My thoughts so far:
(a) Which variation is considered a valid sudoku variation?
I don't think this question makes sense as stated in terms of something being valid or not. I'll try and expand upon this a little more however in terms of what I've heard so far. I have a lot of time for Thomas's suggestion that you have Sudoku, Sudoku Variants, Puzzle-Sudoku Hybrids and Not Sudoku, as a starting point, however, the question about how we separate Sudoku Variants and Puzzle-Sudoku Hybrids is not easy, and I'm not 100% convinced yet this is definitely the best way to think about things. More on this in question (c).
So I think this question is better stated as when can a puzzle be genuinely classified as "Not Sudoku". To begin to answer this I think we need a list of criteria of things that Sudoku definitely need to have.
For example, we definitely need to have a 2-dimensional grid of cells, each of which belongs to (at least) 2 rows/columns and also belongs to a region (a marked group of cells which do not trivially intersect with the rows/columns). We then definitely need to place symbols into this grid. (This is obviously incomplete, I just wanted to make an example).
It is likely that this list "should" apply to all Sudoku Variants, and probably also to some Puzzle-Sudoku Hybrids. This probably isn't going to be entirely satisfactory, but again I think further clarification and guidance is better thought about in question (c).
(b) How do we cope with difficult solving techniques?
My initial reaction to this is that it isn't strictly a relevant question. I certainly have some sympathy with the point of view which says this isn't really a problem of definition - I suppose the reason for including the hard classic as an example was driven by the questions asked in the polls: "Is this suitable for a sudoku competition?" As I've mentioned elsewhere, in the absence of a clear definition, this question I think is easier for people to answer consistently, and for me to be able to interpret more consistently.
Anyhow, the topic has generated some good discussion. From my own point of view, I can't see that it is yet helpful with regards to definitions and classifications, but I'm happy to keep exploring this in case it does reveal something. Certainly one answer to this question is to trust in the judgement of competition organisers and their testing processes.
(c) When do puzzles (sudoku variations) feel like sudoku and when not?
So here we fundamentally need to address what is a Sudoku Variant, and what is Puzzle-Sudoku Hybrid. Again speaking personally I'm not quite sure about this
or even if it's possible to be absolutely sure one way or the other
The Indians in 2017 certainly expressed a clear point of view, but I do not think it has been adequately explored yet. Speaking personally, I also do not believe their experiment was particularly successful either - I think there was much in the WSC round which I thought controversial. I've also thought about things the other way around. I'm not sure the equivalent WPC round was entirely successful either - or perhaps popular is a better word. There are certainly a number of WPC solvers who have a certain animosity towards anything that looks like Sudoku, regardless of how it solves. These solvers would argue that because there is a separate WSC, even the most spurious Puzzle-Sudoku hybrid has no place at the WPC. This seems strange to me, because Sudoku is a type like any other, and it's not like there aren't other puzzle types which are staples at the WPC which have spawned many variations - Tapa, Fillomino, Snake, Kakuro immediately come to mind (I'm sure there are many more) which theoretically you could produce a series of rounds of variants to produce some kind of championship.
This way of thinking kind of leaves the more controversial of our Puzzle-Sudoku hybrids in no-man's land.
Returning to the question, this is going to be the most difficult thing to agree on - different people are going to have different answers about how they feel about this. I've used the ideas of Sudoku Variants and Puzzle-Sudoku hybrids throughout this post, however I'm not convinced it's the best way to think about it. I think my approach is going to (eventually) involve a rigorous classification of additional constraints that you can add to a Sudoku. You can add more than one constraint at a time which is what make things interesting.
An initial example of how I'm thinking goes something like this:
- One family of constraints are the addition additional regions where numbers are not allowed to repeat. This covers things like diagonals, extra regions, but also cages like Renban and Killer. I think, after the example set in 2016, we have to think like this. For those that don't recall, there was a round in this WSC where an Extra Regions puzzle was presented using the rules of Killer, and a Windoku puzzle was presented using the rules of Renban.
- Another family of constraints impose constraints based on the arithmetic properties of how some numbers to be placed grid compare and combine with other numbers to be placed the grid, and require a certain amount of calculation to resolve. This covers things like sums, products, differences (in particular differences of 1 give you a consecutive constraint), ratios. It probably also includes things like whether one number is smaller, bigger or equal to another number. It might even include whether numbers leave a remainder of either 0 or 1 when divided by 2.
From this point of view:
- Diagonal is an additional non-repeating area variant
- Consecutive is an arithmetic variant (in this case with the arithmetic constraint applying to every pair of adjacent cells)
- Killer is both an additional non-repeating area variant, and an arithmetic variant.
This is only a start, and even as I type it doesn't seem entirely satisfactory to me. For one thing, the arithmetic constraints need to have a well-defined domain of application. This might be rows/columns (e.g. Skyscrapers), this might be pairs of cells (e.g. Consecutive), this might be 2x2 areas of cells (e.g. quad max), this might combine with additional grid decorations (e.g. Arrow), it might combine with non-repeating cages (e.g. Killer), and there's plenty more to think about there for sure.
Once you have something rigorous, maybe it will be easier to more precisely draw a line between what feels like Sudoku and what doesn't.