Can you always pair an equal number of red and blue points with no intersection?

The video tutorial explains a geometric problem involving pairing red and blue points in a plane such that no line segments intersect. The problem is based on a 1979 Putnam exam question. The solution involves ordering pairing configurations by the total length of line segments and proving that the configuration with the shortest total length has no intersections. The video also introduces a related problem about point distances.

What new insight or understanding did you gain from this video?