2 ms·
My natural interpretation of "equivalent" would be a 1 wide, 1 tall corridor, and the goal is to maximise the volume instead of the area.
by VorpalWay 9mo ago
My natural interpretation of "equivalent" would be a 1 wide, 1 tall corridor, and the goal is to maximise the volume instead of the area.
- layer8 9mo agoIt seems pretty obvious that the 2D solution is still optimal in that case, by making the sofa maximally tall (1) at all points. Though I don’t know if it has been proven yet.
- VorpalWay 9mo agoThat does seem like a reasonable guess, yet it was only in 1992 that the current (now proven optimal) solution to the 2D case was proven so. You could make the 3D case more interesting by having two corners: one in the plane and one out of the plane. It seems to me that that would need a new solution.
- layer8 9mo agoCertainly, and so would a 2D solution that has to support both left and right turns. To make 3D relevant for a single turn, one of the hallways could be rotated 45° lengthwise.