Question 3
Kolya stands in the plane together with 2020 other grasshoppers. He jumps over each of them once in an arbitrary order. At each jump the grasshopper jumped over is the midpoint of Kolya's starting and finishing positions. A point is a possible finishing point if some order puts Kolya there after 2020 jumps. What is the largest possible number $N$ of finishing points, over all initial placements? (7 points)
Neutral editorial illustration.
Neutral editorial illustration.