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

 Messages: [ Previous | Next ]
 Mark Brader Posts: 88 Registered: 12/10/04
Re: Continous path on square grid
Posted: Feb 5, 2013 2:15 PM

Clive Tooth:
> 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.

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.
--
Mark Brader, Toronto | "My ambition is to see a saying of mine attributed
msb@vex.net | to Dorothy Parker or Mark Twain." -- Joe Fineman