Question 162
Given a polygon with $2016$ vertices. Alisa and Basilio play the following game. In each turn a player draws a diagonal of the polygon which intersects the other drawn diagonals or the sides only at the vertices. When the polygon is cut into triangles the game is finished. For each triangle having exactly zero sides among the sides of the initial polygon Alisa is paid $1$ cent. For each triangle having exactly two sides among the sides of the initial polygon Basilio is paid $1$ cent. Who will get more money and what would be the difference if both are clever players?
Fig. 02
Fig. 02