Handled correctly, a problem like this answers several questions:
1) Can you correctly break down a problem like this into its components parts? 2) Can you recognize the overall class of problems that this falls into? 3) Can you transform this specific problem into the more general class so that you can solve it in a known fashion? 4) Can you think about and implement the movement? 5) Can you communicate while you're doing the above?
No one cares about solving that particular problem. But the answers to the above really are relevant. Being able to map novel problems onto known solutions is absolutely a skill that any competent software engineer needs to have. "Oh, you want me to do X? That looks a lot like Y, this thing we've already solved; maybe I can just implement it in the same fashion (or re-use our existing system!)"
I'm not saying that this particular problem is a wonderful example, or that I'd use it in my own interviews. But this overall class of problems really does have a place in interviewing when it's handled well by the interviewers, and arguments against it on the basis of the specific problem being irrelevant are really rather missing the point.
I don't do many interviews anymore, but I used to, and I had no short supply of problems that I actually had to solve in the course of my work that I could ask about. I don't think whiteboard interviewing is great in general, but if you're going to do it you can at least try to keep it relevant.
As a matter of fact, I did have to do memoization of graph traversals at least once for work (most programmers never have to do this), and I find that problem a lot more interesting (trait matching for Rust). I could easily give a talk about that problem. As for that interview question, though? I don't always do well with time pressure, and so I can't guarantee I'd be able to answer it to your satisfaction.
I've done the "ask a real problem that I've solved before" thing, and I find that it usually gets hung up on details and context around the problem to the detriment of actually solving the problem at hand. That's not to say that such a conversation isn't itself very valuable, but that's a different interview conversation, at least on my team. We find it important to maintain some level of focus just to ensure that we're covering the various signals that we'd like to get from the candidate.
My view is that Google's interview process seems to work because Google gets so many applicants that they can afford to randomly reject most of them. It's not because it's a good process.
So it isn't fair to ask the candidate to solve a real bug or implement a real feature in only 35 minutes unless they've seen something similar before.
This is why big companies like Google are limited to whiteboarding interviews because they need to have an interview process efficient enough to properly vet and filter >1 million applicants Google receives each year.
Personally, I think a better interview process is a pair-programming or work audition for a day. But that is not even close to matching the scale of Google.
Let's say out of a million applications, maybe only 25% are qualified. That is still almost 1000 candidates to interview per day (number of U.S. business days in 2019 is 261; 250,000 candidates / 261 business days = ~957 candidates per business day). Pair-programming or full day work audition will not be able to accommodate 957 candidates every day.
I find that hard to believe.
Moreover, memoized graph traversals don't get you full credit on this question. There's a dynamic programming solution, and in fact the ideal solution is one using matrix math, which is ludicrously divorced from anything most programmers would ever see.
