Although I agree these interview questions are absurd, there is a good amount of merit to seeing peoples responses. I've been to interviews where I didn't answer a single question right and still got the job. I approached each question as a collaborative effort with the interviewers. "Don't look up documentation online" (if it is a good interviewer) really means "Ask me for help".
I will add though, if you're given a task and a set amount of time with no internet/resources while they leave the room. Walk out. Development should never be in a vacuum.
In hindsight I think the hamburger sandwich menu question and the final 2 (number 5 and 6) aren't unusual to test on devs, but seeing how they tackle it without other prompts would definitely be interesting. (Under pressure my tendency is always to write more code than i need-_-) I also do like the ask-for-help thing, if they make themselves available for that.
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