[seqfan] Re: Knight's tour on infinite board
njasloane at gmail.com
Sat May 4 16:56:28 CEST 2019
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
Thanks also for the MO link. I only read the start, so far, which seems
very sketchy and
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:
> 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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