The New Sudoku Players' Forum

[urhegyi]

twodoku1.jpg (61.81 KiB) Viewed 996 times

Any tips on how to solve overlapping variants like these?

[urhegyi]

I found how, but it won't be easy:

[1to9only]

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.

[creint]

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

[urhegyi]

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]

twodoku11.jpg (61.27 KiB) Viewed 964 times

Another with the same jigsaw shape(it seems this shape is popular or easy to generate): both grids are solvable with singles

[urhegyi]

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 955 times

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

[1to9only]

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]

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



[urhegyi]

grid1:

Code: Select all

749283561362194857983541276816725934157468392235679418698312745574836129421957683 111112222114122233444155223644555553644455333667777733668777999668788999688888999

[urhegyi]

grid2:

Code: Select all

745216938129583764683195427517642893964328571396871245238457619871964352452739186 111222224111223244111333244553333344555669994566666994577668999557778988777788888

[1to9only]

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


[urhegyi]

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 913 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 913 times

[urhegyi]

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]

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 874 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 874 times

Code: Select all

......9.....583.6.........7...6..8..9...2..7..9......523......9..1..4.....2...... 999888886999887866999777866447777766444553336455555336422551333442221311222211111