OK then do it on the phone with the interviewer looking at you as you're typing and your brain has suddenly blanked. I've been coding since I was 9 years old, have a massive (relatively) side project with a couple hundred users, have shipped multiple projects in multiple jobs, and I know what a binary tree is and how to traverse one, but I'll be damned if I can figure out how to do it under those conditions. I absolutely hate interview questions where they make you code on the spot. Just look at my Github, I swear I wrote that code.
That's not a puzzle, though. A puzzle would be something barely related to computer science, like "How can I find which ball out of 9 is heavier weighing them twice on a two-sided scale?"
Basic algorithmic knowledge questions are not puzzles, and whoever is calling them that is wrong. Those questions still can be stressful, especially for people that don't do well in interview environment, but puzzle is something else. Puzzle is something that requires some non-trivial insight or trick to solve, usually one that the person has no experience with and it is not obvious even for a person with the knowledge of the basics. That's why they are puzzles - they are "puzzling", which the dictionary defines as "confusing" or "baffling".