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Topic: Continous path on square grid
Replies: 15   Last Post: Feb 6, 2013 7:04 PM

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The Last Danish Pastry

Posts: 736
Registered: 12/13/04
Re: Continous path on square grid
Posted: Feb 5, 2013 8:29 PM
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On Feb 5, 7:15 pm, m...@vex.net (Mark Brader) wrote:

> For a sufficiently asymmetrical path there are 16 variations possible,
> given by combinations of reflection, rotation, and end-to-end reversal.
> In some cases, of course, these will not all be distinct.
>

> > So I would guess that there are about 100 essentially distinct
> > solutions, probably less.

>
> Probably quite a bit less.


I agree with your remark about 16 variations. But my figure of 286
relates only to paths starting at one of the points (0,0) (1,0) (1,1)
(2,0) (2,1) or (2,2) - not every one of the 25 points in the grid.
Anyway, I have now written the code to discard duplicate solutions and
it turns out that there seem to be 118 essentially distinct
configurations. Here they are in a Flickr set...
http://www.flickr.com/photos/lhc_logs/sets/72157632699998440/

--
Clive Tooth



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