The New Sudoku Players' Forum

[SudoKai]

Enter numbers 1-9 in such a way that Rows, Columns, and Squares/Boxes contains each number exactly once on all Sudoku Parquet Boards.

Some cells are larger than others and belong in multiple Rows and Columns.

Additionally 12 Rows and Columns exist.

-There are 5 overlapping Sudoku Parquet Boards.

http://www.SudoKai.com

Sudoku Samurai Parquet 2017-08-22.jpg (141.27 KiB) Viewed 2309 times

[tarek]

Enter numbers 1-9 in such a way that Rows, Columns, and Squares/Boxes contains each number exactly once on all Sudoku Parquet Boards.

Some cells are larger than others and belong in multiple Rows and Columns.

Additionally 12 Rows and Columns exist.

Hi SudoKai,

Very nice visuals.

I think i got my head around how to program this!!!

It is a more restrained (or constrained) form of Sudoku. This should allow a very small number of clues to solve.

Although you say 12 columns & rows, I can see (I can confirm after programming) that there are 5 mini Rows & 5 mini columns per 9 cell square. This means that there should be at least 15 Rows & columns per 81 cell grid.

Can you confirm this or explain further if not. The puzzle validity hangs on the choice of the correct wording of the rules?

Tarek

[Edit: I also noticed that the big cells in each 9 cell square can form a mini row or column (it is a mini diagonal but the shaping of the blocks allows it). The sticky ends of each 9 cell square may give rise therefore to many variations of what a row/column can be defined as!!!]

[SudoKai]

The Rows and Columns are as follow:

rows.png (106.48 KiB) Viewed 2277 times

There does seem to be additional Rows and Columns. But please note they are formed due to Solving Techniques eliminating candidates and not because they are designed that way.

It is a weird and wonderful side effect of Sudoku Parquet which seems to instigate rules where non is outlined.

Below is an example.
The Sudoku Parquet rules are the same.
A self created rule is that all cells of the same large shape forms extra regions and cannot contain duplicate numbers. [Disjoint Groups]

no_candidates_left.png (85.56 KiB) Viewed 2277 times

I sourced as many Sudoku Parquet designs as I could find and the basic rules is the same for all of them. 9 Squares/Boxes, 12 Rows and Columns. So please keep this in mind when programming a solver for this variant.

[tarek]

You example makes it clear.

Programming & building the matrix shouldn't be difficult. I just couldn't find the time over the past few years. hopefully this provides a good stimulus.

From a programming point of view, there are 8 extra columns (4 rows & 4 columns)

The hidden rules appear just like the hidden regions in Windoku. I suspect therefore that this varian makes a very restrained variant & therefore I have a feeling it could go easily to 8 clues.

The diagonal nature of the parquets only allows a diagonal clue symmetry only.

To allow line format presentation I think you still need to think of the big blocks as 1,4,7,11,14,17,21,24,27,.....

Thanks,

Tarek

[SudoKai]

Is this the additional Rows and Columns that you observe?

rows_columns.png (241.73 KiB) Viewed 2261 times

[tarek]

Is this the additional Rows and Columns that you observe?

That is what came to my mind first until you gave the example and made it clear.

Because of the shape of the big cells it is also possible to make a chain of 9 cells travelling from side to side or top to bottom which the solver may consider as rows/columns. The combinations are many. That is why it is important to make it clear in the rules which 12 rows 12 columns you are talking about. that should be easy as your example or something similar in my opinion is enough. The visual example imo is important as it will be tricky to word it

You can try adding the big cell rows and columns as further constraints but imo the puzzle is already very restrained/constrained.

I (and several others like udosuk) have explored some of the restrained/constrained sudoku variants to achieve the 8 clue puzzles (Threads in the forum are available) but haven't explored this interesting design before

In my head I'm still trying to visualise these in the traditional 81 small square format. The rows & columns are not straight lines

Tarek

[tarek]

Here is how the the 1st 4 rows look like when superimposed on the 27 cells as we see them in Sudoku (although it is not a sudoku or latin square anymore).

