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ED=1.9/1.9/1.9 SixySudoku puzzle

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ED=1.9/1.9/1.9 SixySudoku puzzle

Postby 1to9only » Sun Dec 08, 2019 12:06 pm

This puzzle uses the same SixySudoku constraints from post#1 here:

Code: Select all
+-----------+-----------+
| .   .   1 | 2   .   . |
+---+   +---+---+   +---+
| . | 3 | .   4 | . | . |
|   |   |       |   |   |
| . | . | 5   . | . | . |
|   |   |       |   |   |
| . | . | .   . | . | . |
|   +---+-------+---+   |
| .   . | .   . | .   . |
|   +---+       +---+   |
| . | .   .   .   . | . |
+---+---------------+---+

Code: Select all
+----------------------------+--------------------------+
|  456       456      1      | 2        356      356    |
+---------+         +--------+--------+        +--------+
|  256    |  3      | 26       4      | 156    | 156    |
|         |         |                 |        |        |
| *12346  |  246    | 5        136    | 1346   | 12346  |
|         |         |                 |        |        |
| *12346  |  246    | 236      136    | 13456  | 123456 |
|         +---------+-----------------+--------+        |
| *123456   -12456  | 2346     1356   | 123456   123456 |
|         +---------+                 +--------+        |
| *123456 | =12456    2346     1356     123456 | 123456 |
+---------+------------------------------------+--------+

Code: Select all
..12...3.4....5..................... SIXY ED=1.9/1.9/1.9
..12...3.4....5................1.... 1.9, Direct Claiming: Cells R3C1,R4C1,R5C1,R6C1: 1 of column in cage

r6c2=r1c3 always, and r6c5=r1c4 as well.
.
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Re: ED=1.9/1.9/1.9 SixySudoku puzzle

Postby urhegyi » Thu Feb 04, 2021 11:46 pm

Here are two more of them with the same pattern : difficulty 5 stars from the free Peter Ritmeester e-book:
Sudoku_Sixy_Wacky_free_E-pagina's-16-1.png
Sudoku_Sixy_Wacky_free_E-pagina's-16-1.png (68.65 KiB) Viewed 971 times

I understand now the LOL(law of leftovers technique) which makes it a lot easier.
Solution of the first one:
Hidden Text: Show
Code: Select all
251463
364152
542316
136524
425631
613245

Solution of the second one:
Hidden Text: Show
Code: Select all
165432
234561
641253
523614
416325
352146
Last edited by urhegyi on Fri Feb 05, 2021 1:00 pm, edited 3 times in total.
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Re: ED=1.9/1.9/1.9 SixySudoku puzzle

Postby urhegyi » Thu Feb 04, 2021 11:57 pm

Thisone from a post of Hajime came to my attention today:
Image
Same rules as 6x6 jigsaw and 2X3 blocks.
I was able to solve it without the knowledge of the two extra constraints.
solution:
Hidden Text: Show
Code: Select all
625143
431526
542361
316452
164235
253614
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Re: ED=1.9/1.9/1.9 SixySudoku puzzle

Postby urhegyi » Fri Feb 05, 2021 2:34 pm

1to9only wrote:This puzzle uses the same SixySudoku constraints from post#1 here:

Code: Select all
+-----------+-----------+
| .   .   1 | 2   .   . |
+---+   +---+---+   +---+
| . | 3 | .   4 | . | . |
|   |   |       |   |   |
| . | . | 5   . | . | . |
|   |   |       |   |   |
| . | . | .   . | . | . |
|   +---+-------+---+   |
| .   . | .   . | .   . |
|   +---+       +---+   |
| . | .   .   .   . | . |
+---+---------------+---+

Code: Select all
+----------------------------+--------------------------+
|  456       456      1      | 2        356      356    |
+---------+         +--------+--------+        +--------+
|  256    |  3      | 26       4      | 156    | 156    |
|         |         |                 |        |        |
| *12346  |  246    | 5        136    | 1346   | 12346  |
|         |         |                 |        |        |
| *12346  |  246    | 236      136    | 13456  | 123456 |
|         +---------+-----------------+--------+        |
| *123456   -12456  | 2346     1356   | 123456   123456 |
|         +---------+                 +--------+        |
| *123456 | =12456    2346     1356     123456 | 123456 |
+---------+------------------------------------+--------+

Code: Select all
..12...3.4....5..................... SIXY ED=1.9/1.9/1.9
..12...3.4....5................1.... 1.9, Direct Claiming: Cells R3C1,R4C1,R5C1,R6C1: 1 of column in cage

r6c2=r1c3 always, and r6c5=r1c4 as well.
.

