I think the problem with the question is that you asked "what is the term for this?" Which wasn't your real problem, you should have asked "I can only find 4, how come there's 9". It should have been trivial to figure this out with a piece of paper and a pencil. It is obvious now I trust, somebody showed you.
The math experts probably scoffed at the triviality of it. The SO experts may have thought a bit about "is there a different term than derangement", possibly concluding there isn't one. Afaik, derangement is a psychological term, describing a mental disorder. Nobody got to the algorithm part of the question after that hump.
Know what to ask for and formulate it well. Don't make up terms that sound like you know what you are talking about but only obfuscate the issue. Nobody want to test their language skills answering a question, egg on their face when they didn't know that "derangement" is standard verbiage in combinatorics. I trust it isn't but, like many SO contributors, I'm only a practitioner, never been a student.
It wasn't a good question. And thus got closed.