Sudokus have a lot of interesting mathematical properties.

The Phistomefel's ring is interestingly helpful because of the corner squares. (4 & 1) And that its shape is easy to remember.

There are some interesting areas that you can make with this, but nothing quite as memorable.

And yes, there is a minimum amount of clues needed. Like, you can leave out one number, but you cannot leave out two. Because the two numbers could be swapped with both producing proper solutions.