Question 20
Let $n \ge 4$ and $k$ be positive integers. We consider $n$ lines on the plane such that no two of them are parallel and no three of them intersect in a single point. On each of the $\frac{n(n-1)}{2}$ intersection points of these lines there are $k$ coins. Ana and Beto play the following game: each player, in their turn, chooses a point that does not lie on the same line as the point chosen in the previous turn by the other player, and discards one coin from that point. Ana makes the first move and she can choose any point. The player who cannot make a move loses the game.
Determine, for each value of $n$ and $k$, which player has a winning strategy.
Determine, for each value of $n$ and $k$, which player has a winning strategy.