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Re: Path through a 3x3x3 grid
Posted:
Feb 26, 2013 4:59 PM


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 planetoplane 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:
http://www.flickr.com/photos/lhc_logs/sets/72157632868867524/
 Clive Tooth



