How many 15-letter sequences are there which use only A, B, C and D (and not necessarily all of those), where:
A is never immediately followed by B, B is never immediately followed by C, C is never immediately followed by D and D is never immediately followed by A?

There are 4 choices for the first letter.  After that, each letter has only 3 choices, as it is constrained by the preceding letter.  So the answer is 4*(3^14) = 19,131,876

Posted by Steve Herman on 2015-10-13 08:55:36