The 4x4x4x4x4x4 Sudoku Cube is solved when it has been brought into one of the following stages:

Solved State A (Initial State)

1) Base colors are grouped into four 2x2 boxes on all six faces.

2) Circle colors are arranged in 2x2 Sudoku style on two faces.

3) Symbols are arranged in 2x2 Sudoku style on all six faces.

Note: The base color-symbol combination is representing a 4x4 Sudoku.

Initial State

Solved State B

1) Base colors are arranged in 2x2 Supersudoku style on all six faces.

2) Circle colors are arranged in 2x2 Supersudoku style on all six faces.

3) Symbols are arranged in 2x2 Supersudoku style on two faces. Symbols are grouped into four 2x2 boxes on two faces.

Note: The base color-symbol combination is representing a 4x4 Sudoku.

Solved State B

Solved State C1

1) Base colors are arranged in 2x2 Sudoku style on two faces.

2) Circle colors are grouped into four 2x2 boxes on all six faces.

3) Symbols are arranged in 2x2 Sudoku style on two faces. Symbols are grouped into four 2x2 boxes on two faces.

Note: The base color-symbol combination is representing a 4x4 Sudoku.

Solved State C1

Solved State C2

1) Base colors are arranged in 2x2 Supersudoku style on all six faces.

2) Circle colors are grouped into four 2x2 boxes on all six faces.

3) Symbols are arranged in 2x2 Supersudoku style on two faces. Symbols are grouped into four 2x2 boxes on two faces.

Note: The base color-symbol combination is representing a 4x4 Sudoku.

Solved State C2

Solved State D1

1) No remarkable arrangement of the base colors.

2) No remarkable arrangement of the circle colors.

3) Symbols are grouped on all six faces.

Solved State D1

Solved State D2

1) No remarkable arrangement of the base colors.

2) No remarkable arrangement of the circle colors.

3) Symbols are grouped on all six faces.

Solved State D2

Note

Positions where base colors, circle colors and symbols are brought all together either into 2x2 Sudoku or 2x2 Supersudoku positions are not possible.

Glossary

2x2 Sudoku: When on a cube face all four elements of the same group show exactly once on every row and column. In addition they appear exactly once in each of the four 2x2 boxes.

2x2 Supersudoku: When on a cube face all four elements of the same group show exactly once on every row and column as well as on both diagonals. In addition they appear exactly once in each of the four 2x2 boxes.

4x4 Sudoku: When on all six cube faces the combination of two group elements show exactly once. In addition, each of the twelve rows (4 rows per axis), consisting of 16 stickers (along four faces of the cube), must show each combination exactly once as well.

4x4x4x4x4x4 Sudoku Cube

This cube is a Sudoku consisting of up to three levels of '2x2 Sudokus' with base colors, circle colors and symbols on all faces. Therefore the cube name means (4x4x4) cubies x 4 base colors x 4 circle colors x 4 symbols.

In its initial state the cube faces are divided into grids of four colored 2x2 boxes. The four different circle colors are arranged as 2x2 Sudokus on two faces, The four different symbols are arranged as 2x2 Sudokus on all six faces. They appear on every row and column exactly once and they also appear exactly once in each 2x2 box.

The cube can be solved in several 2x2 Sudoku stages with several valid solutions.

1. Base Colors

The cube can be brought into a position where every face shows a different, complete and correct '2x2 Sudoku'. A '2x2 Sudoku' is displayed when all four colors show exactly once on every row and column and exactly once in every 2x2 box. In addition, it becomes a '2x2 Supersudoku' when the four colors are displayed on both diagonals exactly once as well.

In the image above the base colors are arranged in 2x2 Supersudoku style on each of the six faces.

Sudoku Cube: Base Colors Only

It is also possible to have an arrangement where the other six out of twelve possible 2x2 Supersudoku solutions are shown.

2. Circle Colors

In addition to base colors arrangement, circle colors can also be arranged when the following conditions are met:

1) all 16 base color-circle color combinations are shown on all 6 faces.

2) there is only one secondary sticker color of every cubie.

3) secondary stickers show 2x2 Sudokus on all 6 faces.

In the image above the base and circle colors are arranged in a 2x2 Supersudoku style on all six faces.

Sudoku Cube: Base Color-Circle Color Combinations

3. Symbols

Putting it all together one ends up with a cube where each sticker carries markings on three levels: base color, circle color and symbol.

The cube can be played with so that any of the three levels can be grouped (that is identical colors / symbols close to each other). It is also possible to bring the cube to states where at least one of the three levels show 2x2 Sudokus on all 6 faces.

In the image above base and circle colors are arranged in a 2x2 Supersudoku style on all 6 faces as well as the symbols on the front and back face. Note that the symbols of the right and left face are grouped into 2x2 squares and that each symbol shows exactly twice in each row, column and the two diagonals on the upper and down face.

Finally base color-symbol combinations allow displaying '4x4 Sudokus' on the whole cube.

Sudoku Cube: Symbols Only

Sudoku Cube: Base Color-Symbol Combinations

The 4x4x4x4x4x4 Sudoku Cube was invented in 2008 by Ortwin Schenker and introduced in the TwistyPuzzles.com forum.

Faces of the cube: 1024 x 1024, 2048 x 2048

Enlarged view