The debate about what constitutes a sukaku or not is a debate I like to take part in. (But it is a can of worms, who doesn't like worms

)

I (initially) agree that excluding vanilla sudokus from sukakus is silly because vanilla sudokus are a small set

within Sukakus. in that sense it is vanilla that is the restriction (or variant) to Sukaku and not the opposite.

Here is my definition of vanilla sudokus:

Vanilla sudoku: is a sukaku puzzle where

Only a known set of Naked singles is needed to determine puzzle validity/uniqueness.

Now to the fun part (and the reason why a small part of me favours a restriction):

Can we therefore divide Sukaku puzzles into

2 separate groups; vanilla sudokus and Sukaku puzzles that are non-vanilla sudokus?

The answer should be yes (for that it requires some proper definitions) but currently the answer is no!!

Look at the definition of vanilla sudoku that I provided above: Looking at a cell that has a solved naked single (one candidate in a cell) will look like a solved hidden single (unique candidate per sector). If a vanilla sudoku clue is a naked single then you can substitute that known clue with a hidden singles (through adding that candidate to all other cells in a shared sector then adding other candidates to that cell). With our current definitions; this means that a vanilla puzzle has several equivalent non-vanilla forms (And Yes: each known vanilla puzzle can be transformed into a Pencilmark-only version in that way

)

One way to guarantee that we don't have several versions of essentially the same puzzle appearing is to restrict the definition of non-vanilla further:

Desired non-vanilla: Minimal Sukaku with no hidden singles at the start (Minimal guarantees a single version of the puzzle that has cells with 1 candidate (naked singles), No hidden singles will guarantee that we don't have minimal puzzles appearing in a different form). This may need to extend to hidden doubles and hidden triples that are in more than one sector!

unDesired non-vanilla: All other Sukakus that are not vanilla sudokus nor Desired sukakus.

[Edit: corrected a small mix-up]

tarek