10x10 magic square

Special 10x10 magic square

 

Order 10 is double prime number. So a panmagic, symmetric and/or compact result is not possible. Ofcourse there are concentric or inlay results.

 

See below an old 10x10 magic square mailed by Mahdi Alavi. If you split the numbers in the sequences 1 up to 10, 11 up to 20, ..., 91 up to 100, you find exactly one number from each sequence in each row/column/diagonal.

 

I have analyzed the 10x10 magic square and it is easy to find the (first) column grid. But it is very difficult to find a matching (second) row grid.

 

 

Special 10x10 magic square

100

89

79

65

53

46

33

27

12

1

82

22

68

47

10

91

58

32

76

19

77

34

43

7

11

90

92

56

69

26

39

41

2

14

78

25

88

94

60

64

44

9

13

80

66

36

21

86

95

55

6

17

30

35

42

59

67

71

85

93

57

97

81

23

38

63

75

20

3

48

61

52

98

84

28

73

16

8

45

40

24

70

54

99

83

18

5

49

31

72

15

74

37

51

96

4

50

62

29

87

 

 

10 x (number-1) from column grid

10

9

8

7

6

5

4

3

2

1

9

3

7

5

1

10

6

4

8

2

8

4

5

1

2

9

10

6

7

3

4

5

1

2

8

3

9

10

6

7

5

1

2

8

7

4

3

9

10

6

1

2

3

4

5

6

7

8

9

10

6

10

9

3

4

7

8

2

1

5

7

6

10

9

3

8

2

1

5

4

3

7

6

10

9

2

1

5

4

8

2

8

4

6

10

1

5

7

3

9

 

 

+1x number from matching row grid

10

9

8

7

6

5

4

3

2

1

9

3

7

5

1

10

6

4

8

2

8

4

5

1

2

9

10

6

7

3

4

5

1

2

8

3

9

10

6

7

5

1

2

8

7

4

3

9

10

6

1

2

3

4

5

6

7

8

9

10

6

10

9

3

4

7

8

2

1

5

7

6

10

9

3

8

2

1

5

4

3

7

6

10

9

2

1

5

4

8

2

8

4

6

10

1

5

7

3

9

 

 

See in the download below the analysis of the special 10x10 magic square (and the special 14x14 magic square constructed by Jos Luyendijk).

 

Download
10x10 & 14x14 magic square.xlsx
Microsoft Excel werkblad 36.7 KB
Download

 

See also the special 14x14 magic square.

 

10x10 magic square