Interview Question: The Fermi Problem – How many Piano Tuners are there in Chicago?

Strategy and Approach to Answering a Problem Solving Interview Question

If you get asked a problem solving question in an interview, remember that they are NOT looking for the RIGHT answer. They are evaluating the approach you use to think out and solve the problem. A strong candidate demonstrates the following:

1. Evaluates and understand the scope of the problem
2. Communicates assumptions
3. Demonstrates quantitative analytical skills
4. Answers the question that has been asked. You’d be surprised how many candidates get lost in the analysis and solve for a different question than what was asked.

How to Answer this Problem Solving Interview Question

Evaluating this problem, we can see that the solution to this problem would involve multiplying together a series of estimates that would yield the correct answer if the estimates were correct.

For example, we might make the following assumptions:

• There are approximately 5,000,000 people living in Chicago
• On average, there are two persons in each household in Chicago
• Roughly one household in twenty has a piano that is tuned regularly
• Pianos that are tuned regularly are tuned on average about once per year
• It takes a piano tuner about two hours to tune a piano, including travel time
• Each piano tuner works eight hours in a day, five days in a week, and 50 weeks in a year.

From these assumptions we can compute that the number of piano tunings in a single year in Chicago is (5,000,000 persons in Chicago) / (2 persons/household) × (1 piano/20 households) × (1 piano tuning per piano per year) = 125,000 piano tunings per year in Chicago.

And we can similarly calculate that the average piano tuner performs (50 weeks/year)×(5 days/week)×(8 hours/day)×(1 piano tuning per 2 hours per piano tuner) = 1000 piano tunings per year per piano tune. Dividing gives (125,000 piano tuning per year in Chicago) / (1000 piano tunings per year per piano tuner) = 125 piano tuners in Chicago.

Note: For this problem solving job interview question, there is an actual logical answer, however the interviewer will want to evaluate your thinking process.  In answering the interview question, the lead up to your answer will be just as important as the actual answer itself.

For more problem solving, brain teasers, riddles, puzzles, logic job interview questions, please check our out Problem Solving Interview Section.

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