Amadeus Sr Software Engineer interview questions

The hiring process was professional until a senior manager ask me in the last 7 minutes of its interview to calculate how many ping pong balls can be placed inside an airplane with an approximation of 10%. I said that dividing the aircraft volume for the sphere volume overestimate too much, and dividing for the cube volume of side equal to the sphere diameter underestimate too much. So I approached the solution with hexagons that inscribed a circle with a diameter equal to that of the sphere, in order to generalize from 2 to 3 dimensions how much on average each individual sphere occupies, but he drive me away from this solution because too complicated. So I proposed to solve the problem at a smaller dimension, putting some balls in a cube with edges one meter in length, then do the proper proportions, but he didn’t like it too. I explained him that I am sure there is a mathematically rigorous way to do this calculation, obviously not feasible in a few minutes. In response he, with an arrogance that surprised me a lot, challenged me if I want to see how this calculation is done. Without letting myself get nervous about his reaction I politely asked to show me. Then he divided the aircraft volume for the volume of a cube of a side equal to the diameter of the sphere, finally correct the result dividing the volume of the cube for a K constant, that he told me it was worth maybe 0.7 or 0.8. I was shocked by that naive answer, also because there is no evidence that his constant could lead to a solution with an approximation of 10%. In the past I have successfully worked in the company as a contractor for more than a year, during the recruitment process I passed all the tests: C++ coding, system design, English test, personality tests and many other interviews, but at the end, because of that exercise, their feedback was that my mindset overcomplicate the problems. Good luck if you hire your engineers in this way.