MathNet 2015-part-07 — 185 problems (EN–VI) Question 41

Count the number of functions $f: \mathbb{Z} \rightarrow\{\text{'green'}, \text{'blue'}\}$ such that $f(x)=f(x+22)$ for all integers $x$ and there does not exist an integer $y$ with $f(y)=f(y+2)=\text{'green'}$.