MathDB

There is

n

black points in the plane.We do the following algorithm: Start from any point from those

n

points and colour it red. Then connect this point to the nearest black point available and colour this new point red. Then do the same with this point but at any step , but you are never allowed to draw a line which intersects on of the current drawn segments. If you reach an intersection , the algorithm is over. Is it true that for any

n

and at any initial position , we can start from a point st in the algorithm , we reach all the points?

Problem Statement