I am sure you all heard one of these famous interview questions:
- How many gas stations are there in the US?
- How many pennies can you put in Empire States Building?
- How many piano tuners are there in New York?
- How many dentists are there in the Bay Area?
All these interview questions are called "Fermi problems" or "Fermi questions". It simply is an estimation problem about capturing 2 things:
- Being able to explain your assumptions
- And using these assumptions performing an approximation
Let's take a look at the 4th question: How many dentists are there in the Bay Area? We can solve it by:
- There are approximately 10 million people in Bay Area
- Let's assume on average 2 in 5 people go to dentist in Bay Area
- On average people go to dentist twice a year
- A dentist with his/her helpers can see 80 patients a week (1/2 hour per patient)
- On average a dentist takes 2 weeks of vacation per year (They work 50 weeks per year)
- Bay Area has sufficient dentists
Let's say our assumptions and approximations above are correct, then there are 4 million people go to dentist, which results in 8 million visits per year. A dentist can handle 4000 visits per year = 80 visits x 50 weeks. Therefore the Bay Area has approximately 2 thousand dentists = 8 million / 4 thousand.
If you have a lot of time on your hands you can try to solve the following problems with Fermi estimation: