Talk:3125: Snake-in-the-Box Problem

The math problem in question is https://oeis.org/A099155 Mei (talk) 21:57, 6 August 2025 (UTC)

why is d>8 unsolved? stevethenoob 21:59, 6 August 2025 (UTC)

Computational power, I guess, although I'm going to go out on a limb and predict that for N=9 snake=196. 94.73.52.245 23:18, 6 August 2025 (UTC)

I would argue that computer science has one as well with the China room problem. Ctinsman (talk) 22:14, 6 August 2025 (UTC)

Humans aren't cute animals (mostly), so I propose a variant of the problem called the Chinese Red Panda Room 177.12.49.23 22:38, 6 August 2025 (UTC)

Interesting. Just a few days ago I was investigating a very similar idea (looking at a path that transitioned between adjacent faces of a polyhedron, which was effectively going from vertex to connected vertex upon that chosen polyhedron's dual), but for the opposite reason, i.e. looking for the paths that actually maximised proximity (along the path) between neighbouring faces (upon the polyhedra), so that it actually minimised the search back/forth along the path-chain to establish what value the adjacent polyhedron faces (beyond the ones automatically at ±1 positions on the chain) inherited.
As to solving this one (basically disallowing visiting of any nodes adjacent to prior visits other than the single one that the +1 position of the chain has to first go to), I've got a basic idea of how I'd N-dimensionally space-search the possible routes (after all, visiting any given node at {0,1} value for dimensions [a, b, c, ...] rules out now visiting all of [!a, b, c, ...], [a, !b, c, ...], [a, b, !c, ...], etc, except whichever one of these was chosen for the next step of onward travel), for valid foldings across the appropriate N-polytype cuboidal analogue. Though I suspect that the exponental (or greater!) growth in the potential search-trees you'd use would be the sticking point. No point in setting off an exhaustive algorithm if it seemed likely to take three years to check just 1% of possibilities, and no doubt more dedicated analysis than my own brute-forcing method has already hit other problems in trying a more nuanced extrapolation between each level of added dimensionality, which is where the unsolved nature of this starts to bite.
But also think it'd be far more interesting to investigate the possibilities in the N>3-Dimensional extensions of non-cubic platonic solids, like the 600-cell and beyond, and establish what allowable lengths of traversal they would allow, under similar stipulations.
Great! I love getting things like this to think about. If I can spare the time needed... 82.132.245.59 22:22, 6 August 2025 (UTC)

I think you've been nerd-sniped. 177.12.49.23 22:42, 6 August 2025 (UTC)

Psychology is way ahead of y'all, they've been putting actual mice in weird boxes for decades. 177.12.49.23 22:45, 6 August 2025 (UTC)

Reading (just) the comments of the underlying research suggests that 98 is the longest found snake. Perhaps that means a longer one has not been explicitly eliminated (making 8 also not solved to some extent) 2A02:A45B:8867:0:BED8:F2BA:838E:765 22:52, 6 August 2025 (UTC)

I suppose Randall doesn't consider beetles cute, or else philosophy of language would be included. 137.25.230.78 23:15, 6 August 2025 (UTC)