Fermi Problems

Happy Saturday everyone,

It has been a while since we last shared an article about interviews, but we wanted to share a strategy with our followers that is frequently used in interviews to measure candidates' critical and analytical thinking skills.

When preparing for a job interview, most candidates focus on rehearsing their responses to common interview questions about their background, skills, and career goals. However, there is another type of question that is becoming increasingly common in interviews - the Fermi problem.

In today's article, we're going to talk about what Fermi problems are, why they are used in interviews, and how candidates can effectively approach them.

Let's go!

Fermi problems are open-ended questions that ask you to estimate a quantity when you don't have enough information to calculate it precisely. These types of questions can be quite challenging, but they provide valuable insights to interviewers about a candidate's problem-solving abilities, logical thinking, and quantitative skills.

The term "Fermi problem" originates from the physicist Enrico Fermi, who was known for his ability to make rapid, rough calculations to estimate unknown quantities. Fermi problems are named after him because he would frequently pose this type of question to his students as a way to test their critical thinking and numerical reasoning skills.

Understanding Fermi Problems

Fermi problems are questions that involve making educated estimates to arrive at a rough answer. These problems are designed to assess a candidate's ability to apply logical reasoning and mathematical principles to solve complex, open-ended questions. For example, a classic Fermi problem might ask, "How many piano tuners are there in Chicago?" To solve this, one would break down the problem into smaller, manageable parts and make reasonable assumptions to arrive at an estimate.

The Significance of Fermi Problems in Interviews

The primary reason Fermi problems are used in interviews is that they reveal a candidate's problem-solving process. Unlike straightforward technical questions that test specific knowledge, Fermi problems assess how a candidate thinks. This is crucial for roles that require analytical thinking, creativity, and the ability to make decisions based on incomplete information.

Fermi problems also allow interviewers to see how candidates handle ambiguity and uncertainty. In many real-world situations, professionals must make decisions without having all the necessary data. Fermi problems mimic these conditions, giving interviewers insight into how candidates might perform in such scenarios.

Key Skills Assessed by Fermi Problems

When candidates tackle Fermi problems, interviewers look for several key skills:

1. Analytical Thinking: Candidates must demonstrate the ability to break down a large, complex problem into smaller, more manageable parts.
2. Logical Reasoning: Interviewers assess how candidates use logic to make assumptions and connect different pieces of information.
3. Numeracy: Basic mathematical skills are essential for making estimates and performing calculations.
4. Creativity: Candidates often need to think outside the box to come up with reasonable assumptions and approaches to the problem.
5. Communication: It is important for candidates to clearly explain their thought process and reasoning. This not only demonstrates their problem-solving skills but also their ability to communicate complex ideas effectively.

So how should you approach a Fermi problem in a job interview?

1. First and foremost: Don't panic. It's natural to feel overwhelmed when presented with a Fermi problem, as they are designed to be challenging. Take a deep breath and remember that the interviewer is not expecting a precise, perfectly calculated answer.
2. Ask clarifying questions. Before jumping into your estimate, make sure you fully understand what the interviewer is asking. Feel free to ask for additional details or constraints that could help you narrow down the problem.
3. Break the problem down into smaller parts. Identify the key variables or factors that are required to solve the problem, then make reasonable assumptions for each one. For example, if asked to estimate the number of piano tuners in a city, you might need to estimate the city's population, the average number of pianos per household, and the frequency with which pianos are tuned.
4. Use a logical, step-by-step approach. Walk the interviewer through your thought process as you work towards an estimate. Explain your assumptions and the reasoning behind them. This shows your ability to think systematically.
5. Don't be afraid to make educated guesses. Since Fermi problems lack complete information, you'll need to fill in the gaps with your own best estimates. Don't be afraid to make reasonable guesses - the goal is to demonstrate your ability to reason through the problem, not to get the "right" answer.
6. Round your final answer appropriately. When providing your estimate, use sensible rounding to a reasonable order of magnitude. Avoid giving an overly precise number that doesn't align with the level of uncertainty in your assumptions.
7. Reflect on your approach. After providing your answer, take a moment to critique your own problem-solving method. Identify areas where you could have made stronger assumptions or approached the problem differently. This self-awareness is valuable for interviewers to observe.

Common Mistakes to Avoid

While Fermi problems are designed to be challenging, there are common pitfalls candidates should avoid:

1. Overcomplicating the Problem: Fermi problems are meant to be solved with rough estimates, not precise calculations. Avoid getting bogged down in unnecessary details.
2. Ignoring Units: Always pay attention to units and ensure they are consistent throughout your calculations. This can prevent simple mistakes that lead to incorrect estimates.
3. Making Unreasonable Assumptions: While assumptions are necessary, they should be reasonable and based on logical reasoning. Wild guesses can lead to implausible results.
4. Failing to Communicate Clearly: Even if your calculations are correct, failing to clearly explain your thought process can make it difficult for interviewers to follow your reasoning.

Examples of Fermi Problems

To illustrate the application of Fermi problems, here are a few examples:

1. How many golf balls can fit in a school bus?
2. How many cups of coffee are consumed in New York City in a day?
3. How many times does the average person blink in a year?

Each of these problems requires breaking down the question into smaller parts, making reasonable assumptions, and performing calculations to arrive at an estimate.

Step-by-Step Solution Sample

1. Understand the Problem: The goal is to estimate the number of cups of coffee consumed in New York City in a single day.

2. Break Down the Problem: To solve this, we can break the problem down into several smaller questions:

• What is the population of New York City?
• How many people drink coffee?
• How many cups of coffee does a coffee drinker consume per day?

3. Make Assumptions: Let's make reasonable assumptions for each part of the problem:

• Population of New York City: Approximately 8.4 million people.
• Percentage of People Who Drink Coffee: Assume that 70% of the population drinks coffee.
• Average Number of Cups per Day: Assume that the average coffee drinker consumes 2 cups of coffee per day.

4. Perform Calculations:

• Number of Coffee Drinkers:

Number of coffee drinkers = Population of NYC x Percentage of coffee drinkers

our formula is = 8.4 million x 0.70 = 5.88 million people.

• Total Number of Cups of Coffee Consumed:

Total cup of coffee = Number of coffee drinkers x Average?number?of?cups?per?day

= 5.88?million?people×2?cups?per?day=11.76?million?cups?per?day.

5. Check Reasonableness: Review the assumptions and the calculations to ensure they are reasonable. The population and percentage of coffee drinkers are reasonable assumptions, and the average number of cups per day is a typical estimate for coffee consumption.

6. Explain Your Reasoning: Clearly articulate the thought process, assumptions, and calculations:

• We started by estimating the population of New York City at 8.4 million people.
• Assuming 70% of this population drinks coffee gives us 5.88 million coffee drinkers.
• Assuming each coffee drinker consumes an average of 2 cups per day, we estimate a total daily coffee consumption of 11.76 million cups.

In our example, we estimated the number of cups of coffee consumed in New York City in a single day. By considering the population, the percentage of people who drink coffee, and the average number of cups consumed per day, we arrived at an estimate of 11.76 million cups per day. This process highlights the importance of making reasonable assumptions and clearly communicating your thought process.

Fermi problems can be daunting, but with practice and the right mindset, you can turn them into an opportunity to showcase your analytical abilities. You can demonstrate to interviewers that you have the critical thinking skills needed to succeed in their organization by approaching these open-ended questions systematically, making reasonable assumptions, and clearly communicating your thought process.

You got this!

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