Question

To an order of magnitude, how many piano tuners reside in New York City? The physicist Enrico Fermi was famous for asking these questions like this one on oral Ph.D. qualifying examinations.

Answer 1

Hint: To answer such questions, the presence of the mind is the key factor. We don’t have to give an accurate answer as it is impossible but we can estimate the answer i.e. give a close figure to the answer. We need to break down the question into a series of smaller questions and using common sense make educated guesses. We have to use our assumptions to solve the problem.

Complete Step by Step answer:
We will now break our questions into smaller series of questions. Now the first thing that comes to our mind is, how many people line in New York City? Let us assume that approximately $$80,00,000$$ live in New York City. The second question arises, does every person own a piano? The answer is obvious, not every person can own a piano. So, here comes our assumption that families own piano and not every individual. Let on average, each family has $5$ members. The number of families in NYC will be $$16,00,000$$ .
The next question we should ask ourselves is that, does every family owns a piano? The answer here is no. Maybe one in every $$10$$ families has a piano. So, the number of pianos in NYC will be:
${\displaystyle \frac{16,00,000}{10}}=1,60,000$
As per our common sense, tuning of the piano is done mostly once a year. So, let a piano tuner tunes $$4$$ pianos per day $$7$$ and if there are $$200$$ working days then the number of piano tunes in a year would be:
$4\times 200=800$
Lastly, the question arises, how many piano tuners does NYC have? For that, we have to divide the total number of pianos by the number of pianos tuned in a year, we get,
$${\displaystyle \frac{1,60,000}{800}}=200$$
Therefore, $$200$$ piano tuners are there in New York City.
Our answer will be close to the actual answer as our assumptions are sometimes low and sometimes high and thus the guesses cancel each other. It is used to get an order of magnitude of the answer with a reasonable degree of accuracy.

Note:
How much money does a cinema theatre make in a week? How many burgers does McDonald’s sell in a year? These types of problems are used to check the presence of mind of the candidates. These problems are called Fermi problems named after the physicist Enrico Fermi who used these problems to determine the strength of atomic blasts estimated the circumference of the earth, and the possibility of aliens existing in-universe.