## SudokuW/SudokuWX (Windoku)

For fans of Killer Sudoku, Samurai Sudoku and other variants

### SudokuWX: 9-clue Puzzles

.
I have found a 9-clue SudokuWX (WindokuX) puzzle:

Code: Select all
`  +-------+-------+-------+  | . . . | . . . | . 8 . |  | . . . | . 7 . | . . . |  | . . . | . . . | . 5 . |  +-------+-------+-------+  | . . . | 3 . . | . . . |  | . 6 . | . . . | . . . |  | . . . | . . 4 | . 2 . |  +-------+-------+-------+  | . . . | . . . | . . . |  | . . . | . . . | . . 1 |  | 7 . . | . . . | . . . |  +-------+-------+-------+`

I hope that tarek and other pencil-solvers have fun with this one!

I had thought that, since every 10-clue case found by the morph-walker so far is minimal, that 9-clue puzzles might be rare or non-existent, but these were found by checking morphs of the 10-clue puzzles, eg {-2, +1}. So 8-clue puzzles cannot be ruled out by any stretch!

Here are the first 5 x 9-clue puzzles found:
Hidden Text: Show
Code: Select all
`.......8.....7...........5....3......6............4.2..................17........: 123456789456879312897132456942318675368725194571694823685241937234987561719563248....................8...........7.........4.....5........8...32..........69......: 123456789457298361698371245214687593785139426936542817571864932342915678869723154.......8.....7...........5....3......6............4.2.........7........1.........: 123456789456879312897132456942318675368725194571694823685241937234987561719563248..3......4.......2...1...65...2...........9.....................7................: 123456789456789312789132465634298571817564923592317648345621897971845236268973154..3......4...........1.2.65...2...........9.....................7................: 123456789456789312789132465634298571817564923592317648345621897971845236268973154`

Mathimagics
2017 Supporter

Posts: 1870
Joined: 27 May 2015
Location: Canberra

### Re: SudokuWX: 9-clue Puzzles

Mathimagics wrote:.
I have found a 9-clue SudokuWX (WindokuX) puzzle:

Code: Select all
`  +-------+-------+-------+  | . . . | . . . | . 8 . |  | . . . | . 7 . | . . . |  | . . . | . . . | . 5 . |  +-------+-------+-------+  | . . . | 3 . . | . . . |  | . 6 . | . . . | . . . |  | . . . | . . 4 | . 2 . |  +-------+-------+-------+  | . . . | . . . | . . . |  | . . . | . . . | . . 1 |  | 7 . . | . . . | . . . |  +-------+-------+-------+`

I hope that tarek and other pencil-solvers have fun with this one!

Couldn't advance things here!!! congratulations for these discoveries
tarek

tarek

Posts: 3759
Joined: 05 January 2006

### SudokuW: 11-clue Puzzle

.
Here is our first 11-clue SudokuW (Windoku) puzzle. I have found about 100 so far.

Code: Select all
`  +-------+-------+-------+  | . 2 . | . . . | . . 9 |  | . . . | . . . | . . . |  | . . . | . 3 . | . . 1 |  +-------+-------+-------+  | . . . | . . . | . . . |  | 7 . 9 | . . . | . . . |  | 5 . . | . . . | . . . |  +-------+-------+-------+  | 6 . . | . . . | . . . |  | . . . | . . 1 | . 7 . |  | . . . | . . . | . 4 . |  +-------+-------+-------+`

Solution:
Hidden Text: Show
[/code]
123456789467198235895237461284375916719682354536914827641723598952841673378569142
[/code]

For SudokuWX, I have found over 7000 9-clue puzzles on 3000 ED grids. No sign of existence of 8-clue puzzles, but I have an explicit 8-clue tester (using HSets) running that is testing each 9-clue grid.

Mathimagics
2017 Supporter

Posts: 1870
Joined: 27 May 2015
Location: Canberra

### SudokuWX (WindokuX)

I stopped looking for 10-clue SudokuWX puzzles when it became apparent there were so many 9-clue puzzles. At that point I had found 30,554 of the 81,571 ED grids (37.4%) had 10-clue puzzles. This raises the interesting question "how many grids do NOT have 10-clue puzzles?". I will return to this question once the 9-clue puzzles have been identified.

For 9-clue puzzles, I have found 9616 grids (11.8%). A rough estimate of the number of grids with 9-clue puzzles is 27000 (33%) based on random sampling, using explicit HS-based grid testing. Only 100 grids were tested so the estimate error is likely to be relatively high.