solution:
Hidden Text: Show
Code: Select all
541236
632415
125643
463152
254361
316524
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6x6 Jigsaw Blocks (JSBs)

Postby 1to9only » Fri Feb 05, 2021 3:30 pm

It's been over a year since I looked at these sixy (regular) sudokus and (wacky!) jigsaws.
The 2 '5-stars' jigsaws from the e-book are hardly that! Both are rated ED=3.0, needing a naked pair to solve.
As I recall, the free version of the app came with a number of jigsaw types, type 1 being 3Rx2C blocks.
For regular sixy sudokus, I posted a solver here.

The wacky jigsaws are essentially JSBs. I generated this a year ago:
Image
Code: Select all
.2........3.4.......6...........5... 111222113322413325443355446655466665

Analysis (without Generalized Intersections), ED=6.6: Show
26 x Hidden Single
1 x Direct Claiming
1 x Direct Hidden Pair
3 x Naked Single
6 x Pointing
4 x Claiming
2 x X-Wing
3 x XY-Wing
2 x XYZ-Wing
1 x Generalized X-Wing
2 x Forcing X-Chain

Analysis (with Generalized Intersections), ED=4.2: Show
28 x Hidden Single
1 x Direct Hidden Pair
2 x Naked Single
6 x Pointing
6 x Claiming
9 x Generalized Intersection
1 x X-Wing
1 x Hidden Pair
1 x XY-Wing

Here are some non-symmetric sixy jigsaws I made:
Image
Code: Select all
......3.....6....54....3......2...36 112333112334512434512444552266556666

Analysis, ED=4.2: Show
28 Hidden Single
2 Pointing
2 X-Wing
1 XY-Wing

Image
Code: Select all
....4...4.......2......15.....3..... 112222111123444423544333555663556666

Analysis, ED=6.6: Show
28 Hidden Single
2 Direct Claiming
2 Pointing
1 Claiming
1 X-Wing
1 XY-Wing
1 Turbot Fish

Finally, here is a real '5-star' hard sixy jigsaw:
Image
Code: Select all
......6..........1......3......5.2.. 122233111233141223444443555566556666

Analysis, ED=7.1: Show
30 Hidden Single
1 Naked Single
12 Pointing
7 Claiming
11 Generalized Intersection
4 Naked Pair
2 Naked Triplet
3 XY-Wing
1 XYZ-Wing
1 BUG type 2
1 Generalized X-Wing
1 Bidirectional Y-Cycle
1 Forcing Chain

Forum post: here, I posted a SixySolver: here. It will brute-force solve a sixy sudoku (including jigsaws).
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Re: ED=1.9/1.9/1.9 SixySudoku puzzle

Postby urhegyi » Fri Feb 05, 2021 5:47 pm

sixy.gen02.66.png
sixy.gen02.66.png (11.16 KiB) Viewed 931 times

I applied a few times the law of leftovers and a generalized form of remote pair and came to this
solution:
Hidden Text: Show
Code: Select all
263145
154362
415623
632451
541236
326514
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Re: ED=1.9/1.9/1.9 SixySudoku puzzle

Postby urhegyi » Sat Feb 06, 2021 5:00 pm

Solved thisone with x-wing and xy-wing:
sixy.gen01.42.png
sixy.gen01.42.png (11.23 KiB) Viewed 909 times

Solution:
Hidden Text: Show
Code: Select all
542361
361524
613245
425613
136452
254136
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Re: ED=1.9/1.9/1.9 SixySudoku puzzle

Postby urhegyi » Sat Feb 06, 2021 11:05 pm

I found a site with 60 examples of a SixyWacky sudoku generated by a maple package(source available)
https://sites.math.rutgers.edu/~zeilberg/Sixy/Problems.html
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Re: ED=1.9/1.9/1.9 SixySudoku puzzle

Postby urhegyi » Tue Jan 17, 2023 6:01 pm

Today I was looking to sixy jigsaw sudoku's from Peter Ritmeester in a Dutch newspaper "De Telegraaf".
The hardest level wasn't hard at all, so I decided to look at the Jigsaw variant.
This was the 17 jan 2023 puzlle:
Image
After solving it on paper with pencilmarks I found some strange behaviour:
solution:
Code: Select all
314652
256143
563214
421536
142365
635421

The 56 pair at R2C23 moved to R3C12.
The 14 pair at R2C45 moved to R3C56.
The 42 pair at R5C23 moved to R4C12.
The 36 pair at R5C45 moved to R4C56.
Is this typical for this jigsaw design, or can it be explained through the law of leftovers?
If 1to9only has a generator for jigsaw, is it possible to generate another one with the same jigsaw design, so I can find out if this rule I found was coincidence or not.
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Postby 1to9only » Tue Jan 17, 2023 8:52 pm

urhegyi wrote:Is this typical for this jigsaw design, or can it be explained through the law of leftovers?
If 1to9only has a generator for jigsaw, is it possible to generate another one with the same jigsaw design, so I can find out if this rule I found was coincidence or not.

