

P

be a convex polygon. Prove that there exists a convex hexagon that is contained in

P

and whose area is at least

\frac34

of the area of the polygon

P

.
Alternative version. Let

P

be a convex polygon with

n\geq 6

vertices. Prove that there exists a convex hexagon with
a) vertices on the sides of the polygon (or) b) vertices among the vertices of the polygon
such that the area of the hexagon is at least

\frac{3}{4}

of the area of the polygon.
Proposed by Ben Green and Edward Crane, United Kingdom

Problem Statement