Examples of Fermi Problems
The classic Fermi problem, generally attributed to Fermi, is "How many piano tuners are there in Chicago?" A typical solution to this problem involves multiplying a series of estimates that yield the correct answer if the estimates are correct. For example, we might make the following assumptions:
- There are approximately 5,000,000 people living in Chicago.
- On average, there are two persons in each household in Chicago.
- Roughly one household in twenty has a piano that is tuned regularly.
- Pianos that are tuned regularly are tuned on average about once per year.
- It takes a piano tuner about two hours to tune a piano, including travel time.
- Each piano tuner works eight hours in a day, five days in a week, and 50 weeks in a year.
From these assumptions, we can compute that the number of piano tunings in a single year in Chicago is
- (5,000,000 persons in Chicago) / (2 persons/household) × (1 piano/20 households) × (1 piano tuning per piano per year) = 125,000 piano tunings per year in Chicago.
We can similarly calculate that the average piano tuner performs
- (50 weeks/year)×(5 days/week)×(8 hours/day)/(2 hours to tune a piano) = 1000 piano tunings per year per piano tuner.
Dividing gives
- (125,000 piano tunings per year in Chicago) / (1000 piano tunings per year per piano tuner) = 125 piano tuners in Chicago.
A famous example of a Fermi-problem-like estimate is the Drake equation, which seeks to estimate the number of intelligent civilizations in the galaxy. The basic question of why, if there is a significant number of such civilizations, ours has never encountered any others is called the Fermi paradox.
Read more about this topic: Fermi Problem
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