The New Sudoku Players' Forum

[enxio27]

Clarification of terminology here: NC+ refers to Non-Consecutive, yes? Is that the same thing as NC? (I believe it was djApe who first came up with the non-consecutive variant idea.) And they are non-consecutive with respect to row and column only, not diagonally, correct? Any other constraints that I missed?

[m_b_metcalf]

Clarification of terminology here: NC+ refers to Non-Consecutive, yes? Is that the same thing as NC? (I believe it was djApe who first came up with the non-consecutive variant idea.) And they are non-consecutive with respect to row and column only, not diagonally, correct? Any other constraints that I missed?

NC+ has also {1, 9} (or {1,N}) as a forbidden pair. And, of course, the NC+ condition must hold for the diagonals of an X-sudoku. What's sauce for the goose is sauce for the gander.

Regards,

Mike

[Mathimagics]

What he means, enxio, is that NC+ regards values 1 and 9 as being consecutive also.

Now, Mike, just hang on one second, when did we agree that if diagonals apply, they have to be NC too?

It's certainly a valid variation, but I think it's not what most people would regard as standard NC (if there is such a thing). Call it XNC perhaps?

[tarek]

the NC+ condition must hold for the diagonals of an X-sudoku. What's sauce for the goose is sauce for the gander.

I don’t share this view. The NC should follow a chess piece move. If non is explicitly specified then the rule applies to Adjacent cells only (aka the chess piece “Wazir” move). Adjacent cells means that the cells share an edge which in our sudoku format means 1 orthogonal cell in any direction.

Anything other than that should be explicitly specified!

I love the idea of X diagonals NC but IMO they have to be explicitly declared!

Tarek

[enxio27]

Thanks to you both for the explanation. It appears that JSudoku and RCB SudokuSolver don't have options for NC+, but I can work with it.

So Mike's first sample puzzle (copied below) in post #5 of this thread is legit, since the givens in R1C2 and R2C1 are diagonally adjacent and not horizontally or vertically adjacent?

Code: Select all

  .  1 15  8  .  . 10  .  .  7  .  .  9  2 12  .
  2  .  3  5  . 15  .  .  .  .  8  . 13 11  . 16
  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .
  .  .  .  .  .  .  .  4  2  .  .  .  .  .  .  .
  .  .  .  .  .  .  . 13 15  .  .  .  .  .  .  .
  .  .  .  3  .  .  . 10  8  .  .  .  1  .  .  .
  5  .  . 13  .  9 11  3 16  2  6  . 12  .  . 14
  .  2  9  .  . 12 16  7 13  4 14  .  . 15  6  .
  .  5  2  .  .  3 13 15  7  1 10  .  .  6  9  .
 13  .  . 12  .  1  8 11  5  3 16  .  7  .  .  4
  .  .  . 16  .  .  .  9 12  .  .  . 10  .  .  .
  .  .  .  .  .  .  .  2  4  .  .  .  .  .  .  .
  .  .  .  .  .  .  . 14 10  .  .  .  .  .  .  .
  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .
  6  .  8  1  . 10  .  .  .  . 12  .  2  4  .  7
  . 11  4  9  .  .  1  .  . 13  .  .  8 10 15  .

[hkociemba1]

I played a bit around with my added NC+ functionality and found a few things:
5. For N=3 here is a Sudoku which is NC+, X and P which needs only 4 givens
.....................................................3...1.................7..4..

Herbert, Could you kindly provide your solution for this?

Thanks,

Mike

My solution which should be unique if my implementation of the NC+ part ist correct is
729461538164835792538297146853972614416358279972614853297146385641583927385729461

[tarek]

So Mike's first sample puzzle (copied below) in post #5 of this thread is legit, since the givens in R1C2 and R2C1 are diagonally adjacent and not horizontally or vertically adjacent

The world federation defines adjacent cells as cells sharing an edge which means vertically or horizontally in this case. They use the term “neighboring” cells to describe cells that share an edge or point. So a neighbouring cell could be a cell in any direction!!

