What is a sudoku? My answer.

[berni]

Having a little time to think about the original question I found the following answer.

For me a sudoku consist of a grid of n times n cells, which is dissected into n regions of size n. Some cells may contain a number and the goal is to fill a single number into each cell, such that in every row, column and region, every number from 1 to n appears exactly once. (Less formally, this should be a description of what is called "Irregular Sudoku". In my oppinion a "Classic Sudoku" with square regions is just a popular special case of a sudoku.)

For me a variation of a sudoku (and this is something, that holds for variations of every other puzzle type too) is similar to a sudoku, but some (but not too many) constraints may be changed, that is

1. Constraints may be removed (for example a Sudoku with penrose grid, like the one I created for the 24h in 2016: Download round 4)
2. Constraints may be replaced (for example a Scattered Sudoku)
3. Constraints may be added (for example a Greater-Than-Sudoku)

Especially:

• For me a bare latin square is a sudoku (just make all regions rectangles of width 1).
• A Starbattle-Sudoku is a sudoku variant, as the constraint "digits from 1 to n" is replaced by "digits from 1 to n-2 and two stars"; and a new constraint "stars may not touch" is added.
• It's possible to have sudokus where symbols repeat. As far as I know, some people have the ability to spot missing numbers immediately, when all numbers have to be distinct, while this ability does not work anymore when symbols repeat. Other people (including me) do not have this ability. I don't think that this should be a reason to remove types from the variants lists. People who can spot missing numbers, should still be able to cope with puzzles, where they cannot use their special ability. In that case, they have to use other means and I think, that's fair.

[detuned]

Thanks Berni, I am insanely overworked right now so haven't really had time to think about things over the last week or so - and nor will I likely to be over the next week or so - but I am very glad to see some of the elements we have discussed so far put together in a coherent whole. I'm sure there'll be others who have much to say about this!

[Fred76]

I'm happy that you change your mind about the fact that it is possible to define what is a sudoku.

For the b. you mention scattered sudoku. I don't see which constraint has been replaced?

My main question about your definition is: How do you judge the "but not too many" in your text: "some (but not too many) constraints may be changed"?

If I take 2 examples:
The puzzle "Tic-tac logic" has 3 constraints changed from your definition. Do you think it's a sudoku variation?
I don't have right to publish it, but in the italian sudoku championship last year, there was a puzzle which had 8 constraints (rossini, killer, kropki, arrows, parity,group sum, thermo and greater than) added to your definition. Would you say it's intrinsically a problem?
Have you more thoughts about how this "not too many" should be judge?

Speaking about variations, I'm less experienced as you in the field of puzzles, but my point of view would be only "c. constraints may be added" should be done. Of course it depends on how you formulate the definition of the puzzle. For example, from your definition I think some constraints can be removed or replaced, basically "number from 1-n" could be "set of n distinct symbols" in my opinion, and the grid has not to be a square (your example of sudoku with penrose grid is totally ok for me as a geometrical variation).

I would say a puzzle X is a minimal set of constraints, and variations of puzzle X is a puzzle which satisfies same set of constraints, but can have more of them and/or can take alternate shape (if the shape is not in the minimal set of constraint).

Set of regions being distinct of rows or columns is in my minimal set of constraints about sudoku, thus I don't see bare latin square as a sudoku variation.

To take few other examples where we could disagree, my opinion is:
A thermo-sudoku is a variation of sudoku, but classic sudoku is not a variation of thermo-sudoku.
Classic sudoku is a variation of latin square, but latin square is not a variation of sudoku.
Skyscrapers is a variation of latin square, but latin square is not a variation of skyscrapers (if you remove the skyscraper constraint to a skyscraper puzzle, I don't think the puzzle is a variation of skyscraper).

For each puzzle type, the difficulty is to define what are the minimal constraints.

If we compare our 2 conceptions of variations:
In your conception, "if a puzzle X is a variation of puzzle Y, then puzzle Y is a variation of puzzle X" which is not the case in my conception.
In my conception, "if a puzzle X is a variation of puzzle Y and puzzle Y is a variation of puzzle Z, then puzzle X is a variation of puzzle Z", which is not always the case in your conception (there is a point where we can reach your limit "but not so many").

Fred

[berni]

I'm happy that you change your mind about the fact that it is possible to define what is a sudoku.

This is probably a misunderstanding. In the post Three different questions? I talked about a definition of sudoku variations not about the definition of the puzzle type sudoku. In the last case it's just a question if people think of 3x3-region-sudoku as the base type or of irregular-sudoku (as I do). But that's a matter of taste. My oppinion about clear borders of variations has not changed.

For the b. you mention scattered sudoku. I don't see which constraint has been replaced?

For me, a region implies, that all the cells of the region are connected. (It's difficult to find a better example using sudokus. Take fences: Replacing the meaning of the numbers from "count of edges" to "count of grid intersections" would create a variation.)

My main question about your definition is: How do you judge the "but not too many" in your text: "some (but not too many) constraints may be changed"?

Not at all. That's exacly, where I think, that clear borders should be avoided.

A thermo-sudoku is a variation of sudoku, but classic sudoku is not a variation of thermo-sudoku.

A thermo-sudoku is a variation of sudoku. A classic sudoku is a (special case of a) thermo-sudoku (with not thermometer appearing).

Classic sudoku is a variation of latin square, but latin square is not a variation of sudoku.

Classic sudoku is a variation of latin square. Latin square is a sudoku (with superflous regions).

Skyscrapers is a variation of latin square, but latin square is not a variation of skyscrapers (if you remove the skyscraper constraint to a skyscraper puzzle, I don't think the puzzle is a variation of skyscraper).

Skyscrapers is a variation of latin square. A latin square is a skyscrapers puzzle (the constraint is not removed, but just not used as there are no numbers around the grid, to make the puzzle have a unique solution you probably need numbers inside the grid).

In your conception, "if a puzzle X is a variation of puzzle Y, then puzzle Y is a variation of puzzle X" which is not the case in my conception.

No. In my conception, there are base types. Sudoku is a base type as well as fences or tapa or skyscrapers. A variation is something, that is based on that base type.

[Fred76]

Thanks for your answer.
I'm sorry to ask so many questions, but there is still something that I would like to understand better.

My main question about your definition is: How do you judge the "but not too many" in your text: "some (but not too many) constraints may be changed"?

Not at all. That's exacly, where I think, that clear borders should be avoided.

I'm not sure I understand well what you say. For you, there are no clear borders of variations. I think I more or less understand it. But my question about judgement was about the real application. There are situations where you HAVE to judge if a puzzle is a sudoku or not: if you are an author for a sudoku competition or the responsible of puzzle selection for sudoku competition. Then I think you can't avoid the question. How in practice do you do when you're in such situations? How do you judge personally if a puzzle is a sudoku variation or not?

Fred

[berni]

There are situations where you HAVE to judge if a puzzle is a sudoku or not: if you are an author for a sudoku competition or the responsible of puzzle selection for sudoku competition. Then I think you can't avoid the question. How in practice do you do when you're in such situations? How do you judge personally if a puzzle is a sudoku variation or not?

If the puzzle feels like a sudoku variation it is one. If it doesn't feel like a sudoku variation it is not one. And everything in between depends on the circumstances and maybe the feeling of others (if available).