I regularly look things like that up. I am a builder and a problem solver, not a reference manual.
"I'm your Google, anything you'd need to look up just ask me and I'll give you the answer".
Great way to take the pressure off plus it gives you a good idea on how well they ask questions/are comfortable leaning on others. It's a huge plus if I can get a reasonable candidate to admit that there might be parts of the problem at hand they don't understand.
I've written code tests where I'm expected to read the code, find the issues and fix them on paper. But when they take it too far beyond the spirit of what I believe to be a reasonable test of understanding and fixing code, then I write that I'd just for example compile the program and look at the output.
The companies that are most into questions like these seem to be the classic (failing agile) body shops with ridiculous turnover of their talent, which causes them to have to interview even more, which causes in turn for their tests to become even more abstract and worthless.
6 months to get into things is kinda long though. Unless it's super complex things, it should be less. Are you sure you are not exaggerating?
Most engineers can be productive in a month. The 3x engineers take half that.
Do you see how that putting-words-in-others-mouths looks? It's rude and does not contribute too any kind of productive discussion.
I can relate to this. I have pretty good resume - good schools, advanced degree, impressive sounding projects, a long list of publications. My track-record suggests I am at least a 3x engineer.
So when I get into a coding interview, I'm expected to perform as such... but I usually come off as a 0.3x engineer. Like really bad. Forget syntax bad. Forget algorithms bad. I've bombed so bad in a technical interview, the interviewer questioned if I even knew basic trigonometry. They had spent 10 hours interviewing me prior and felt good, but got me in person and suddenly thought I was an idiot.
In each of my jobs, I've had a considerable ramp-up period. I'm talking 6 months or more of feeling completely lost and unproductive. I get in my head and it makes me perform worse.
If I'm not fired in that first period, I'm lucky. Only after about a year on the job I can perform at the level my resume would suggest.