Difficult Windoku

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Difficult Windoku

Postby urhegyi » Tue Oct 27, 2020 9:37 am

122859418_2775466659377122_8562093601238633413_n.png
122859418_2775466659377122_8562093601238633413_n.png (44.77 KiB) Viewed 168 times
I have found a windoku that really keeps me struggeling. After the basics and applaying the hidden constraints of windoku, I have to try other methods like coloring or contradiction and xy-wing or xy-chain. Is there someone who can give a way to start after the basics without having to apply the hidden constraints and perhaps a less complicated way of solving like I did?
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Re: Difficult Windoku

Postby 1to9only » Tue Oct 27, 2020 11:09 am

Image
After singles, my modified SE 1.2.1.3 shows a UR type 4 (above image), and a turbot fish follows (ED=6.6/1.2/1.2).
I think SukakuExplainer 1.17.11 solves this differently.
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Re: Difficult Windoku

Postby Hajime » Tue Oct 27, 2020 11:17 am

    3 candidate elimination using Generalized Intersection.
    one XY-chain (Windoku not involved) to elinate two "9"s.
    Rest is hidden/naked singles, BUT the hidden constraints of windoku are needed.
Possible Solution path:
Hidden Text: Show
Code: Select all
Step Row Col Val Why
   1   7   2   5   Naked Single
   2   7   3   2   Naked Single
   3   5   2   9   HS in col
   4   5   4   7   HS in col
   5   5   5   6   HS in col
   6   6   8   6   HS in col
   7   1   9   7   HS in col
   8   4   4   5   HS in box
   9   2   4   2   HS in windoku
   10   8   4   3   HS in windoku
   11   8   2   6   HS in windoku
   12   6   2   7   HS in windoku
   13   8   1   7   HS in windoku
   14   7   1   1   Naked Single
   15   7   5   9   Naked Single
   16   7   8   4   Naked Single
   17   9   1   4   Naked Single
   18   9   3   8   Naked Single
   19   3   3   7   HS in row
   20   4   3   6   HS in row
   21   7   7   3   HS in row
   22   2   3   3   HS in col
   23   3   5   3   HS in col
   24   6   6   9   HS in col
   25   5   6   8   HS in box
   26   1   1   9   Naked Single
   27   6   5   2   Naked Single
   28   9   7   9   HS in row
   29   4   5   1   HS in col
Generalized Intersection  | (4)W2r2b3 => (-4)r2c9 | (5)c8r6b6W4 => (-5)r6c7 | (5)r6c9W8 => (-5)r8c9
   30   6   7   8   Naked Single
   31   8   9   8   Naked Single
XY_Chain  |  (9=5)r2c9 (5=8)r2c1 (8=2)r4c1 (2=9)r4c8 [4] => (-9)r2c8 (-9)r4c9
   32   2   9   9   HS in row
   33   4   8   9   HS in row
   34   6   9   5   HS in col
   35   1   7   5   HS in box
   36   5   3   5   HS in box
   37   5   9   3   HS in box
   38   8   8   5   HS in box
   39   1   3   4   HS in windoku
   40   5   7   4   HS in windoku
   41   3   9   4   HS in windoku
   42   2   1   5   HS in windoku
   43   4   1   8   HS in windoku
   44   6   1   3   HS in windoku
   45   9   9   1   HS in windoku
   46   5   1   2   HS in windoku
   47   4   2   4   Naked Single
   48   4   9   2   Naked Single
   49   5   8   1   Naked Single
   50   8   7   2   Naked Single
   51   9   4   6   Naked Single
   52   9   6   2   Naked Single
   53   1   4   1   HS in row
   54   1   6   6   HS in row
   55   2   2   1   HS in row
   56   2   6   4   HS in row
   57   2   8   8   HS in row
   58   3   7   1   HS in row
   59   3   8   2   HS in row
   60   3   2   8   HS in row
   61   8   6   1   HS in row
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Re: Difficult Windoku

Postby urhegyi » Tue Oct 27, 2020 12:09 pm

1to9only wrote:After singles, my modified SE 1.2.1.3 shows a UR type 4 (above image), and a turbot fish follows (ED=6.6/1.2/1.2).
I think SukakuExplainer 1.17.11 solves this differently.

