I don’t need to “prove” that I can write code by memorizing an algorithm. I have made more than enough code available on my GitHub which I’d be happy to explain in depth with anyone who is interested. Not interested? Great, you’ve made it easier for me to make my decision.

Sounds to me like the uninterested person is the one who made the decision.

Yeah if they’re not interested in the only evidence of ability you’re willing to provide, then I think you’re not being considered in the first place.

Depending on what those 30 lines are supposed to do and whether they have to be asymptotically optimal at doing it, writing down 30 lines of code while talking about every decision you’re making, to show the “thought process” might very well be more than a 30 minute task.