define a box packing as *gap-less* if 
- all inner boxes have disjoint interior
- the sum of volumes of the inner box equals that of the outer box
- the sum of the extents of the inner boxes in each principal direction equals that of the outer box  

define a box paxking as *stable* if 
- for every hyperplane with a point inside the outer box there is an inner box with inner points to both sides of that hyperplane.  

**Questions:**  
>- for which $k$, depending on dimension $n$ of the boxes do stable gap-less packings of boxes with boxes exist?  
>- how can such packings be found, given $k$ and $n$?  

In $2{-}d$ there are many examples from [squaring the square](https://en.wikipedia.org/wiki/Squaring_the_square) which is a very special case of this question for $n=2$; this question allows boxes of equal size and arbitrary extents in each principal direction.