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

CentsLord Jul 10, 2020

#1**+1 **

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.

ryanthemathboi Jul 10, 2020

#2**+6 **

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

#3**+1 **

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