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### What is sudoku?

Posted: **Tue 30 Nov, 2010 5:48 am**

by **AndreyBogdanov**

The first reflection after looking at a phrase "Standard puzzles, and their variants have their own separate forum area." is - What is sudoku?

Which puzzle (I hope we understand what is puzzle

) could be named sudoku? And which could not. What is general rule for sudoku?

I'm sure about some "magic rule" - digits cannot repeat in some areas. But are digits obligatory? Or there may be any other figures (or pictures)? Are there any restriction for size or number of "magic area"?

### Re: What is sudoku?

Posted: **Tue 30 Nov, 2010 12:11 pm**

by **PuzzleScot**

Fair point. The distinction was intended to differentiate puzzles seen at a WSC or WPC.

In retrospect, I see no real reason to separate the categories.

Unless there are any objections, I will merge the 2 topics...

### Re: What is sudoku?

Posted: **Tue 30 Nov, 2010 2:27 pm**

by **Fred76**

It's hard to define exactly which puzzles are sudoku or aren't. The limit is not clear and I think we can't write a clear definition that is valuable for each case.

There are so many kind of sudoku variants; most of them are based on standard sudoku rules + constraints, what is clearly a sudoku. But others are geometrically different; use of digit is not an obligation, etc...

The sign that shows that limit is not clear is that on WSC final in Zilina, second puzzle was not a sudoku in my opinion: It was a diagonal latin square with constraints.

### Re: What is sudoku?

Posted: **Tue 30 Nov, 2010 5:41 pm**

by **ronaldx**

Hahaha this is a great question! "What is sudoku?": I was thinking about it too.

In my mind, a sudoku includes any puzzle where you have to place a certain fixed number of symbols into cells:

- so that one such symbol appears in each cell,

- certain given subsets of the cells must contain each symbol exactly once.

(no other rules are necessary to place the symbols uniquely)

In my mind, a latin square *is* a type of sudoku, it's just a primitive type.

I haven't looked the relevant Zilina puzzle up, so perhaps I am missing something, but it sounds very much like a sudoku:

the Zilina puzzle is a latin square with diagonals;

a 'classic' sudoku is a latin square with boxes.

Is there a strong difference? I'm not sure about it.

### Re: What is sudoku?

Posted: **Tue 30 Nov, 2010 6:42 pm**

by **AndreyBogdanov**

PuzzleScot wrote:Unless there are any objections, I will merge the 2 topics...

My post was not a complaint. I think it's really interesting and important question. I think in future we could divide puzzlesport to some "events" - to have different championsips for different events and one "absolute championship" (as in gymnastics). So we should determine rules for each event. I don't know which division is the best, but division on types of puzzles (Sudokus, Batleships, Kakuros and so on) may be one of the variants. And now we should understand what is Sudoku because definition for other puzzle types would be more difficult.

I could define Sudoku as puzzle where solver have to fill some grid with symbols from the given set. No more then one symbol per cell. There are some areas with "magic rule" - no symbols could repeat in this areas. Each cell should be in at least two (or even three - do we want to consider Latin square as Sudoku?) areas. Any additional restrictions may apply.

### Re: What is sudoku?

Posted: **Tue 30 Nov, 2010 7:29 pm**

by **nickdeller**

I think it's a great question. I wonder whether the 3 puzzles below fit into the picture?

* A 7x7 latin square, with sufficient cells pre-filled to make the solution unique, no other information given

* A 9x9 sudoku grid, no duplicates in the 3x3 boxes, no cells pre-filled, but with Skyscrapers clues given

* A 7x7 standard Skyscrapers puzzle.

In my book, the first two would be counted as variant sudoku, the third one wouldn't... but I can't easily explain why not. Any thoughts?

### Re: What is sudoku?

Posted: **Tue 30 Nov, 2010 9:15 pm**

by **detuned**

ronaldx wrote:Hahaha this is a great question! "What is sudoku?": I was thinking about it too.

In my mind, a sudoku includes any puzzle where you have to place a certain fixed number of symbols into cells:

- so that one such symbol appears in each cell,

- certain given subsets of the cells must contain each symbol exactly once.

(no other rules are necessary to place the symbols uniquely)

In my mind, a latin square *is* a type of sudoku, it's just a primitive type.

I haven't looked the relevant Zilina puzzle up, so perhaps I am missing something, but it sounds very much like a sudoku:

the Zilina puzzle is a latin square with diagonals;

a 'classic' sudoku is a latin square with boxes.

Is there a strong difference? I'm not sure about it.

This reminds me of a long running dialogue I've had with Thomas Snyder and others. Basically our definition comes down to the so-called "3rd constraint".

Re the zilina example, the 3rd constraint is the diagonals. But this by definition means that some cells have only 2 constraints (rows and columns) and some have 3. Unless all cells have three constraints on them , then as far as our consensus goes, it ain't a sudoku. I said as much to the newspapers, so I'd better stick with that

. Anyhow, this definitely rules out latin squares as sudoku - and if you compare and contrast the solving process you'll see why this is a good thing to do.

The only ambiguity here is with "hex" grids, but this is an easy modification to take care of.

### Re: What is sudoku?

Posted: **Tue 30 Nov, 2010 9:27 pm**

by **detuned**

nickdeller wrote:I think it's a great question. I wonder whether the 3 puzzles below fit into the picture?

