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Re: Continous path on square grid
Posted:
Feb 1, 2013 10:29 AM
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On Feb 1, 3:23 pm, Willem <wil...@turtle.stack.nl> wrote:
> Willem wrote:
> ) clive tooth wrote:
>
> ) ) Let a P(n,s) be a continuous path, made of s straight sections, which
> ) ) passes exactly once through each of n^2 points arranged in a square
> ) ) array.
> ) )
> ) ) So, here is a P(3,4)...
> ) )http://www.flickr.com/photos/lhc_logs/8435448440/in/photostream
> ) )
> ) ) I know of a P(4,6). But I cannot find a P(5,8). Any takers?
> )
> ) IIRC, I figured out a way to get P(n,n*2-2) by beginning at P(4,6) in
> ) such a way that adding a row and column required two extra lines.
> )
> ) I can't remember exactly what that beginning sequence was though.
>
> Ah yes, now I remember. If you take the 3x3 solution you posted, the last
> line can be extended upward, and then you can draw lines right and down,
> adding a row and column to the top and right respectively. From there on
> you can keep on spiraling outward.
>
> (Fixed width)
>
> 8-O-O-O-O-9
> | |
> O 4-O-O-5 O
> | | | |
> O 1-O-O-2 O
> | |\ /| |
> O O O O O O
> | | X | |
> O O O # O O
> | |/ | |
> 7-3-O-O-6 10
Your line 34 passes through point 1.
I think you have overlooked the "... passes exactly once through each
[point] ..." condition.
--
Clive
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