Guesstimate Questions to Practise, With Worked Answers
Eight guesstimate questions of the kind consulting, product and quant interviews ask, each worked from figures you already know, what interviewers listen for, and where to practise with an answer key.
Introduction
A guesstimate question asks for a number nobody in the room knows: how many piano tuners in Chicago, how many cups of coffee Starbucks sells in a day, how many golf balls fit in a bus. Consulting, product and quant interviews ask them because the answer is beside the point; the reasoning is the answer. Below are eight worked the way an interviewer wants to hear them, then the fastest way to practise with an answer key.
The Method in One Paragraph
Split the quantity into pieces you can estimate, state each piece aloud with its assumption, multiply, then check the result against something you know. Aim for the right power of ten, not the right first digit: an estimate within a factor of two or three is a good one. Two habits matter more than knowledge. Round every number to something you can multiply in your head, and when a piece has a wide range, take the middle in powers of ten: between 1,000 and 100,000 the middle is 10,000, not 50,500.
1. How Many Piano Tuners Are There in Chicago?
Fermi's original. Chicago has about 2.7 million people, roughly 2.5 per household, so about a million households. Perhaps one in twenty owns a piano: 50,000 pianos. A piano is tuned about once a year, and a tuner doing four a day for 250 days manages a thousand. So 50,000 tunings a year at 1,000 per tuner is about 50 tuners. Directory counts have always landed within a factor of two of that.
2. How Many Cups of Coffee Does Starbucks Sell in a Day?
Roughly 40,000 stores worldwide. A busy store serves perhaps 500 customers a day and a quiet one 200; call it 350, at a little over one drink each. 40,000 times 400 is 16 million drinks a day. That is the right order of magnitude, and the sanity check is that it is a few drinks a year for every person on Earth, which sounds like Starbucks.
3. How Many Golf Balls Fit in a School Bus?
A school bus is about 12 metres long and roughly 2.5 wide and 2 high inside: about 60 cubic metres. A golf ball is about 4.3 cm across, so a cube around it is about 80 cubic centimetres, or 0.00008 cubic metres. 60 divided by 0.00008 is 750,000. Spheres pack to about 65% of the space, and seats take some of it, so call it half a million.
4. How Many Heartbeats in a Football Match?
A resting heart runs about 70 beats a minute. A match is 90 minutes, so about 6,300 for a fan sitting still and more like 9,000 for one on their feet shouting. If the question is about the players, use 150 beats a minute for 90 minutes: about 13,500.
5. How Many Eggs Would Fill an Olympic Swimming Pool?
An Olympic pool is 50 by 25 by 2 metres: 2,500 cubic metres, or 2.5 billion cubic centimetres. A large egg is about 55 cubic centimetres. Divided out, about 45 million eggs before packing gaps. Say 40 million.
6. How Many Cars Are There in the United States?
About 340 million people, 130 million households, and a little under two vehicles per household: about 250 million. Official counts put registered vehicles, trucks included, closer to 280 million, so the estimate is a little low and comfortably within a factor of two.
7. How Much Does the Air in a Room Weigh?
A bedroom of 4 by 4 by 2.5 metres is 40 cubic metres. Air is about 1.2 kilograms per cubic metre at sea level. So about 50 kilograms, which surprises most people, and is the point of the question.
8. How Many Words Does a Person Say in a Lifetime?
Around 15,000 words a day is a fair average across talkative and quiet days. Times 365 is about 5.5 million a year, times 80 years is about 440 million. Under half a billion.
What Interviewers Are Listening For
Structure before numbers: name the pieces before you estimate any of them. Assumptions said aloud, so a wrong one can be corrected instead of hidden. A sanity check at the end against something known. And composure when a piece is unknown: a stated guess with a range beats a pause.
Where to Practise With an Answer Key
Worked examples run out, and the real gap in guesstimate practice is feedback: you rarely learn how far off you were. Fermi Unlimited is a game built on exactly this. It deals Fermi estimation questions about real quantities, across everyday life, sport, space and the human body, one after another, and after every guess it shows a worked estimate from published figures with the sources. You are marked on how many times off you were, so a good estimate survives and a cold one ends the run. There is also a guide to getting better at Fermi with the anchor figures worth memorising.
Sources
Weinstein, L. and Adam, J. A., Guesstimation: Solving the World's Problems on the Back of a Cocktail Napkin (Princeton University Press, 2008).
About the author
Jeffery is a student and longtime puzzle enthusiast who grew up on grid games and brain teasers. He covers strategy and the small optimizations that turn an average score into a great one.