## Sudoku-DG with 11 clues

For fans of Killer Sudoku, Samurai Sudoku and other variants

### Sudoku-DG with 11 clues

One of my programs found a few Sudokus with Disjoint Groups, with only 11 clues in the puzzle.
Below is a nice example.

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

Posts: 14
Joined: 10 December 2021

### Re: Sudoku-DG with 11 clues

.................1....1............2..2.....3.....4....5........6....47.....8....

Hi Ruud. This looks like SudokuP to me. There are currently 14 known 11 clue such puzzles, which are listed here.

If your puzzle is in minlex form you might have discovered a new one.

Leren

<edit> Unfortunately not a new SudokuP puzzle, it's a morph of O5. However, it's clever in that it also solves as a Sudoku PX puzzle.

If you morph the puzzle by taking the F transform (Row 1 -> Box1, Row 2 -> Box 2, Row 3 -> Box 3 and similarly for the other 2 Tiers) you get another morph of O5

................1......1........2...........4..2..3....5..6...........8....47....

which solves as a SudokuP but not as a Sudoku PX.

Leren
Leren

Posts: 4648
Joined: 03 June 2012

### Re: Sudoku-DG with 11 clues

Hi Leren,
Several sources outside this forum, including Wikipedia, call this format Sudoku-DG, where DG stands for Disjoint Groups. Forgive me for not being to-to-date with the latest terminology.

I translated the canonicalization code in the thread from your link to C#, and it produces the ED grids (with the solution grid normalized).
It seems I have found 12 of the 14 known 11-clue puzzles, and no new additions.

I did not find the code written by Serg (or description thereof) how to convert the ED grids to the min-lex format you used above. If you have a pointer to sample code for this conversion or an explanation of the steps to perform, I would appreciate it very much.

Ruud
Ruud from Sudocue

Posts: 14
Joined: 10 December 2021

### Re: Sudoku-DG with 11 clues

Hi Ruud,

My puzzle was not in minlex form, it was simply a morph (an F transform) of your puzzle, such that it remained a SudokuP puzzle but not a SudokuPX puzzle.

I found Sudoku-DG on the Sudopedia site, and from that I assumed that it was the same as what we call SudokuP, so I put that in my SudokuP solver and it solved uniquely.

However, when I examined the solution I noticed that it was also a SudokuPX solution, so I put that into my Sudoku PX solver and it also solved.

So a morph of O5 can also be a Sudoku PX puzzle, but not the minlex form, which serg has given. That was a very intriguing result, that was never mentioned in the SudokuP thread.

Leren
Last edited by Leren on Thu Dec 30, 2021 4:17 am, edited 2 times in total.
Leren

Posts: 4648
Joined: 03 June 2012

### Re: Sudoku-DG with 11 clues

I had never heard this called "SudokuP" until just now. Good to know.
mith

Posts: 890
Joined: 14 July 2020

### Re: Sudoku-DG with 11 clues

The SudokuP threads start here and here. The SudokuPX thread starts here. In the first thread Mathimagics mentions both names for the SudokuP/DG variant. Happy reading. Leren
Leren

Posts: 4648
Joined: 03 June 2012

### Re: Sudoku-DG with 11 clues

Thanks Leren.

I am a little late in the game for the minimum clues search, but I ran my code anyway and found the 14 SudokuP puzzles with 11 clues, as well as the 3 SudokuPX puzzles with 9 clues.

But I would like to check if any other forum members have noticed that the B-P space has the same structure as the R-C space in a SudokuP or SudokuPX. (the F-transform confirms it)
As a result, any pattern normally spotted in the R-C space could also be present in the B-P space. Let's call it the "boxed" version of these patterns.
This includes X-Wing, Swordfish, Jellyfish, skyscraper, 2-string kite, empty rectangle, and every other type of turbot, finned, sashimi and franken fish. (in B-P space, the rows become the boxes)

I am currently implementing some of these in my solver and will hopefully have some examples soon.

Happy New Year to all,
Ruud
Ruud from Sudocue

Posts: 14
Joined: 10 December 2021

### Re: Sudoku-DG with 11 clues

Ruud from Sudocue wrote:But I would like to check if any other forum members have noticed that the B-P space has the same structure as the R-C space in a SudokuP or SudokuPX. (the F-transform confirms it)

True indeed. I think blue pointed this out originally ...

Mathimagics
2017 Supporter

Posts: 1921
Joined: 27 May 2015
Location: Canberra

### Re: Sudoku-DG with 11 clues

Thanks for the confirmation, Mathimagics.

As promised, here is an example. The first Boxed Swordfish found by my solver:

Box positions (1,6,8) have all the candidates for digit 8 in boxes (6,8,9), eliminating 6 surplus candidates.

The Sudoku-P puzzle: 090500100080060040000000007600300000005001000900020000701000000000000000000000509

Without the boxed techniques, my solver suggested 2 Sue De Coq, some coloring steps and an empty rectangle. Others may have selected different techniques, but all of a higher order than simple fish.
Ruud from Sudocue

Posts: 14
Joined: 10 December 2021

### Re: Sudoku-DG with 11 clues

Hi, Ruud!
Ruud from Sudocue wrote:I did not find the code written by Serg (or description thereof) how to convert the ED grids to the min-lex format you used above. If you have a pointer to sample code for this conversion or an explanation of the steps to perform, I would appreciate it very much.

Are you currently need a code to convert Sudoku-DG (aka SudokuP) puzzles to minlex form? I have such canonicalizer, but the code is very primitive, i.e. ineffective.

Serg
Serg
2018 Supporter

Posts: 803
Joined: 01 June 2010
Location: Russia

### Re: Sudoku-DG with 11 clues

Thanks for the offer, Serg, but I figured it out with the posted samples. I am storing the puzzles locally in the format returned by sudokup_canonicalize_sp(). For exports I wanted to use the minlex format.