Tarek

[m_b_metcalf]

I played a bit around with my added NC+ functionality and found a few things:
5. For N=3 here is a Sudoku which is NC+, X and P which needs only 4 givens
.....................................................3...1.................7..4..

Herbert, Could you kindly provide your solution for this?

My solution which should be unique if my implementation of the NC+ part ist correct is
729461538164835792538297146853972614416358279972614853297146385641583927385729461

By what I regard as a consistent definition of NC+, the diagonals must also fulfil that condition. Thus, IMHO, a NC+ X for N=3 cannot exist.

Regards,

Mike

Code: Select all

  7  2  9  4  6  1  5  3  8
  1  6  4  8  3  5  7  9  2
  5  3  8  2  9  7  1  4  6
  8  5  3  9  7  2  6  1  4
  4  1  6  3  5  8  2  7  9
  9  7  2  6  1  4  8  5  3
  2  9  7  1  4  6  3  8  5
  6  4  1  5  8  3  9  2  7
  3  8  5  7  2  9  4  6  1

[enxio27]

Since (as near as I can tell), djApe invented the non-consecutive variation (about 2010, I believe), I think we should stick with his definition:

http://www.djape.net/non-consecutive-sudoku/

He also introduced a Sudoku-X variation of the NC puzzle, which did NOT require that the diagonals be non-consecutive.

If you want to come up with other variations on the NC theme, I have no issue with that, but please call them by a new name so that there is no confusion with existing puzzle types.


BTW: JSudoku doesn't seem to be handling non-consecutive letters very well. And RCB SudokuSolver doesn't handle 16x16 puzzles at all.

[hkociemba1]

With a bit patience within about 20 min I also found a NC+ SudokuW grid for N=4. As I already said no such grid exists for N=3

Hidden Text: Show

Code: Select all

 +-------------+-------------+-------------+-------------+
 |  3  6 10 12 |  9 16  7 15 |  8  1 13  2 | 14  4 11  5 |
 |  1 13  5  8 | 14 12  3 10 | 15 11  6  4 |  2  7  9 16 |
 | 14 16 11  4 |  6  8  5  2 |  9  7  3 10 | 12  1 15 13 |
 |  7  2  9 15 |  1 11 13  4 | 12 16  5 14 |  3  6  8 10 |
 +-------------+-------------+-------------+-------------+
 |  9  7  3 10 | 12  4  8 14 |  1  6  2 16 | 13 11  5 15 |
 |  4 15  1 14 |  2  7 16 11 |  5 13 10  3 |  6  8 12  9 |
 | 11  8 13  2 |  5  9  6  1 |  7  4 12 15 | 10 16 14  3 |
 |  5 12 16  6 | 10 13 15  3 | 11  8 14  9 |  4  2  7  1 |
 +-------------+-------------+-------------+-------------+
 | 15  3 14  9 |  7  2 12 16 | 13 10  8  6 | 11  5  1  4 |
 |  6 11  4  1 | 15 10 14  9 |  2  5 16 12 |  8 13  3  7 |
 | 12  5  8 13 |  3  1  4  6 | 14  9 11  7 | 15 10 16  2 |
 | 16 10  2  7 | 13  5 11  8 |  3 15  4  1 |  9 12  6 14 |
 +-------------+-------------+-------------+-------------+
 | 10  1 15  5 |  8  3  9 13 |  6  2  7 11 | 16 14  4 12 |
 |  2 14  6 11 |  4 15  1  5 | 16 12  9 13 |  7  3 10  8 |
 | 13  9 12  3 | 16  6 10  7 |  4 14  1  8 |  5 15  2 11 |
 |  8  4  7 16 | 11 14  2 12 | 10  3 15  5 |  1  9 13  6 |
 +-------------+-------------+-------------+-------------+

I used this to create a symmetric SudokuW/NC+ puzzle (eventually not minimal) with 48 givens

