The New Sudoku Players' Forum

[Albania]

I have idea to remake my old rubik cube.
Make it whole white and add numbers to make it Sudoku 3D.

Is it possible to make it proper to solve like classic sudoku? No doubles in 3x3 + all horizontal lines + all vertical lines in 3D?
How to math this? And is it will be 1 solve only or multiple solves?
Someone could help me to math this and arrange on the grid? I'm beginner.

Here are some graphics for better understanding:

[Albania]

Here are layered Lines on the 3D Cube & Flattened Cube Grid:

[denis_berthier]

.
What you're asking is not clear.
About the constraints, do you mean two kinds of conditions:
1) side conditions:
- no doubles in any of the 2 horizontal and 4 vertical 3x3 sides
2) mini-lines conditions (version already guaranteed by the side conditions):
- no doubles in any of the 12 horizontal mini-rows of the 2 horizontal sides:
- no doubles in any of the 12 horizontal mini-columns of the 4 vertical sides
- no doubles in any of the 12 vertical mini-columns of the 4 vertical sides
or 2bis)
- no double for any couple of mini-lines with a common edge in any horizontal or vertical slice? (suggested by your 1st drawing; the last one conveys no information).
Moreover, your 1st drawing suggests only the external slices have this condition; what about the median slices?

About the ways of playing, do you mean only Rubik cube rotations are allowed?
Do you mean some cells may not be marked at the start?

About the global question, there are several stages to analyse:
1) are there any solutions?
2) how to find solutions if all the cells are marked at the start?
3) how to find solutions if not all the cells are marked at the start?

[Edit]: for some unknown reason, the second post was not visible when I answered. It makes my answer pointless.
However, regarding the long lines, how do you put 9 digits in 12 cells without repetitions?
.

[SudoKai]

The Sudoku you are describing is a Sudo-Kurve variant as well as an extension on perspective types.

[Albania]

However, regarding the long lines, how do you put 9 digits in 12 cells without repetitions?

Right! I didn't saw this. Thx! It's impossible! It looks like every line have 12 numbers.

So I looked around and there is a variation with 12 characters. There are numbers 1 - 9 & A, B, C letters.

Now. How this variation is called? 12x12 Sudoku? How I can implement it on a rubik cube flattened grid? This variation has squares 3x4. Rubik cube has 3x3.
So in this variation no doubles in 3x4 + all horizontal lines + all vertical lines on 12x12 grid. Which has 12*12=144 cells
But I wanna no doubles in 3x3 + all horizontal lines + all vertical lines on flattened cube grid. Which has 6*9=54 cells

Is there any advanced sudoku maker software or online with this 12x12 variation where I can built sudoku on different grids or check is there no doubles in lines etc.?

[Albania]

The Sudoku you are describing is a Sudo-Kurve variant as well as an extension on perspective types.

Thx for the info SudoKai. But it looks like Sudo-Kurve variant can't be implemented on physical 3D cube in the way I want. There is like second line from row on side is connected with first line on top etc. You can do this on the computer program and it will show you visualization of it on flattened grid & highlight different lines on 3D cube but physical 3D cube can't do this. Also I see there is 5 sides instead of 6, like on 3D cube it will be missing 1 side. Is there 6 sides variant of this? Maybe it could be implemented, not in the way I want but could be and I could make it as a second project. Just for solving you will need an image how rows & columns are connected on different sides.

[creint]

Is this one you are looking for?

[Albania]

Is this one you are looking for?

Yes. This grid you send. 12 characters variation (numbers from 1-9 and letters A, B, C).
No doubles in 3x3 + all horizontal lines + all vertical lines on flattened cube grid.
There is 9 lines (6 main lines +3 lines just straight). Every line has 12 cells. There can't be doubles in the cells where the same colour line is.

Here is the grid with lines:

[creint]

Solution was:

Code: Select all

      2 7 9
      B 4 5
      C A 6
C 2 4 1 6 A 7 9 8 C 2 3
3 8 1 7 C 3 5 C A 7 1 5
6 7 B 9 B 8 3 6 1 4 8 6
      8 9 2
      A 3 1
      4 5 B

But you probably wanted the following 3 rows also distinct:

Code: Select all

C 2 4 1 6 A 7 9 8 C 2 3
3 8 1 7 C 3 5 C A 7 1 5
6 7 B 9 B 8 3 6 1 4 8 6

So distinct every side + distinct every rotate on X Y Z axes
Well then there is no possible solution with only 123456789ABC

[Hajime]

So distinct every side + distinct every rotate on X Y Z axes
Well then there is no possible solution with only 123456789ABC

OK. But now for a slightly different constraint.
If you look at a cube you only see 3 sides.
Is it possible that all 3 visible sides have distinct figures, for each point of view?

[creint]

For hexadoku it is possible:

So distinct every side + distinct every rotate on X Y Z axes
Well then there is no possible solution with only 123456789ABC

OK. But now for a slightly different constraint.
If you look at a cube you only see 3 sides.
Is it possible that all 3 visible sides have distinct figures, for each point of view?

I don't know what you mean, do you have more information?

[Hajime]

When you look at a cube, always only 3 sites are visible.
The other 3 sites are at the back.
Sites are 3x3 and must contain 123456789.
Each visible bended line holds 6 different digits.

I figured it out:

Code: Select all

    +---+
    |698|
    |374|
    |512|
+---+---+---+---+
|789|123|987|321|
|123|456|321|654|
|456|789|654|987|
+---+---+---+---+
    |512|
    |374|
    |698|
    +---+


for example
Edit: swapped 73 in top and bottom box to 37

[creint]

This one is valid for you Hajime


You had duplicate 7 in column 4
6 7 5 1 4 7
1 4 7 5 7 6

And column 4 + 12
6 7 5 1 4 7
1 4 7 5 7 6

[Albania]

For hexadoku it is possible:

From Hexadoku grid you can make 2 x 3D Cubes
It is little like driving a car instead of walking 10 meters.
Waste of "Sudoku Material"
You know what I mean?
Hexadoku 16 Characters - 16x16=256 cells
12x12 Sudoku 12 Characters - 12x12=144 cells
Flattened Cube Grid - 6x9=54 cells - Max Cells in 1 Line - 12 & it gives 9 Lines x 12 Cells = 108 Cells From 144 Cells Slots
It looks like you just need to rearrange 12x12 Sudoku and it should be possible but how?

[creint]

Your flattened cube idea has no valid solution, it is not possible.

Possible candidates in a cell 123456789ABC
6 box constraints for 9 cells
3 ring like constraints for 12 cells (red blue green)
3 column like constraints for 12 cells (gray pink yellow)
3 row like constraints for 12 cells (row 4,5,6)
Am I missing some constraints?
(Even if you remove the 6 box constraints it has no valid solution)