Tim Little wrote: > On 2012-10-01, quasi <email@example.com> wrote: > > Let C be a cube in R^3 and suppose S is a subset of C such that > > each (closed) face of C contains at least one point of S. > > > > Prove or disprove: > > > > Of all cubes that contain S, C has the least volume. > > Disproof: Let S = intersection of unit cube centered at the origin > with the coordinate axes. There is a smaller cube that contains S; > one that is not aligned with the coordinate axes.
Seems plausible, but not obvious. Can you show the explicit such smaller cube?