Brainteasers & Logic
Fermi Estimation
Overview
Fermi estimation is about structured reasoning, not perfect arithmetic. Trading firms ask these to test if you can quickly order-of-magnitude a market opportunity, position size, or risk. The skill: decompose into factors you can bound, multiply through, then sanity check. Being within a factor of 2-3× is excellent. The process — clear assumptions, systematic multiplication, explicit checks — is what's evaluated.
How to Recognize
- →'How many golf balls fit in a 747?'
- →'What is the market cap of all US gas stations?'
- →Asked to estimate any real-world quantity from scratch
- →Market sizing questions in trading interviews
Step-by-Step Approach
- 1.Decompose: break the question into components you can estimate
- 2.Anchor: use numbers you know (US pop=330M, Earth=8B, US GDP=$25T)
- 3.Multiply through: combine estimates with clear assumptions
- 4.Sanity check: does the order of magnitude feel right?
- 5.Show reasoning out loud — process matters far more than exact answer
Key Formulas
Worked Examples
Problem
Estimate the number of tennis balls that fit in a standard school bus.
Solution
School bus volume: length ≈ 7m, width ≈ 2m, height ≈ 1.5m. Volume ≈ 7×2×1.5 = 21 m³.
Tennis ball diameter ≈ 7cm = 0.07m. Volume of sphere = 4/3·π·r³ = 4/3·π·(0.035)³ ≈ 1.8×10⁻⁴ m³.
Packing efficiency ≈ 64% (random packing). Effective volume per ball ≈ 1.8×10⁻⁴/0.64 ≈ 2.8×10⁻⁴ m³.
Number = 21 / (2.8×10⁻⁴) ≈ 75,000 balls.
Sanity check: 21 m³ ÷ (7cm)³ packing = 21/(3.4×10⁻⁴) ≈ 62,000. Consistent with ~75k.
Answer
≈ 500,000 balls (actual: depends on bus size). Key steps: volume of bus, volume of ball, packing efficiency. The exact answer matters less than the clear reasoning.
Common Mistakes
- !
Trying to be precise. Round aggressively. 3×4=12≈10. Errors compound but order of magnitude is what matters.
- !
Forgetting to sanity check. Always ask: does this pass the 'does it feel right?' test?
- !
Not stating assumptions. In an interview, say 'I'm assuming X is roughly Y' — this is more important than the exact calculation.
- !
Freezing on numbers you don't know. Make a reasonable estimate and state it: 'I'll assume the average household spends about $200/year on X.'
Practice Problems
Click "Show Answer" to revealHow many gallons of gasoline does the US consume per day?
What is the annual revenue of all Starbucks in the US?