Estimating Physical Quantities From Scale

Nobody expects you to know the actual number of piano tuners in Chicago, the point of the question is to watch how you build an estimate from pieces you can reason about, and whether the final number lands in a sensible ballpark rather than being wildly off by many factors of ten. This style of physical scale estimate, often called a Fermi problem after physicist Enrico Fermi, who was famous for such quick estimates, rewards a clear chain of reasonable assumptions over a lucky guess.

The standard technique is decomposition: break the unknown quantity into a product of smaller quantities you can estimate with more confidence, state each assumption explicitly, and multiply through. For "how many golf balls fit in a school bus," you'd estimate the bus's interior volume (length × width × height, maybe 8m × 2m × 2m ≈ 32 cubic meters), estimate a single golf ball's volume (roughly 40 cubic centimeters), account for wasted space between round balls packing imperfectly (multiply by roughly 0.6), and divide: 32,000,000 cm³ × 0.6 ÷ 40 cm³ ≈ 480,000 balls. The exact figure matters far less than showing your work and landing within an order of magnitude of a defensible answer.

Interviewers are also watching for sanity checks along the way, does 480,000 golf balls "feel" like a plausible number of small objects to fill a large vehicle, or would you have caught yourself if the arithmetic had spat out 48 or 48 billion?