Problem

Source: Belarusian MO 2023

Tags: geometry, algebra



Positive integer $n$ is called good if there exist $n$ points on plane($X_1, \ldots, X_n$), such that for all $1 \leq i \leq n$ vectors $X_iX_1, \ldots, X_iX_n$ can be partitioned into two groups with equal sums. Find all good numbers