I have also HS-tested half of the 9616 grids for 8-clue puzzles and none have been found.

The 9-clue search and 8-clue testing is ongoing.

Mathimagics
2017 Supporter

Posts: 1870
Joined: 27 May 2015
Location: Canberra

### SudokuW/SudokuWX (Windoku)

.
I have independent corroboration (twice in fact) of my figure for the number of SudokuW grids:

This was given by "aeb" here, and apparently confirmed by Red Ed.

https://homepages.cwi.nl/~aeb/games/sudoku/nrc.html

6,337,174,388,428,800 = 17,463,553,760 x 9!

Mathimagics
2017 Supporter

Posts: 1870
Joined: 27 May 2015
Location: Canberra

### Re: SudokuWX: 9-clue Puzzles

tarek wrote:
Mathimagics wrote:.
I have found a 9-clue SudokuWX (WindokuX) puzzle:

Code: Select all
`  +-------+-------+-------+  | . . . | . . . | . 8 . |  | . . . | . 7 . | . . . |  | . . . | . . . | . 5 . |  +-------+-------+-------+  | . . . | 3 . . | . . . |  | . 6 . | . . . | . . . |  | . . . | . . 4 | . 2 . |  +-------+-------+-------+  | . . . | . . . | . . . |  | . . . | . . . | . . 1 |  | 7 . . | . . . | . . . |  +-------+-------+-------+`

I hope that tarek and other pencil-solvers have fun with this one!

Couldn't advance things here!!! congratulations for these discoveries
tarek

Sukaku Explainer Difficulty rating: 8.9 (Dynamic Region Forcing Chains) so this is beyond what most can do with P&P

tarek

Posts: 3759
Joined: 05 January 2006

### Re: SudokuW: 11-clue Puzzle

Mathimagics wrote:.
Here is our first 11-clue SudokuW (Windoku) puzzle. I have found about 100 so far.

Code: Select all
`  +-------+-------+-------+  | . 2 . | . . . | . . 9 |  | . . . | . . . | . . . |  | . . . | . 3 . | . . 1 |  +-------+-------+-------+  | . . . | . . . | . . . |  | 7 . 9 | . . . | . . . |  | 5 . . | . . . | . . . |  +-------+-------+-------+  | 6 . . | . . . | . . . |  | . . . | . . 1 | . 7 . |  | . . . | . . . | . 4 . |  +-------+-------+-------+`

This one certainly can be fun to solve manually
SE Difficulty rating: 4.1 (Two-string Kite)

tarek

Posts: 3759
Joined: 05 January 2006

### Re: SudokuW/SudokuWX (Windoku)

I'm bumping this thread because it's become of interest again. At the time it was active I had no code for W. I recently realized that I had some solution grids with symmetry of givens that also fulfilled both the W and X constraints. That's when I started looking for low clue counts (aka reinventing the wheel). Ten such grids are hidden below.

Mike
Hidden Text: Show
Code: Select all
`968257143253419687417683529592831476871546932634972815186725394325194768749368251917635428852714639643928517461859273529347186738162945396281754174593862285476391651973428897124536423658197945816273162347859738592641319265784576489312284731965712864539694735182538219647961587324253941768487326951345198276829673415176452893468379152591428376723516498376841529952763841184952637215694783637285914849137265135768492468192735792435168657324981384951627921687354249576813573819246816243579517692483394178625862345179658724931243961758971583246139457862486239517725816394842639571597241683613587429268413957479852136351796248186325794724968315935174862917658243453912687682437519561729438839546172274183956196374825325891764748265391754829316621345798389671245175493862936258471842716539568934127213567984497182653`

m_b_metcalf
2017 Supporter

Posts: 13094
Joined: 15 May 2006
Location: Berlin

### Re: SudokuW/SudokuWX (Windoku)

10 more very extreme windoku-x with the same design:
Code: Select all
`.3.....547......2....3.7.................................1.4....8......615.....3. ED=9.7/1.2/1.2.3.....547......2....3.7.................................1.4....8......267.....4. ED=9.6/1.2/1.2.3.....547......2....3.7.................................1.4....8......297.....4. ED=9.6/1.2/1.2.3.....547......2....3.7.................................1.4....8......915.....3. ED=9.7/1.2/1.2.3.....547......2....3.7.................................1.4....9......615.....3. ED=9.7/1.2/1.2.3.....547......2....3.7.................................1.4....9......267.....4. ED=9.6/1.2/1.2.3.....547......2....3.7.................................1.4....9......287.....4. ED=9.6/1.2/1.2.3.....547......2....3.7.................................1.4....9......815.....3. ED=9.7/1.2/1.2.3.....547......2....3.7.................................1.4....6......915.....3. ED=9.7/1.2/1.2.3.....547......2....3.7.................................1.4....6......287.....4. ED=9.6/1.2/1.2`

SiSeSuSo Program seems to create duplicates!
urhegyi

Posts: 611
Joined: 13 April 2020

### Re: SudokuW/SudokuWX (Windoku)

urhegyi wrote:SiSeSuSo Program seems to create duplicates!

