Date modified: Thu 2023-05-11 . 11:51 AM
Date created: Sat 2023-10-07 . 09:02 PM
# Pairing points with disjoint line segments. Given $2n$ points in the plane in **general position**, that is, **no three are colinear**. Color $n$ of them blue and $n$ of them red. Is it always possible to pair off a blue and a red point with a **straight line segment** in such a way that the line segments **never intersect**? ![[---images/--- pairing with disjoint line segments 2023-05-06 15.41.37.excalidraw.svg]] If so, why? If not, can you come up with a configuration of points so no matter you pair them, there will be two line segments that intersect? --- If you randomly pair them off, then you might run into intersections. Is it possible to fix them? #puzzle #discrete-geometry