## Jigsaw Twodoku

For fans of Killer Sudoku, Samurai Sudoku and other variants

### Jigsaw Twodoku

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

Posts: 538
Joined: 13 April 2020

### Re: Jigsaw Twodoku

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.
urhegyi

Posts: 538
Joined: 13 April 2020

### Re: Jigsaw Twodoku

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.
1to9only

Posts: 3416
Joined: 04 April 2018

### Re: Jigsaw Twodoku

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

Posts: 325
Joined: 20 January 2018

### Re: Jigsaw Twodoku

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.
urhegyi

Posts: 538
Joined: 13 April 2020

### Re: Jigsaw Twodoku

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
urhegyi

Posts: 538
Joined: 13 April 2020

### Re: Jigsaw Twodoku

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 (108.07 KiB) Viewed 396 times

What have to be the digits in grid 2 that correspond to the symmetry?
urhegyi

Posts: 538
Joined: 13 April 2020

### Re: Jigsaw Twodoku

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.
1to9only

Posts: 3416
Joined: 04 April 2018

### Re: Jigsaw Twodoku

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 1362194857983541276816725934157468392235679418698312    745  386 <- block 9 rotated 180 degrees574836    129  921421957    683  547456728931   -> remap    681937254 <- grid 2932147685      numbers  253469178    this can be rotated 180 degrees764831529               916754832319685472               542178693683592147               175823469275914863               398246715891376    254 -> 386    724591    386148253    796    921    467385    921527469    318    547    839612    547`
1to9only

Posts: 3416
Joined: 04 April 2018

### Re: Jigsaw Twodoku

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

Posts: 538
Joined: 13 April 2020

### Re: Jigsaw Twodoku

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

Posts: 538
Joined: 13 April 2020

### Re: Jigsaw Twodoku

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.

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..... 111112222113122244333155224633555554633355444667777744668777999668788999688888999grid 2:.....6.3....583..........27.......93.64........6...24.23.....1....9..3....2...... 999888886999887866999777866447777766444553336455555336422551333442221311222211111`
1to9only

Posts: 3416
Joined: 04 April 2018

### Re: Jigsaw Twodoku

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 (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 (19.91 KiB) Viewed 354 times
urhegyi

Posts: 538
Joined: 13 April 2020

### Re: Jigsaw Twodoku

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   . | .   .   .   .   . |                        +---------------+-------------------+`
urhegyi

Posts: 538
Joined: 13 April 2020

### Re: Jigsaw Twodoku

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 (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 (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
Joined: 13 April 2020

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