I see a pattern which I'm sharing just to make sure I'm understanding correctly. Starting with \$$2x\$$ and repeatedly getting the right adjoint, I see:

\$$2x\$$, \$$\lfloor\frac{n}{2}\rfloor\$$, \$$2x+1\$$, \$$\lfloor\frac{n-1}{2}\rfloor\$$, \$$2x+2\$$, \$$\lfloor\frac{n-2}{2}\rfloor\$$, ...

So Puzzle 12 would be \$$\lfloor\frac{n}{2}\rfloor\$$ and Puzzle 13 would be \$$\lfloor\frac{n+1}{2}\rfloor\$$. Am I crazy?