# Fermi problems

Enrico Fermi, the Nobel Laureate for Physics in 1938, was known for his ability to make good approximate calculations with little or no actual data – hence the problem type named after him. One example is his estimate of the strength of the first atomic bomb detonated in New Mexico in 1945, based on the distance travelled by pieces of paper in the blast wave dropped from his hand during the explosion. Fermi's estimate of 10 kilotons of TNT was within an order of magnitude of the now-accepted value of around 19 kilotons.

Many Fermi problems require only a pencil and the back of an envelope – a calculator might also be useful! They typically involve estimating the number of service providers appropriate for some occupation in a city or other population hub.

## Piano tuners

As a lecturer Fermi used to challenge his classes with problems that, at first glance, seemed impossible. One such problem was that of estimating the number of piano tuners in Chicago given only the population of the city.

How many piano tuners are there in **your** state or territory capital?

## Estimation: dentists

Fermi problems are mainly to do with estimating quantities relevant to addressing real world problems.

Estimate how many dentists are needed in the city of Toowoomba.

## Average: service stations

** **

In Fermi problems some experienced modellers favour finding the average. They use the Goldilocks Principle where M

_{2 }

is too big and M

_{1 }

is too small. What is just right?

How many service stations are needed (in a provincial city)?