Given the four letters: A , B , C , D . ABCAD and ABABD are two examples of a five
letter movement. In a five letter movement, one must start with the letter A and end with the
letter D. No two consecutive spots in a five letter movement can consist of the same letter.
For example, ABBCD would not be a five letter movement. Choosing only from the four
given letters, find the number of distinct five letter movements.

Question

Given the four letters: A , B , C , D . ABCAD and ABABD are two examples of a five
letter movement. In a five letter movement, one must start with the letter A and end with the
letter D. No two consecutive spots in a five letter movement can consist of the same letter.
For example, ABBCD would not be a five letter movement. Choosing only from the four
given letters, find the number of distinct five letter movements.

anonymous · Answer

ABABD   ABACD ABCAD ABCBD ABDAD ABDBD ABDCD 
too long hh I think almost 21or more