How many piano tuners are there in the entire world?

Job: Product Manager

Photo: delgaudm

Answer: We'd answer "However many the market dictates. If pianos need tuning once a week, and it takes an hour to tune a piano and a piano tuner works 8 hours a day for 5 days a week 40 pianos need tuning each week. We'd answer one for every 40 pianos."

On Wikipedia, they call this a Fermi problem.

The classic Fermi problem, generally attributed to Fermi,[2] is "How many piano tuners are there in Chicago?" A typical solution to this problem would involve multiplying together a series of estimates that would yield the correct answer if the estimates were 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.

And we can similarly calculate that the average piano tuner performs

(50 weeks/year)×(5 days/week)×(8 hours/day)×(1 piano tuning per 2 hours per piano tuner) = 1000 piano tunings per year per piano tuner.

Dividing gives

(125,000 piano tuning 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 are a significant number of such civilizations, ours has never encountered any others is called the Fermi paradox.