/sci/ - Science & Math

Hi, Kim. I've got some mathematics questions for you.

I was looking at a clock face and it got me wondering about something. What are the minimum amount of numbers necessary in a set of numbers that would allow them to be scrambled so that:

A) No two consecutive numbers remain as such, including the first and last numbers (as though they were the ends of a line conjoined as a circle).
B) No number can remain in or in immediate proximity to the same place it was initially.

For example, five wouldn't work for several reasons:
1.) Simply reversing the order of the numbers 1-5 still leaves 3 as the third number in the list, 5&4, 4&3, 3&2, 2&1 are still consecutive, and 1&5 would still be able to loop back to each other (fails A and B).
2.) 31524 fails because 1 is second and 4 is fifth in this arrangement (fails B), and even though 3 and 4 are not at the ends of the original list, they could be considered "consecutive" in this context as 1 and 5 are normally (fails A).t

I came up with eight as the minimum number, with 35827146 as a satisfactory example (if not the only one). I almost thought seven would work as well. This brings me to my actual questions:

1.) Does eight being the minimum imply that any greater amount of numbers will also satisfy the conditions?
2.) Is this already a thing that mathematicians have worked out?
3.) If the answer is yes, what is it called?