Question 2
Suppose there are $997$ points given in a plane. If every two points are joined by a line segment with its midpoint coloured in red, show that there are at least $1991$ red points in the plane. Can you find a special case with exactly $1991$ red points?
Schematic: only a few of the given points and one midpoint are shown.
Schematic: only a few of the given points and one midpoint are shown.