Jigsaw + Windoku + X

For fans of Killer Sudoku, Samurai Sudoku and other variants

Re: Jigsaw + Windoku + X

Postby urhegyi » Thu Feb 18, 2021 7:24 pm

The search for new layouts continues:
arriving at 9 clues JSWX example:
Image
attention windoku windows not marked on picture
Code: Select all
7.......35.......4......................2......................1.......98.......6 444111122444111222544112266543332266555333666558833376558899776888999777889999777

Edit:
The one I posted before with 10 clues was much harder, but I posted thisone for the nice form and the fact it has only 9 clues the numbers from 1 to 9!
Looks easy but will know more after trying it by hand. When looking at the number of eliminations by naked/hidden quad it can be more difficult to solve by hand then I thought.
This can be an interesting one to keep with a nice solvepath?
Code: Select all
Eliminated candidates per Method and per Sudoku

Method   \  Sudoku |   SER |     1
                   |-------|------
Not counted elims  |     0 |    98
Naked Singles      |   0.1 |    18
Hidden Singles     |   0.2 |   127
Naked Single  [1]  |   2.5 |     2
Naked Pair    [2]  |     3 |    13
Naked Quad    [4]  |     5 |     6
Hidden Quad   [5]  |   5.4 |    42
Hidden Pair   [7]  |   3.4 |     6
Locked Singles[2]  |   2.8 |    90
Locked Singles[3]  |   2.9 |    20
Locked Singles[4]  |     3 |    20
                   |-------|------
Eliminated Cand's  |   442 |   442
Sum(SER * Cand's)  | 718.4 | 718.4

Initial Candidates :   442
Maximum SER rating :   5.4 - Approach
Labour rating      : 718.4 - Experimental rating

But this layout permits also very hard ones like:
Code: Select all
#1/WX/B4,JS
............7.8..............5...7..4.7...6.1..6...9..............3.6............
444111122444111222544112266543332266555333666558833376558899776888999777889999777

Code: Select all
Eliminated candidates per Method and per Sudoku

Method   \  Sudoku |   SER |     1
                   |-------|------
Not counted elims  |     0 |    86
Naked Singles      |   0.1 |    34
Hidden Singles     |   0.2 |   146
Naked Pair    [2]  |     3 |    10
Naked Triple  [3]  |   3.6 |    10
Hidden Quad   [5]  |   5.4 |     4
Locked Singles[2]  |   2.8 |    76
Locked Singles[3]  |   2.9 |    13
Locked Singles[4]  |     3 |     8
Locked Singles[5]  |   3.1 |     1
WXYZ Wing     [4]  |   5.5 |     5
VWXYZ Wing    [5]  |   6.3 |     1
Turbot-fish   [4]  |   4.2 |     5
                   |-------|------
Eliminated Cand's  |   399 |   399
Sum(SER * Cand's)  | 452.6 | 452.6

Initial Candidates :   399
Maximum SER rating :   6.3 - Approach
Labour rating      : 452.6 - Experimental rating

Can the rating of 6.3 be confirmed by SE?
Last edited by urhegyi on Thu Feb 18, 2021 8:11 pm, edited 1 time in total.
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JSWX SE Ratings

Postby 1to9only » Thu Feb 18, 2021 8:10 pm

Code: Select all
.6.4.2.8..............1...................................3..............2.8.7.9. 111222233111123338114422238444552338475555538477655888476668899477769999776666999 JSWX ED=7.9/7.9/2.9

7.......35.......4......................2......................1.......98.......6 444111122444111222544112266543332266555333666558833376558899776888999777889999777 JSWX ED=7.7/7.7/2.8

............7.8..............5...7..4.7...6.1..6...9..............3.6............ 444111122444111222544112266543332266555333666558833376558899776888999777889999777 JSWX ED=7.1/1.5/1.5

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Re: Jigsaw + Windoku + X

Postby Hajime » Fri Feb 19, 2021 9:05 am

urhegyi wrote:
Code: Select all
7.......35.......4......................2......................1.......98.......6 444111122444111222544112266543332266555333666558833376558899776888999777889999777

Edit:
The one I posted before with 10 clues was much harder, but I posted thisone for the nice form and the fact it has only 9 clues the numbers from 1 to 9!

