@Alex #38

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

I get a different form of the answer to Puzzle 13: \$$g(n) = \lceil \frac{n}{2} \rceil\$$. But \$$\lfloor \frac{n+1}{2} \rfloor\$$ is the same as \$$\lceil \frac{n}{2} \rceil \$$: if n is even, we get \$$\frac{n}{2}\$$; if n is odd, we get \$$\frac{(n+1)}{2}\$$. So I think we agree (obviously still assuming \$$f, g : \mathbb{N} \to \mathbb{N} \$$).

Is there a name for this kind of "gauge"-like transformation between functions? Our forms are different but in the given domain and range, they behave identically.