## Difficult Windoku

For fans of Killer Sudoku, Samurai Sudoku and other variants

### Difficult Windoku

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?
urhegyi

Posts: 96
Joined: 13 April 2020

### Re: Difficult Windoku

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.
1to9only

Posts: 2119
Joined: 04 April 2018

### Re: Difficult Windoku

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 colGeneralized Intersection  | (4)W2r2b3 => (-4)r2c9 | (5)c8r6b6W4 => (-5)r6c7 | (5)r6c9W8 => (-5)r8c9   30   6   7   8   Naked Single   31   8   9   8   Naked SingleXY_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`

Hajime

Posts: 230
Joined: 20 April 2018
Location: Netherlands

### Re: Difficult Windoku

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.
urhegyi

Posts: 96
Joined: 13 April 2020

### Re: Difficult Windoku

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 boxNaked/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 boxPointing, Claiming  | (1)J4r8 => (-1)r8c9 | (2)J4r8 => (-2)r8c9Generalized 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 SingleXY_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 colXY_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`

Hajime

Posts: 230
Joined: 20 April 2018
Location: Netherlands

### Re: Difficult Windoku

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.
urhegyi

Posts: 96
Joined: 13 April 2020

### Re: Difficult Windoku

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.

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.
1to9only

Posts: 2119
Joined: 04 April 2018

### Re: Difficult Windoku

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.
urhegyi

Posts: 96
Joined: 13 April 2020

### Re: Difficult Windoku

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

m_b_metcalf
2017 Supporter

Posts: 11305
Joined: 15 May 2006
Location: Berlin

### Re: Difficult Windoku

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.
urhegyi

Posts: 96
Joined: 13 April 2020

### Re: Difficult Windoku

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

Posts: 96
Joined: 13 April 2020

### Re: Difficult Windoku

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.
urhegyi

Posts: 96
Joined: 13 April 2020