In 1945, physicist Enrico Fermi estimated the yield of the first nuclear bomb test by dropping scraps of paper and watching how far the blast carried them.
No instruments. No calculations. Just observation, reasoning, and a surprisingly accurate answer.
That instinct - to break an impossible question into answerable pieces - gave rise to one of the most enduring tools in science, business, and hiring: the Fermi Problem.
Here are six that became genuinely famous, and what made each one stick.
1. How Many Piano Tuners Are There in Chicago?
The original. Fermi reportedly posed this to his students at the University of Chicago, and it's been copied, adapted, and celebrated ever since.
Nobody knows the answer off the top of their head - which is precisely the point. Instead, you construct it:
- Chicago has roughly 3 million people, or about 1 million households
- Maybe 1 in 20 owns a piano - that's 50,000 pianos
- A piano needs tuning once or twice a year: roughly 75,000 tunings annually
- A tuner can do perhaps 4 appointments a day, 250 days a year - about 1,000 tunings per tuner
Divide through and you land somewhere around 75 piano tuners. The actual number, when people have checked, tends to sit in that range.
The reason this question endures isn't the answer. It's the realisation that the answer was reachable - from nothing but common sense and arithmetic.
2. How Many Gas Stations Are There in the United States?
This one became a staple of consulting interviews in the 1980s and 90s, and it's still used today.
On the surface it sounds like a question that needs a database. It doesn't. You can reconstruct it:
- Around 240 million licensed drivers
- Each car needs refuelling roughly once a week
- A busy station might serve 1,000 cars a week
That points toward roughly 150,000 stations. The real figure is close to 145,000.
What made this a classic interview question is that it tests something specific: can you build a logical model of a system you've never studied? That's a transferable skill. The gas stations are just the vehicle.
3. How Many Golf Balls Can Fit Inside a Boeing 747?
The one that went mainstream.
This question spread through Silicon Valley and Wall Street hiring in the 2000s and became so well-known it spawned a minor industry of practice guides, YouTube explainers, and consulting prep courses.
The structure is elegant:
- The interior volume of a 747 is roughly 800 cubic metres
- A golf ball has a diameter of 4.3cm - volume of about 40 cubic centimetres
- Spheres pack at around 64% efficiency
Multiply through and you get somewhere in the range of 20–25 million golf balls.
The reason it works as a problem is that it demands three distinct skills in sequence: spatial reasoning, unit conversion, and packing geometry. Miss any one of them and your answer falls apart. Nail all three and you feel like you've done something genuinely clever - because you have.
4. How Many Manhole Covers Are There in New York City?
Microsoft made this one famous in the 1990s as one of their signature interview questions. Candidates who said "I have no idea" failed. Candidates who immediately rattled off a number failed too.
What interviewers wanted was the pause, and then the reasoning:
- New York City covers about 780 square kilometres
- Manholes appear roughly every 50–100 metres in urban areas
- Density varies - Midtown has far more than Staten Island
A reasonable estimate lands somewhere between 250,000 and 300,000. The question became famous not because the number is interesting but because it revealed something about how people handle problems they've never encountered before. That turns out to be a reasonable proxy for job performance.
5. How Many Petrol Stations Would You Pass Driving Across Australia?
A more recent addition to the Fermi canon, and a favourite in Australian business and education contexts.
Driving coast to coast - say, Sydney to Perth - covers roughly 4,000 kilometres. The breakdown is stark:
- The first few hundred kilometres out of Sydney: stations every 10–20km
- Through regional New South Wales: every 50–80km
- Across the Nullarbor: some stretches exceed 200km between stops
Total? Perhaps 80–120 stations, depending on your exact route.
What makes this one unusual is that it teaches geography as a side effect. You can't solve it without confronting just how vast and empty the Australian interior really is. The maths is simple. The perspective shift is the point.
6. How Many Cups of Coffee Are Consumed Around the World Each Day?
The most accessible Fermi Problem on this list - and the one with the most reliably shocking answer.
Work through it:
- Roughly 8 billion people in the world
- About a third drink coffee - call it 2.5 billion drinkers
- Average consumption among drinkers: perhaps 1.5 cups a day
That's around 3–4 billion cups daily. Every single day.
This problem is useful precisely because the answer feels wrong. Our intuitions about global scale are almost always off. Problems like this recalibrate them.
What These Six Have in Common
Each of these questions became famous for a reason - and it's not that the answers are surprising (though they often are).
It's that the process is surprising. Most people assume that not knowing an answer means you can't find it. Fermi Problems prove that wrong, repeatedly, using nothing but structured thinking.
That's a lesson worth sitting with.
Where Magnitudle Comes In
Magnitudle is a daily estimation game built on exactly this idea.
Every day, one question. One attempt. No multiple choice, no hints - just you and your reasoning.
Some questions will feel impossible. That's the point. The satisfaction isn't in knowing the answer. It's in discovering that you could figure it out.