“How many piano tuners are there in Chicago?”
This is the original Fermi problem, from which the entire genre of “Fermi estimation” takes its name. Enrico Fermi, the Italian-American physicist, used to ask versions of this at the University of Chicago in the 1940s and 50s as a teaching tool. The question was older than tech interviewing by half a century. By the time Google adopted Fermi-style questions in the 2000s, the piano tuners problem had been used to teach decomposition reasoning to generations of physics and engineering students.
The Google version of the question is dead — Laszlo Bock retired it in 2013 along with the rest of the brainteaser canon. But the underlying lineage from Fermi’s classroom continues, and the question is alive in product manager, consulting, and senior system design interviews in 2026.
The structured calculation
The standard approach decomposes the question into a chain of multiplicative ratios. Each ratio is something you can estimate from general knowledge.
Population of Chicago. About 2.7 million people in the city proper, or about 9 million in the metropolitan area depending on how the question is interpreted. Use 3 million for the city.
Households. Roughly 2.5 people per household, so 3M / 2.5 = 1.2 million households.
Pianos per household. Most households do not own a piano. Maybe 1 in 20 households does. So 1.2M × (1/20) = 60,000 pianos in Chicago.
Tunings per piano per year. A regularly-used piano needs tuning about once a year. Many pianos go years without tuning. Use 0.5 tunings per piano per year on average. So 60,000 × 0.5 = 30,000 tunings per year.
Tunings per piano tuner per year. A tuner can do maybe 2 tunings per day, working 250 days a year, so 500 tunings per tuner per year.
Tuners required. 30,000 / 500 = 60 piano tuners.
Final answer: approximately 60 piano tuners in Chicago. Anywhere in the range 30 to 200 is defensible with reasonable assumptions. The actual number, when checked against trade-association data, is in the range 100–200, which makes the estimate accurate within a factor of 2 — which is exactly the order-of-magnitude precision Fermi estimation aims for.
Why it is the prototype Fermi problem
The piano tuners problem is structurally clean in a way most estimation problems are not. It decomposes into exactly five multiplicative components, each of which you can estimate with reasonable accuracy from general knowledge. None of the components requires specialized knowledge. The errors at each step partially cancel — overestimating pianos per household offsets underestimating tunings per piano — so the final answer is more accurate than any individual component would suggest.
This is the property that makes Fermi estimation a useful skill rather than a guessing game. A practiced estimator gets within a factor of 3 of the right answer for problems they have never thought about before, even when individual estimates are off by 50% in either direction. The technique works because it is a chain of related approximations, and the law of large numbers (in a loose sense) applies to the multiplicative composition.
Fermi’s original use
Fermi used these problems pedagogically. The story most often told is that during the Trinity nuclear test in 1945, Fermi dropped pieces of paper from his hand and watched how far they were blown by the blast wave. From that observation alone, he produced an estimate of the bomb’s yield that was within a factor of two of the actual measurement that came later.
The piano tuners problem in his classroom was not a yield estimate, but the technique was the same: take a question with no obvious answer, break it into pieces you can estimate, multiply them out, and accept that the answer is approximate. Generations of physicists were taught this method as a way to develop intuition about quantities that are too unfamiliar to know directly.
From physics classroom to Google interview
The transit from physics teaching tool to Google interview question happened in the late 1990s and early 2000s. Multiple senior people at Google had science backgrounds, and the Fermi-style question fit the company’s hiring philosophy at the time — testing for general reasoning ability rather than specific technical skill. The piano tuners question was canonical, so it became the template for variants like “golf balls in a school bus” and “weighing a 747”.
The retirement, like the rest of the brainteaser era, came from internal data. Google found that Fermi-question performance had near-zero correlation with on-the-job software engineering performance. Bock’s 2013 statement effectively ended the format at Google, and Microsoft and the rest of FAANG followed within a few years.
Where the format survives
- Product manager interviews. Market sizing questions (“how many ride-share rides happen in Tokyo on a Friday night?”) are core to PM loops at FAANG, AI labs, and most large tech companies.
- Management consulting interviews. McKinsey, BCG, and Bain still use Fermi-style market sizing extensively.
- Senior+ system design rounds. “Estimate the storage cost of running this at 100x scale” is structurally a Fermi problem with engineering numbers.
- Finance and trading interviews. Mental math estimation problems used in superday rounds at investment banks.
- Physics and engineering classrooms. Still taught as a foundational skill in many undergraduate programs, often using Fermi’s original problems.
The signal in a strong answer
The interviewer is watching for the same things as in any other Fermi-style question:
- Clarification. “Chicago city or metro area? Are we counting hobbyists who tune their own piano?”
- Structured decomposition. Population → households → pianos → tunings → tuners. Each ratio explicit.
- Defensible numbers. Each estimate justified with general knowledge.
- Order-of-magnitude reasonableness. Final answer in the right ballpark; visibly so.
- Optional: cross-check. “Let me sanity-check by estimating the other way: tuners as a fraction of total Chicago workforce.”
The cross-check is what separates polished from competent. Strong candidates produce the answer one way, then estimate it a second way using a different decomposition, and check that the two estimates agree to within a factor of 3. This is the technique Fermi himself used and is the gold standard for these questions.
Variations interviewers ask
- “Pizza shops in New York.” Same shape, different city and product.
- “Total annual revenue of the dental market in Germany.” Multiple-step decomposition involving demographics and pricing.
- “How many trains run on the New York subway in a day?” Combines time (peak vs off-peak), capacity, and frequency.
- “How many windows are in Manhattan?” Buildings × floors × windows per floor; harder because of the variation in building types.
- “What is the total mass of all the bicycles in Amsterdam?” Population × bicycle ownership × mass per bike.
Is the literal question still asked in 2026?
In tech engineering interviews, no. The pure piano-tuners question is dead. Asking it earnestly in 2026 would signal an outdated process. The Fermi-estimation skill, however, is alive and useful, and any candidate preparing for a PM or consulting interview should drill the technique using a few canonical problems including this one.
Frequently Asked Questions
Where does the name “Fermi problem” come from?
Enrico Fermi, the Italian-American physicist who pioneered nuclear physics in the 20th century. He used estimation problems as a teaching tool at the University of Chicago, and the genre took his name posthumously.
What is the actual number of piano tuners in Chicago?
Trade-association data suggests 100–200 in the city, depending on how “piano tuner” is defined and which year. The standard Fermi estimate of 60 is within a factor of 2–3, which is the expected accuracy for a problem of this kind.
Should I prepare for Fermi questions in 2026?
For tech engineering, no. For PM, consulting, finance, or senior+ system design, yes. The technique is the same regardless of the specific problem; drill the structure on a few canonical examples.
Why does the technique work?
Because errors in different multiplicative factors partially cancel. Overestimating one ratio offsets underestimating another, so the final answer is more accurate than the individual components. This is sometimes called the “central limit theorem of estimation”.
What is the difference between Fermi and brainteaser questions?
Fermi questions ask for a defensible numerical estimate. Brainteasers (like the manhole cover) ask for a clever insight. Fermi survives in roles where estimation is job-relevant; brainteasers have mostly died in tech.