5x5x5 magic cube

 

Read on http://nl.wikipedia.org/wiki/Perfect_magische_kubus all about the features of the perfect magic cube. The smallest perfect magic cube is the 5x5x5 magic cube. 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

http://www.trump.de/magic-squares/magic-cubes/cube-5-mid-t.gif

Walter Trump and Christian Boyer, 2003-11-13

http://www.trump.de/magic-squares/magic-cubes/perfect-5-small-t.gif

 

 

This 5x5x5 magic cube has as magic features:

  • the 5 rows, the 5 columns and the 2 diagonals in each level give the magic sum of 315;
  • the 25 pilars give the magic sum of 315;
  • the 20 diagonals through the 5 levels give the magic sum of 315 (e.g. 115+64+38+87+11=315 or 106+44+58+87+20=315);
  • the 4 tridiagonals give the magic sum of 315 (e.g. 67+39+63+87+59=315).

 

Use the same method to construct the panmagic 5x5 square (shift) to construct a symmetric & semi panmagic 5x5x5 cube.
 
Choose as first row of the first grid in the first level: 2-3-4-0-1. Construct row 2 up to 5 of the first grid of the first level by shifting the first row each time 2 places to the left. Construct the first grid of level 2 up to 5 by shifting the columns of the first grid of the first level each time 2 places to the left.
 
Choose as first row of the second grid in the first level: 0-1-2-3-4. Construct row 2 up to 5 of the second grid of the first level by shifting the first row each time 2 places to the right. Construct the second grid of level 2 up to 5 by shifting the columns of the second grid of the first level each time 2 places to the left.
 
The third grid is the same as the second grid, but the levels must be put in reversed order (5 up to 1 instead of 1 up to 5).
 
Take 1x digit from first grid + 5x digit from second grid + 25x digit from third grid to get a symmetric & semi (pan)magic 5x5x5 cube.
 

 

1x digit +1               +    5x digit                     +    25x digit                   =    5x5x5 cube, first level

2

3

4

0

1

   

0

1

2

3

4

   

3

4

0

1

2

   

78

109

15

41

72

4

0

1

2

3

   

3

4

0

1

2

   

1

2

3

4

0

   

45

71

77

108

14

1

2

3

4

0

   

1

2

3

4

0

   

4

0

1

2

3

   

107

13

44

75

76

3

4

0

1

2

   

4

0

1

2

3

   

2

3

4

0

1

   

74

80

106

12

43

0

1

2

3

4

   

2

3

4

0

1

   

0

1

2

3

4

   

11

42

73

79

110

                                                   
                                                   

1x digit +1               +    5x digit                     +    25x digit                   =    5x5x5 cube, second level

4

0

1

2

3

   

2

3

4

0

1

   

1

2

3

4

0

   

40

66

97

103

9

1

2

3

4

0

   

0

1

2

3

4

   

4

0

1

2

3

   

102

8

39

70

96

3

4

0

1

2

   

3

4

0

1

2

   

2

3

4

0

1

   

69

100

101

7

38

0

1

2

3

4

   

1

2

3

4

0

   

0

1

2

3

4

   

6

37

68

99

105

2

3

4

0

1

   

4

0

1

2

3

   

3

4

0

1

2

   

98

104

10

36

67

                                                   
                                                   

1x digit +1               +    5x digit                     +    25x digit                   =    5x5x5 cube, third level

1

2

3

4

0

   

4

0

1

2

3

   

4

0

1

2

3

   

122

3

34

65

91

3

4

0

1

2

   

2

3

4

0

1

   

2

3

4

0

1

   

64

95

121

2

33

0

1

2

3

4

   

0

1

2

3

4

   

0

1

2

3

4

   

1

32

63

94

125

2

3

4

0

1

   

3

4

0

1

2

   

3

4

0

1

2

   

93

124

5

31

62

4

0

1

2

3

   

1

2

3

4

0

   

1

2

3

4

0

   

35

61

92

123

4

                                                   
                                                   

1x digit +1               +    5x digit                     +    25x digit                   =    5x5x5 cube, fourth level

3

4

0

1

2

   

1

2

3

4

0

   

2

3

4

0

1

   

59

90

116

22

28

0

1

2

3

4

   

4

0

1

2

3

   

0

1

2

3

4

   

21

27

58

89

120

2

3

4

0

1

   

2

3

4

0

1

   

3

4

0

1

2

   

88

119

25

26

57

4

0

1

2

3

   

0

1

2

3

4

   

1

2

3

4

0

   

30

56

87

118

24

1

2

3

4

0

   

3

4

0

1

2

   

4

0

1

2

3

   

117

23

29

60

86

                                                   
                                                   

1x digit +1               +    5x digit                     +    25x digit                   =    5x5x5 cube, fifth level

0

1

2

3

4

   

3

4

0

1

2

   

0

1

2

3

4

   

16

47

53

84

115

2

3

4

0

1

   

1

2

3

4

0

   

3

4

0

1

2

   

83

114

20

46

52

4

0

1

2

3

   

4

0

1

2

3

   

1

2

3

4

0

   

50

51

82

113

19

1

2

3

4

0

   

2

3

4

0

1

   

4

0

1

2

3

   

112

18

49

55

81

3

4

0

1

2

   

0

1

2

3

4

   

2

3

4

0

1

   

54

85

111

17

48

 


Less & extra magic features:

  • The vertical diagonals through the levels give not the magic sum;
  • The pandiagonals in each level give the magic sum of 315;
  • The vertical pandiagonals through the levels give the magic sum of 315

 

 

Download
5x5x5, semi [pan]magic 5x5x5 cube.xls
Microsoft Excel werkblad 80.5 KB