Question 198
Given an integer $n \ge 16$, consider the set
$$
G = \{(x, y) : x, y \in \{1, 2, \dots, n\}\}
$$
consisting of $n^2$ points in the plane. Let $A$ be any subset of $G$ containing at least $4n\sqrt{n}$ points. Prove that there are at least $n^2$ convex quadrangles with all their vertices in $A$ such that their diagonals intersect in one common point.
$$
G = \{(x, y) : x, y \in \{1, 2, \dots, n\}\}
$$
consisting of $n^2$ points in the plane. Let $A$ be any subset of $G$ containing at least $4n\sqrt{n}$ points. Prove that there are at least $n^2$ convex quadrangles with all their vertices in $A$ such that their diagonals intersect in one common point.