On Feb 20, 3:46 pm, Clive Tooth <cli...@gmail.com> wrote:
> There is a (well known) continuous path, made of four straight > sections, which passes exactly once through each of 9 points arranged > in a square 3x3 array. > > Using three of these paths, plus two plane-to-plane straight sections, > it is clearly possible to make a continuous path, made of 14 straight > sections, which passes exactly once through each of 27 points arranged > in a 3x3x3 grid. > > However, there is at least one such path made up of only 13 straight > sections.
I believe that there are exactly 26 essentially distinct paths through the 27 points of the 3x3x3 grid. Here are images of all of them: