The New Sudoku Players' Forum

[Albania]

Even if you remove the 6 box constraints it has no valid solution

Little pitty, but ok.
I think Hexadoku for now is ok. Thx!
Maybe future brings something smaller than 16 characters, maybe AI will be better and help creating something

[Albania]

For hexadoku it is possible:

Wait. It isn't possible. Rubik cube is 3x3. Here you have 4x4.
How you fit 16 characters into 3x3 square?
Looks like Hexadoku can't be implemented into standard 3x3 rubik cube.
But also 12x12 Sudoku can't be implemented into standard rubik cube 3x3 for same reason or any other characters.
Square is 9 cells and lines have 12 cells. It is impossible to put full Sudoku on standard Rubik Cube 3x3.
It is only possible if you remove 1 side from cube, leave it empty or something like this but I don't wanna do this. I wanna have full 3D cube.
Ehh

It looks like it is only possible with Hexadoku & 4x4 Rubik Cube.

[denis_berthier]

For hexadoku it is possible:

Wait. It isn't possible. Rubik cube is 3x3. Here you have 4x4.

Hi Albania
Rubik's cubes can be any size. You can even buy 4x4 physical Rubik's cubes.
The same is true of Sudoku: it is not restricted to 9x9.

creint's modification of your idea is the best 3D version of Sudoku one can imagine. It leads to a clean game, with easy to write rules, similar to those of Sudoku: for each possible value in {1, 2 ... 9, A ... G}, only one position in each side, in each horizontal slice and in each vertical slice.
I suggest we call it RubiDoku ("SudoCube" and "CubeDoku" are already used commercially.)
I would be quite surprised if this game had not already been invented - though I haven''t been able to find it by a quick search on the web.

Complexity-wise, with 16*6 = 96 cells, it's intermediate between 9x9 (81 cells) and 16x16 (256 cells) classical Sudoku.
Mathematically-wise, it's a beautiful object of study - same as Sudoku. It has isomorphisms slightly different from Sudoku*: digit permutations, reflections in each dimension, central symmetry, arbitrary permutations of slices in each dimension.
Contrary to Sudoku, it can physically exist in only one size (unless you want to create puzzles in 4D, 5D... space, but they will be hard to build in the real world).

Also same as Sudoku, it has g-candidates and whips[1] (which Latin Squares don't have) and they are easy to define and use (as "intersections"). It makes it all the more interesting as a game and as an object of study.

I don't have a generator of puzzles, but I think it wouldn't be too hard for those who have one to adapt it to produce minimal RubiDoku puzzles.

I think we also need some notation for the sides; I suggest the following (Top, Bottom, West, South, East, North), in the above flat representation of the cube:

Code: Select all

   T
W  S  E  N
   B


(*) I've modified my original version of isomorphisms. I no longer stick to those respecting Rubik's cube markings on different sides of small cubes.
.

[Hajime]

This one is valid for you Hajime

Finally I solved this nice puzzle with Paper&Pencil and a lot of Eraser; and some guessing...