Reversible magic square

 

Paul Michelet constructed a 9x9 reversible panmagic (and 3x3 compact & symmetric) square.

 

In the square are the numbers 11/19, 21/29, 31/39, 41/49, 51/59, 61/69, 71/79, 81/89 and 91/99.

 

If you reverse the digits of all numbers in the 9x9 panmagic square (i.e. 19 reversed is 91) you get another 9x9 panmagic (and 3x3 compact & symmetric) square.

 

 

9x9 reversible panmagic (and 3x3 compact & symmetric) square

88

81

86

18

11

16

68

61

66

38

31

36

58

51

56

78

71

76

48

41

46

98

91

96

28

21

26

83

85

87

13

15

17

63

65

67

33

35

37

53

55

57

73

75

77

43

45

47

93

95

97

23

25

27

84

89

82

14

19

12

64

69

62

34

39

32

54

59

52

74

79

72

44

49

42

94

99

92

24

29

22

 

 

Reversed 9x9 panmagic (and 3x3 compact & symmetric) square 

88

18

68

81

11

61

86

16

66

83

13

63

85

15

65

87

17

67

84

14

64

89

19

69

82

12

62

38

58

78

31

51

71

36

56

76

33

53

73

35

55

75

37

57

77

34

54

74

39

59

79

32

52

72

48

98

28

41

91

21

46

96

26

43

93

23

45

95

25

47

97

27

44

94

24

49

99

29

42

92

22

 

Download
Reversible 9x9 magic square.xls
Microsoft Excel werkblad 52.0 KB

 

It is possible to construct a reversible 9x9 magic square, which is not only panmagic, 3x3 compact and symmetric, but also 1/3 of each row and 1/3 of each column gives 1/3 of the magic sum.

 

 

Take 1x digit from first grid

1

5

9

6

7

2

8

3

4

8

3

4

1

5

9

6

7

2

6

7

2

8

3

4

1

5

9

1

5

9

6

7

2

8

3

4

8

3

4

1

5

9

6

7

2

6

7

2

8

3

4

1

5

9

1

5

9

6

7

2

8

3

4

8

3

4

1

5

9

6

7

2

6

7

2

8

3

4

1

5

9

 

 

+ 10x digit from second grid

1

8

6

1

8

6

1

8

6

5

3

7

5

3

7

5

3

7

9

4

2

9

4

2

9

4

2

6

1

8

6

1

8

6

1

8

7

5

3

7

5

3

7

5

3

2

9

4

2

9

4

2

9

4

8

6

1

8

6

1

8

6

1

3

7

5

3

7

5

3

7

5

4

2

9

4

2

9

4

2

9

 

 

= Ultra magic 9x9 reversible square

11

85

69

16

87

62

18

83

64

58

33

74

51

35

79

56

37

72

96

47

22

98

43

24

91

45

29

61

15

89

66

17

82

68

13

84

78

53

34

71

55

39

76

57

32

26

97

42

28

93

44

21

95

49

81

65

19

86

67

12

88

63

14

38

73

54

31

75

59

36

77

52

46

27

92

48

23

94

41

25

99

 

 

If you reverse the digits of each number, you get:

 

 

Reversed ultra magic 9x9 square

11

58

96

61

78

26

81

38

46

85

33

47

15

53

97

65

73

27

69

74

22

89

34

42

19

54

92

16

51

98

66

71

28

86

31

48

87

35

43

17

55

93

67

75

23

62

79

24

82

39

44

12

59

94

18

56

91

68

76

21

88

36

41

83

37

45

13

57

95

63

77

25

64

72

29

84

32

49

14

52

99

 

Download
Ultra magic reversible 9x9 square.xls
Microsoft Excel werkblad 56.5 KB