Years ago Zynga asked me how would I design a vending machine for blind people which was annoying because I asked it immediately back and clearly they hadn't even thought about it themselves. But then I brought up Ian Bogost and it was a hard stop basically, lol.
edit: Is it health? Like health tracking / indication? Not all games require it but maybe in the right context this would be the most important. This is snarky but I think you could run with it (health being the most important "number").
response to your edit: Your interpretation of the question makes a little more sense. He was talking about a specific number, not a concept\variable that is common in games. For Zynga I'd probably say energy or money or something, although any tracked resource that determines loss, victory or progression would work for your version.
Edit: doing any "technical" work prior to doing research is a display of technical INcompetence.
Who is this “we”?
If I ask you "How can you attempt to get the answer to this in under a minute" or "what's the first thing you would do" and you don't say "search for existing solution" (it doesn't have to be Google), you fail. You don't have to read my mind; I want to know where YOUR mind goes first. And if it goes to anything more complicated than "I'll try to look it up" you just simply fail; I can't afford to have you wasting any more of my business' time.
Which answer is better? Which were they looking for? Who knows.
Renting a bus and filling it with golf balls is significantly more effort intensive than calculating, but it might give interesting, real world insights if the values differ.
For the purpose of running a business, the choice, to my mind, hinges on how much your revenue / customer satisfaction / product depends on the real world intelligence such an endeavour might bring. The situation illustrated is contrived, so it's hard to contrive an answer to that question.
There's hybridized approaches. Here's a 3D/AV interactive developer's contribution to your approach list:
I've used lidars and depth cameras as a hammer quite a bit over the last year, so I'd do thus - Realsense D435 capture the inside of a bus. Use meshlab to align and stitch all your pointsets. Perform reconstruction on it so you get a 3d mesh. Use your tool of choice to perform a physics simulation on golf balls (I'd probably use Unity3d, because customers love simulations they can play with.)
Run your simulation a ton of times with epsilon changes to initial conditions. Maybe even do it with an evolutionary algorithm that tries to maximize the count!
Either way, report back with a distribution. Also capture frames every once in a while so you can give them a timelapse. God customers love timelapses.
I was interviewing during the time covid started and everyone started working from home. I was interviewing with a company. I had a call with recruiter then with a hiring manager. I also got a project to work on over weekend.
Then got response something like, we really like you, but currently our hiring is suspended, we will let you know when it is back up.
Like, why did you wasted my time if you knew that I can't proceed to the on-site interview and you won't do it remotely?
Its sort of like companies doing subconscious window shopping...absolutely infuriating stuff
In this case, it sounds like the mood was right in the room for it to be taken well candidly.
Memorizing is not knowing.
One time an interviewer asked me "how would you go about counting the ridges of a US quarter?"
I rattled off some ideas about counting the ridges in an arc and then multiplying to get total ridges but the interviewer kept prodding and eventually ended the question and said he was looking for me to say "google it" (I didn't realize it was a known, fixed number).
I just rolled my eyes and laughed and said "Huh, good one, but how would you go about counting the ridges of a foreign coin assuming it's freshly minted and the number of ridges is unknown?" The interviewer shifted uncomfortably and just said "yeah, I'd probably do something like what you said - count the ridges in an arc and multiply..."
(i.e. "if you are going to give me bogus lateral thinking puzzles to test my competence I'm going to fire them back to see how you handle them")