* A 7x7 latin square, with sufficient cells pre-filled to make the solution unique, no other information given

* A 9x9 sudoku grid, no duplicates in the 3x3 boxes, no cells pre-filled, but with Skyscrapers clues given

* A 7x7 standard Skyscrapers puzzle.

In my book, the first two would be counted as variant sudoku, the third one wouldn't... but I can't easily explain why not. Any thoughts?

Under what I've just outlined above:

1) No

2) Yes

3) No

### Re: What is sudoku?

Posted: **Wed 01 Dec, 2010 12:01 am**

by **ronaldx**

Under what I outlined:

1) Yes

2) No (an additional non-sudoku rule is required; though I'd agree it's a sudoku-variant, it's also a skyscrapers-variant)

3) No (an additional non-sudoku rule is required; Skyscrapers is clearly a relative of sudoku)

If you presented a lay-person with a puzzle and gave no rules but "this is a sudoku", would they immediately understand what they were expected to do?

With a 7x7 latin square - I think the answer is yes.

With a skyscrapers variant, the answer is definitely not.

The third constraint rule is interesting, but what makes the third constraint "specialler" than the second constraint that it requires vastly different solving techniques? (I'm not disagreeing, I'm asking for opinion on why that becomes special)

### Re: What is sudoku?

Posted: **Wed 01 Dec, 2010 12:54 am**

by **detuned**

The first two constraints are non-repeating digits in rows and columns (there are three of these in a hex grid for what is called "isosudoku"). The third constraint blends together information from both rows and columns. It adds an extra dimension to the puzzle that makes solving sudoku a subtly different solving experience than filling in a latin square. It introduces a somewhat "local" constraint to the puzzle.

It strikes me that any definition worth its salt should classify 1) and 3) as either both yes or both no, as you could take puzzle 1), add some clues on the outside and suddenly its an example of puzzle 3).

### Re: What is sudoku?

Posted: **Wed 01 Dec, 2010 1:38 am**

by **Fred76**

I agree with Tom, with the 3rd constraint. If I take part in a sudoku tournament and there are only latin squares, I'll think it's not a sudoku tournament !

For me it's even more than a 3rd constraint; it must be a "local constraint" (as explained Tom):

Some sudoku can have more than 2 directional constraints, for example star sudoku (see

http://www.sachsentext.de/gif/starsudoku1.gif for example). There are 3 directions + 1 box constraint. From my point of view, if there were not box constraint, it should not be called "sudoku" (but... sort of... "latin star"?) even if there are 3 (directional) constraint.

ronaldx wrote:- so that one such symbol appears in each cell,

- certain given subsets of the cells must contain each symbol exactly once.

- What about: sudoku 0-9 (http://www.sachsentext.de/gif/sudok09b.gif) or tight fit sudoku (http://www.stanford.edu/~tsnyder/tightfit2.jpg) ? it must have more than one such symbol in some cells.
- I've seen variants of sudoku, for example subsets3*3 on argio-logic.net (Italian site), where each symbol appears more than one in every subsets (in this example you have to fill grids with digits 1, 2 and 3 so that each digit appears exactly 3 times in every row, column and box. Can we call this sudoku or not?

ronaldx wrote:
2) No (an additional non-sudoku rule is required; though I'd agree it's a sudoku-variant, it's also a skyscrapers-variant)

If you presented a lay-person with a puzzle and gave no rules but "this is a sudoku", would they immediately understand what they were expected to do?

With a 7x7 latin square - I think the answer is yes.

In my opinion a sudoku-variant can be called sudoku. Of course, to solve this one, you have to know the meaning of outside clues. But it is sufficiant to explain the meaning of these and say that sudoku rules apply. If you present a 9*9 latin square saying only "this is a sudoku", I think someone can think that people who make this grid forget to design 3*3 boxes and try to solve using this constraint, even if boxes are not apparent... Of course with 7*7 example, it's not the same because 7*7 sudoku are less common.

### Re: What is sudoku?

Posted: **Wed 01 Dec, 2010 10:05 am**

by **drsteve**

I'd go with the third constraint, or tighten it up slightly by insisting that every cell is belongs to (at least 1) outlined area in the grid in which the digit cannot repeat.

So, No, Yes, No for the three examples, but this does rule out one thing that I'd call Sudoku, which is one of Tom S's mutants where each outlined area contains a repeated digit - so a 5x5 contains 4 boxes of 6 cells and an individual one. Definitely sudoku, but hard to fit into a standard definition.

### Re: What is sudoku?

Posted: **Sat 04 Dec, 2010 6:05 pm**

by **detuned**

I've seen variants of sudoku, for example subsets3*3 on argio-logic.net (Italian site), where each symbol appears more than one in every subsets (in this example you have to fill grids with digits 1, 2 and 3 so that each digit appears exactly 3 times in every row, column and box. Can we call this sudoku or not?

I've not come across those Argio logic examples before - although I've certainly seen "sudoku" puzzles where instead of no repeats you have a specific letter/number repeating - I think there was a sudoku using the letters of HALLOWEEN in Zilina. Very much a grey area I think. I think I'd just about put the halloween puzzle as a sudoku, but I'd be less inclined to count the argio logic example.

Of course if we stick to the letter of the law of what has previously been said, we should exclude these examples. They certainly have a different solving flavour to them, but they certainly retain a certain flavour of a sudoku puzzle...