Hidden Text: Show

Code: Select all

+-------------+-------------+-------------+-------------+
 |  .  6  .  . |  9  .  .  . |  .  .  .  2 |  .  . 11  . |
 |  1  .  .  . |  .  .  .  . |  .  .  .  . |  .  .  . 16 |
 |  . 16  .  . |  .  .  .  . |  .  .  .  . |  .  . 15  . |
 |  7  2  .  . |  . 11  .  . |  .  .  5  . |  .  .  8 10 |
 +-------------+-------------+-------------+-------------+
 |  .  7  .  . |  .  .  .  . |  .  .  .  . |  .  .  5  . |
 |  .  .  .  . |  .  .  .  . |  .  .  .  . |  .  .  .  . |
 |  .  .  .  2 |  .  .  .  . |  .  .  .  . | 10  .  .  . |
 |  .  . 16  . |  .  . 15  3 | 11  8  .  . |  .  2  .  . |
 +-------------+-------------+-------------+-------------+
 |  .  . 14  . |  .  . 12 16 | 13 10  .  . |  .  5  .  . |
 |  .  .  .  1 |  .  .  .  . |  .  .  .  . |  8  .  .  . |
 |  .  .  .  . |  .  .  .  . |  .  .  .  . |  .  .  .  . |
 |  . 10  .  . |  .  .  .  . |  .  .  .  . |  .  .  6  . |
 +-------------+-------------+-------------+-------------+
 | 10  1  .  . |  .  3  .  . |  .  .  7  . |  .  .  4 12 |
 |  . 14  .  . |  .  .  .  . |  .  .  .  . |  .  . 10  . |
 | 13  .  .  . |  .  .  .  . |  .  .  .  . |  .  .  . 11 |
 |  .  4  .  . | 11  .  .  . |  .  .  .  5 |  .  . 13  . |
 +-------------+-------------+-------------+-------------+

@Mike: I can confirm that there is not even a SudokuNC+ where neighbors on the diagonals are all nonconsecutive. For N=4 there are such SudokuNC+ with also are SudokuX.

[Mathimagics]

Ok Mike, the tribe has spoken!

This is Waziristan and we are a fundamentally orthocratic society. There is no adjacency but orthogonal.

Adjacent cells in Waziristan are those that share an EDGE (of unit length), neighbouring cells need only have some common point.

MM
Ministry of Orthogonal Affairs

[tarek]

Ministry of Orthogonal Affairs

Away from all of the Python references, these ministry rules pre-date me ... So I can't take full credit

[Mathimagics]

That's good, then, since we were never offering it!

But perhaps I can show you a ComfyDown orthogonal mattress?

[Hajime]

the NC+ condition must hold for the diagonals of an X-sudoku.

He also introduced a Sudoku-X variation of the NC puzzle, which did NOT require that the diagonals be non-consecutive.

It is not possible to have adjacent cells AND diagonals to be non-consecutive. The middle cell r5c5 has 8 neighbors which should not have non-consecutive values, but at the same time the middle box needs all digits.

[hkociemba1]

Another quite obvious NC+ variation is not only to disallow consecutive values but (cyclically) disallow |value1-value2|<=K, with some K>=1. Let's call this NCK+. For K=2 there exist grids for N=3:

Code: Select all

 +-------+-------+-------+
 | 5 2 8 | 4 1 7 | 3 9 6 |
 | 1 7 4 | 9 6 3 | 8 5 2 |
 | 6 3 9 | 5 2 8 | 4 1 7 |
 +-------+-------+-------+
 | 3 9 6 | 2 8 5 | 1 7 4 |
 | 7 4 1 | 6 3 9 | 5 2 8 |
 | 2 8 5 | 1 7 4 | 9 6 3 |
 +-------+-------+-------+
 | 8 5 2 | 7 4 1 | 6 3 9 |
 | 4 1 7 | 3 9 6 | 2 8 5 |
 | 9 6 3 | 8 5 2 | 7 4 1 |
 +-------+-------+-------+

But N=3 does not allow NC3+ grids.
A very hard question is which is the minimal N such that there exists a NCK+ grid. I do not know the answer even for K=3.
EDIT: I see that the solution just uses the minirows types 1,4,7 / 2,5,8 / 3,6,9 though I did not make any assumptions about this.