Question: Let a point in 3D space. Let cubes with edges of arbitrary sizes. How many cubes with disjoint interiors can actually contain this point? The cubes of the solution can be of different sizes.
Ideas: There is a possible answer of 8 cubes of the same arbitrary size a. Make a cube where each edge is equal to $2∗a$ using 8 cubes. The center of this cube touches 8 cubes. Can you think of a better arrangement?
The problem seems somehow relevant to the kissing number, but it seems more general. Any feedback would be welcome