# Famous Fermi Problems

Your 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 math will you use to solve the problem?

http://hgse.balancedassessment.org/docs/e011.pdf

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/

https://www.mathcircles.org/files/Fermi_Estimates_Lesson_Plan.pdf

https://www.eduweb.vic.gov.au/edulibrary/public/teachlearn/student/mathscontinuum/fermiquestionsvels.pdf