The law of leftovers will apply to many of the sixysudoku 'wacky' puzzles.
If my memory serves me right, there were 12 jigsaw types, of which 1 was duplicated - so only 11 jigsaw types. I'll post them here if I find them!
I've not tried, but I think the latest of my SudokuExplainers (2023.1.4) will generate these puzzles!! The 17 jan 2023 puzzle:
Code: Select all
3.4.....6............5.....3.......1
AAABBBACCCCBAACCBBDDEEFFDEEEEFDDDFFF
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Re: ED=1.9/1.9/1.9 SixySudoku puzzle

Postby urhegyi » Tue Jan 17, 2023 9:23 pm

Thank you,
I tried generating one:
Code: Select all
........62...............3..4.2....5
AAABBBACCCCBAACCBBDDEEFFDEEEEFDDDFFF
JSB
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Postby 1to9only » Wed Jan 18, 2023 8:59 am

1to9only wrote:If my memory serves me right, there were 12 jigsaw types, of which 1 was duplicated - so only 11 jigsaw types. I'll post them here if I find them!

grid_01 is the standard sixy sudoku, grid_03 and grid_08 are duplicates.
sixy sudoku layouts: Show
Code: Select all
+-------+-------+-------+       grid_01
| .   . | .   . | .   . |       112233112233112233445566445566445566
|       |       |       |
| .   . | .   . | .   . |
|       |       |       |
| .   . | .   . | .   . |
+-------+-------+-------+
| .   . | .   . | .   . |
|       |       |       |
| .   . | .   . | .   . |
|       |       |       |
| .   . | .   . | .   . |
+-------+-------+-------+

+-----------+-----------+       grid_02
| .   .   . | .   .   . |       111222113422133442533446553466555666
|       +---+---+       |
| .   . | . | . | .   . |
|   +---+   |   +---+   |
| . | .   . | .   . | . |
+---+       |       +---+
| . | .   . | .   . | . |
|   +---+   |   +---+   |
| .   . | . | . | .   . |
|       +---+---+       |
| .   .   . | .   .   . |
+-----------+-----------+

+-----------+-----------+       grid_03 (same as grid_08)
| .   .   . | .   .   . |       111222113322413325443355446655466665
|       +---+---+       |
| .   . | .   . | .   . |
+---+   |       |   +---+
| . | . | .   . | . | . |
|   +---+       +---+   |
| .   . | .   . | .   . |
|       +-------+       |
| .   . | .   . | .   . |
|   +---+       +---+   |
| . | .   .   .   . | . |
+---+---------------+---+

+-----------+-----------+       grid_04
| .   .   . | .   .   . |       111222314425314425314425336655366665
+---+   +---+---+   +---+
| . | . | .   . | . | . |
|   |   |       |   |   |
| . | . | .   . | . | . |
|   |   |       |   |   |
| . | . | .   . | . | . |
|   +---+-------+---+   |
| .   . | .   . | .   . |
|   +---+       +---+   |
| . | .   .   .   . | . |
+---+---------------+---+

+-----------+-----------+       grid_05
| .   .   . | .   .   . |       111222113322143352443355466665446655
|       +---+---+       |
| .   . | .   . | .   . |
|   +---+       +---+   |
| . | . | .   . | . | . |
+---+   |       |   +---+
| .   . | .   . | .   . |
|   +---+-------+---+   |
| . | .   .   .   . | . |
|   +---+       +---+   |
| .   . | .   . | .   . |
+-------+-------+-------+

+-----------+-----------+       grid_06
| .   .   . | .   .   . |       111222311224331244335644355664555666
+---+       |       +---+
| . | .   . | .   . | . |
|   +---+   |   +---+   |
| .   . | . | . | .   . |
|       +---+---+       |
| .   . | . | . | .   . |
|   +---+   |   +---+   |
| . | .   . | .   . | . |
+---+       |       +---+
| .   .   . | .   .   . |
+-----------+-----------+

