MathDB

Let

n \ge 4

and

k

be positive integers. We consider

n

lines in the plane between which there are not two parallel nor three concurrent. In each of the

\frac{n(n-1)}{2}

points of intersection of these lines,

k

coins are placed. Ana and Beto play the following game in turns: each player, in turn, chooses one of those points that does not share one of the

n

lines with the point chosen immediately before by the other player, and removes a coin from that point. Ana starts and can choose any point. The player who cannot make his move loses. Determine based on

n

and

k

who has a winning strategy.

Problem Statement