Covering Problems
Place equal discs over a container without leaving any hole, then make their shared radius as small as possible. This hub collects the site's continuous-covering families: every construction is scored by its hardest-to-reach point.
Covering reverses packing
Packing forbids overlap and asks how large the circles can be. Covering allows any overlap but requires every point of the container to lie in at least one disc, and asks how small the shared radius can be. Centres that look evenly spread are not enough: boundaries, corners and holes between several discs can all become the worst point that sets the score.
The verifier does not blindly sample the plane. It checks the finite candidates that can be worst in the Voronoi structure: container vertices, boundary intersections and interior Voronoi vertices. A submission is therefore still just a list of centres, and the server can recompute its covering radius deterministically.
Three containers, three independent frontiers
Place n points in the unit square and grow a disc of the same radius around each. The discs must cover the whole square, leaving nothing out; make that shared radius as small as you can.
31 sub-problems · 29 open · 26 with external sourcesPlace n centres in a unit equilateral triangle and minimise the common radius needed to cover every point of it.
34 sub-problems · 32 open · 30 with external sourcesPlace n centres in a regular pentagon and minimise the common radius needed to cover the whole container.
29 sub-problems · 29 open · 4 with external sources