+-----------+-----------+       grid_07
| .   .   . | .   .   . |       111222133442135642135642335644555666
|   +-------+-------+   |
| . | .   . | .   . | . |
|   |   +---+---+   |   |
| . | . | . | . | . | . |
|   |   |   |   |   |   |
| . | . | . | . | . | . |
+---+   |   |   |   +---+
| .   . | . | . | .   . |
+-------+   |   +-------+
| .   .   . | .   .   . |
+-----------+-----------+

+-----------+-----------+       grid_08 (same as grid_03)
| .   .   . | .   .   . |       111222113322413325443355446655466665
|       +---+---+       |
| .   . | .   . | .   . |
+---+   |       |   +---+
| . | . | .   . | . | . |
|   +---+       +---+   |
| .   . | .   . | .   . |
|       +-------+       |
| .   . | .   . | .   . |
|   +---+       +---+   |
| . | .   .   .   . | . |
+---+---------------+---+

+-----------+-----------+       grid_09
| .   .   . | .   .   . |       111222113422133442335644355664555666
|       +---+---+       |
| .   . | . | . | .   . |
|   +---+   |   +---+   |
| . | .   . | .   . | . |
+---+   +---+---+   +---+
| .   . | . | . | .   . |
|   +---+   |   +---+   |
| . | .   . | .   . | . |
+---+       |       +---+
| .   .   . | .   .   . |
+-----------+-----------+

+-----------+-----------+       grid_10
| .   .   . | .   .   . |       111222113322133332444555446655466665
|       +---+---+       |
| .   . | .   . | .   . |
|   +---+       +---+   |
| . | .   .   .   . | . |
+---+-------+-------+---+
| .   .   . | .   .   . |
|       +---+---+       |
| .   . | .   . | .   . |
|   +---+       +---+   |
| . | .   .   .   . | . |
+---+---------------+---+

+---+---------------+---+       grid_11 (is a variant of grid_02 rotated 90 degrees)
| . | .   .   .   . | . |       122223112233111333444555446655466665
|   +---+       +---+   |
| .   . | .   . | .   . |
|       +---+---+       |
| .   .   . | .   .   . |
+-----------+-----------+
| .   .   . | .   .   . |
|       +---+---+       |
| .   . | .   . | .   . |
|   +---+       +---+   |
| . | .   .   .   . | . |
+---+---------------+---+

+-----------+-----------+       grid_12
| .   .   . | .   .   . |       111222113322133332445566455556444666
|       +---+---+       |
| .   . | .   . | .   . |
|   +---+       +---+   |
| . | .   .   .   . | . |
+---+---+-------+---+---+
| .   . | .   . | .   . |
|   +---+       +---+   |
| . | .   .   .   . | . |
|   +-------+-------+   |
| .   .   . | .   .   . |
+-----------+-----------+

I've looked at some of the sixy sudokus on 'De Telegraaf', some layouts are variants of the above.
De Telegraaf layouts: Show
Code: Select all
+-----------+-----------+       2023_01_15 (is a variant of grid_06)
| .   .   . | .   .   . |       111222331244311224355664335644555666
+-------+   |   +-------+
| .   . | . | . | .   . |
|   +---+   |   +---+   |
| . | .   . | .   . | . |
|   +-------+-------+   |
| . | .   . | .   . | . |
|   +---+   |   +---+   |
| .   . | . | . | .   . |
+-------+   |   +-------+
| .   .   . | .   .   . |
+-----------+-----------+

+-----------+-----------+       2023_01_17 (is a variant of grid_12)
| .   .   . | .   .   . |       111222133332113322445566455556444666
|   +-------+-------+   |
| . | .   .   .   . | . |
|   +---+       +---+   |
| .   . | .   . | .   . |
+-------+-------+-------+
| .   . | .   . | .   . |
|   +---+       +---+   |
| . | .   .   .   . | . |
|   +-------+-------+   |
| .   .   . | .   .   . |
+-----------+-----------+

Some jigsaw layouts are a variant of this, in various combinations and rotations: Show
Code: Select all
+-------+-------+-------+
| .   . | .   . | .   . |
|   +---+       +---+   |
| . | .   .   .   . | . |
|   +-------+-------+   |
| .   .   . | .   .   . |
+-------+---+---+-------+
| .   . | .   . | .   . |
|   +---+       +---+   |
| . | .   .   .   . | . |
|   +-------+-------+   |
| .   .   . | .   .   . |
+-----------+-----------+
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