Long-time player here. Strangely enough, the hardest part of these exercises is the uncomfortable brief moment of getting acquainted with (or being teleported to) a random board position.
A couple days ago I was really captivated solving chess puzzles on lichess and I encountered a particular puzzle that didn't make sense to me (my puzzle rating is ~1800). Then I realized it's white to move, and I've been pondering on black moves for the last 10 minutes... Mistakes a human mind can make while playing chess really surprise me, even while doing another intellectual activity like programming, learning math, reading a book etc you don't realize how notoriously prone your brain to errors until you have an objective measure to compare your reasoning to. Fascinating.
Mercifully Lichess actually tells you who has the move. ChessTempo didn't (you have to figure it out from who moved last,) and thereby made this feeling of disorientation much worse than it had to be.
It's a moment that actually requires paying attention to. Occasionally I find myself unable to find a winning move. To the point where I just try all possible legal moves. And they all fail! That's when I realize the last opponent move was actually a pawn move that can be captured en passant:-(