Problem
COM-B1-M10-P018 No Equal Neighbors
#18
★★★☆☆ Level 3 of 5
How many strings of length \(8\) over letters \(A,B,C\) have no two equal adjacent letters?
The first letter has \(3\) choices, each next letter has \(2\).
There are \(3\) choices for the first position. Each next letter must differ from the previous one, so it has \(2\) choices. Total: \(3\cdot2^7=384\).
Not every sequence problem needs a complicated recurrence.