xkcd #3125: Snake-in-the-Box Problem
Title text:
Chemistry grad students have been spotted trying to lure campus squirrels into laundry hampers in the hope that it sparks inspiration.
Transcript:
Transcript will show once it’s been added to explainxkcd.com
Source: https://xkcd.com/3125/
What about goats in circular pens? A goat is tied to the fence of a circular pen. How long does the rope need to be so that the goat can reach exactly half of the pen's area? What sounds like a high school math problem was eventually solved in 2020 via complex analysis.
Here's the answer:
I feel like the answer should be much simpler than that equation salad.
Equation salad? It's elegant. Well, according to my father who was a math professor.
Deriving that monstrosity must be something out of a grad school horror novel.
What's really neat about this problem is that the 3D example, a bird in a cage, was solved sooner and is much simpler
Randall forgot psychology, which has involved a ton of putting animals in boxes...
Also zoology
Either I'm misunderstanding the problem or a length of 8 is possible.
Edit: found my mistake, far left edge has two non-consecutive segments on adjacent corners. Leaving this up in case anyone else tries for a better score.
Unless your snake is an ouroboros, I don't think folks will count the head and tail as consecutive
The head and tail aren't adjacent if you only look at my blue line and not the original. But my attempt fails due to the far left edge.
I'm just nodding along and hoping no one notices i don't know what's happening
I'm still trying to fill that hotel with infinite monkeys
My combinatorics professor used gnomes!
There really is an xkcd for everything.
I'd expect something around ~200 for n=9 and ~400 for n=10, but I imagine this is too big to be brute forced by raw computing
Some trivial bounds: F(n-1) + 1 <= F(n) <= F(n-1) * 2 + 1.
Also F(n) <= 2^(n-1)
I guess a key thought experiment doesn’t qualify as a reason, and also we are supposed to conveniently forget about putting spherical cows in a vacuum just because.
This is not my wheelhouse, and presumably were what I am about to suggest be right a million other people would have already pointed it out (not on lemmy necessarily, just in general). But aren't all of those sides equal so the relationship between snake's and any cube side's length effectively (as we see it anyway) shrinks/grows as it moves around the hypercube.
To be honest I don't even understand what the cartoon means by 'two non-consecutive parts of its coils' so I wouldn't take my word for anything.
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