# An algebra problem

Algebra Level 3

Let $$S=\left\{ 1,2,3,4,5,6,7,8,9 \right\}$$. Consider a function $$f:S\rightarrow S$$ defined in the following table:

$\begin{array} { | c | c | } \hline x & f(x) \\ \hline 1 & 8 \\ 2 & 3 \\ 3 & 5 \\ 4 & 7 \\ 5 & 2 \\ 6 & 9 \\ 7 & 6 \\ 8 & 1 \\ 9 & 4 \\ \hline \end{array}$

Then, the minimum integer value of $$n$$ such that $$\underbrace { f(f(...(f } (x)))=x$$ $$\quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad$$$$n$$ times

for every $$x\in S$$ is...

×