Jigsaw Twodoku

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Jigsaw Twodoku

Postby urhegyi » Mon Nov 30, 2020 10:58 pm

twodoku1.jpg
twodoku1.jpg (61.81 KiB) Viewed 437 times
Any tips on how to solve overlapping variants like these?
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Re: Jigsaw Twodoku

Postby urhegyi » Mon Nov 30, 2020 11:10 pm

I found how, but it won't be easy:
Last edited by urhegyi on Mon Dec 14, 2020 3:43 pm, edited 1 time in total.
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Re: Jigsaw Twodoku

Postby 1to9only » Mon Nov 30, 2020 11:44 pm

In grid 1, in (overlapping) block 9, eliminate candidates from givens in grid 2 -> results in naked single r8c8=9. The grid solves with singles.
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Re: Jigsaw Twodoku

Postby creint » Tue Dec 01, 2020 8:18 pm

Can be solved using only hidden singles. Using a solver is an option.
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Re: Jigsaw Twodoku

Postby urhegyi » Tue Dec 01, 2020 8:45 pm

creint wrote:Can be solved using only hidden singles. Using a solver is an option.

A solver can be used to detect if one or more of the grids are solvable on it's own, but I prefer solving them by hand. When looking better I see now that the only possible value for R8C8=9, as 1to9only suggested too. I don't know how I could miss something that is so obvious, perhaps I was tired as it was late. I suppose not all of the Jigsaw Twodokus have a complete solvable grid, but it was my first thought to look for, instead of looking for singles in the overlapping area.
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Re: Jigsaw Twodoku

Postby urhegyi » Tue Dec 01, 2020 9:28 pm

twodoku11.jpg
twodoku11.jpg (61.27 KiB) Viewed 405 times
Another with the same jigsaw shape(it seems this shape is popular or easy to generate): both grids are solvable with singles
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Re: Jigsaw Twodoku

Postby urhegyi » Tue Dec 01, 2020 10:46 pm

Looking closer at the two examples: the given digits in grid 1 from left to right and up down come in exactly the same position in grid 2 but then from right to left and down up, so they are mirrored. Is there a way when generating grid 1 to determine the coresponding digits in grid 2 to make the twodoku valid?
So I generate this grid1:
2020-12-01 (6).png
2020-12-01 (6).png (108.07 KiB) Viewed 396 times

What have to be the digits in grid 2 that correspond to the symmetry?
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Re: Jigsaw Twodoku

Postby 1to9only » Tue Dec 01, 2020 11:27 pm

urhegyi wrote:Is there a way when generating grid 1 to determine the coresponding digits in grid 2 to make the twodoku valid?

JigsawExplainer generates random grids, dont think it can be used to generate 2 jigsaws with the same pattern of givens. If this were possible, block 9 would be empty or have a symmetry of givens, and grid 2 would have to be rotated 180 degrees. E.g. the 1st twodoku:
Code: Select all
grid 1:         grid 2: rotated:

..5...9..       ..4...7..
.3.164.2.       .5.781.3.
6.......4       8.......4
.5.....8.       .4.....8.
.4..9..6.       .7..6..2.
.8.....5.       .2.....7.
3........       9........
.2.457...       .3.142...
..6......       ..3......


I would probably write custom code to generate such jigsaw twodoku. Either as noted above, or as a 15x15 grid containing both sudokus and removing clues symmetrially.
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Re: Jigsaw Twodoku

Postby 1to9only » Wed Dec 02, 2020 12:01 am

Generating 2 solution grids for the jigsaw twodoku is relatively easy!
Generate 2 grids, keep solutions, for grid 2, the numbers need remapping, and the grid rotated. E.g.
Code: Select all
749283561 <- grid 1
362194857
983541276
816725934
157468392
235679418
698312    745  386 <- block 9 rotated 180 degrees
574836    129  921
421957    683  547

456728931   -> remap    681937254 <- grid 2
932147685      numbers  253469178    this can be rotated 180 degrees
764831529               916754832
319685472               542178693
683592147               175823469
275914863               398246715
891376    254 -> 386    724591    386
148253    796    921    467385    921
527469    318    547    839612    547

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Re: Jigsaw Twodoku

Postby urhegyi » Wed Dec 02, 2020 12:57 am

grid1:
Code: Select all
749283561362194857983541276816725934157468392235679418698312745574836129421957683 111112222114122233444155223644555553644455333667777733668777999668788999688888999
Last edited by urhegyi on Wed Dec 16, 2020 12:20 am, edited 2 times in total.
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Re: Jigsaw Twodoku

Postby urhegyi » Wed Dec 02, 2020 12:59 am

grid2:
Code: Select all
745216938129583764683195427517642893964328571396871245238457619871964352452739186 111222224111223244111333244553333344555669994566666994577668999557778988777788888
Last edited by urhegyi on Wed Dec 16, 2020 12:21 am, edited 1 time in total.
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Re: Jigsaw Twodoku

Postby 1to9only » Wed Dec 02, 2020 3:44 pm

You can run the 2 Explainers with the 2 solution grids, side-by-side, remove clues symmetrically, checking that the jigsaws are still valid each time, E.g.
Image

