## 3d Sudoku

For fans of Killer Sudoku, Samurai Sudoku and other variants

### 3d Sudoku

I developed my own version of 3d sudoku because everything I could find online seemed gimmicky, whereas this is (in my opinion) a true generalisation of sudoku to three dimensions. While regular sudoku has vertical columns and horizontal rows, my 3d sudoku adds what I decided to call towers for lack of a better description, which are essentially the same as rows and columns, just in the perpendicular direction.

Each number 1-8 must be used exactly once in each row, column and "tower" (I visualise the different layers on top of each other, and so it would appear to stick out from the ground like a tower when rested on a flat surface) and 2x2x2 box. In the image attached I drew each layer of the 8x8x8 cube next to eachother and connected them by arrows that mean that one is on top of or below the next. The two 8x8 square layers next to eachother share a 2x2x2 box.

Despite my best efforts, what I drew is not, strictly, an extension of sudoku into 3 dimensions, but rather an extension of 4x4 sudoku into 3 dimensions. To extend regular 9x9 sudoku into 3 dimensions I would need to draw a 27x27x27 cube containing nearly 20,000 cells as opposed to the 512 of my 8x8x8 sudoku or the mere 81 of regular sudoku.

I thought of it just a few hours ago and spent the time since them drawing it, writing this and writing something similar on a reddit post, so I don't know whether the regular strategies will continue to apply. Singles definitely will, and I think doubles, triples and quads will still apply, but I can't easily visualise pointing pairs and box-line reduction in three dimensions, nor X-Wings and other more complicated tactics. I suspect that most methods of working out sudokus will either work in my 3d sudoku or have a close analogue in my 3d sudoku, but that is just conjecture.

I couldn't attach the image because of the file size, so here's a website that I uploaded it to instead. https://imgur.com/a/HDMuCZ2
Last edited by 3dsudoku on Wed Mar 13, 2019 6:21 am, edited 1 time in total.
3dsudoku

Posts: 4
Joined: 11 March 2019

### Re: 3d Sudoku

In case someone want to try to manually solve a different grid:
Singles only, should be very easy
Hidden Text: Show
Code: Select all
`. . . . 4 2 . .   . 2 . 1 . . . .. . 8 . . . . .   3 . . . . . . 66 . . . . . . .   . . . . . . 5 .. . . . . . . .   . . . . . 7 . .. . . . 8 . . .   . . . . . . 3 .. 1 . 2 . . . .   . . . 6 . . . .. . . . . 8 . .   . . 5 . . . . 3. . . . 5 . . .   . . . 8 . . 2 .                                 7 5 . 6 . . . .   . . . . . . . .. . . . . . . .   . . . . 8 . . .. . . 8 1 3 . .   . . 2 . . 7 . .. . . . 2 . . .   . 4 1 . . . . .. . . . . . . .   . . . . . . 4 .4 . . . . . . 5   . . 7 . 4 2 3 .. . . . . . . .   . . . . . . . .2 . . 3 . 8 . .   . . . . . . . .                                 . . 5 . . . . 3   . . . . . 8 . .5 . 6 . . . . .   . 3 . 4 . . . .. . . . . . . 1   . . 3 . . . . .. . . . 3 . 4 .   . . . . . . . .2 . 1 . 6 . . 7   . 8 . . . . . .. . . . . . . .   5 . . . . . . .. . . . 8 . . .   . . . . . 2 3 .. . 4 2 . . 8 .   . . . . . 1 . .                                 . . . . 1 . . .   . . . . . . . 8. 8 . 7 . . . .   2 . . . 6 . . .. . . . . . . 2   . 1 . . . 5 . .8 6 . . . . 3 .   . . . . . . 7 .1 . 2 4 . . . .   5 . . . . 3 . .. . . . . . . .   . . . . . . 1 .. . . . 7 . 8 .   . . 8 . . . . .. . . . . . . 5   . 6 . . . . . .                                 `

Very easy to generate more.
creint

Posts: 160
Joined: 20 January 2018

### Re: 2x2x2 3d Sudoku

This thread definitely has an extra dimension to it as it literally disappeared before re-appearing again a few days later.

1st of all, well done & best of luck in your attempts to popularize this sudoku variant.

A 3D explanatory post will go a long way to help explain what this variant is about (a cube to demonstrate your concept will be great.)

I like the idea of the 2x2x2 box but IMO this thing about it which I like the most is essentially the most challenging to bring out to manual solvers. A single cell will directly see cells in many different grids. This will suit better a fancy app where you can flip/rotate the cube to see your cell and the effects it has.

The concept IMO should stay at the 2x2x2 level and shouldn't go to 3x3x3 (27x27 Cube face) or to 4x4x4 (The lovely 64x64 cube face).

There are enough constraints IMO for you to be able to present the cube using a 3 face only cube puzzle as I demonstrated in my WYSIWYG 3D sudoku. This would allow you to show a cube with 3 faces containing all the clues.

The manual solver would still need 24 grids to work around the cube in 2D nevertheless! IMO you need to show each grid with the 2x2 squares clearly separated from the rest of the cells & I would even suggest having different colours, one for each of the 2x2x2 boxes so it can be easily migrated into the 2x2 squares in the 2d grids

In the few years after 2005, sudoku became so popular to a degree that I wouldn’t be surprised if your concepts has been visited by others several times. I’ve seen so many variations of the sudoku cube that I lost count. I’m not sure if you have read or seen an app exploring a sudoku cube puzzle variation called Kuboku. From the brief descriptions I found it sounds and looks very similar which doesn’t surprise me.

