[seqfan] Re: Knight's tour on infinite board

[Neil Sloane]

Hans, Thanks for that comment.  If we don't have an explicit construction
for any of the 8 "tours", how can we be sure that they don't get trapped
after a while?  (Compare the tours I talked about in the Numberphile video
on Youtube)

Thanks also for the MO link. I only read the start, so far, which seems
very sketchy and
hand-wavy.


Best regards
Neil

Neil J. A. Sloane, President, OEIS Foundation.
11 South Adelaide Avenue, Highland Park, NJ 08904, USA.
Also Visiting Scientist, Math. Dept., Rutgers University, Piscataway, NJ.
Phone: 732 828 6098; home page: http://NeilSloane.com
Email: njasloane at gmail.com



On Sat, May 4, 2019 at 10:45 AM Hans Havermann <gladhobo at bell.net> wrote:

> > And are there really only 8 solutions?
>
> The 8 sequences likely show the 8 possible first moves of a knight at
> position 1 in a particular (but presently undefined) knight's tour spiral
> construction. That other constructions exist (perhaps even other spiral
> constructions) appears to be certain:
>
>
> https://mathoverflow.net/questions/296549/does-knight-behave-like-a-king-in-his-infinite-odyssey
>
> Joel David Hamkins: "My answer can also be used to make non-spiral tours,
> since you can assemble the 5×5 blocks in any tiling, as long as each block
> is attached by a side to the next. It follows that there are continuum many
> such tours."
>
>
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