Question 141
Gari took a 6-item multiple choice test with 3 choices per item, labelled $A$, $B$, and $C$. After the test, he tried to recall his answers to the items. He only remembered that he never answered three consecutive $A$'s, he never answered three consecutive $B$'s, and he did not leave any item blank. How many possible sets of answers could Gari have had?