Office Applications and Entertainment, Magic Cubes  
Index  About the Author 
3.12 Quaternary Composition (1)
Any number m = 0 ... 63 can be written as m = b_{1} + 4 * b_{2}
+ 16 * b_{3}
with b_{i} = 0, 1, 2, 3 for i = 1, 2, 3 (Quaternary representation).
3.12.2 Sudoku Comparable Cubes
Quaternary Cubes for which the rows, columns and pillars contain each the four integers 0, 1, 2 and 3 are also referred to as Sudoku Comparable Cubes.
The rows, columns and pillars of Sudoku Comparable Cubes sum to 6.
3.12.3 Almost Perfect Magic Cubes
Sudoku Comparable Cubes, with also the plane diagonals summing to 6, can be obtained by applying the equations as deducted in Section 3.2.2, however for a Magic Sum 6.
Almost Perfect Magic Cubes can be generated by selecting combinations of Sudoku Comparable Cubes
(B1, B2, B3)
while ensuring that the resulting Cube C contains all integers 1 thru 64.
3.12.4 Pantriagonal Magic Cubes
Quaternary Pantriagonal Magic Cubes can be obtained by applying the equations as deducted in Section 3.7.2, however for a Magic Sum 6.
Pantriagonal Magic Cubes can be generated by selecting combinations of Quaternary Cubes
(B1, B2, B3)
while ensuring that the resulting Cube C contains all integers 1 thru 64.
3.12.5 Pandiagonal/Triagonal Magic Cubes
Quaternary Pan Diagonal/Triagonal Magic Cubes can be obtained by applying the equations as deducted in Section 3.8.2, however for a Magic Sum 6 under the restriction that the elements of each Pan Triagonal should be different.
Pan Diagonal/Triagonal Magic Cubes can be generated by selecting combinations of Quaternary Cubes
(B1, B2, B3)
while ensuring that the resulting Cube C contains all integers 1 thru 64.
Associated Sudoku Comparable Magic Cubes can be obtained by applying the equations as deducted in Section 3.9.2, however for a Magic Sum 6.
Associated Magic Cubes can be generated by selecting combinations of Sudoku Comparable Cubes (B1, B2, B3) while ensuring that the resulting Cube C contains all integers 1 thru 64.
3.12.7 Pantriagonal/Associated Magic Cubes
Pantriagonal/Associated Sudoku Comparable Magic Cubes can be obtained by applying the equations as deducted in Section 3.10.2, however for a Magic Sum 6.
Pantriagonal/Associated Magic Cubes can be generated by selecting combinations of Sudoku Comparable Cubes
(B1, B2, B3)
while ensuring that the resulting Cube C contains all integers 1 thru 64.
The obtained results regarding the miscellaneous types of order 4 Magic Cubes as deducted and discussed in previous sections are summarized in following table: 
Class
Main Characteristics
Method
Tag
Subroutine
Results
Almost Perfect
General
Sudoku
B1/2/3
Attachment 3.6.1
27648Simple
Associated
Sudoku
B1/2/3
Attachment 3.6.6
15360 (Note 1)Pantriagonal
2D Compact and Complete
Sudoku
B1/2/3
Attachment 3.6.4
91506 (Note 1)Pandiagonal
Sudoku
B1/2/3
Attachment 3.6.5
6144 (Note 1)Associated
Sudoku
B1/2/3
Attachment 3.6.7
55296
Note 1: Produced with B1 = constant.

Index  About the Author 