MathDB

5

Part of 1995 Rioplatense Mathematical Olympiad, Level 3

Problems(1)

game with sum of distances betewen 2n points

Source: Rioplatense 1995 L3 P5

9/19/2022
Consider 2n2n points in the plane. Two players AA and BB alternately choose a point on each move. After 2n2n moves, there are no points left to choose from and the game ends. Add up all the distances between the points chosen by AA and add up all the distances between the points chosen by BB. The one with the highest sum wins. If AA starts the game, describe the winner's strategy.
Clarification: Consider that all the partial sums of distances between points give different numbers.
geometry