Solved in next version coming soon, also with vicinity search.

Hajime

Posts: 1003
Joined: 20 April 2018
Location: Netherlands

### Re: SudokuW/SudokuWX (Windoku)

My best 12 from a longer file of X-windokus. Maybe a vicinity search would get still higher?

Mike
Code: Select all
`...1...2...........3........2...45.......6...................74..8..............8    ED=9.4/1.2/1.2   1..2...........2...3..............45.........3.5..6........785...1...............    ED=9.5/4.0/2.9 ....1.......2.34............4...2..15..................67............5.8.........    ED=9.6/4.0/2.9   ..1...2.....1...34.......1..5......................6..3...7.........1.....4.8....    ED=9.7/2.9/2.9   ...1.......2..3.........4..5............3..6.........7...68.........7....2.......    ED=9.8/4.3/2.9      ..1...2....34.....5...63.....51..................2............6......7....8...9..    ED=9.9/9.9/2.9     <---- A nice pearl1..2...3......42.5.............1...........................6....6.472.....8......   ED=10.0/2.9/2.9.1.........21.3.......4..........5..67........2.7........8........4..8...........   ED=10.1/1.5/1.5.1.2.345..63...2..............1....5.7............8......4.......................   ED=10.2/2.9/2.9...1..2.....2.34.5.........14.......6............7.............8.......6.6.......   ED=10.6/1.2/1.2....1..2..............3...4......5..........64........17....6.3...6.....8.6......   ED=10.7/1.5/1.5............1..2....3............4..5.........6.....7..1.......8....9........7...   ED=11.2/1.5/1.5`

m_b_metcalf
2017 Supporter

Posts: 13094
Joined: 15 May 2006
Location: Berlin

### Re: SudokuW/SudokuWX (Windoku)

FWIW, from an old file of randomly generated X-Windokus:
Code: Select all
`..........1....9.......3.........8..7.1.29.........3........6....4....7.......... 12 ED=10.0/10.0/2.9...9.......2....3..4......6....5.7.1..........5.......6.......3.............1.... 12 ED=10.1/10.1/2.9....2..9....17.....8.......3..7............1......5.......96...............3..... 12 ED=10.1/10.1/2.9.............24........6.583..................1................2....1.6....698... 13 ED=10.1/10.1/2.9....6....5..9..2........5......1.9.....7......4.......1..63..4................... 13 ED=10.1/10.1/2.9.....7............8.9....6.31.8.....5..............................36..1...2..6.3 14 ED=10.6/10.6/2.9..8.....................74..81.6........5....5..............1....7...9.2.......7. 13 ED=10.6/10.6/2.9...................1.6.8...4...1..6.5..7..............3..9.................5..72. 13 ED=10.7/10.7/2.9....4.......................3...6.1.........6..9.....8..2.......4..1...3........5 12 ED=10.8/10.8/2.9`

SE Ratings are from SudokuMonster's SukakuExplainer.
1to9only

Posts: 3994
Joined: 04 April 2018

### Re: SudokuW/SudokuWX (Windoku)

All very high ratings: 10+ is rare.
SiSeSuSo still can not produce these.
I have now implemented in a beta version: Vicinity search and no x.y/1.2/1.2 and unique givens per band/stack.
Later some extra info in "interactive games" topic.