It still has the sudoku 3x3 boxes. the 1st and 4th rows are similar to Latin square's (and sudoku's) 1st and 3rd rows. So it is a special type of Jigsaw. Where most variants build the extra regions on a Latin square template. This one builds it on the 3x3 sudoku boxes template

tarek

[SudoKai]

If you have Row 1 and Row 3, then Row 2 will automatically be imposed. So it is still a Sudoku, albeit a Mutant representation thereof.

hidden_row1.png (36.96 KiB) Viewed 2232 times

The other Rows and Columns I have highlighted might just as well be part of the Rules as they seem to help in solving this particular Parquet design. I think it is because of all the Locked Candidates and Common Peer Eliminations.

hidden_row2.png (45.51 KiB) Viewed 2232 times

Here is a Sudoku Parquet with 9 clues.

Updated Rules for this Sudoku Parquet design:
Enter numbers 1-9 in such a way that Rows, Columns, and Squares/Boxes contains each number exactly once.

Some cells are larger than others and belong in multiple Rows and Columns.

There are 12 Rows and Columns.
6 Additional Rows and Columns exists which aids in solving.

sudoku_parquet_9clues.png (16.25 KiB) Viewed 2232 times

[tarek]

If you have Row 1 and Row 3, then Row 2 will automatically be imposed. So it is still a Sudoku

That is true. Those hidden regions are forced which means that you could be also correct that there will be more hidden regions that will appear in addition to forced LOLs.

Nevertheless still interesting and lovely sudoku variant

Tarek

[tarek]

I like how we are updating stuff as we discuss it more.

To complement your 9 big cell region here are the 2 non intersecting regions to complete the 27 cells.

I think that these 3 regions (9 in the 81 cells) are probably what force the parquets' non orthogonal intersecting regions in my original image

Tarek

[SudoKai]

I did a quick test and got the following results.

rows_columns_red_cells.png (70.45 KiB) Viewed 2213 times

Now players have even more hidden regions they can utilize when solving this variant.

Here are your Rows and Columns outlined.

rows_columns.png (153.46 KiB) Viewed 2213 times

[tarek]

Anther take on the wording of the puzzle

Fill in each 9-cell row, column and 3x3 box so that it contains the numbers 1-9
This puzzle has 12 rows, 12 columns and 9 3x3 boxes
There are additional hidden 9 cell regions that may help in solving the puzzle

[tarek]

Here are 4 symmetric puzzles with 10 clues (I double checked my software but they should be valid)
These need more than singles to solve even when using known and hidden constraints

SudokuParquet_da_10_04.jpg (86.07 KiB) Viewed 2164 times

SudokuParquet_da_10_03.jpg (91.32 KiB) Viewed 2164 times

SudokuParquet_da_10_02.jpg (87.31 KiB) Viewed 2164 times

[tarek]

SudokuParquet_da_10_01.jpg (92.34 KiB) Viewed 2164 times

Puzzles in line format

Code: Select all

..1.2.............3.4...............5.......6...............7.3.............8.9..
..1....2.........34.............5...............6.............47.........8....9..
..1............2..3......4......5...............6......7......3..8............9..
.......1.........2......3......4.......5.6.......7......8......9.........1.......

[tarek]

But I think that this following puzzle will appeal to you SudoKai as it can't be solved with singles using the declared constraints .... But if you know that you can use sudoku constraints and the Big cell rows and columns ( so 3 hidden rows & 3 hidden columns) then you will solve it using singles

SudokuParquet_ns_10_01.jpg (89.95 KiB) Viewed 2163 times

Code: Select all

.1.2...3....4..56...........5....7................8.........................1....

As I coded this as a sudoku variant, I didn't remove rows/columns 2,5,8 from the known constraints.

I had a look at other parquets construction & variations. I think that this one is the most pleasing to the eye and has the double diagonal symmetry

Thanks for letting me enjoy this again

tarek