What I did was take R6C7 as 5 which eliminates 5 from R8C78(in window)so R8C9 must be 5 and R2C9 can't be 5 and R2C1 must be 5.
This leads to R1C3 must be 4 and eliminates 4 from R1C67(pair 1/6) and gives R1C7 =5 which is in contradiction with R6C7=5, so r6c7 must be 8!
This eliminates 8 from R8C78 so R8C9 must be 8 and R3C9 can't be 8 =(2/4).
So I found an xy-wing R4c1=(2/8), R4C2=(4/8) and R3C9=(2/4).
When I take R3c9=2 then R3C78 can't be 2 and R4C8 must be 2(in window).
This leads to R4C1=8 and R4C2=4.
In the other case R3C9=4. So R3c9 must be 4 or R4C2 must be 4, or both.R3C2 and R4C9 which can see both begin and endpoints can't be 4.
With that the rest solves with singles.
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Re: Difficult Windoku

Postby Hajime » Tue Oct 27, 2020 12:19 pm

Actually there is a solution without the windoku constraints.
Imagine the 4 visible regions as 4 jigsaw pieces. The rest is a vanilla sudoku.
Now you need 2 XY-chains, one of length 6 and one of length 4.

Hidden Text: Show
Code: Select all
Step Row Col Value Why
   1   7   2   5   Naked Single
   2   7   3   2   Naked Single
   3   5   2   9   HS in col
   4   5   4   7   HS in col
   5   4   4   5   HS in box
   6   2   4   2   HS in jigsaw
   7   8   4   3   HS in jigsaw
   8   7   7   3   HS in row
   9   3   5   3   HS in col
   10   2   3   3   HS in jigsaw
   11   7   8   4   HS in jigsaw
   12   7   1   1   Naked Single
   13   7   5   9   Naked Single
   14   6   6   9   HS in col
   15   5   6   8   HS in box
Naked/Hidden Pairs,Triplets,Quads  | NSS (67)c2r68 => (-7)r3c2 (-6)r4c2
   16   4   3   6   HS in jigsaw
   17   3   3   7   HS in jigsaw
   18   8   2   6   HS in jigsaw
   19   6   2   7   HS in jigsaw
   20   6   8   6   HS in jigsaw
   21   6   5   2   Naked Single
   22   1   9   7   HS in row
   23   5   5   6   HS in row
   24   8   1   7   HS in row
   25   9   3   8   HS in col
   26   4   5   1   HS in col
   27   9   1   4   HS in box
Pointing, Claiming  | (1)J4r8 => (-1)r8c9 | (2)J4r8 => (-2)r8c9
Generalized Intersection  | (4)J2r2b3 => (-4)r2c9 | (1)J2r2b3 => (-1)r2c9 | (5)c8r6b6J4 => (-5)r6c7 | (5)J4b9 => (-5)r8c9
   28   6   7   8   Naked Single
   29   8   9   8   Naked Single
XY_Chain  |  (9=5)r1c1 (5=4)r1c3 (4=5)r5c3 (5=3)r6c1 (3=5)r6c9 (5=9)r2c9 [6] => (-9)r2c1
   30   1   1   9   HS in col
   31   9   7   9   HS in col
XY_Chain  |  (9=5)r2c9 (5=8)r2c1 (8=2)r4c1 (2=9)r4c8 [4] => (-9)r2c8 (-9)r4c9
   32   2   9   9   HS in row
   33   4   8   9   HS in row
   34   1   7   5   HS in box
   35   8   8   5   HS in box
   36   1   3   4   Naked Single
   37   5   3   5   Naked Single
   38   6   1   3   Naked Single
   39   6   9   5   Naked Single
   40   2   6   4   HS in row
   41   2   1   5   HS in row
   42   3   9   4   HS in row
   43   4   2   4   HS in row
   44   4   1   8   HS in row
   45   5   9   3   HS in row
   46   5   7   4   HS in row
   47   5   1   2   HS in col
   48   3   8   2   HS in col
   49   2   8   8   HS in col
   50   9   9   1   HS in col
   51   4   9   2   HS in col
   52   3   2   8   HS in box
   53   3   7   1   HS in box
   54   5   8   1   HS in box
   55   8   6   1   HS in box
   56   9   6   2   HS in box
   57   9   4   6   HS in box
   58   8   7   2   HS in box
   59   2   2   1   HS in jigsaw
   60   1   4   1   Naked Single
   61   1   6   6   Naked Single
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Re: Difficult Windoku

