The New Sudoku Players' Forum

[coloin]

Going to go off on a tangent here ....
A varient here is OWB [One Wonky Box] sudoku
Heres an example of an easy puzzle [ not sure how to remove more clues manually]

Code: Select all

+---+---+---+
|385|...|71.|
|..7|...|689|
|691|...|.34|
+---+---+---+
|...|62.|897|
|...|179|.56|
|...|.5.|1.3|
+---+---+---+
|15.|9.8|.4.|
|.68|731|2..|
|739|5.2|..1|
+---+---+---+      44 clues


The WB [Wonky Box] is Box 9, and it only has numbers 1-6
There are 3 positions in Box 9 without a clue [ but here not defined]

looking at it structurally
Ive only found 4 possible solution grid forms with OWB [One Wonky Box]in Box 9

Code: Select all

 
+---+---+---+
|175|839|462|
|364|215|789|
|982|764|153|
+---+---+---+
|546|927|318|
|813|456|297|
|729|183|645|
+---+---+---+
|697|341|52x|
|458|672|931|
|231|598|x74|
+---+---+===+    2 loci with no possible clue in B9, Type 1

Code: Select all

+---+---+---+
|175|839|246|
|364|215|978|
|982|764|315|
+---+---+---+
|546|927|831|
|813|456|729|
|729|183|564|
+---+---+---+
|697|342|15x|
|231|598|4x7|
|458|671|x92|
+---+---+---+    3 loci with no possible clue in B9, Type 2 

Code: Select all

+---+---+---+
|127|598|463|
|439|762|851|
|568|314|972|
+---+---+---+
|614|823|597|
|783|159|246|
|952|647|138|
+---+---+---+
|895|231|6x4|
|346|975|x1x|
|271|486|3x5|
+---+---+---+   4 loci with no possible clue in B9 Type 3   

Code: Select all

+---+---+---+
|698|237|145|
|743|815|629|
|215|946|873|
+---+---+---+
|976|458|231|
|132|769|458|
|854|321|796|
+---+---+---+
|569|183|xx2|
|327|594|x1x|
|481|672|3xx|
+---+---+---+   6  loci with no possible clue  in in B9     Type 4 

Removing clues wont necessarily give challenging puzzles, or maybe they will ....

Ive shown B9 as the box with the wonky clues [IMO B9 is easier to visualize] but B5 might be more aesthetic.

The clues in B9 could easily be limited to 1-7,1-6,1-5 or 1-3. and the no-clue positions could be defined, this would give us puzzles with less clues than above.

With computer solvers the difficulty would step up if the wonky box was not defined, and if the clue numbers in the WB was also not defined
although it would have to be that only one of the 9 potential wonky boxes has a unique valid OWB puzzle !

Looking at it structurally...The filling of the B9 box is primarily / solely dependant on the filling of B3B6B7B8
There must therefore be more ways to these OWB solution grids than vanilla 9*9 sudoku solution grids
in 100000 random B3B6B7B8 fillings only 12.9% had a valid B9 [ as in non-wonky], the remaining 87% had Wonky Boxes
in a smaller sample, of the 4 invalid types 1:2:3:4 found their incidence ratio was 24:10:1:0
In the most common type with 2 impossible cells, for example , there are 2 other cells with 2 more options, and these would have to be givens

Code: Select all

+---+---+---+
|...|...|123|
|...|...|569|
|...|...|784|
+---+---+---+
|...|...|618|
|...|...|352|
|...|...|497|
+---+---+---+
|893|765|...|
|465|312|..X|
|127|489|X..|
+---+---+---+

+----------------------+----------------------+----------------------+
| 5679   4578   4689   | 5689   4579   4678   | 1      2      3      |
| 237    13478  1248   | 128    2347   13478  | 5      6      9      |
| 23569  135    1269   | 12569  2359   136    | 7      8      4      |
+----------------------+----------------------+----------------------+
| 23579  3457   249    | 259    234579 347    | 6      1      8      |
| 679    1478   14689  | 1689   479    14678  | 3      5      2      |
| 2356   1358   1268   | 12568  235    1368   | 4      9      7      |
+----------------------+----------------------+----------------------+
| 8      9      3      | 7      6      5      | 2      4      1      |
| 4      6      5      | 3      1      2      | 89     7      X      |
| 1      2      7      | 4      8      9      | X      3      56     |
+----------------------+----------------------+----------------------+

+---+---+---+
|...|...|123|
|...|...|569|
|...|...|784|
+---+---+---+
|...|...|618|
|...|...|352|
|...|...|497|
+---+---+---+
|893|765|241|
|465|312|.7X|
|127|489|X3.|
+---+---+---+

......123......569......784......618......352......49789376524146531287.127489.35
......123......569......784......618......352......49789376524146531287.127489.36
......123......569......784......618......352......49789376524146531297.127489.35
......123......569......784......618......352......49789376524146531297.127489.36

Anyhow

The whole point of this is whether anyone can easily program a simple solver ...
...and remove more clues and see how hard the puzzles might be ,

or maybe more usefully a program to count the number of OWB solutions [9] for multi solution puzzles ....

