Question 155
By a *strip* of breadth $b$ we mean a closed part of the plane consisting of all points that lie between two parallel lines at distance $b$ from each other. Let $S$ be a finite set of $n$ ($n \ge 4$) points in the plane, such that any three points from $S$ can be covered by a strip of breadth 1. Prove that $S$ can be covered by a strip of breadth 2.