Kearting [Dividing plane to convex sets]
Source: Iranian National Math Olympiad (Final exam) 2006
September 19, 2006
geometry proposedgeometry
Problem Statement
We have finite number of distinct shapes in plane. A "convex Kearting" of these shapes is covering plane with convex sets, that each set consists exactly one of the shapes, and sets intersect at most in border.
http://aycu30.webshots.com/image/4109/2003791140004582959_th.jpg
In which case Convex kearting is possible?
1) Finite distinct points
2) Finite distinct segments
3) Finite distinct circles