Hajime

Posts: 1003
Joined: 20 April 2018
Location: Netherlands

### Re: SudokuW/SudokuWX (Windoku)

I figured out today how to rate a batchfile created with SiSeSuSo of windoku-x with sukakuexplainer (1to9only version), but when it gets ratings above 10.1/10.1/2.6 it shows SE 20.0 and aborts.
example here:
Hidden Text: Show
Code: Select all
`.83..296.........1........32.........................53........4.........172..54. ED=9.8/9.8/2.6.83..296.........1........32.........................53........4.........192..45. ED=9.4/2.8/2.6.83..296.........1........32.........................53........4.........124..85. ED=9.7/9.5/2.6.83..296.........1........32.........................53........4.........126..84. ED=8.9/2.5/2.5.83..296.........1........32.........................53........4.........126..58. ED=7.2/2.5/2.5.83..296.........1........32.........................53........4.........129..58. ED=7.2/2.5/2.5.83..296.........1........32.........................53........4.........129..85. ED=7.2/2.5/2.5.83..296.........1........32.........................53........4.........927..45. ED=9.8/9.8/2.6.83..296.........1........32.........................53........4.........927..81. ED=8.3/2.5/2.5.83..296.........1........32.........................53........4.........924..81. ED=9.6/2.5/2.5.83..296.........1........32.........................53........4.........924..58. ED=9.5/2.5/2.5.83..296.........1........32.........................53........4.........921..45. ED=10.0/9.8/2.6.83..296.........1........32.........................53........4.........962..41. ED=9.5/2.5/2.5.83..296.........1........32.........................53........4.........962..14. ED=9.4/2.5/2.5.83..296.........1........32.........................53........4.........972..45. ED=10.1/10.1/2.6.83..296.........1........32.........................53........4.........629..54. ED=20.0/2.5/2.5.83..296.........1........32.........................53........4.........629..15. ED=20.0/2.5/2.5.83..296.........1........32.........................53........4.........629..14. ED=9.6/2.5/2.5.83..296.........1........32.........................53........4.........621..45. ED=9.7/9.7/2.6.83..296.........1........32.........................53........4.........627..45. ED=9.8/9.8/2.6.83..296.........1........32.........................53........4.........627..14. ED=9.5/9.4/2.6.83..296.........1........32.........................53........4.........624..58. ED=9.4/2.5/2.5.83..296.........1........32.........................53........4.........692..14. ED=9.4/2.5/2.5.83..296.........1........32.........................53........4.........692..54. ED=9.3/2.5/2.5.83..296.........1........32.........................53........4.........692..41. ED=9.4/2.5/2.5.83..296.........1........32.........................53........4.........672..45. ED=10.1/10.1/2.6.83..296.........1........32.........................53........4.........612..54. ED=10.1/2.8/2.6.83..296.........1........32.........................53........4.........279..81. ED=8.3/2.5/2.5.83..296.........1........32.........................53........4.........297..45. ED=9.9/9.9/2.6.83..296.........1........32.........................53........4.........269..14. ED=9.5/2.5/2.5.83..296.........1........32.........................53........4.........269..41. ED=9.7/2.5/2.5.83..296.........1........32.........................53........4.........762..14. ED=10.0/10.0/2.6.83..296.........1........32.........................53........4.........726..81. ED=8.3/2.5/2.5.83..296.........1........32.........................53........4.........721..45. ED=9.9/9.9/2.6.83..296.........1........32.........................53........4.........729..81. ED=8.3/2.5/2.5.83..296.........1........32.........................53........4.........724..18. ED=20.0/8.3/2.6.83..296.........1........32.........................53........4.........712..45. ED=9.7/9.7/2.6.83..296.........1........32.........................53........6.........271..54. ED=9.6/9.6/2.6.83..296.........1........32.........................53........6.........279..41. ED=9.6/2.8/2.6.83..296.........1........32.........................53........6.........241..57. ED=9.6/9.6/2.6.83..296.........1........32.........................53........6.........249..71. ED=9.6/2.8/2.6.83..296.........1........32.........................53........6.........412..75. ED=3.4/2.8/2.6.83..296.........1........32.........................53........6.........429..71. ED=9.6/2.8/2.6.83..296.........1........32.........................53........6.........927..51. ED=9.5/2.8/2.6.83..296.........1........32.........................53........6.........927..54. ED=9.1/2.8/2.6.83..296.........1........32.........................53........6.........924..51. ED=9.5/2.8/2.6.83..296.........1........32.........................53........6.........924..57. ED=9.1/2.8/2.6.83..296.........1........32.........................53........6.........972..85. ED=9.4/2.5/2.5.83..296.........1........32.........................53........6.........972..51. ED=9.5/2.8/2.6.83..296.........1........32.........................53........6.........942..51. ED=9.5/2.8/2.6.83..296.........1........32.........................53........6.........942..85. ED=9.4/2.5/2.5.83..296.........