Indeed a very nice layout/puzzle with all 9 givens symmetrical.
And when omitting the naked/hidden quad it is still possible to solve with basic methods and locked singles (generalized intersections).
Code: Select all
Method   \  Sudoku |   SER |     1
                   |-------|------
Not counted elims  |     0 |    98
Naked Singles      |   0.1 |    18
Hidden Singles     |   0.2 |   127
Naked Single  [1]  |   2.5 |     2
Naked Pair    [2]  |     3 |    19
Naked Triple  [3]  |   3.6 |     4
Hidden Pair   [7]  |   3.4 |     8
Locked Singles[2]  |   2.8 |   126
Locked Singles[3]  |   2.9 |    20
Locked Singles[4]  |     3 |    20
                   |-------|------
Eliminated Cand's  |   442 |   442
Sum(SER * Cand's)  | 601.6 | 601.6

Initial Candidates :   442
Maximum SER rating :   3.6 <- Approach
Labour rating      : 601.6 <- Experimental rating
Time needed        : 00:00:02.204


The elimination of candidates is shifted to locked singles.
Especially the singles locked in 4 ! houses that eliminated 20 candidates will be hard.

Maybe that rating should not be "3" , but much higher.
What is the highest rated method in SE (with ED=7.7) ?
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Re: Jigsaw + Windoku + X

Postby 1to9only » Fri Feb 19, 2021 12:51 pm

The ED=7.7 and ED=7.9 are Nishio Forcing Chains.
The ED=7.1 is a Bidirectional Cycle.

Interestingly, the 2 in r5c5 can be removed to make an 8-clues JSWX:
Code: Select all
7.......35.......4.............................................1.......98.......6 444111122444111222544112266543332266555333666558833376558899776888999777889999777 JSWX ED=9.1/9.0/2.8

The ED=9.x are Cell/Region/Double/Conradiction Forcing Chains.
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Re: Jigsaw + Windoku + X

Postby urhegyi » Fri Feb 19, 2021 1:53 pm

Hajime wrote:
urhegyi wrote:
Code: Select all
7.......35.......4......................2......................1.......98.......6 444111122444111222544112266543332266555333666558833376558899776888999777889999777

Edit:
The one I posted before with 10 clues was much harder, but I posted thisone for the nice form and the fact it has only 9 clues the numbers from 1 to 9!

Indeed a very nice layout/puzzle with all 9 givens symmetrical.
And when omitting the naked/hidden quad it is still possible to solve with basic methods and locked singles (generalized intersections).
Code: Select all
Method   \  Sudoku |   SER |     1
                   |-------|------
Not counted elims  |     0 |    98
Naked Singles      |   0.1 |    18
Hidden Singles     |   0.2 |   127
Naked Single  [1]  |   2.5 |     2
Naked Pair    [2]  |     3 |    19
Naked Triple  [3]  |   3.6 |     4
Hidden Pair   [7]  |   3.4 |     8
Locked Singles[2]  |   2.8 |   126
Locked Singles[3]  |   2.9 |    20
Locked Singles[4]  |     3 |    20
                   |-------|------
Eliminated Cand's  |   442 |   442
Sum(SER * Cand's)  | 601.6 | 601.6

Initial Candidates :   442
Maximum SER rating :   3.6 <- Approach
Labour rating      : 601.6 <- Experimental rating
Time needed        : 00:00:02.204


The elimination of candidates is shifted to locked singles.
Especially the singles locked in 4 ! houses that eliminated 20 candidates will be hard.

Maybe that rating should not be "3" , but much higher.
What is the highest rated method in SE (with ED=7.7) ?

Even the Naked triple isn't needed:
The reduced analysis for the 9 clues variant:
Code: Select all
Eliminated candidates per Method and per Sudoku

Method   \  Sudoku |   SER |     1
                   |-------|------
Not counted elims  |     0 |    98
Naked Singles      |   0.1 |    18
Hidden Singles     |   0.2 |   127
Naked Single  [1]  |   2.5 |     6
Naked Pair    [2]  |     3 |    19
Hidden Pair   [7]  |   3.4 |     8
Locked Singles[2]  |   2.8 |   126
Locked Singles[3]  |   2.9 |    20
Locked Singles[4]  |     3 |    20
                   |-------|------
Eliminated Cand's  |   442 |   442
Sum(SER * Cand's)  | 597.2 | 597.2

