MathDB

A regular hexagon in the plane is called sweet if its area is equal to

1

. Is it possible to place

2000000

sweet hexagons in the plane such that the union of their interiors is a convex polygon of area at least

1900000

?
Remark: A subset

S

of the plane is called convex if for every pair of points in

S

, every point on the straight line segment that joins the pair of points also belongs to

S

. The hexagons may overlap.

Problem Statement