This still makes the jigsaws solvable on their own!
Code: Select all
+-------------------+---------------+
| .   .   .   .   . | .   5   .   . |
|       +---+   +---+       +-------+
| .   . | 2 | . | .   4   . | .   . |
+-------+   |   +-------+   +---+   |
| .   8   . | . | .   . | .   7 | 6 |
+---+       +---+       +-------+   |
| . | 1   6 | .   .   .   9   . | . |
|   |       +---+       +-------+   |
| . | .   .   . | .   . | 3   9   . |
|   +---+-------+-------+---+       |
| 2   3 | .   .   .   .   . | .   . |
|       +---+           +---+-------+-------------------+---+
| 6   9 | . | .   .   . | .   .   . | .   .   6   .   3 | . |
|       |   |   +-------+           |       +---+   +---+   |
| .   . | . | 8 | 3   6 | .   .   . | 5   8 | 3 | . | .   . |
|   +---+   +---+       |           +-------+   |   |       |
| . | 2   .   9   .   . | .   .   . | .   .   . | . | 2   7 |
+---+-------------------+-------+---+           +---+       |
                        | .   . | .   .   .   .   . | 9   3 |
                        |       +---+-------+-------+---+   |
                        | .   6   4 | .   . | .   .   . | . |
                        |   +-------+       +---+       |   |
                        | . | .   6   .   .   . | 2   4 | . |
                        |   +-------+       +---+       +---+
                        | 2 | 3   . | .   . | . | .   1   . |
                        |   +---+   +-------+   |   +-------+
                        | .   . | .   9   . | . | 3 | .   . |
                        +-------+       +---+   +---+       |
                        | .   .   2   . | .   .   .   .   . |
                        +---------------+-------------------+

For matching jigsaw colors!:
Code: Select all
grid 1:
......5....2..4....8.....76.16...9........39.23.......69..........836....2.9..... 111112222113122244333155224633555554633355444667777744668777999668788999688888999
grid 2:
.....6.3....583..........27.......93.64........6...24.23.....1....9..3....2...... 999888886999887866999777866447777766444553336455555336422551333442221311222211111
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Re: Jigsaw Twodoku

Postby urhegyi » Wed Dec 02, 2020 5:06 pm

This makes the Jigsaws solvable on their own. In principe I can confirm this but I found an 18 clues example with rating 11.5 and 3.0 for both grids.
grid1:
Code: Select all
......5.....1..8..9......7681...........6..92..5..9...6.........7.836............ 111112222113122244333155224633555554633355444667777744668777999668788999688888999

grid-01.png
grid-01.png (20.44 KiB) Viewed 354 times

grid2:
Code: Select all
............583.6.........7...6..8..96..2...........4523......9..1..4.....2...... 999888886999887866999777866447777766444553336455555336422551333442221311222211111

grid-02.png
grid-02.png (19.91 KiB) Viewed 354 times
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Re: Jigsaw Twodoku

Postby urhegyi » Wed Dec 02, 2020 5:53 pm

Code: Select all
+-------------------+---------------+
| .   .   .   .   . | .   5   .   . |
|       +---+   +---+       +-------+
| .   . | . | 1 | .   .   8 | .   . |
+-------+   |   +-------+   +---+   |
| 9   .   . | . | .   . | .   7 | 6 |
+---+       +---+       +-------+   |
| 8 | 1   . | .   .   .   .   . | . |
|   |       +---+       +-------+   |
| . | .   .   . | 6   . | .   9   2 |
|   +---+-------+-------+---+       |
| .   . | 5   .   .   9   . | .   . |
|       +---+           +---+-------+-------------------+---+
| 6   . | . | .   .   . | .   .   . | .   .   .   .   . | . |
|       |   |   +-------+           |       +---+   +---+   |
| .   7 | . | 8 | 3   6 | .   .   . | 5   8 | 3 | . | 6   . |
|   +---+   +---+       |           +-------+   |   |       |
| . | .   .   .   .   . | .   .   . | .   .   . | . | .   7 |
+---+-------------------+-------+---+           +---+       |
                        | .   . | .   6   .   .   8 | .   . |
                        |       +---+-------+-------+---+   |
                        | 9   6   . | .   2 | .   .   . | . |
                        |   +-------+       +---+       |   |
                        | . | .   .   .   .   . | .   4 | 5 |
                        |   +-------+       +---+       +---+
                        | 2 | 3   . | .   . | . | .   .   9 |
                        |   +---+   +-------+   |   +-------+
                        | .   . | 1   .   . | 4 | . | .   . |
                        +-------+       +---+   +---+       |
                        | .   .   2   . | .   .   .   .   . |
                        +---------------+-------------------+
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Re: Jigsaw Twodoku

Postby urhegyi » Thu Dec 03, 2020 3:19 pm

Today I did some more experiments with the same solution grids. Yesterday's example had respectively ratings 11.5 and 3.0. So I started solving with the second grid. I wondered if the first grid is always the hardest and human unsolvable due to the concept of creating the solution grids. It isn't always the case. I found an 19 clues example today with respectively ratings 2.9 and 11.2. What seems to be so remarkable at this example is that solving the first grid and putting the overlapping digits in the second one reduces the 11.2 rating to 2.9 and not to singles. So it's still hard to solve.
grid1:
03-12-19c-01.png
03-12-19c-01.png (21.09 KiB) Viewed 315 times

Code: Select all
......5.....1..8..9......768......3..5..6...2..5..9...6.........7.836.....1...... 111112222113122244333155224633555554633355444667777744668777999668788999688888999

grid2:
03-12-19c-03.png
03-12-19c-03.png (20.98 KiB) Viewed 315 times

Code: Select all
......9.....583.6.........7...6..8..9...2..7..9......523......9..1..4.....2...... 999888886999887866999777866447777766444553336455555336422551333442221311222211111
urhegyi
 
Posts: 538
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