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Topic: Path through a 3x3x3 grid
Replies: 3   Last Post: Feb 26, 2013 5:01 PM

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The Last Danish Pastry

Posts: 739
Registered: 12/13/04
Re: Path through a 3x3x3 grid
Posted: Feb 26, 2013 4:59 PM
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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:


Clive Tooth

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