The way to solve this is ask everyone in NYC how many piano tuners they think there are, add up the answers, and divide by 8,244,910. Do this in 2011 or you have to divide by some other number.
How many piano tuners can dance on the head of a pin?
I’m actually quite impressed by how close Shagnasty got, lo those many moons ago. Take a late bow, sir.
No, real scientists confuse meters and yards.
People who actually play their pianos get them tuned twice a year. My guess is that only about 10% of pianos are owned by people who actually play them. That’s based on my limited experience, as a piano player, bumping into pianos. Half of them are garbage that just hasn’t been hauled out yet. In any case, it’s beside the point. All Shagnasty’s constants were wild guesses off the top of the head, but most of which could actually be researched.
However, in addition to trying a formula like Shagnasty’s, I’d check the guild (Registered Piano Tuners), the yellow pages, and google. When checking the yellow pages, I’d be sure to note whether I’m contacting an individual or a company. For companies, I’d select a random sample and ask them how many tuners they represented, and whether the tuners were full-time employees or associates (since they could also be associates for another company).
IMHO, a more interesting question would be “what’s the error term on your answer?” That’s the kind of question an engineer has to be able to answer.
:bows:
I would like to thank everyone for this opportunity, especially my mom. Stay cool and be sure to have your pets neutered.
The basic idea behind these kinds of analyses is that your individual assumptions will not be correct individually but the errors you make will tend to be both high and low and tend to cancel each other out so that you converge on a reasonably correct answer just based on what you know.
If you think that 1 billion people live in NYC and 75% of households own pianos then you will get a completely wrong answer but anyone with any sense can approximate the real values well enough. Once you combine enough reasonably accurate assumptions, that becomes a really powerful tool to getting close to the real answer without anything more than the knowledge you started with. The key is to know how to pick those assumptions, have some reasonable idea of the facts to support them, and then do accurate math based on those.
It is simple fuzzy logic but works remarkably well if you set it up correctly.
I believe that my mother’s upright piano has been sitting in a basement for over ten years, not being played. I have been told that it is basically now a piece of trash.
You can also bring in fragments of information that you do happen to know, even if they’re things that most folks wouldn’t. As an example, a friend and I were once working on a test that had a question on it “Estimate the total area that would need to be covered by solar panels to meet all of the US’s electricity needs”. Well, my friend started by saying “The solar constant at Earth is about a kilowatt per square meter, but I’m not sure what the energy consumption of the US is.”. I, on the other hand, didn’t know the solar constant off the top of my head, but for the energy consumption of the US, I just assumed “Oh, call it the equivalent of about 5 100-watt light bulbs per person”. Meanwhile, although I didn’t know the solar constant off the top of my head, I did happen know all of the following facts, which were enough to derive it:
The Schwarzschild radius of the Sun
The gravitational constant and the speed of light
The efficiency of hydrogen fusion
The fraction of a star’s hydrogen that will be fused in its main sequence lifespan
The main sequence lifespan of the Sun
All I know is you can tune a piano, but you can’t tuna fish.
Show your work.
Some. How many are any good? A piano technician != a “tuner.”
Pardon my French but it is not a good question.
Perfectly understandable. Meters are the things that fall from space and land in people’s yards. I always get it backwards.
This.
In the tech industry this is a very common type of question to ask engineers and product manager candidates in interviews.
Personally I’ve been asked “How would you figure out how many time pieces there are in the bay area? and How would you figure out how many planes are in flight over california at a given time?”
Shagnasty’s answer was very good even if he just used variables instead of actual guesses. The exercise is to showcase your problem solving method.
I once asked the time piece question to a product manager interviewee and he paused for a while and then responded “About 10 million”. He didn’t get the job. 
Yep. Though I find that the real value of the question has nothing to do with their answer. A candidate that thinks the question is dumb doesn’t understand why I’m asking it, and is thus unsuitable for the job. Any engineering task of any significance requires doing ballpark estimates and similar mental simplifications almost continuously, and often subconsciously.
I see what you mean. I usually frame the question by saying things like: “I just want to get a sense of how your gears work” or some such language to encourage them to make even a half-hearted attempt.
I’m a PM and therefore I’m a bit more soft-hearted than you engineering types so I give them a bit of encouragement.
Yeah, we engineers can be brutal… I’ve never personally driven a candidate to tears, but I know people who have :).
Honestly, though, I usually stick to more traditional tech questions. Sometimes I’ll ask these kinds of questions during phone screens since “whiteboard questions” are basically impossible.
So why do we need dedicated piano tuners anyway? Is tuning a piano really that much more complicated than tightening some strings with a wrench (screwdriver?) and sitting there with a tuner? Tedious, to be sure, but it doesn’t sound herculean. I suppose the strings breaking is a concern, as getting piano strings probably requires some special orders here and there, but it seems odd that one can make a whole profession out of it.
It’s not impossible to tune a piano yourself, but you need a set of special tools to tighten the strings, a very high-quality tuner, and a trained ear because even the best digital tuner isn’t quite precise enough. To perfectly match the tuning of two or three strings for most notes, and tune not-quite-perfect intervals used in equal temperament tuning schemes, you need to be able to hear and precisely adjust beat frequencies.
If you’re willing to drop a couple hundred bucks on tools, spend an entire weekend tuning, and probably end up with imperfect results, go ahead. Most people would rather spend $100 for a professional tuning every few years. That’s a lot of money to spend on a crappy piano that nobody plays anyways, but it’s not much money compared to piles of sheet music, lessons, or professional expenses.
I suppose it’s comparable to some of the more tedious and fiddly car repairs. There’s some that are easy for anyone with a wrench and a bit of common sense, but others are difficult enough that most shade tree mechanics will go to a professional.
And then, you may wind up with a piano that’s in technically perfect tune, but it will probably be soulless. The art comes in voicing the subtle nuances and de-tunings to make it sound right.
A Fermi problem I often thought of while commuting to and from San Francisco was “How heavy is BART?”
My estimations started with the basics that it is a heavy rail system, the rails weigh 110 pounds per foot, there are 10,560 feet of rail per mile of track, the third rail is lighter material at probably 75 pounds per foot, there are about 100 miles of route, all of which is double-track, and there’s probably 10 miles of track in the various train yards, which comes to about 353,000 tons of rails. Ties and track ballast are probably another 175,000 tons. They have about 650 cars that weigh 56,000 pounds each for another 18,000 tons, so about 530,000 tons just for the tracks and trains, which is less than I expected.