An 8×8 chessboard is in the shape of a torus. (This means that the board "wraps around" - you can go left from a2 and come out on h2, for instance. It also works vertically - you can go up from f8 and come out on f1.) What's the minimum number of knights you can place on the board so every square is attacked, even ones with pieces on them?
I was looking for a possible duplicate of this problem, then I found
but it doesn't imply that your question is less fascinating.
I'd answer by saying that the worst best case should be:
as is evident from this article.
Also, I'm currently writing a program for the best case scenario, hope will do t without bugs :)
I've always been intrigued by Torus, especially because of K-map :D