MEMO 2017 ekipno problem 4
Let be an integer. A sequence of distinct points in the plane is called good if no three of them are collinear, the polyline is non-self-intersecting and the triangle is oriented counterclockwise for every . For every integer determine the greatest possible integer with the following property: there exist distinct points in the plane for which there are distinct permutations such that is good.
(A polyline consists of the segments .)