You are given a list of points. Connect all points with the minimum total cost. The cost of connecting two points is the Manhattan distance between them. This is an MST problem on a complete graph.
Every pair of points has an edge. The job: find the MST. The twist: edges are implicit, not given directly. You compute them on demand. This tests whether you can apply MST to geometric problems. With points, there are edges, so you need an efficient MST algorithm.