Initial Candidates :   442
Maximum SER rating :   3.4 - Approach
Labour rating      : 597.2 - Experimental rating
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Re: Jigsaw + Windoku + X

Postby urhegyi » Mon Feb 22, 2021 2:42 pm

A very hard new example with a new layout:
Code: Select all
#1/WX/B4,JS
7.......3....................61.92.....9.3.....32.48....................5.......6
112222255111222555111125555666649999666444999766444998777434888777333888773333388

Can SE confirm the rating of 8+ found by SiSeSuSo?
Or a slightly adapted layout with an example a bit less hard as the one before:
Code: Select all
#1/WX/B4,JS
....9........3........8......4...2..8..243..5..6...7......7........6........2....
332222244333222444333121444355111664555111666555516666777789999777888999778888899

Rated 5.0 by SiseSuSo but it counts Turbot-fish as 4.2 so I guess SE will give 6.6?
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Re: JSWX SE Ratings

Postby urhegyi » Mon Feb 22, 2021 5:34 pm

1to9only wrote:
Code: Select all
.6.4.2.8..............1...................................3..............2.8.7.9. 111222233111123338114422238444552338475555538477655888476668899477769999776666999 JSWX ED=7.9/7.9/2.9

7.......35.......4......................2......................1.......98.......6 444111122444111222544112266543332266555333666558833376558899776888999777889999777 JSWX ED=7.7/7.7/2.8

............7.8..............5...7..4.7...6.1..6...9..............3.6............ 444111122444111222544112266543332266555333666558833376558899776888999777889999777 JSWX ED=7.1/1.5/1.5


Using the extra hidden constraints of windoku would considerably reduce this ratings!
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Re: Jigsaw + Windoku + X

Postby Hajime » Tue Feb 23, 2021 9:48 am

urhegyi wrote:Rated 5.0 by SiseSuSo but it counts Turbot-fish as 4.2 so I guess SE will give 6.6?

This is what is listed in SE Rating here
Code: Select all
    '3.6, 3.8, 4.0: Naked Triplet, Swordfish, Hidden Triplet
    '4.0-4.3: Skyscraper, 2-String Kite, Turbot Crane
    '4.2, 4.4: XY-Wing, XYZ-Wing

So Turbot Fish is about 4.2 , isn't ?
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Re: Jigsaw + Windoku + X

Postby urhegyi » Thu Feb 25, 2021 7:30 pm

In the original SE rating there are no skyscrapers, kites, cranes only Turbot-Fish (verity or contradiction) with a rating of 6.6.
Because SE don't know of WXYZ-wing I think this example will be rated 7.1 or so.
Can this be confirmed?
Code: Select all
#1/WX/B4,JS
...5.1................4....35.....67.........28.....56....1................4.5...
444478888444477788111477788111373782113333322196363222996665222996665555999965555

Code: Select all
Eliminated candidates per Method and per Sudoku

Method   \  Sudoku |   SER |     1
                   |-------|------
Not counted elims  |     0 |    95
Naked Singles      |   0.1 |    23
Hidden Singles     |   0.2 |   155
Locked Singles[2]  |   2.8 |    43
Locked Singles[3]  |   2.9 |    13
Locked Singles[4]  |     3 |    12
Locked Singles[5]  |   3.1 |     5
WXYZ Wing     [4]  |   5.5 |     4
Turbot-fish   [4]  |   4.2 |     8
                   |-------|------
Eliminated Cand's  |   358 |   358
Sum(SER * Cand's)  | 298.5 | 298.5

Initial Candidates :   358
Maximum SER rating :   5.5 - Approach
Labour rating      : 298.5 - Experimental rating

This example was constructed without generalized intersection methods and without WXYZ-wings. So it must be solvable with 4.2 rating(SiSeSuSo) or 6.6 rating(SE).
This is the SiSeSuSo log after disabling wings and Locked Singles. Only pointing/claiming, subsets and turbot-fish allowed:
Code: Select all
Eliminated candidates per Method and per Sudoku

Method   \  Sudoku |   SER |     1
                   |-------|------
Not counted elims  |     0 |   125
Naked Singles      |   0.1 |    42
Hidden Singles     |   0.2 |   107
Naked Pair    [2]  |     3 |     4
Naked Triple  [3]  |   3.6 |     8
Locked Singles[2]  |   2.8 |    60
Turbot-fish   [4]  |   4.2 |    12
                   |-------|------
Eliminated Cand's  |   358 |   358
Sum(SER * Cand's)  | 284.8 | 284.8

