Problem

Source:

Tags: combinatorial geometry, game strategy



An integer $n > 1$ is given. Two players in turns mark points on a circle. First Player uses red color while Second Player uses blue color. The game is over when each player marks $n$ points. Then each player nds the arc of maximal length with ends of his color, which does not contain any other marked points. A player wins if his arc is longer (if the lengths are equal, or both players have no such arcs, the game ends in a draw). Which player has a winning strategy?