Fermi estimation can also be useful in job hunting interview preparation by solving problems many times. However, it will be difficult to solve the problem in time unless you know the prerequisite numbers, points to solve the problem, and techniques in advance.
In this article, I will explain the points to solve the Fermi estimation problem and the basic numbers that I want to memorize. We have also compiled examples of Fermi estimation exercises and ideas for answers. If you are looking for a job hunting and want to work on Fermi estimation, please take a look to the end.
Points to solve the Fermi estimation problem
I will explain two points that you should be aware of when solving the Fermi estimation problem in practice.
Remember the prerequisite numbers
In Fermi estimation, knowledge of statistical values that you want to know as prerequisite knowledge is indispensable. It will be difficult to solve a problem in time unless you memorize the statistics of common sense level and the statistics that are often required for a problem.
Practice putting together answers in a limited amount of time
If you practice solving the Fermi estimation problem as a job hunting measure, you need to practice solving it within a limited time. The more accurate numbers you try to get, the more numbers you have to consider and the longer it takes to put them together.
It is also important to make some divisive assumptions in order to put the problem together in time. By practicing to put together the answers in time, you will be able to take a bird’s-eye view of the whole and identify the parts that are divisible and the parts that are particular about, and you will be able to answer in time.
Basic numbers to keep in mind to solve the Fermi estimation
To solve the Fermi estimation, let’s know some basic statistics. Some of the statistics are highly variable, so it’s easier to remember the approximate values. However, just in case, I will also introduce a public site where you can refer to detailed values.
Statistics that can be used for Fermi estimation (Japan version)
Approximate values of statistics on Japan and reference sites for detailed data are as follows.
|Name of statistics||Approximate value||Reference site|
|population||127 million people||Ministry of Internal Affairs and Communications “Population, Vital Statistics and Number of Households Based on Basic Resident Register”|
|Household||60 million households||Ministry of Internal Affairs and Communications “Population, Vital Statistics and Number of Households Based on Basic Resident Register”|
|Land area||Approximately 378 million km2||JICE “Other than the big land of Japan”|
|Resident||About 30%||JICE “Japanese city spreading in the lowlands”|
|Average life||84 years old||Ministry of Health, Labor and Welfare “Simple Life Table (Core Statistics)”|
|Labor force population||About 66 million people||Statistics Bureau, Ministry of Internal Affairs and Communications “Labor Force Survey Survey Results Table of Contents (National Results)”|
|Number of births per year||About 870,000 people||Ministry of Health, Labor and Welfare “Vital Statistics”|
|University entrance rate||About 54%||Ministry of Education, Culture, Sports, Science and Technology “About publication of basic school survey (preliminary figures) for the first year of Reiwa”|
|Number of large companies||11,000 companies||Small and Medium Enterprise Agency “Number of SMEs / Business establishments”|
|Number of medium-sized enterprises||3.5 million companies||Small and Medium Enterprise Agency “Number of SMEs / Small Businesses”|
Memorizing this amount of information will give you more drawers to come up with an answer when tackling the Fermi estimation problem.
Statistics that can be used for Fermi estimation (world version)
Here are some of the world’s statistics that will help you think about the Fermi estimation problem.
|Name of statistics||Approximate value|
|population||7.7 billion people|
|Surface area of the earth||500 million km2|
|Ratio of sea to land area||7: 3|
|Number of countries in the world||195 countries|
To find out the statistics of the world, “World Statistics” of the Statistics Bureau of the Ministry of Internal Affairs and Communications is convenient. The latest information is posted, so please use it when you want to check and remember the statistical values you care about.
Other basic numbers
Other numbers you should know to solve the Fermi estimation include the GDP of the United States, China, and Japan, the number of stations in Japan, and the population and area of Tokyo.
Also, if you remember basic figures such as the area and population of the prefecture where you live, you can often use it as a base when answering questions, so it is recommended to check it.
If you come up with a number you want to know while actually solving the Fermi estimation problem, it is a good idea to look it up and remember it yourself.
Fermi estimation exercises
Here are some exercises for Fermi estimation. We arranged the solution by presenting the premise confirmation, formulating the calculation formula from the premise, and applying the numerical value to solve it.
Consider that there are omissions in the premise in how to solve the problem presented here, and consider the premise yourself.
1. How many utility poles are there in Tokyo?
1km2It is assumed that the number of utility poles per unit is estimated and calculated.
