AMM Problem 12548 Solution

In this article, I provide the solution to AMM Problem 12548. This article is being published a day after the AMM deadline!
This is part of my December 31st 2025 deadline, of which I solved 5/7 problems that I'm sharing here! This is the 3rd such article.

This problem is about counting, for all $n \in \mathbb{N}$, the number of functions $f: [n^2] \rightarrow [n]$ such that $\exists g: \mathbb{Z} \rightarrow [n]$ surjection such that for every $a+b$ even:

$$f(g(a), g(b)) = g(\frac{a+b}{2})$$

The solution can be found clicking here

I hope you enjoyed reading the article

Any feedback is greatly appreciated!