I made up this interesting problem playing with wire sculptures:
If I have a $10 \times 10 \times 10$ clear box and inside I can put wireframe unit cubes, what's the maximum number of unit edges (or total edge length) I can get if I must have exactly $800$ unit cubes in my box? Every unit cube is clear and you can see all $12$ edges, and if two unit cubes are connected by an edge it only counts as a single edge. The unit cubes can float, too and must be on lattice points.
My guess would be to spread out the unit cubes as much as possible to get the most unique edges. Is this equivalent to spreading out the "air pockets" as well as possible? I believe this is some kind of packing problem, but I don't have any experience with those.