This puzzle serves as the more concrete sequel to my previous post; in particular, see that post for the rules of the game. Rather than (implicitly) demanding a description of a polynomial-time algorithm for solving all such puzzles—an answer I myself didn't/still don't have—this post has a smaller, well-defined scope: Which of the three arrow sequences below are admissible, and which are inadmissible?
These puzzles are meant to be analyzed by hand (in particular, I solved them by hand with less than a single sheet of scrap paper each), and any solutions should be human-derivable and human-checkable. I made them of such a size that a brute force algorithm I coded fails to be feasible at about the ~25 arrow size and only gets exponentially worse from there (the above are of size 30, 32, and 40), but I'll hedge my bets that someone might have better hardware or more efficient implementation and so add the no-computers tag (but feel free to use computers to try to understand the problem in general!).
Here are some example sequences that may be useful for practice before tackling the big ones up above:
Concerning the three big sequences that officially comprise this puzzle, it may happen that they are first figured out by different posters. In that case, I will accept whoever's answer attains the most points according to the scheme (1) = 30 points, (2) = 32 points, (3) = 40 points.