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

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]


Fermi questions are neat, but not nearly as useful as Churchill questions. Long before he was Prime Minister Winston Churchill was Chancellor of the Exchequer, something like our Secretary of the Treasury. One day the then-Prime Minister Stanley Baldwin called him up and asked how long it would take to estimate the total cost to Great Britain of the Great War (WW-I). Churchill called in his chief economist and put the question to him. The economist thought about it for a bit and replied that if he put his entire staff on the project they could develop an authoritative estimate in ten years. Churchill thanked him, pickup up the phone, rang the PM and told him he would have an estimate later that afternoon.

The economist was apoplectic. "Didn't you hear what I just said?" he sputtered?

"Yes", replied Churchill. "I heard you say that it will be ten years before anyone knows whether my best guess today is right or wrong".

I pretty much made a career out of providing Churchill answers to more or less unanswerable technical/economic/political questions.