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Perfect magic 8x8x8 cube
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How to use a panmagic 4x4 square to produce a perfect magic 8x8x8 cube?
 
 
Read on http://en.wikipedia.org/wiki/Perfect_magic_cube everything about the features of the perfect magic cube.
Perfect magic cubes exist from the size (order) of 5x5x5 and bigger.
 
See on www.trump.de/magic-squares/magic-cubes/cubes-1.html the following perfect magic 5x5x5 cube.


The first known perfect magic cube of order 5



Walter Trump and Christian Boyer, 2003-11-13
 


 
The above mentioned 5x5x5 magic cube has the following magic features:
-         the 5 rows, the 5 columns and the 2 diagonals in each level give the magic sum of 315:
-         the 25 pillars give the magic sum of 315;
-         the 30 diagonals (for example 115+64+38+87+11=315 or 106+44+58+87+20=315) through the 5 levels give
the magic sum of 315;
-         The four space diagonals (for example 67+39+63+87+59=315) give the magic sum of 315.
 
 
You can use a 4x4 panmagic square to produce a perfect magic 8x8x8 cube in the next four steps:
 
 
■ Use the pattern of a 4x4 panmagic square to produce the basic pattern of the 1st level of the 8x8x8 magic cube:
 
 
  panmagic 4x4                ->      column 2&3 swapped
1
8
10
15
 
 
1
10
8
15
12
13
3
6
 
 
12
3
13
6
7
2
16
9
 
 
7
16
2
9
14
11
5
4
 
 
14
5
11
4
 
 
  4x4 in right half                                      left half       <-          right half                             fill in crosswise
1
5
11
15
 
 
12
16
2
6
1
5
11
15
 
 
12
16
2
6
1
5
11
15
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
2
6
12
16
11
15
1
5
12
16
2
6
 
 
1
5
11
15
12
16
2
6
 
 
1
5
11
15
12
16
2
6
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
11
15
1
5
2
6
12
16
14
10
8
4
 
 
7
3
13
9
14
10
8
4
 
 
7
3
13
9
14
10
8
4
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
13
9
7
3
8
4
14
10
7
3
13
9
 
 
14
10
8
4
7
3
13
9
 
 
14
10
8
4
7
3
13
9
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
8
4
14
10
13
9
7
3
 
 
■ The basic pattern of the 3th level is the basic pattern of the 1st level of the 8x8x8 magic cube vertical mirrored:
 
 
1st level 8x8x8 cube, vertical mirrored          =         3rd level 8x8x8 magic cube
12
16
2
6
1
5
11
15
 
 
15
11
5
1
6
2
16
12
2
6
12
16
11
15
1
5
 
 
5
1
15
11
16
12
6
2
1
5
11
15
12
16
2
6
 
 
6
2
16
12
15
11
5
1
11
15
1
5
2
6
12
16
 
 
16
12
6
2
5
1
15
11
7
3
13
9
14
10
8
4
 
 
4
8
10
14
9
13
3
7
13
9
7
3
8
4
14
10
 
 
10
14
4
8
3
7
9
13
14
10
8
4
7
3
13
9
 
 
9
13
3
7
4
8
10
14
8
4
14
10
13
9
7
3
 
 
3
7
9
13
10
14
4
8
 
 
 
■ Produce the basic patterns of the remaining levels of the 8x8x8 magic cube by swapping the 4x4 sub-squares of the
1st respectively 3rd level:
 
-         Produce the basic patterns of the 2nd, 7th and 8th level by swapping the 4x4 sub-squares in the basic pattern
of the 1stlevel (see below colours yellow, red, pink and blue);
-         Produce the basic patterns of the 4th, 5th and 6th level by swapping the 4x4 sub-squares in the basic pattern
of the 3rdlevel (see below colours grey, white, green and brown).
 
 
■ Add in each level two fixed Sudoku patterns to the basic patterns and produce the level by adding 1x digit from the
basic pattern to 16x the digit from the same cell of Sudoku pattern [1] and by adding 64x digit from the same cell of
Sudoku pattern [2]:
 
 
  Basic pattern, 1st level                                      Sudoku pattern [1], 1st level                 Sudoku pattern [2], 1st level
12
16
2
6
1
5
11
15
 
