“How many golf balls fit in a plane?” is the most famous estimation question, and it is also one the company that made it famous publicly dropped. In 2013 Laszlo Bock, then Google’s head of people operations, told the New York Times that brainteasers such as “How many golf balls can you fit into an airplane?” were “a complete waste of time” that “don’t predict anything”, according to ABC News’s report of the interview.
Yet the format has not disappeared. Yale’s Office of Career Strategy lists market-sizing questions and brain teasers as standard parts of consulting case interviews, and says market sizing tests “your thought process, ability to structure, general business and numbers sense”. So if you are applying for consulting, or for analytical roles where interviewers like to see you reason with numbers, it is worth knowing how to handle them.
This article works through four scenarios, each a different type of estimation question, using the same method throughout.
The method in five moves
OpenStax’s university physics textbook calls these “Fermi calculations”, after the physicist Enrico Fermi, and makes the point that “estimating does not mean guessing a number or a formula at random.” Its strategies translate well to an interview room:
- Clarify. Which plane? Cabin only, or the hold too? Are seats still in place? Ask one or two questions, then commit.
- Break it down. Turn one unknown into several smaller ones you can estimate: big volumes from lengths, totals from a rate times a population.
- Round hard. OpenStax says one significant figure is fine, and that the goal is a ballpark figure, so “keep the arithmetic as simple as possible”.
- Bound it when you are stuck. If you cannot estimate a figure, state numbers it must be above and below, then pick a value between them.
- Sanity-check. OpenStax’s last strategy is “Does this make any sense?” Cross-check with a second route if you can.
Throughout, speak your assumptions aloud. The interviewer cannot give credit for reasoning they cannot hear.
Scenario 1: The physical-volume question
“How many golf balls would fit inside a commercial aircraft?”
The figures for the aircraft below are illustrative assumptions, of the kind a candidate might make on the spot. They are not manufacturer specifications.
Clarify
“I’ll assume a single-aisle passenger jet, the cabin only, with seats left in place. Is that reasonable?” If the interviewer says yes, carry on.
Estimate the ball
The R&A’s Rules of Equipment state that the diameter of a golf ball “must not be less than 1.680 inches (42.67 mm)”. Call it about 4 cm across. A quick way to count balls is to treat each one as a 4 cm cube: 4 × 4 × 4 = 64 cm³ per ball.
If you want to refine that: a sphere of that size has a volume of roughly 41 cm³, but balls poured into a space do not fill it. A 2010 article in the American Physical Society’s journal Physics notes that disordered sphere packings cannot be compressed beyond roughly 64% of the volume. At about 64% packing, each ball effectively takes up about 41 ÷ 0.64, or roughly 64 cm³. The cube shortcut and the careful version land in the same place, which is worth saying out loud.
Estimate the space
- Cabin length: assume 30 m.
- Width: assume 3.5 m.
- Height: assume 2.2 m.
- Volume: 30 × 3.5 × 2.2 ≈ 230 m³.
- Take off about 20% for seats, galleys and lavatories: roughly 185 m³.
Combine and check
One cubic metre is 1,000,000 cm³, so it holds about 1,000,000 ÷ 64 ≈ 15,600 balls. Multiply by 185 m³ and you get roughly 2.9 million. Round it: about 3 million golf balls.
Sanity check: a cubic metre is roughly the size of a large washing-machine box. Does 15,000 golf balls in that box sound plausible? Twenty-five balls fit along each 1-metre edge, and 25 × 25 × 25 is about 15,600. The two routes agree.
Then add one line of judgement: “If we included the cargo hold or removed the seats, the figure would rise, but it would stay in the low millions.”
Scenario 2: The demand-side market question
“How many haircuts happen in a week in a city of 2 million people?”
This is a market-sizing question in disguise. All the figures below are illustrative assumptions.
- Population: 2,000,000 (given).
- Assume the average person, across all ages, has a haircut roughly every six weeks.
- Haircuts per week: 2,000,000 ÷ 6 ≈ 330,000.
A stronger candidate splits the population into groups whose habits differ (for example, adults with short hair, adults with long hair, children) and states a frequency for each. Splitting shows structure; just make sure the arithmetic stays manageable.
