A strip of width w is the set of all points which lie on, or between, two parallel lines distance w apart. Let S be a set of n (n≥3) points on the plane such that any three different points of S can be covered by a strip of width 1.
Prove that S can be covered by a strip of width 2. inductiongeometrytrigonometrycombinatorics proposedcombinatoricsExtremal combinatorics