Answer quickly: how many piano tuners are there in the city of Chicago?

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Remember: I said quickly. We need an answer, and we need it in the next sixty seconds. Oh, and no using Google, either.

Did you give up? A lot of people do. A lot of people don't even know where to begin answering a question like that. But then, a lot of people are also unfamiliar with Fermi problems.


Named after physicist Enrico Fermi (who had a knack for solving seemingly unsolvable or overwhelming estimation problems with impressive speed and accuracy), one of the best ways to approach Fermi problems is a clever trick known as order of magnitude estimation. In this expertly animated TEDEd video, educator Michael Mitchell gives a great introduction to Fermi problems and how to go about solving them.

Fun fact: Fermi problems are notorious for popping up during interviews for positions with companies like Google and Microsoft. One reason for this is that these problems can often be as complex, or as simple, as you want to make them. For example: as Mitchell explains, one can choose to consider how often pianos are tuned, how many pianos a piano tuner can tune in one day, or how many days a year your typical piano tuner works (alternatively, one can just say a piano tuner works on approximately X pianos in a given year). In this way, a single Fermi problem can often be deconstructed into a subset of other Fermi problems.


Opting to explore these lower-level Fermi problems is one way to highlight your ability to think in creative or abstract ways — but it can also indicate that you don't know when the hell to stop overanalyzing and just answer the freaking question. Try to keep that in mind the next time you're up for a position as an Associate Product Manager at Google.

[TEDEd via Joe Hanson]