[alehul]

I'm fairly sure that he was speaking his calculations aloud in the process of reaching the dollar value when the interviewer stopped him and asked for an answer.

It's a great interview question in the sense of a Fermi problem (I was once asked by a startup "how many window washers are there in [CITY]?"). The premises you choose and how you evaluate them, however, are so much more important in a Fermi problem than a correct answer. I remember being about 5x off but it was only because of a drastic underestimation on the time it takes to clean a window.

[vonmoltke]

Fermi problems are terrible questions when asked about things the questionee has no concept of. The point of a Fermi problem is to make an educated guess, and doing so requires knowledge of the problem space the guess is being made in. Pulling random constraints out of your ass for a domain you do not know does not demonstrate this ability.

[alehul]

If you're saying that in regards to the window washer question, I actually enjoyed it!

The point of a Fermi problem is to arrive at a reasonable estimation for a fairly unknown value by extrapolating and connecting from known values (by known, I mean there's a more narrow lower and upper bound).

I wouldn't say that a Fermi problem about how many window washers are in a city is a terrible question; it is more challenging than something in which you already have domain expertise, but that just makes you have to extrapolate further, which is the real point of the Fermi problem. In fact, pretty easy (and knowable) starting points are the population of the city, windows per individual, etc.

Doesn't a Fermi problem without domain expertise display more critical thinking and reasoning style, while a Fermi problem with domain expertise is less of a Fermi problem, and more of a knowledge test?

[vonmoltke]

> Doesn't a Fermi problem without domain expertise display more critical thinking and reasoning style, while a Fermi problem with domain expertise is less of a Fermi problem, and more of a knowledge test?

A Fermi problem is both a test of knowledge and a test of reasoning skills. The types of estimates Enrico Fermi was known for were only possible because he had the domain knowledge for his reasoning to leverage. If you remove the domain knowledge from the problem you remove a significant amount of the signal from trying to concoct the estimate. It is a much easier problem if you can just make up numbers rather than infer accurate guesses from the domain.