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