Initial Candidates :   358
Maximum SER rating :   4.2 - Approach
Labour rating      : 284.8 - Experimental rating

Now I'm very interested in the SE approach of the story.
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Re: Jigsaw + Windoku + X

Postby 1to9only » Fri Feb 26, 2021 11:46 am

urhegyi wrote:In the original SE rating there are no skyscrapers, kites, cranes only Turbot-Fish (verity or contradiction) with a rating of 6.6.
Because SE don't know of WXYZ-wing I think this example will be rated 7.1 or so.

From past ratings, SE substitutes/solves these using Forcing Chains and Nishio Forcing Chains.
Code: Select all
...5.1................4....35.....67.........28.....56....1................4.5... JSWX ED=7.6/1.5/1.5

444478888444477788111477788111373782113333322196363222996665222996665555999965555

Difficulty rating: 7.6
This Windoku Jigsaw can be solved using the following logical methods:
64 x Hidden Single (1.0-1.5)
1 x Direct Pointing (1.7)
2 x Direct Claiming (1.9)
6 x Cage Pointing (2.6)
14 x Claiming (2.8)
18 x Generalized Intersection (2.9)
4 x Forcing Chain (7.1-7.2)
1 x Aligned Triplet Exclusion (7.5)
1 x Nishio Forcing Chains (7.6)

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Re: Jigsaw + Windoku + X

Postby urhegyi » Fri Feb 26, 2021 11:08 pm

Another example which generates very quickly:
Code: Select all
#1/WX/B4,JS
.6.....8............5...1............3.5.9.6............4...9............7.....3.
111222233112223333411253363411256666445555566444457996848857996888877799887777999
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Re: Jigsaw + Windoku + X

Postby urhegyi » Sun Feb 28, 2021 7:14 pm

I found a nice JSWX example with only 10 clues and solvable by turbot-fish and xy-chains.
SiseSuso takes its time to calculate, but finds a solvepath.
What about SE?
Code: Select all
#1/WX/B4,JS
...................3.....6....9.8...8.......2...2.5....7.....4...................
441118833444118333441118833441888893699999993697777255667722255666722555667722255

analyse log:
Code: Select all
Eliminated candidates per Method and per Sudoku

Method   \  Sudoku |   SER |     1
                   |-------|------
Not counted elims  |     0 |   109
Hidden Singles     |   0.2 |   247
Locked Singles[2]  |   2.8 |    59
Locked Singles[3]  |   2.9 |     6
Turbot-fish   [4]  |   4.2 |     4
XY-chain      [4]  |   4.6 |     2
                   |-------|------
Eliminated Cand's  |   427 |   427
Sum(SER * Cand's)  |   258 |   258

Initial Candidates :   427
Maximum SER rating :   4.6 - Approach
Labour rating      :   258 - Experimental rating

hints:
Hidden Text: Show
Code: Select all
Generalized Intersection  | (4)/r2c5 => (-4)r2c5 | (4)W7c9 => (-4)r1c9 | (3)/r8c5 => (-3)r8c5 | (3)W8J6 => (-3)r9c1 | (3)r9c7W6 => (-3)r5c7 | (4)J1c3W5 => (-4)r5c3
2-string-Kite,SkyScraper,TurbotCrane  |
X-Chain [4]  (3) r1c9=r5c5-r8c8=r8c4 => (-3)r1c4 |
Turbot Crane (3) r5c3=r5c5-r2c5=r1c3 => (-3)r6c3 |
Skyscraper (4) r2c6=r2c2-r5c5=r5c7 => (-4)r9c6 |
Skyscraper (4) r4c2=r2c2-r2c6=r3c6 => (-4)r4c7
XY_Chain W  |  (3=1)r1c9 (1=4)r3c9 (4=1)r3c6 (1=3)r4c7 [4] => (-3)r4c9
XY_Chain J  |  (4=1)r6c3 (1=3)r7c4 (3=1)r7c1 (1=4)r9c1 [4] => (-4)r6c1

Code: Select all
#1/WX/B4,JS
7...9...3...................1.....2...........8.....1...................4...5...6
441118833444118333441118833441888893699999993697777255667722255666722555667722255

