In how many ways can the letters A, B, C and D be arranged so that no letter is adjacent to any letter that comes immediately before it or immediately after it alphabetically?


I understand there are 4! ways to arrange the letters A, B, C, D without any constraints.


What method should I use here? Complementary or constructive?

I will start with complementary.


There are 4! ways w/out constraints. 

Let's see how many ways there are to arrange the letters so that every letter IS adjacent to the letter that comes immediately before or immediately after it.




o _ O How will I find this? Help is appreciated! :D

 Jul 10, 2020

I might not be correct, but I think it's 2. I don't have time to show a solution, but I will about 30 min. later.

 Jul 10, 2020

xD I think I might have figured it out!

There's just BDAC and CADB


So it's just 2 ways, I think? 

CentsLord  Jul 10, 2020

Yes, but I wanted to give a big explanation. Since you got it, I don't need to do it xD

ryanthemathboi  Jul 10, 2020

28 Online Users