2007 OIM Problems/Problem 3

Problem

Two teams, $A4 and$ B $, dispute the territory limited by a circle.$ A $has$ n $blue flags and$ B $has$ n $white flags ($ n \ge 2 $, fixed). They play alternately and the game begins. Each team, in turn, places one of its flags at a point on the circumference that has not been used in a previous play. Once a flag is placed you can't change its location. Once the$ 2n $flags have been placed, the territory is divided between the two teams. A territory point belongs to team$ A $if the flag closest to it is blue, and to team$ B $if the flag closest to it is white. If the blue flag closest to a point is the same distance as the nearest white flag to that point, then the point is neutral (it is neither$ A $nor$ B $).$ A $team wins the game if its points cover an area greater than the area covered by the other team's points. There is a tie if both areas covered are equal. Show that, for all$ n $, team$ B$ has a strategy to win the game.