3 ms·
OK. I took your rough square as: left side, front, right side all have teeth along them; the rear of the square opens into your throat with no teeth. Since we'r
by abecedarius 11y ago
OK. I took your rough square as: left side, front, right side all have teeth along them; the rear of the square opens into your throat with no teeth. Since we're taking it to be a unit square, each side is of length 1. Knuth's toothbrush travels a total distance of 12 in those units, plus the upper-to-lower distance, which'd be some moderate fraction of 1.
I don't understand by what units you're counting, that they uniformly measure a distance. Maybe you're tallying moves that are not brushing? That'd be 1 for Knuth, the upper-to-lower transition. But it's OK! We don't need to argue about a joke.
- davidivadavid 11y agoThe square is the cartesian product upper/lower X left/right (upper left, upper right, lower left, lower right). I was only counting moves from left to right or top to bottom (along the sides of the square), so I suppose those are moves that aren't brushing (because I assume the actual brushing varies little). How would that be 1 for Knuth?
- abecedarius 11y agoBecause Knuth's path never interrupts brushing except the one time it moves from upper to lower teeth.
- davidivadavid 11y agoThat seems a little arbitrary to me. You have to switch how you hold the brush to go left/right (unless your brush is double-sided). For example, I can't imagine his first move, from upper left outside, to upper right outside, to be continuous. And you might as well argue that you're not interrupting either when going from top to bottom. I mean you're just continuing the same movement after all. Damn, who knew brushing teeth could be so complex.