On the subject of B-P space: A "boxed" version of the skyscraper has now been implemented.

Puzzle: 100080007000700000040005006000000000200000000400000013700000030008000650300000000

Here is a skyscraper with 2 candidates each for digit 2 in position groups (6,7) with a weak link in box 9.
This technique is like a box of chocolates: you never know where eliminations will show up!
Ruud from Sudocue

Posts: 14
Joined: 10 December 2021

### Re: Sudoku-DG with 11 clues

Indeed, another chocolate, same puzzle but another X-chain of length 4 (2stringKite in stead of Skyscraper) with a weak link in a DG-group:
Hidden Text: Show
Code: Select all
`[1,1] r8c1=9 Naked Single[2,2] r3c1=8 Naked Single[3,3] r2c1=5 Naked Single[3,4] r4c1=6 Naked Single[4,5] r1c7=5 Hidden Single in row 7[4,6] r3c5=3 Hidden Single in row 5[4,7] r3c3=7 Hidden Single in row 3[4,8] r2c7=3 Hidden Single in col 2[4,9] r5c8=6 Hidden Single in col 5[4,10] r1c3=3 Hidden Single in box 3[4,11] r2c8=8 Hidden Single in box 5[4,12] r5c2=3 Hidden Single in box 5[4,13] r6c2=8 Hidden Single in box 8[4,14] r4c4=3 Hidden Single in box 1[4,15] r8c6=3 Hidden Single in box 6[4,16] r5c6=7 Hidden Single in sudokuP 5[5,17] r6c3=9 Naked Single[5,18] r6c6=2 Naked Single[5,19] r6c7=7 Naked Single[6,20] r4c2=7 Hidden Single in row 2[6,21] r8c5=7 Hidden Single in row 5[6,22] r9c8=7 Hidden Single in row 8[7,22] Naked/Hidden Pairs,Triplets,Quads  | NPair (15)c3r45 => (-15)r7c3 (-1)r9c3 | NTriple (145)c3r459 => (-4)r7c3 | NPair (56)b5e78 => (-5)r4c5 | NTriple (129)P7e239 => (-129)r9c4 | 1 (4)r9c3 => (-4)r9c6 (-4)r9c9 | NTriple (148)r9c369 => (-1)r9c7[8,23] r9c3=4 Naked Single[9,24] r3c7=1 Hidden Single in col 3[10,24] 2-String-Kite,SkyScraper,TurbotCrane  | 2-String Kite (1)r2c5=r2c6-r5c3=r4c3 => (-1)r4c5[11,24] Naked/Hidden Pairs,Triplets,Quads  | NTriple (249)P2e356 => (-29)r1c2 (-2)r7c2 (-249)r7c5stte`

2-String Kite (1)r2c5=r2c6-r5c3=r4c3 => (-1)r4c5
The link r2c6-r5c3 is in same DG

Hajime

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Joined: 20 April 2018
Location: Fryslân

### Re: Sudoku-DG with 11 clues

Sudoku P basics, then Row Skysrcaper (9) => - 9 r4c7, r7c9, then

Code: Select all
`*--------------------------------------------------*| 1 269  3  | 249   8     469  | 5     249   7     || 5 29   26 | 7     1249  1469 | 3     8     24-9  || 8 4    7  | 29    3     5    | 1    d29    6     ||-----------+------------------+-------------------|| 6 7    15 | 3     19    1489 | 248   24-9  24589 || 2 3    15 | 148  b149   7    | 48    6    a459   || 4 8    9  | 56    56    2    | 7     1     3     ||-----------+------------------+-------------------|| 7 1256 26 | 2489  12569 1489 | 2489  3     1248  || 9 12   8  | 14    7     3    | 6     5     124   || 3 256  4  | 56   c2569  18   | 29    7     18    |*--------------------------------------------------*`

Row/P House Skyscraper (9) r5c9 = r5c5 - r9c5 = (9) r3c8 => - 9 r2c9, r4c8; lclste

Leren
Leren

Posts: 4648
Joined: 03 June 2012

### Re: Sudoku-DG with 11 clues

These are all X-chains of length 4 that I could find:

2-String Kite (1)r2c5=r2c6-r5c3=r4c3 => (-1)r4c5 |
Turbot Crane (1)r2c6=r2c5-r7c5=r7c2 => (-1)r7c6 |
Skyscraper (1)r4c3=r4c6-r9c6=r9c9 => (-1)r7c9 |
2-String Kite (2)r2c3=r7c3-r8c2=r8c9 => (-2)r2c9 |
X-Chain [4] (2)r2c3=r8c9-r9c7=r3c4 => (-2)r2c5 |
2-String Kite (2)r3c4=r3c8-r9c5=r7c5 => (-2)r7c4 |
X-Chain [4] (2)r3c8=r1c8-r7c5=r9c5 => (-2)r9c2 |
Turbot Crane (2)r7c3=r2c3-r2c2=r8c2 => (-2)r7c2 |
X-Chain [4] (2)r7c5=r9c5-r3c8=r1c8 => (-2)r1c2 (-2)r4c8 |
Turbot Crane (4)r1c8=r2c9-r8c9=r8c4 => (-4)r1c4 |
2-String Kite (9)r1c2=r2c2-r5c5=r5c9 => (-9)r4c8 |
Skyscraper (9)r2c2=r1c2-r1c8=r3c8 => (-9)r2c9 |
Skyscraper (9)r5c9=r5c5-r9c5=r9c7 => (-9)r7c9 (-9)r4c7

Hajime

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Location: Fryslân