Fermi problems, also called Fermi estimates or order-of-magnitude problems, are designed to test your ability to make rough estimations rather than solve for exact answers. They’re named after physicist Enrico Fermi, who was famous for his back-of-the-envelope calculations.
The key to Fermi problems is to break down the problem into smaller, more manageable chunks. You then make educated guesses about each chunk, using common knowledge and basic math. Finally, you multiply or add your estimates to arrive at a final answer.
Here are some key aspects of Fermi problems:
- Focus on Estimation: The goal isn’t a precise answer, but an answer within a reasonable range.
- Order of Magnitude: Often, answers are expressed in scientific notation, focusing on the number’s order of magnitude (how many zeroes are after the leading digits).
- Back-of-the-Envelope Calculations: Ideally, these problems can be solved with basic math operations and common knowledge.
Here’s a classic Fermi problem example:
- Question: How many blades of grass are there on a football field?
There’s no way to count every blade of grass, but we can estimate. We can figure out the area of the field, estimate the average density of blades of grass per square meter, and multiply those values to get a rough idea of the total number.
Fermi problems are great for:
- Developing estimation skills: They help you think critically and make reasonable guesses based on limited information.
- Understanding complex problems: By breaking down a problem into smaller parts, you gain a better understanding of the big picture.
- Enhancing critical thinking: They encourage you to analyze information, identify assumptions, and justify your reasoning.
If you search online for “Fermi problems,” you’ll find many examples and resources to practice your estimation skills!
Also, from another source:
Fermi problems, named after physicist Enrico Fermi, are estimation problems that involve making rough calculations based on limited information and assumptions to arrive at a reasonable estimate. These problems are often used to develop problem-solving skills, critical thinking, and the ability to make quick and educated guesses.
Fermi problems typically involve a series of steps:
- Identification of key factors: Determine the key factors or variables involved in the problem. This may include quantities such as population size, distances, rates of change, or physical properties.
- Making assumptions: Make reasonable assumptions or approximations about the values of the key factors. These assumptions simplify the problem and allow for easier estimation.
- Estimation: Use basic mathematical operations such as multiplication, division, addition, and subtraction to estimate the unknown quantity based on the given information and assumptions.
- Sensitivity analysis: Assess the sensitivity of the estimate to changes in the assumptions or input parameters. This helps evaluate the reliability of the estimate and identify factors that have the greatest impact on the result.
Fermi problems can cover a wide range of topics, including physics, engineering, economics, and everyday life. Some classic examples of Fermi problems include:
- How many piano tuners are there in Chicago?
- How many grains of sand are there on a beach?
- How many liters of gasoline does a typical gas station sell in a day?
- How many golf balls can fit inside a school bus?
- How many people in the world are currently wearing hats?
Fermi problems are valuable because they teach problem-solving skills and encourage creative thinking. They demonstrate that it’s possible to arrive at reasonable estimates even when faced with limited information or complex problems.