Delaunay Triangulation

On this topic:
https://en.wikipedia.org/wiki/Delaunay_triangulation

Trangulating a polygon means to split it up into smaller triangles.
Your Program could generate some random points and triangulate the konvex hull of them.

Then the challenge would be to find out which triangles are needed to be flipped to make a delaunay trangulation out of it.

Next you could make a voronoi diagram, which tells you areas that are closest to one of the point.
This is to be imagines like having multiples schools and finding the areas for each school to pull pupils from, based on travel distance.
To do so, you would have to make lines that are perpendicular to the edges of the triangles of the delaunay triangulation and they are cut off by each other.

I think you would be able to do the delaunay triangulation in one ~15 min coding challenge, but the voronoi diagram might be a bit harder.