Question 73
Determine all positive integers $n \ge 2$ for which the following statement is true:
Given any $n$ distinct points on the plane such that the distance between each pair of points is distinct, there exists a pair of points $A$, $B$ for which the difference between the number of points lying on either side of the perpendicular bisector of segment $AB$ is not greater than $1$.
Given any $n$ distinct points on the plane such that the distance between each pair of points is distinct, there exists a pair of points $A$, $B$ for which the difference between the number of points lying on either side of the perpendicular bisector of segment $AB$ is not greater than $1$.