Sometimes we are not in the mood to resolve a particular problem and just want to see a new one. I agree that a skip button would not be appropriate, as we would skip all but the ones we found the solution.
So my suggestion is a Postpone button, allowing you to see a new puzzle then go back to the postponed one another day. The postponed puzzle would be listed in a small box below the board like all others, but with a grey Pause symbol. Each account would be allowed to accumulate only up to 5 postponed puzzles and must resolve them before they leave the list of last 15 puzzles.
PS: Many of us want ratings for their long games, but we need your vote, please www.strawpoll.me/11093155