Background
The idea of this article originated from a contest (Petrozavodsk Summer-2016. Petr Mitrichev Contest 14), which I believe is attributed to Petr. In this contest, an interesting problem is proposed:
"Cosider this process: pick a random number ni uniformly at random between 10 and 100. Generate ni random points with integer coordinates, picking each coordinate independently and uniformly at random from all integers between 0 and 109, inclusive. Find the convex hull of those points.
Now you are given 10000 polygons generated by this program. For each polygon, you need to guess the value ni that was used for generating it."
