|How I Can Tell I Am A Huge Nerd
||[Mar. 24th, 2011|11:42 pm]
In the checkout line this evening, I was thumbing through Reader's Digest, reading the humorous interstitials. They had one labeled something like "ridiculous interview questions" that had the question "How many basketballs would fill this room?"|
And I thought, that's not ridiculous at all. That's actually quite an interesting question. Not for the most basic answer, that's pretty trivial -- just guesstimate how many basketballs fit along each dimension and multiply -- but to see whether the candidate asks any interesting followup questions. Like "Hexagonal close-pack, face-centered cubic, or just stuffed in randomly?" Or "Should I assume we've removed the furniture first?" Or "Do you want to use inflated basketballs?"
(And because I was overcome by curiosity, Google & Wikipedia tells me that a regulation basketball is about 30" in circumference, or 9.5 inches in diameter, and that FCC and HCP have the same (optimal) density of ~74%, while random packing is more like 50-60%, with a limit of 64%. The More You Know!)
Yeah. This is my brain.
odd that FCC and HCP have the same packing density.
I thought so too, at first, but it turns out to be not odd at all because they're almost the same arrangement. In both cases you have planes of spheres in a triangular lattice, with each layer nestled into the hollows of the layer below it. It's just a question of whether the offsets from layer to layer go ABABAB or ABCABC.
Edited at 2011-03-25 07:06 am (UTC)
I knew you were a nerd when you used Interstitial in a sentence.
Oh, you knew LONG before THAT! ;)
My sister gets the Digest, and I'd not picked it up in ages, and I saw *exactly* that question, and thought the same thing. Admittedly, after the initial thought about how I'd approach answering the question, I didn't go look up a basketball's dimensions, but, yeah. In the end I concluded that the list of questions was largely not ridiculous, and so, the headline was, to me, a disappointment.
Just read this but I'm trying to figure out ... oh, wait, I got it. With hexagonal stacking each ball loses the dimension relative to 60° * its circumference. Liking things tidy, I just assumed this would be hexagonal :)
If I didn't want the job, I would probably reply "That depends quite a lot on the size of your basketball."
That might well be one of my questions even if I did want the job.
I think a good interviewer would counter with something like, "Good point. Regulation NBA size. Go."
(nods) I wouldn't ask it for a job I wanted because I would expect most interviewers to treat it as evidence of being uncooperative.
That said, if someone actually gave me that response, I would pretty much have to update my evaluation of whether I wanted the job on the spot.
The most ridiculous interview question I've gotten was "Have you ever been in a fistfight?" I'm curious how you'd approach that one.
As an aside, that was in an interview for VR-1, so it's quite meaningful in hindsight.
I can't think of any answer other than "Uh... no."
Or maybe, "No. Why?"
Unless you're interviewing for a job as a bouncer, that one is a ridiculous question.
I'm trying to remember where I read that, oddly enough, random sphere packing is not well understood from a fundamental mathematical POV. As in, you can physically measure or simulate, but there's not a from-first-principles theoretical workup.https://secure.wikimedia.org/wikipedia/en/wiki/Random_close_pack
says "Experiments have shown that (random close pack) gives a maximum density of about 49-50%"
and I'd demote it to about 40% for basketballs, b/c their high-grip surfaces would hinder them moving around to find their optimal arrangement.
Well, it really depends on how well you can shake your office building, now doesn't it?