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Retrieved October 2, June 17, Retrieved February 1, Archived from the original on Retrieved June 24, September 9, Recording Industry Association of America. Retrieved January 18, Keep this in mind and take it off the estimate at the end. Assumption 4: To estimate the number of pianos in Chicago, you might guess that 1 out of people have a piano—again, a wild guess, but probably within an order of magnitude. In addition, there are schools and other institutions with pianos, many of them with multiple pianos.
This estimate is trickier to base on facts, but assume that when these are factored in, they roughly equal the number of private pianos, for a total of 2 pianos for every people. Now to estimate the number of people in Chicago. You might guess 2. We decided to double this number to account for institutional pianos, so the result is 50, pianos.
So, here are the various estimates: 1.
There are 2. There are 2 pianos for every people. There are 50, pianos in Chicago.
Pianos are tuned once a year. It takes 2 hours to tune a piano. Piano tuners work 2, hours a year. Add 15 percent to that number to account for travel time, meaning that there are approximately 58 piano tuners in Chicago. What is the real answer? The Yellow Pages for Chicago lists This includes some duplicates businesses with more than one phone number are listed twice , and the category includes piano and organ technicians who are not tuners.
Deduct 25 for these anomalies, and an estimate of 58 appears to be very close. Back to the Google interview and the Empire State Building question. If you were sitting in that interview chair, your interviewer would ask you to think out loud and walk her through your reasoning.
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One way to start would be to estimate its size, and then estimate the weight based on that. For size I need to know height, length, and width. My boundary conditions are that it is between 50 and stories; 50 stories work out to being — feet tall 10—15 feet per story , and stories work out to be 1,—1, feet tall. So my height estimate is between and 1, feet.
Now for its footprint. A lemon? These are skills that can be nurtured beginning at a young age. Most jobs require some degree of creativity and flexible thinking. If the building is square, it is x feet in its length x width. There are several ways to go from here. All rely on the fact that most of the building is empty—that is, it is hollow.
The weight of the building is mostly in the walls and floors and ceilings. I imagine that the building is made of steel for the walls and some combination of steel and concrete for the floors. The volume of the building is its footprint times its height. My footprint estimate above was 60, square feet.
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My height estimate was 1, feet. I could estimate the thickness of the walls and floors and estimate how much a cubic foot of the materials weighs and come up then with an estimate of the weight per story. Alternatively, I could set boundary conditions for the volume of the building.
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That is, I can say that it weighs more than an equivalent volume of solid air and less than an equivalent volume of solid steel because it is mostly empty. The former seems like a lot of work. That means that the walls on each side, and any interior supporting walls, total 13 feet.
I happen to remember from school that a cubic foot of air weights 0.
Obviously, the building is not all air, but a lot of it is—virtually the entire interior space—and so this sets minimum boundary for the weight. The volume times the weight of air gives an estimate of 60,, cubic feet x 0. But I can estimate that, based on some comparisons. It seems to me that 1 cubic foot of steel must certainly weigh more than a cubic foot of wood.
This gives me two boundary conditions: 6 million pounds if the building were all air, and 30 billion pounds if it were solid steel. This hypothetical interviewee stated her assumptions at each stage, established boundary conditions, and then concluded with a point estimate at the end, of , tons. Nicely done!
Another job interviewee might approach the problem much more parsimoniously. Using the same assumptions about the size of the building, and assumptions about its being empty, a concise protocol might come down to this. Skyscrapers are constructed from steel. Imagine that the Empire State Building is filled up with cars. I know that a car weighs about 2 tons and it is about 15 feet long, 5 feet wide, and 5 feet high. The floors, as estimated above, are about x feet each. How many rows will fit?