Analyze log:
Code: Select all
Eliminated candidates per Method and per Sudoku

Method   \  Sudoku |   SER |     1
                   |-------|------
Not counted elims  |     0 |    88
Naked Singles      |   0.1 |    49
Hidden Singles     |   0.2 |    97
Naked Pair    [2]  |     3 |     7
Naked Triple  [3]  |   3.6 |     4
Naked Quad    [4]  |     5 |     7
Locked Singles[2]  |   2.8 |   107
Locked Singles[3]  |   2.9 |    13
Locked Singles[4]  |     3 |    18
Locked Singles[5]  |   3.1 |     9
Turbot-fish   [4]  |   4.2 |    18
XY-chain     [11]  |   7.3 |     4
                   |-------|------
Eliminated Cand's  |   421 |   421
Sum(SER * Cand's)  | 618.7 | 618.7

Initial Candidates :   421
Maximum SER rating :   7.3 - Approach
Labour rating      : 618.7 - Experimental rating
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Re: Jigsaw + Windoku + X

Postby urhegyi » Mon Mar 01, 2021 11:21 am

A long time ago I did some tests with JSWX and the H-layout which wasn't working. Now I have found out why. I did 2 little swaps on the layout which is now JSWX compliant.
examples:
Code: Select all
#1/WX/B4,JS
..9...4......................39.46....5...3....82.15......................2...1..
111223333112223333112225663411525666444555666444585996744588899777788899777788999

solution:
Hidden Text: Show
Code: Select all
619327485457682913724193856283954671145876329978231564836519247591468732362745198
111223333112223333112225663411525666444555666444585996744588899777788899777788999

Code: Select all
#1/WX/B4,JS
.........45.....13...1.3.....3...6.............8...5.....5.9...59.....32.........
111223333112223333112225663411525666444555666444585996744588899777788899777788999

solution:
Hidden Text: Show
Code: Select all
619327485457682913724193856283954671145876329978231564836519247591468732362745198
111223333112223333112225663411525666444555666444585996744588899777788899777788999
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Re: Jigsaw + Windoku + X

Postby Hajime » Mon Mar 01, 2021 3:56 pm

urhegyi wrote:
Code: Select all
#1/WX/B4,JS
.........45.....13...1.3.....3...6.............8...5.....5.9...59.....32.........
111223333112223333112225663411525666444555666444585996744588899777788899777788999

14 Turbots fish of length 4. Amazing. Is that a record?
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Re: Jigsaw + Windoku + X

Postby urhegyi » Mon Mar 01, 2021 6:16 pm

What do you think of thisone?
Code: Select all
#1/WX/B4,JS
.1.....8.4.......3..................1.......9..................5.......2.6.....9.
111223333112223333112225663411525666444555666444585996744588899777788899777788999

It's the first time I see a locked singles[6]!
Then those wings and the number of turbot-fishes makes this a hard nut to crack.
Analyze log:
Code: Select all
Eliminated candidates per Method and per Sudoku

Method   \  Sudoku |   SER |     1
                   |-------|------
Not counted elims  |     0 |    97
Naked Singles      |   0.1 |    33
Hidden Singles     |   0.2 |   104
Naked Single  [1]  |   2.5 |     4
Naked Pair    [2]  |     3 |     7
Naked Triple  [3]  |   3.6 |     8
Hidden Triple [6]  |     4 |    29
Hidden Pair   [7]  |   3.4 |     5
Locked Singles[2]  |   2.8 |    68
Locked Singles[3]  |   2.9 |    22
Locked Singles[4]  |     3 |    24
Locked Singles[5]  |   3.1 |    17
Locked Singles[6]  |   3.2 |     2
XYZ Wing      [3]  |   4.4 |     2
WXYZ Wing     [4]  |   5.5 |     4
UVWXYZ Wing   [6]  |   6.6 |     3
Turbot-fish   [4]  |   4.2 |    24
                   |-------|------
Eliminated Cand's  |   453 |   453
Sum(SER * Cand's)  | 753.6 | 753.6

Initial Candidates :   453
Maximum SER rating :   6.6 - Approach
Labour rating      : 753.6 - Experimental rating
urhegyi
 
Posts: 539
Joined: 13 April 2020

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