G2.2 Let $f_{1}=9$ and $f_{n}=\left\{\begin{array}{ll}f_{n-1}+3 & \text { if } n \text { is a multiple of } 3 \\ f_{n-1}-1 & \text { if } n \text { is not a multiple of } 3\end{array}\right.$.
If $B$ is the number of possible values of $k$ such that $f_{k}<11$, determine the value of $B$.
$$
f_{1}=9, f_{2}=8, f_{3}=11, f_{4}=10, f_{5}=9, f_{6}=12, f_{7}=11, f_{8}=10, f_{9}=13, \cdots
$$

There are 5 values of $k$ such that $f_{k}<11, B=5$
Note: The Chinese version $\cdots$ where $k$ satisfies $f_{k}<11 \cdots$ should be changed to $\cdots$ such that $f_{k}<11 \cdots$