I made an effort to unify terminology & coordinates in such puzzles which IMO is better than describing lines in a band/stack/tower terminology but this is your variant & your effort which means you're free to dictate your rules.

Here are some of the links:
http://forum.enjoysudoku.com/re-introducing-the-sudoku-cube-3d-sudoku-sudoku3d-9-9-9-t30044.html
http://forum.enjoysudoku.com/tarek-s-sudoku-cube-puzzles-sudoku-3d-sudoku3d-t30045.html
http://forum.enjoysudoku.com/kuboku-the-real-3d-sudoku-t6159.html#p58592
http://www.kuboku.com
tarek

tarek

Posts: 3531
Joined: 05 January 2006

### Re: 3d Sudoku

I logged back on to update this and say that I found it had been done earlier by Hideki Tsuiki and Yasuyuki Tsukamoto*, but the kuboku website that Tarek provided the link for is older still.

I would also like to reassess my earlier statement about strategies for solving this. I am no longer of the belief that the only strategies are simply the same as in regular 9x9 sudoku, but rather that they will be significantly more complicated. More advanced wings, for instance, may utilize the additional third dimension.

I am currently working on determining whether X-wings and swordfishes will work properly in this 3d sudoku, and whether they are “less effective” with the extra dimensions to worry about.
3dsudoku

Posts: 4
Joined: 11 March 2019

### Re: 3d Sudoku

An old and badly maintained website regarding 3D Sudoku
http://www.realsudoku3d.com
SudoKai

Posts: 43
Joined: 07 June 2014
Location: South-Africa

### Re: 3d Sudoku

3dsudoku wrote:I would also like to reassess my earlier statement about strategies for solving this. I am no longer of the belief that the only strategies are simply the same as in regular 9x9 sudoku, but rather that they will be significantly more complicated. More advanced wings, for instance, may utilize the additional third dimension.

I am currently working on determining whether X-wings and swordfishes will work properly in this 3d sudoku, and whether they are “less effective” with the extra dimensions to worry about.

I think the logic will remain the same but there will be a challenge when you try to visualise an intersecting 3d box with a line on a 2d grid. So, short of the kuboku 3d app which you can flip turn & slice IMO for a 2d representation, you would need two 8x8 grids appearing next to each other with the 2x2x2 box appearing as 2 2x2 squares for each grid with the same colour code (or shade). With 64 boxes in your 8x8x8 3d sudoku, colour coding is a challenge by itself so consider the above as me thinking out loud rather than giving you a concrete brilliant idea

tarek

Posts: 3531
Joined: 05 January 2006

### Re: 3d Sudoku

Yeah, X-Wings still work, and by the same logic, so do Swordfishes, Jellyfishes, etc. The only issue with them is that they are still two-dimensional strategies, and so only effect things on a plane. Take this excerpt of a grid (cube?):

Code: Select all
`. . a . . . . .     . . . . . . . .. . a . . a . .     . . a . . . . .. . . . . . . .     . . . . . . . .. . . . . . . .     . . . . . . . .. . a . . a . .     . . . . . . . .. . . . . a . .     . . . . . . . .. . . . . . . .     . . . . . . . .`

Where anything with a represents a place where there is a candidate A that can go there, pencilled in rather than just where a is. There is an X-wing on the layer on the left which can eliminate two candidates, but it is unable to eliminate the candidate on-top of it, represented on the grid to the right.

I think that there's a way to connect multiple X-Wings on various layers utilising the third dimension, perhaps an X-Wing cube with 8 cells or some such, but I haven't worked out the logic of that just yet, and it is extremely difficult as I have so far been working entirely on pen-and-paper. I'd download kuboku (as it seems to have an identical ruleset to my 3d sudoku), but unfortunately, my computer runs OSX instead of Linux or Windows.
3dsudoku

Posts: 4
Joined: 11 March 2019

### Re: 3d Sudoku

Coding basic fish on a 2d plane is only part of fish logic. If you look st the UFG, This extends to franken and mutant fish which should cover regions outside your single grid because the logic still holds. I didn’t even mention fins or Obi-Wahn’s fish logic which should also hold for any sudoku variant too. Jsudoku coded fish that covers variants under generalised “fish”. Because Hudoku coded the fish catcher embracing the UFG, it would require only minor tweaks on that to suit variants including 3d sudoku.

You will find all these complex techniques which you mention “wings, chains, fish, sets, ... etc” coded in most variant solvers under “generalised” or “complex” but they follow an extension of the same logic as the basic technique 1st described in vanilla sudoku.

Tarek

tarek

Posts: 3531
Joined: 05 January 2006

### Re: 3d Sudoku

3dsudoku wrote:...I think that there's a way to connect multiple X-Wings on various layers utilising the third dimension...

Perhaps a free 3D Software application like Blender will assist you in your efforts.
http://blender.org/

I am not an expert on advanced solving techniques but I think this makes an X-Wing cube.

xwing_cube_colour.jpg (36.17 KiB) Viewed 318 times
SudoKai

Posts: 43
Joined: 07 June 2014
Location: South-Africa

### Re: 3d Sudoku

But it's very rare to find one X-Wing cube. I have not seen many 3d sudoku that are rated hard.
It is possible to design a puzzle that contains the X-Wing cube but to create one were it is the first easiest tactic would be almost impossible.
You only need 2 fishes not covering each other. More will result in less possible exclusions.
You find 2 fishes, you do the exclusions and then you find max 2 fishes again on the same 8 points.
For X-Wings redundant tactic, and looking further the same for larger fishes.
creint

Posts: 160
Joined: 20 January 2018