Question 96
Suppose there are $2019$ points $A_1, A_2, \dots, A_{2019}$ on a circle that form the regular $2019$-gon $A_1A_2\dots A_{2019}$. Olesya and Andrew take turns, Olesya is the first to go. According to certain rules, Olesya makes a move to form an obtuse triangle, and Andrew – an acute triangle. The rules for forming triangles are as follows. At the beginning vertices $A_1$ and $A_2$ are supposed to be marked. In the first step Olesya marks an unmarked vertex $A_i$ so that $\Delta A_1A_2A_i$ is formed and vertex $A_i$ becomes marked. Let in the next step Olesya (Andrew) marked an unmarked earlier vertex $A_j$ and formed an obtuse (acute) $\Delta A_kA_lA_j$. Then in the next step Andrew (Olesya) can mark such an unmarked vertex $A_m$, for which an acute (obtuse) triangle $\Delta A_nA_jA_m$ is formed, where $n=k$ or $n=l$. One loses if not able to follow the rules to make another move, that is to mark the vertex to form a proper triangle. Who wins the game if both players play correctly?