Aren't the examples of brainteasers actually Fermi problems? Maybe they sound like brainteasers if asked without the appropriate context, but when you're doing a system design interview and you have to estimate your throughput or storage requirements, you're effectively solving a Fermi problem just like the one that asks you to estimate the number of windows in NYC.
Most of the "estimate foo" problems are Fermi problems. E.g. The classic one I've heard is "estimate the number of piano tuners in the world". The route I took to do so is:
number of people in the world
/ average number people per piano
* average number of times a piano is tuned per year
* average amount of hours to tune a piano
/ average number of hours a piano tuner works per day
/ average number of days a piano tuner works per year
So in terms of units, the flow is:
people
-> pianos
-> piano tunings per year
-> hours spent tuning pianos per year
-> workdays spent tuning pianos per year
-> piano tuners
This is all very similar to dimensional analysis most people will learn in a highschool science class.
Just to plug in some random numbers, let's pick 7 billion people, 100 people per piano, 0.3 tunings per year, 1 hour to tune a piano, 3 hours of tuning per day and 100 days per year(I imagine it's part-time for most piano tuners...). We arrive at:
7,000,000,000 / 100 * 0.3 * 1 / 3 / 100 == 70,000
And, for what it's worth, at least in my field, we do these sorts of ballpark estimations all the time to determine feasibility of systems.
I've never had one of these in an interview setting, but I imagine the important thing is to demonstrate the line of reasoning rather than actually arriving at a concrete number.
I love the term "Fermi problem", because the origin is, of course, the Fermi paradox. The idea that multiplying a series of uncertainties together does something other than blow your error range out is such a weird idea.
> The idea that multiplying a series of uncertainties together does something other than blow your error range out is such a weird idea
Might seem weird but it is massively useful. Having an educated estimate that is _only_ out by an order of magnitude is a massive improvement over wild-ass guesses that are 4-5 orders of magnitude off -- especially in systems design where over- or under-provisioning leads to millions wasted in effort.
