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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: 740 Registered: 12/13/04
Re: Continous path on square grid
Posted: Feb 5, 2013 6:32 AM

On Feb 5, 5:56 am, fom <fomJ...@nyms.net> wrote:

> Assuming that that photo of the P(3,4) was yours,
> will you be posting it?

My program has found 286 examples of a P(5,8).

Start Sols
point
(0,0) 100
(1,0) 54
(1,1) 68
(2,0) 12
(2,1) 12
(2,2) 40
---
286

However, these solutions are not all essentially distinct, in
particular a path and its reversal are both counted. So I would guess
that there are about 100 essentially distinct solutions, probably
less.

Here is a picture of three paths...
http://www.flickr.com/photos/lhc_logs/8446539821/in/photostream

Here are the coordinates of the 9 vertices of each path:

Solution "11,4"
0: ( 2 1)
1: ( 0 1)
2: ( 0 4)
3: ( 4 0)
4: (-3 0)
5: ( 5 4)
6: ( 1 4)
7: ( 4 1)
8: ( 4 3)

Solution "11,5"
0: ( 2 1)
1: ( 2 3)
2: ( 5 3)
3: ( 1 -1)
4: ( 1 6)
5: ( 5 -2)
6: ( 0 13)
7: ( 0 -12)
8: ( 4 4)

Solution "5,6"
0: (1 0)
1: (5 0)
2: (1 4)
3: (4 4)
4: (0 0)
5: (0 5)
6: (7/3 1/3)
7: (11/2 7/2)
8: (1 2)

--
Clive Tooth