Postby urhegyi » Tue Oct 27, 2020 12:38 pm

2020-10-27.png
2020-10-27.png (91.68 KiB) Viewed 146 times
I pasted this string in Jigsaw explainer:
Code: Select all
.2..8..3.....7.6..6..9.5........37.............14........8.7..6..9.4.....3..5..7. 955596669711172227711172227711172227955596669833384448833384448833384448955596669

I will be surprised what's the result of this.
Because it don't know the 9 normal boxes from a vanilla sudoku it will have multiple solutions. This program considers the rules of a Latin square.
When implementing the sudoku rueles into it, I think it will be possible to make a Windoku solver from it.
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Re: Difficult Windoku

Postby 1to9only » Tue Oct 27, 2020 2:48 pm

urhegyi wrote:I pasted this string in Jigsaw explainer:
Code: Select all
.2..8..3.....7.6..6..9.5........37.............14........8.7..6..9.4.....3..5..7. 955596669711172227711172227711172227955596669833384448833384448833384448955596669

I will be surprised what's the result of this.
Because it don't know the 9 normal boxes from a vanilla sudoku it will have multiple solutions. This program considers the rules of a Latin square.
When implementing the sudoku rueles into it, I think it will be possible to make a Windoku solver from it.

AFAIK, (of the free downloadable solvers) only SukakuExplainer 1.17.x solves the windoku.
Download 1.17.7 from: https://github.com/SudokuMonster/SukakuExplainer/releases
Or download a later version 1.17.11 I built from: https://github.com/1to9only/SukakuExplainerPlus/releases

The currently pre-released SudokuJigsawExplainer will show multiple solutions. I have a version with JSB (jigsaw + blocks) enabled, but I have not used it for a couple months, it had new features added recently and not much testing done. As it's still using SE 1.2.1.3 techniques, I think after singles it will show the UR type 4 as the next step.
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Re: Difficult Windoku

Postby urhegyi » Tue Oct 27, 2020 4:28 pm

I tested it with version 1.17.7 from sukakuexplainer and it confirms my solution in post from 12.09 pm. What I did with contradiction is in fact generalized intersection which removes 5 from R6C7. Then it shows the xy-wing, which is the same as what I described in my earlier post. Nice my work from yesterday is confirmed by the solver.
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Re: Difficult Windoku

Postby m_b_metcalf » Sun Nov 01, 2020 10:13 am

urhegyi wrote:I have found a windoku that really keeps me struggeling.

I'd just like to point out that this puzzle is not minimal. The following clues are individually redundant: r3c1, r4c6, r4c7, r6c4, r8c5, r9c8, and various subsets of them can be removed, as here
Code: Select all
 . 2 . . 8 . . 3 .
 . . . . 7 . 6 . .
 . . . 9 . 5 . . .
 . . . . . . 7 . .
 . . . . . . . . .
 . . 1 4 . . . . .
 . . . 8 . 7 . . 6
 . . 9 . . . . . .
 . 3 . . 5 . . . .   4 clues removed -> minimal windoku


Regards,

Mike
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Re: Difficult Windoku

Postby urhegyi » Sun Nov 22, 2020 5:34 pm

2020-11-22 (2).png
2020-11-22 (2).png (93.4 KiB) Viewed 43 times
The new version of JSB explainer also finds the xy-wing and not more the UR type 4.
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Re: Difficult Windoku

Postby urhegyi » Sun Nov 22, 2020 5:39 pm

2020-11-22 (3).png
2020-11-22 (3).png (92.95 KiB) Viewed 41 times
Or the same as windoku:
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Re: Difficult Windoku

Postby urhegyi » Mon Nov 23, 2020 8:58 am

2020-11-23 (1).png
2020-11-23 (1).png (98.94 KiB) Viewed 18 times
When I remove the 4 clues like Mike Metcalf suggested it keeps it's ER 4.2 and stays human solvable.
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