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Re: Continous path on square grid
Posted:
Feb 6, 2013 6:36 AM
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clive tooth wrote:
>
> 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/
That's neat. What algorithm did you use to find the paths? The answer
may be long and complicated, and if so I'll not press you for it; but if
it's short and simple I wouldn't mind knowing.
--
When a true genius appears in the world, you may know him by
this sign, that the dunces are all in confederacy against him.
Jonathan Swift: Thoughts on Various Subjects, Moral and Diverting
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