Now check from the supply side. Assume a barber or stylist does 10 cuts a day, six days a week: 60 a week. To deliver 330,000 cuts you would need about 5,500 working barbers and stylists, or roughly one for every 360 residents. Ask yourself whether that sounds possible for a city. If one route gave you 330,000 haircuts and the other implied one barber per 20 people, you would know an assumption was wrong.
Scenario 3: The capacity question
“How many petrol stations does a city of 2 million need?”
Bock’s own examples included “How many gas stations in Manhattan?” Capacity questions like this one combine demand with how much one unit can serve. Again, the numbers are illustrative.
| Step | Assumption | Result |
|---|---|---|
| Cars in the city | One car per three residents | About 670,000 cars |
| Refuelling frequency | Once a week | About 95,000 fills a day |
| Capacity of one station | 8 pumps, 5 minutes per fill, 12 busy hours, pumps in use half the time | 8 × 144 × 0.5 ≈ 580 fills a day |
| Stations needed | 95,000 ÷ 580 | About 165 stations |
Present it in this table-like order on your notepad. Then name the assumption with the biggest effect (here, how often people refuel) and say what would happen if it were wrong: “If people fill up every ten days rather than seven, the answer drops to around 115.”
Scenario 4: The question with no numbers
“Why are manhole covers round?”
Yale lists this as an example of a brain teaser and says such questions “may or may not have a definite answer”. The approach is the same as with the numerical questions: say what the object has to do, then test shapes against those requirements. A cover must not fall through its own hole; it must be practical to move; it must sit securely. Then reason about whether a circle, a square or another shape meets each requirement better, and say where you are unsure. The interviewer is watching how you build the argument, not checking it against an answer key.
What to do when it goes wrong mid-answer
- You realise an assumption is off. Say so and fix it: “Actually, 30 metres seems short for the whole aircraft, but it’s about right for the cabin, so I’ll keep it.”
- Your arithmetic slips. Slow down and redo the step aloud. Rounding to friendlier numbers is allowed.
- The interviewer challenges a figure. Take the challenge as information, not as criticism. Adopt their number and carry on.
- Your mind goes blank. Restate the question and write down the first breakdown that comes to mind. It is easier to improve a structure than to invent one under pressure.
How to practise
Pick everyday objects and spaces (a lift, a bus, your city’s coffee shops) and estimate one a day in under three minutes. Then check: look up the real figure if one exists, and see which assumption was furthest off. Over a few weeks you build a store of reference points, such as typical room sizes, daily footfall and transport speeds, that make the next estimate quicker.
If the job you are targeting involves quantitative work, make sure your CV shows it with real figures from your own experience. The resume examples show how numbers can sit in achievement bullets, and the data analyst resume builder is set up for analytical roles.
Frequently asked questions
Will I fail if my number is far from the real one?
Usually not. Yale’s Office of Career Strategy notes that for market-sizing questions there is often a broad range of acceptable answers. Interviewers are watching the structure, the assumptions and the arithmetic. A sensible method that lands at 2 million when the ‘real’ figure is 4 million is far better than a lucky guess with no reasoning.
Can I use pen and paper?
In most in-person and video interviews, yes; ask if you are unsure. Writing your assumptions in a column also makes them easier for the interviewer to follow and challenge.
What if I genuinely have no idea about a starting figure?
Say so, then bound it. If you do not know the length of an aircraft cabin, you might say it is certainly more than 10 metres and less than 100, pick a reasonable value in between, and invite correction. That is a technique, not a weakness.
Do employers still ask brain teasers?
Some do, and some do not. Google’s former people chief, Laszlo Bock, told the New York Times in 2013 that the company had found brainteasers did not predict anything, but estimation still appears in consulting case interviews and some analytical roles. Prepare for it if your target field uses cases.
Sources
- Google Skips ‘Waste of Time’ Brainteaser Interview Questions (ABC News)
- The Case Interview (Yale Office of Career Strategy)
- University Physics Volume 1, 1.5 Estimates and Fermi Calculations (OpenStax, Rice University)
- Rules of Equipment, Part 4: Conformance of Balls (The R&A)
- The tetrahedral dice are cast . . . and pack densely (Physics (American Physical Society))