The full name of this cube design is '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 and symbols are arranged as 2x2 Sudokus on all six faces. They appear on every row and column exactly once.
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. In addition, it becomes a '2x2 Supersudoku' when the four colors are displayed on both diagonals exactly once as well.
It is also possible to have an arrangement where the other six out of twelve possible 2x2 Sudoku 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.
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 any of the three levels show 2x2 Sudokus on all 6 faces.
Finally base color-symbol combinations allow displaying 4x4 Sudokus on the whole cube (Euler squares can also be found all over the place).
Glossary
2x2 Sudoku: When on a cube face all four elements of the same group show exactly once on every row and column.
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.
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.
The 4x4x4x4x4x4 Sudoku Cube is © 2008 by Ortwin Schenker.
An introductory article can be found in the TwistyPuzzles.com forum.
http://twistypuzzles.com/forum/viewtopic.php?f=15&t=11933
Werner Randelshofer Jan 25, 2009 12:53:34 PM