[coloin]

ok ... ive managed to construct a puzzle which has at least one OWB solution... but i dont know if it is unique
wonky box is not defined, neither are the clues....

Code: Select all

+---+---+---+
|1..|4..|..9|
|.5.|.8.|.2.|
|.98|1.2|..4|
+---+---+---+
|..1|..5|89.|
|58.|92.|.67|
|.79|841|2.5|
+---+---+---+
|.67|518|.42|
|81.|294|.76|
|...|...|5..|
+---+---+---+


[coloin]

It took a while ..... but I eventually nmanaged to make a solution grid with 9 WB

There are nine wonky boxes, box 1 has no 1, box 2 has no 2, box 3 has no 3 ... box 9 has no 9
All in a disjoint template !

Code: Select all

4523678.936.891745897.5461212594837.68327.591.791362849.6423158534619.272187.5436

Not sure if there can be worthwhile puzzles by removing clues .....

[Hajime]

Looks a lot like my post about "sudoku in error",
See http://forum.enjoysudoku.com/sudoku-in-error-t37999.html

[creint]

Are there any sample puzzles.
Empty boxes must be defined (or directly impossible) before you can start to solve.
If they are not defined then you could get different solutions based on which cells you solve first.

[coloin]

Yes Hajime these constrained solution grids are similar - except for the rows and columns..... here its only the box which is constrained....

it was quite difficult to construct the solution grid ...

Empty boxes must be defined (or directly impossible) before you can start to solve.
If they are not defined then you could get different solutions based on which cells you solve first.

Maybe .... i think a simple back tracking solver could be employed perhaps .... if there are few solution grids [ if there are] , then few clues are needed
the proviso is that there is no 1 in box 1 , no 2 in box 2 .....
the impossible cells are disjoint
the puzzles may well only be computor solvable

It maybe that the solution grid should be that the impossible cell is doubly [r and c] constrained
In the solution grid I constructed the 3 in box 3 is prevented by a 3 in the row and also a 3 in the column, whilst the 1 in box 1 is only constrained by a 1 in r2 but not in c3 ... so not perfect
but i dont know if a solution grid like that exists even ...

[HATMAN]

I terms of making interesting puzzles within the format you might consider adding the NC constraint.
For my ORC puzzles (even rows and columns allow repeats) I found it necessary to add NC to give a viable solution space.

Maurice

[Hajime]

To make a "sudoku in error" from your puzzle above with the restriction that there is exactly 1 error per digit and all digits are present (rule 1 to 6):

Code: Select all

candidates per pink box/cell are:
4589 1678 2567
2358 1349 2589
2458 3469 3568
(choose the digits of the box NOT in the same row or column, and of course NOT the remaining digit of that box)

with a possible solution:

5 1 7
2 9 8
4 6 3
on the pink cells.


Now there is exactly 1 error per row/col/box and your only activity is to make a puzzle from this solution

[coloin]

Indeed that would be a solution grid for invalid and extra clues in each row, column and box.

It took a while but eventually was able to construct a true Nine Wonky Box solution grid
The rows and columns are all valid, just the boxes are invalid
These would be the pencilmarks in the empty grid

Code: Select all

                                                         
+-----------------------------+----------------------------+----------------------------+
|           23456789 23456789 | 13456789 13456789 13456789 | 12456789 12456789 12456789 |
| 23456789  23456789 23456789 |          13456789 13456789 | 12456789 12456789 12456789 |
| 23456789  23456789 23456789 | 13456789 13456789 13456789 |          12456789 12456789 |
+-----------------------------+----------------------------+----------------------------+
| 12356789           12356789 | 12346789 12346789 12346789 | 12345789 12345789 12345789 |
| 12356789  12356789 12356789 | 12346789          12346789 | 12345789 12345789 12345789 |
| 12356789  12356789 12356789 | 12346789 12346789 12346789 | 12345789          12345789 |
+-----------------------------+----------------------------+----------------------------+
| 12345689  12345689          | 12345679 12345679 12345679 | 12345678 12345678 12345678 |
| 12345689  12345689 12345689 | 12345679 12345679          | 12345678 12345678 12345678 |
| 12345689  12345689 12345689 | 12345679 12345679 12345679 | 12345678 12345678          |
+-----------------------------+----------------------------+----------------------------+


Here is a solution grid with 8 clues in each row box and column
There is no 1 in box 1 at r1c1, no 2 in box 2 at r2c4, no 3 in box 3 at r3c7 .... no 9 in box 9 at r9c9.
Each invalid position is doubly covered by the respective clue - eg the pink box in box 1 has a 1 in r1c7 and a 1 in r4c1

Code: Select all

+---+---+---+
|.37|958|164|
|469|.71|285|
|582|643|.79|
+---+---+---+
|1.5|487|392|
|976|3.2|851|
|328|169|4.7|
+---+---+---+
|24.|536|718|
|851|29.|643|
|693|714|52.|
+---+---+---+
 

Better visualised with this image