Question 21
Let $n$ be a given positive integer. For a finite set $M$ of points in the plane, we say that distinct points $A, B \in M$ are connected if the line $AB$ contains exactly $n+1$ points in $M$.
Determine the smallest positive integer $m$ for which there exists a set $M$ of $m$ points in the plane with the property that any point $A \in M$ is connected to exactly $2n$ other points in $M$.
Determine the smallest positive integer $m$ for which there exists a set $M$ of $m$ points in the plane with the property that any point $A \in M$ is connected to exactly $2n$ other points in $M$.