
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

