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.

Related: https://arxiv.org/abs/1806.02404

This was 13 years ago, and Google has since had many "revelations" about its misuse of useless tools like brainteasers. The current process and interviewer training/selection process is nothing like the process in 2005.

Perhaps that true, but I think it's a recent change. I vaguely remember having a brain teaser question as recently as 6 years ago, but I concede it was a long time ago and I could be remembering wrong.

BI had an article about it as recently as 2015. https://www.businessinsider.com/google-brain-teaser-intervie...

BI... is an interesting publication. With an interesting relationship to facts.

That question doesn't seem great. People who've spent more time in NYC will likely perform better, since they'll immediately start describing classes of buildings where they've spent time and generalizing, but how familiar you are with NYC is irrelevant to the job.

Depending on your applicant pool, that might be correlated with a protected class, like race, gender, or national origin.

I don't think classes of buildings are that imporant. Just multiply the resident population by the number of windows per person. Just throwing a number out there, I'd estimate something like 10 windows per resident, counting residential and commercial.