- The area of Tokyo is about 2,200km2(Statistics)
- The number of utility poles per area is about 1 in 5m, 5m based on experience.2Estimated to be 2 (value by assumption)
- Japan’s habitable land is about 30%, but Tokyo’s is assumed to be about 60% (value based on assumption)
1. 1km2Number of utility poles around = (1km2÷ 5m2) × 2
2. Number of utility poles in Tokyo = Area of Tokyo x number of utility poles per area x 60%
1. 1km2Number of utility poles around = 200 x 2 = 400 / km2
2. Number of utility poles in Tokyo = 2,200km2× 400 / km2× 60% = 528,000
Let’s look for other factors to validate this issue. For example, the utility poles are underground, but it is necessary to consider that amount.
2. How many PCs are used in Japan?
Since each person uses a personal computer, the number of users is assumed to be equal to the number of PCs used. Some people have multiple kitchens by themselves, but I don’t think there are many, so I won’t think about it here. In addition, elderly people think that they do not use a personal computer very much, so we will ignore it here.
- Japan’s population is 120 million (statistics)
- Person using a personal computer (assumed)
- People using PCs at work = Approximately 60 million workers (statistics)
- Those who use PCs at school = Elementary school students and above (* Including programming education from 2020)
- People who use PCs in private = Younger generation is smartphone main, 40s and over thinks that there are many PCs, and it is set at 50% of the worker population
People who use a personal computer are considered to be the total number of people who use a personal computer at work, school, or private life.
- People using a PC at work
People using PCs at work = worker population
- People using a PC at school
Number of students over elementary school = Number of births per year x 12 years (elementary, middle and high school) + Number of births per year x University admission rate 50% x 4 years
- People who use a PC in private
People who use PCs in private = Worker population x 50%
- People using a PC at work
People who use PCs at work = about 60 million
- People using a PC at school
People using PCs at school = Approximately 1 million people x 12 years + Approximately 1 million people x University enrollment rate 50% x 4 years = 12 million people + 2 million people = 14 million people
- People who use a PC in private
People who use PCs in private = about 60 million x 50% = 30 million people
60 million + 14 million + 30 million = 104 million units
Here are some other Fermi estimation problems that are good for practicing.
- How many cats are there in Japan?
- How many ants are there on earth?
- How many golf balls can fit in a large bus?
- Who is sleeping at this moment in the world?
Let’s actually solve the problem by the same procedure as before and get used to how to solve the Fermi estimation.
How to summarize after solving the Fermi estimation
After solving the Fermi estimation, it is necessary to put it together in a logical structure that can be communicated to the interviewer. I will introduce three points when summarizing, so let’s summarize the answer according to this form.
The composition of the story brings the conclusion first
First, I will explain what was the result of answering the Fermi estimation. If you are asked “the number of utility poles in Japan”, first come to the conclusion that “the number of utility poles in Japan is 〇〇”.
Also note: How many utility poles are there in Japan? Let’s find the answer with “Fermi estimation”
Communicate the process of making a hypothesis in detail
Next to the conclusion, I will explain the calculation formulas in order from the hypothesis, but the important point here is to convey the process of thinking about the hypothesis in detail.
For example, suppose that when you consider the demand for taxis, you simply list the demand.
We have identified the demand for taxis as follows.
・ Return home after the last train
・ Movement when there are many items such as shopping
・ Travel of travelers
This alone does not tell you how to consider and identify demand, and it is difficult to convey the whole picture of the hypothesis to the interviewer.
We have identified the demand for taxis by assuming the following.
1. Resident’s work relations: Return home after the last train
2. Resident’s private relationship: Movement when there is a lot of shopping etc.
3. Non-resident travel: Traveler travel
If you summarize the examination process in this way so that you can see it, it will be easier for the interviewer to point out any omissions.
Create a calculation formula according to the hypothesis
After organizing the hypothesis, we will present the necessary information. Let’s explain the specific numbers by grouping the statistical values that you already remember and the numbers that you derived from your inference. Don’t forget to explain that the part where the premise was decided by dividing it to some extent is “I decided this as the premise here”.
Once you have done this, let’s assemble the calculation formula while showing the process of examination in detail. The interviewer is informed that he built the logic while thinking for himself, unlike when he applied it to the framework and made it mechanically.
The problem of Fermi estimation can be difficult if you are not used to it. However, by practicing a few times, you will be able to understand the knack of answering, and you will be able to build logic faster and with less omissions.
In addition to solving the problem yourself, practice scrutinizing the content of the answer to look for omissions and brushing up the answer several times yourself. In an actual interview, it is also important to refine the answer in the interaction with the interviewer. Let’s try to solve the Fermi estimation problem by yourself so that we can respond flexibly and quickly.