Search All of the Math Forum:

Views expressed in these public forums are not endorsed by NCTM or The Math Forum.

Notice: We are no longer accepting new posts, but the forums will continue to be readable.

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

 Messages: [ Previous | Next ]
 The Last Danish Pastry Posts: 740 Registered: 12/13/04
Path through a 3x3x3 grid
Posted: Feb 20, 2013 10:46 AM

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.

Can you find such a path?

Suggested notation:

The grid consists of all points (x,y,z) with x, y and z being integers
satisfying 0 <= x, y, z <= 2. For a path, give the starting point and
all subsequent "target points".

So a path might begin:
(0, 0, 2)
(-2, 2, 0)
...

--
Clive Tooth