 
1
3
3
1
2
0
0
2
 
 
0
7
3
4
6
1
5
2
2
6
12
16
11
15
1
5
 
 
2
0
0
2
1
3
3
1
 
 
4
3
7
0
2
5
1
6
1
5
11
15
12
16
2
6
 
 
0
2
2
0
3
1
1
3
 
 
5
2
6
1
3
4
0
7
11
15
1
5
2
6
12
16
 
 
3
1
1
3
0
2
2
0
 
 
1
6
2
5
7
0
4
3
7
3
13
9
14
10
8
4
 
 
2
0
0
2
1
3
3
1
 
 
7
0
4
3
1
6
2
5
13
9
7
3
8
4
14
10
 
 
1
3
3
1
2
0
0
2
 
 
3
4
0
7
5
2
6
1
14
10
8
4
7
3
13
9
 
 
3
1
1
3
0
2
2
0
 
 
2
5
1
6
4
3
7
0
8
4
14
10
13
9
7
3
 
 
0
2
2
0
3
1
1
3
 
 
6
1
5
2
0
7
3
4
 
 
  Basic pattern, 2nd level                                     Sudoku pattern [1], 2nd level               Sudoku pattern [2], 2nd level
7
3
13
9
14
10
8
4
 
 
0
2
2
0
3
1
1
3
 
 
2
5
1
6
4
3
7
0
13
9
7
3
8
4
14
10
 
 
3
1
1
3
0
2
2
0
 
 
6
1
5
2
0
7
3
4
14
10
8
4
7
3
13
9
 
 
1
3
3
1
2
0
0
2
 
 
7
0
4
3
1
6
2
5
8
4
14
10
13
9
7
3
 
 
2
0
0
2
1
3
3
1
 
 
3
4
0
7
5
2
6
1
12
16
2
6
1
5
11
15
 
 
3
1
1
3
0
2
2
0
 
 
5
2
6
1
3
4
0
7
2
6
12
16
11
15
1
5
 
 
0
2
2
0
3
1
1
3
 
 
1
6
2
5
7
0
4
3
1
5
11
15
12
16
2
6
 
 
2
0
0
2
1
3
3
1
 
 
0
7
3
4
6
1
5
2
11
15
1
5
2
6
12
16
 
 
1
3
3
1
2
0
0
2
 
 
4
3
7
0
2
5
1
6
 
 
  Basic pattern, 3rd level                                      Sudoku pattern [1], 3rd level                Sudoku pattern [2], 3rd level
15
11
5
1
6
2
16
12
 
 
3
1
1
3
0
2
2
0
 
 
4
3
7
0
2
5
1
6
5
1
15
11
16
12
6
2
 
 
0
2
2
0
3
1
1
3
 
 
0
7
3
4
6
1
5
2
6
2
16
12
15
11
5
1
 
 
2
0
0
2
1
3
3
1
 
 
1
6
2
5
7
0
4
3
16
12
6
2
5
1
15
11
 
 
1
3
3
1
2
0
0
2
 
 
5
2
6
1
3
4
0
7
4
8
10
14
9
13
3
7
 
 
0
2
2
0
3
1
1
3
 
 
3
4
0
7
5
2
6
1
10
14
4
8
3
7
9
13
 
 
3
1
1
3
0
2
2
0
 
 
7
0
4
3
1
6
2
5
9
13
3
7
4
8
10
14
 
 
1
3
3
1
2
0
0
2
 
 
6
1
5
2
0
7
3
4
3
7
9
13
10
14
4
8
 
 
2
0
0
2
1
3
3
1
 
 
2
5
1
6
4
3
7
0
 
 
  Basic pattern, 4th level                                      Sudoku pattern [1], 4th level                Sudoku pattern [2], 4th level
4
8
10
14
9
13
3
7
 
 
2
0
0
2
1
3
3
1
 
 
6
1
5
2
0
7
3
4
10
14
4
8
3
7
9
13
 
 
1
3
3
1
2
0
0
2
 
 
2
5
1
6
4
3
7
0
9
13
3
7
4
8
10
14
 
 
3
1
1
3
0
2
2
0
 
 
3
4
0
7
5
2
6
1
3
7
9
13
10
14
4
8
 
 
0
2
2
0
3
1
1
3
 
 
7
0
4
3
1
6
2
5
15
11
5
1
6
2
16
12
 
 
1
3
3
1
2
0
0
2
 
 
1
6
2
5
7
0
4
3
5
1
15
11
16
12
6
2
 
 
2
0
0
2
1
3
3
1
 
 
5
2
6
1
3
4
0
7
6
2
16
12
15
11
5
1
 
 
0
2
2
0
3
1
1
3
 
 
4
3
7
0
2
5
1
6
16
12
6
2
5
1
15