1........32.........................53........6.........172..54. ED=9.1/2.6/2.6.83..296.........1........32.........................53........6.........142..57. ED=9.1/2.6/2.6.83..296.........1........32.........................53........6.........712..45. ED=3.4/2.8/2.6.83..296.........1........32.........................53........6.........729..41. ED=9.6/2.8/2.6.83..296.........1........32.........................53........9.........472..15. ED=10.1/10.1/2.6.83..296.........1........32.........................53........9.........472..85. ED=9.5/7.2/2.6.83..296.........1........32.........................53........9.........472..81. ED=9.5/7.2/2.6.83..296.........1........32.........................53........9.........462..51. ED=9.5/2.8/2.6.83..296.........1........32.........................53........9.........427..58. ED=9.5/7.2/2.6.83..296.........1........32.........................53........9.........426..57. ED=9.6/9.5/2.6.83..296.........1........32.........................53........9.........426..81. ED=9.4/2.5/2.5.83..296.........1........32.........................53........9.........426..17. ED=9.4/2.8/2.6.83..296.........1........32.........................53........9.........426..15. ED=9.6/9.0/2.6.83..296.........1........32.........................53........9.........421..58. ED=9.5/7.2/2.6.83..296.........1........32.........................53........9.........412..75. ED=7.5/2.8/2.6.83..296.........1........32.........................53........9.........712..45. ED=7.5/2.8/2.6.83..296.........1........32.........................53........9.........726..15. ED=9.6/9.0/2.6.83..296.........1........32.........................53........9.........726..14. ED=9.4/2.8/2.6.83..296.........1........32.........................53........9.........726..81. ED=9.4/2.5/2.5.83..296.........1........32.........................53........9.........726..54. ED=9.6/9.5/2.6.83..296.........1........32.........................53........9.........721..58. ED=9.5/7.2/2.6.83..296.........1........32.........................53........9.........724..58. ED=9.5/7.2/2.6.83..296.........1........32.........................53........9.........762..51. ED=9.5/2.8/2.6.83..296.........1........32.........................53........9.........742..15. ED=10.1/10.1/2.6.83..296.........1........32.........................53........9.........742..85. ED=9.5/7.2/2.6.83..296.........1........32.........................53........9.........742..81. ED=9.5/7.2/2.6.83..296.........1........32.........................53........9.........247..81. ED=7.3/2.8/2.6.83..296.........1........32.........................53........9.........247..85. ED=9.4/7.2/2.6.83..296.........1........32.........................53........9.........247..58. ED=9.3/7.2/2.6.83..296.........1........32.........................53........9.........274..85. ED=9.4/7.2/2.6.83..296.........1........32.........................53........9.........274..81. ED=7.3/2.8/2.6.83..296.........1........32.........................53........9.........274..58. ED=9.3/7.2/2.6.83..296.........1........32.........................53........9.........217..54. ED=2.9/2.8/2.6.83..296.........1........32.........................53........9.........214..57. ED=2.9/2.8/2.6.83..296.........1........32.........................53........1.........246..17. ED=9.7/9.7/2.6.83..296.........1........32.........................53........1.........249..15. ED=9.7/9.5/2.6.83..296.........1........32.........................53........1.........276..14. ED=9.7/9.7/2.6.83..296.........1........32.........................53........1.........279..15. ED=9.7/9.5/2.6.83..296.........1........32.........................53........1.........629..57. ED=8.4/2.5/2.5.83..296.........1........32.........................53........1.........629..54. ED=8.4/2.5/2.5.83..296.........1........32.........................53........1.........627..54. ED=9.4/2.8/2.6.83..296.........1........32.........................53........1.........627..45. ED=9.5/2.8/2.6.83..296.........1........32.........................53........1.........624..75. ED=9.5/2.8/2.6.83..296.........1........32.........................53........1.........624..57. ED=9.4/2.8/2.6.83..296.........1........32.........................53........1.........642..51. ED=9.8/2.8/2.6.83..296.........1........32.........................53........1.........672..51. ED=9.8/2.8/2.6.83..296.........1........32.........................53........1.........429..57. ED=9.7/9.5/2.6.83..296.........1........32.........................53........1.........426..58. ED=20.0/2.5/2.5.83..296.........1........32.........................53........1.........462..15. ED=9.8/2.8/2.6`
urhegyi

Posts: 611
Joined: 13 April 2020

### Re: SudokuW/SudokuWX (Windoku)

urhegyi wrote:I figured out today how to rate a batchfile created with SiSeSuSo of windoku-x with sukakuexplainer (1to9only version), but when it gets ratings above 10.1/10.1/2.6 it shows SE 20.0 and aborts.

The 1to9only version lacks many solving techniques.
You can rate all (or just the 20.0's) using SudokuMonster's version.
The command line options are different for the 2 versions!
1to9only

Posts: 3994
Joined: 04 April 2018

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