Thanks Patrick and Thomas, your question clarified puzzle 11 for me also.

Patrick, regarding puzzles 12 and 13, I think the answers you gave are indeed adjoints but flipped (right -> left, left -> right). For example, take m=2, n=3 for puzzle 12:

$$f(2)\leq 3 \textrm{ if and only if } 2\leq g(3)$$
$$4 \leq 3 \textrm{ if and only if } 2 \leq \lceil \frac{3}{2} \rceil = 2$$

which is no good. Of course, I may have made a thinko myself...