Question

Define a good word as a square of letters that consists only of the letters $A,B$ and $C$ and in which never immediately followed by $B$,$B$ is never immediately followed by $C$, and $C$ is never immediately followed by $A$. If the number of $n-$ letter good words are $384$, find the value of $n$.

Answer 1

A,B,C $\to 3$letters

$384=3\times 2^7=3\times 2^n$

$\therefore n=7$