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>which most people never have nor will need to do

That doesn't mean that someone would be unable to program it. Inverting a binary tree tests if you know how to traverse a tree. I may not traverse trees all day at work, but I can easily do a tree traversal if I needed to and I expect that to be true of most people who can actually program and not just talk the talk.

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I understand what you mean, I could also probably pass the test. But what is the utility in an arcane test like this? If I'm hiring web developers, I'd want them to see how they apply their knowledge to a realistic scenario. There is a real chance that a potentially great hire with decent experience in a desirable technology will fail the inversion task.

sure, I often have to do tree and graph traversals in my day to day but, I will 100% fail to do that under pressure with people looking at me and expecting me to "talk throught my thought process".

If you really really care about me traversing a graph, leave me alone with the task for a while, let me take my time, give me access to the internet even. Why do you care that I can write it on the spot? If anything that just proves that I memorised it just before the interview, not that I actually had to think much about it

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