Here’s a hybrid option: I’ll assume that on any given floor, 95 percent of the volume is air, and 5 percent is steel.I’m just pulling this estimate out of the air, really, but it seems reasonable.Divide this by the number of hours each tuner works, and you have the number of tuners. One time a year seems like a reasonable guesstimate. Assumption 3: How many hours a year does the average piano tuner work?

Here’s a hybrid option: I’ll assume that on any given floor, 95 percent of the volume is air, and 5 percent is steel.I’m just pulling this estimate out of the air, really, but it seems reasonable.Divide this by the number of hours each tuner works, and you have the number of tuners. One time a year seems like a reasonable guesstimate. Assumption 3: How many hours a year does the average piano tuner work?

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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 100 people. If you don’t know the answer to this, you might know that it is the third-largest city in the United States after New York (8 million) and Los Angeles (4 million). If you were sitting in that interview chair, your interviewer would ask you to think out loud and walk her through your reasoning.

You might guess 2.5 million, meaning that 25,000 people have pianos. There is an infinity of ways one might solve the problem, but to give you a flavor of how a bright, creative, and systematic thinker might do it, here is one possible “answer.” And remember, the final number is not the point—the thought process, the set of assumptions and deliberations, is the answer. One way to start would be to estimate its size, and then estimate the weight based on that. I’m going to calculate the weight of the building empty—with no human occupants, no furnishings, appliances, or fixtures.

In this case, it might be easier to start with the number of pianos that you think are in Chicago and then figure out how many tuners it would take to keep them in tune. How many hours a year the average piano tuner works4.

In any Fermi problem, we first lay out what it is we need to know, then list some assumptions:1. The number of pianos in Chicago Knowing these will help you arrive at an answer.

Google isn’t interested in the answer, though; they’re interested in the process. By “weight of the Empire State Building,” do you mean with or without furniture? The fourth response is the correct one, using approximating, or what some people call guesstimating.

They want to see a reasoned, rational way of approaching the problem to give them insight into how an applicant’s mind works, how organized a thinker she is. People throw up their hands and say “that’s impossible” or they try to look up the answer somewhere. These types of problems are also called estimation problems or Fermi problems, after the physicist Enrico Fermi, who was famous for being able to make estimates with little or no actual data, for questions that seemed impossible to answer.

Approximating involves making a series of educated guesses systematically by partitioning the problem into manageable chunks, identifying assumptions, and then using your general knowledge of the world to fill in the blanks.

How would you solve the Fermi problem of “How many piano tuners are there in Chicago? As with many Fermi problems, it’s often helpful to estimate some intermediate quantity, not the one you’re being asked to estimate, but something that will help you get where you want to go.

Consider the following question that has been asked at actual Google job interviews: How much does the Empire State Building weigh?

Now, there is no correct answer to this question in any practical sense because no one knows the answer. They don’t bring you any closer to solving the problem; they only postpone being able to start it.

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