Question 52
A strip of breadth $\ell$ is the set of those points in the plane, situated between or on two parallel lines at distance $\ell$ one from the other.
Consider a finite set $S$ of $n \geq 3$ (distinct) points in the plane, with the property that any three points of $S$ can be covered by a strip of breadth 1. Prove the set $S$ can be covered by a strip of breadth 2.
Consider a finite set $S$ of $n \geq 3$ (distinct) points in the plane, with the property that any three points of $S$ can be covered by a strip of breadth 1. Prove the set $S$ can be covered by a strip of breadth 2.