Library / Fermi Questions
Fermi Questions
Order-of-magnitude estimation questions used in quant and trading interviews, break the unknown into parts, reason to a defensible answer, and track your progress as you solve.
- The Nursery Heavyweight
- The Office Skyline
- The Shoreline Problem
- The Sidewalk Business
- The Tollbooth Deal
- The Weight of a Full Bathtub
- The Weight of a Million Dollars
- The Wired Tower
- The Workday Peak
- The Working Cab
- The Working Fleet at Sea
- The Worldwide Box Office
- Toothpaste Tubes in a Lifetime
- Waking a Nation
- Wall-to-Wall Packing
- Water on Every Block
- Weighing a Skyline Icon
- Years Spent Asleep
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What are Fermi questions?
Fermi questions ask you to estimate a quantity you can’t look up, like “how many piano tuners are there in Chicago?”, by breaking it into parts you can reason about and combining sensible assumptions. Trading and quant interviewers love them because they reveal how you decompose a problem, handle uncertainty, and sanity-check a number under pressure.
On Tradermath, each question is graded by order of magnitude: get within a factor of ten and you’re on track. Work through the curated set, reveal hints when you’re stuck, and compare your estimate against a full worked solution to build the instinct that matters most in interviews.
Tips & Tricks for solving Fermi Questions
What is a Fermi Question?
A Fermi question is a problem-solving question that requires estimation to arrive at a rough answer. Named after physicist Enrico Fermi, these questions typically involve making educated guesses and assumptions based on limited information.
What if I have no clue about an assumption?
When faced with a Fermi question in an interview and you have no clue about a certain assumption, follow these steps:
- Acknowledge the Uncertainty: Start by acknowledging that you are unsure about the assumption. This shows honesty and transparency.
Example: "I'm not entirely sure about the exact value for this assumption, but I will make an educated guess." - Use General Knowledge: Draw on any general knowledge you might have related to the topic to make a reasonable estimate.
Example: "I know that the population of a large city can range from 1 to 10 million people, so I'll use 5 million as a middle-ground estimate." - Explain Your Reasoning: Clearly explain the logic behind your guess. This demonstrates your problem-solving approach and how you handle uncertainty.
Example: "Given that many major cities have populations in the range of a few million, I'll assume 5 million for simplicity, which seems reasonable for a large metropolitan area." - Seek Feedback: If possible, ask the interviewer if the assumption seems reasonable. This can provide guidance and show that you are open to input.
Example: "Does that assumption sound reasonable, or would you suggest a different approach?" - Proceed with the Estimate: Use your assumption to continue solving the problem. Ensure that your subsequent calculations are logical and consistent with the assumption made.
Example: "Based on the assumption of 5 million people, I'll calculate the proportion who might use a certain service..."
By following these steps, you demonstrate your ability to handle uncertainty effectively, think critically, and communicate clearly, all of which are valuable skills in any problem-solving scenario.
How to approach a Fermi Question?
A general good approach for solving Fermi Questions is to follow these steps:
- Break down the problem: Try to break the problem down into solvable questions.
- Make reasonable assumptions: Identify and state any assumptions you are making.
- Use approximations: Simplify the calculations by using rounded numbers where appropriate.
- Check your work: Verify if the answer makes sense and is plausible given the context.
How detailed should my assumptions be?
Your assumptions should be detailed enough to provide a logical basis for your estimates but not so detailed that they overcomplicate the problem. Strive for a balance that allows you to make reasonable approximations.
What skills are interviewers assessing with Fermi questions?
Interviewers are assessing your problem-solving abilities, logical reasoning, quantitative skills, ability to make and justify assumptions, and how you handle uncertainty.
Are there any common traps to avoid when answering Fermi questions?
- Avoid overcomplicating the problem with unnecessary details.
- Don't get stuck on finding the "perfect" assumption.
- Ensure your assumptions are reasonable and explainable.