How many ping pong balls can you fit into a Boeing 747?

This question is a brainteaser aimed at understanding your ability to make reasonable estimates and assumptions. As improbable as this question might seem for an interview, it serves a clear purpose. It's not essential to blurt out the exact number, the interviewer is interested in your thought process, how you approach the problem, the assumptions you make and how you eventually bring these factors together to provide a logical estimate.

Steps to approach the question:

1. Understand the dimensions: Figure out the dimensions of a Boeing 747. If you don't already know this, you will have to make a reasonable estimation.
2. Calculate the volume: Use the dimensions to estimate the total physical space (volume) inside the jet in a unit that is easy to deal with, such as cubic meters.
3. Estimate Ping Pong Ball Size: Based on an average size, calculate the volume of a ping pong ball.
4. Calculate the number of balls: Divide the total volume of the plane by that of a single ping pong ball to get the estimated number of balls.
5. Factor in additional space: You also need to consider that spheres don’t perfectly pack, so you'll need to make a further assumption about how much space is wasted.
6. Provide your estimate: Do all the math and provide your estimate ensuring you share your thought process.

The dimensions of a Boeing 747 are approximately 70 meters in length, the width is 6 meters and height is approximately 6 meters as well. These dimensions give a gross estimate of the volume as 2520 cubic meters (7066).

For the ping pong ball, it's known to have a diameter of roughly 40mm, so its radius is 20mm or 0.02 meters. Using the volume formula for spheres 4/3pir^3, the volume is approximately 0.0000335 cubic meters.

If we divide the volume of the plane by the volume of a single ping pong ball, we get approximately 75,223,880 or 75 million ping pong balls.

Now keeping in mind spheres don’t pack perfectly (scientifically, the densest packing in fact is around 74%) let's use 70% to adjust the above figure, to account for the spaces between the balls which gives us about 52.6 million balls. So I would estimate that we could fit around 52.6 million ping pong balls in a Boeing 747.

The process begins by estimating the size of the Boeing 747. By approximation, it is 70 meters long, 6 meters wide, and 6 meters high. So the volume would be: 7066=2520 cubic meters.

Next, estimate the size of a ping pong ball which is usually about 40mm in diameter or 0.04m. Its volume is calculated using the formula for volume of a sphere, which gives approximately 0.0000335 cubic meters.

Dividing the volume of Boeing by volume of the ping pong ball gives us about 75 million balls. However, they won't perfectly fit together, hence we can assume that only 70% of the space will be occupied, resulting in approximately 52.5 million balls.

Therefore, I estimate we can fit about 52.5 million ping pong balls inside the Boeing 747.