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?