Question 100
There are $n$ rays $OA_1, OA_2, ..., OA_n$ that start at point $O$ and are enumerated counterclockwise on a plane so that $\angle A_1OA_n \lt 180^\circ$. Determine the smallest $n$ such that there exists a pair of $60^\circ$ angles, a pair of $45^\circ$ angles and a pair of $30^\circ$ angles among angles $\angle A_iOA_j$, $1 \le i \lt j \le n$.
(Bogdan Rublyov)
Fig. 1
(Bogdan Rublyov)
Fig. 1