Golf Balls in a Plane: Volume-Packing Estimates

Like the piano tuners question, "how many golf balls fit in a Boeing 747?" isn't testing whether you happen to know the answer — it's testing whether you can build a defensible estimate from a chain of simple, stated assumptions, catching obviously wrong intermediate steps along the way. The key insight for this particular puzzle is that it reduces to two separate estimates multiplied together: the usable interior volume of the container, and the volume each item effectively occupies once you account for gaps between round objects.

A reasonable approach: estimate the plane's cabin as a cylinder roughly 50 meters long and 4 meters in diameter, giving a rough volume of $\pi r^2 \times \text{length} \approx \pi \times 2^2 \times 50 \approx 630$ cubic meters; then subtract, say, half for seats, aisles, and unusable space, leaving about 300 cubic meters. A golf ball is roughly 4cm across, so its own volume is small, but spheres don't pack perfectly — random packing of spheres typically fills only about 60% of the surrounding space, with the rest being gaps. Dividing the usable volume by a golf ball's effective "packed" volume (its own volume divided by that 60% packing efficiency) gives an estimate in the tens of millions of golf balls.

The exact number matters far less than whether the candidate explicitly separated "container volume" from "packing efficiency" rather than pretending balls tile space perfectly, and whether each assumption (cabin size, usable fraction, packing density) was stated as a number that could be sanity-checked and revised on the spot.