game with sum of distances betewen 2n points
Source: Rioplatense 1995 L3 P5
September 19, 2022
geometry
Problem Statement
Consider points in the plane. Two players and alternately choose a point on each move. After moves, there are no points left to choose from and the game ends.
Add up all the distances between the points chosen by and add up all the distances between the points chosen by . The one with the highest sum wins.
If starts the game, describe the winner's strategy.Clarification: Consider that all the partial sums of distances between points give different numbers.