Advent calendar 2025
14 December
There are five ways to make a list of four As and Bs that don't contain an odd number of consecutive As:
- B,B,B,B
- A,A,B,B
- B,A,A,B
- B,B,A,A
- A,A,A,A
How many ways are there to make a list of eleven As and Bs that don't contain an odd number of consecutive As?
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A valid sequence of length \(n\) can be made by either adding a single B to the right of a valid sequence of length \(n-1\)
or two As to a valid sequence of length \(n-2\). Therefore, the number of sequences of length \(n\) can be calculated by
adding the previous two terms (ie it's the Fibonacci sequence).
Using this, we can work out that the number of sequence of length eleven is 144.
