Question 168
Find the minimal integer $n \ge 3$ such that there exist $n$ points $A_1, A_2, \dots, A_n$ on a plane with no three being collinear, such that for every $1 \le i \le n$, the midpoint of the segment $A_iA_{i+1}$ is contained in the segment $A_jA_{j+1}$ for some $j \ne i$. Here, $A_{n+1} = A_1$.