Question 94
Let $P_1, P_2, \dots, P_{2021}$ be $2021$ points in the quarter plane $\{(x, y) \mid x \ge 0, y \ge 0\}$.
The centroid of these $2021$ points lies at the point $(1, 1)$.
Show that there are two distinct points $P_i, P_j$ such that the distance from $P_i$ to $P_j$ is no more than $\sqrt{2}/20$.
The centroid of these $2021$ points lies at the point $(1, 1)$.
Show that there are two distinct points $P_i, P_j$ such that the distance from $P_i$ to $P_j$ is no more than $\sqrt{2}/20$.