Famous Fermi Problems


cropped-diagonals_polygon.gifYour parents tell you that if you are good for 1 million minutes that you can get a cell phone.

Let’s have a math chat! Leave me a response to this math happening.

What do you wonder about?

What do you know or notice?

What information do you need?

What assumptions can you make?

What math will you use to solve the problem?


cropped-diagonals_polygon.gif Will you have to be good for 12 hours, or 12 days or 12 weeks?

This I call a Fermi Problem! Discover the amazing mathematician, Enrico Fermi

A “Fermi question” is a question in physics which seeks a fast, rough estimate of quantity which is either difficult or impossible to measure directly

“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:

  1. There are approximately 9,000,000 people living in Chicago.
  2. On average, there are two persons in each household in Chicago.
  3. Roughly one household in twenty has a piano that is tuned regularly.
  4. Pianos that are tuned regularly are tuned on average about once per year.
  5. It takes a piano tuner about two hours to tune a piano, including travel time.
  6. 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

(9,000,000 persons in Chicago) ÷ (2 persons/household) × (1 piano/20 households) × (1 piano tuning per piano per year) = 225,000 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.

Dividing gives

(225,000 piano tunings per year in Chicago) ÷ (1000 piano tunings per year per piano tuner) = 225 piano tuners in Chicago.

The actual number of piano tuners in Chicago is about 290.[3]

Other Fermi problems

Try our Family of Problems – Fermi Collection on http://completemath.onmason.com/family-of-problems/geometry-and-measurement/

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