Method of Strachey

 

Take a 7x7 magic square and construct the second, third and fourth 7x7 magic square by adding (7 x 7 =) 49, (2 x 49 = ) 98 respectively (3 x 49 = ) 147 to all numbers of the first 7x7 magic square. Put the first square in the top left corner, put the second square in the bottom right corner, put the third square in the top right corner and put the fourth square in the bottom left corner.

 

 

46 31 16 1 42 27 12 144 129 114 99 140 125 110
5 39 24 9 43 35 20 103 137 122 107 141 133 118
13 47 32 17 2 36 28 111 145 130 115 100 134 126
21 6 40 25 10 44 29 119 104 138 123 108 142 127
22 14 48 33 18 3 37 120 112 146 131 116 101 135
30 15 7 41 26 11 45 128 113 105 139 124 109 143
38 23 8 49 34 19 4 136 121 106 147 132 117 102
193 178 163 148 189 174 159 95 80 65 50 91 76 61
152 186 171 156 190 182 167 54 88 73 58 92 84 69
160 194 179 164 149 183 175 62 96 81 66 51 85 77
168 153 187 172 157 191 176 70 55 89 74 59 93 78
169 161 195 180 165 150 184 71 63 97 82 67 52 86
177 162 154 188 173 158 192 79 64 56 90 75 60 94
185 170 155 196 181 166 151 87 72 57 98 83 68 53

 

 

The columns and the diagonals give already the magic sum. To get the right sum in the rows, you must swap numbers, as follows. We split the 7x7 square in the top left corner and the 7x7 square in the bottom left corner in 'quarters' (marked by the blue numbers). The (yellow marked) ‘quarters’ top left and (red marked) 'quarters' bottom left of the 7x7 square in the top left corner must be swapped with the ‘quarters’ top left and bottom left of the 7x7 square in the bottom left corner. Also the (green marked) blue numbers on the border between the two 'quarters’  from the second cell up to the crossing point must be swapped. Finally the (pink marked) numbers of the top half of the last column(s) must be swapped with the numbers of the bottom half of the last column(s). Because the numbers of the first three columns must be swapped, the numbers of the last (3 – 1 = ) 2 columns must be swapped. See below the result.

 

 

14x14 magic square

193 178 163 1 42 27 12 144 129 114 99 140 76 61
152 186 171 9 43 35 20 103 137 122 107 141 84 69
160 194 179 17 2 36 28 111 145 130 115 100 85 77
21 153 187 172 10 44 29 119 104 138 123 108 93 78
169 161 195 33 18 3 37 120 112 146 131 116 52 86
177 162 154 41 26 11 45 128 113 105 139 124 60 94
185 170 155 49 34 19 4 136 121 106 147 132 68 53
46 31 16 148 189 174 159 95 80 65 50 91 125 110
5 39 24 156 190 182 167 54 88 73 58 92 133 118
13 47 32 164 149 183 175 62 96 81 66 51 134 126
168 6 40 25 157 191 176 70 55 89 74 59 142 127
22 14 48 180 165 150 184 71 63 97 82 67 101 135
30 15 7 188 173 158 192 79 64 56 90 75 109 143
38 23 8 196 181 166 151 87 72 57 98 83 117 102

 

 

ór

 

 

1x number from grid with 4x 7x7 magic square

32

40

48

7

8

16

24

32

40

48

7

8

16

24

38

46

5

13

21

22

30

38

46

5

13

21

22

30

44

3

11

19

27

35

36

44

3

11

19

27

35

36

1

9

17

25

33

41

49

1

9

17

25

33

41

49

14

15

23

31

39

47

6

14

15

23

31

39

47

6

20

28

29

37

45

4

12

20

28

29

37

45

4

12

26

34

42

43

2

10

18

26

34

42

43

2

10

18

32

40

48

7

8

16

24

32

40

48

7

8

16

24

38

46

5

13

21

22

30

38

46

5

13

21

22

30

44

3

11

19

27

35

36

44

3

11

19

27

35

36

1

9

17

25

33

41

49

1

9

17

25

33

41

49

14

15

23

31

39

47

6

14

15

23

31

39

47

6

20

28

29

37

45

4

12

20

28

29

37

45

4

12

26

34

42

43

2

10

18

26

34

42

43

2

10

18

 

 

+49x number from grid with numbers 0, 1, 2 and 3

0

0

0

0

3

3

3

2

2

2

2

2

1

1

0

3

3

3

0

0

0

2

2

2

2

2

1

1

0

3

3

3

0

0

0

2

2

2

2

2

1

1

0

3

3

3

0

0

0

2

2

2

2

2

1

1

0

3

3

3

0

0

0

2

2

2

2

2

1

1

0

3

3

3

0

0

0

2

2

2

2

2

1

1

0

0

0

0

3

3

3

2

2

2

2

2

1

1

3

3

3

3

0

0

0

1

1

1

1

1

2

2

3

0

0

0

3

3

3

1

1

1

1

1

2

2

3

0

0

0

3

3

3

1

1

1

1

1

2

2

3

0

0

0

3

3

3

1

1

1

1

1

2

2

3

0

0

0

3

3

3

1

1

1

1

1

2

2

3

0

0

0

3

3

3

1

1

1

1

1

2

2

3

3

3

3

0

0

0

1

1

1

1

1

2

2

 

 

= 14x14 magic square

32

40

48

7

155

163

171

130

138

146

105

106

65

73

38

193

152

160

21

22

30

136

144

103

111

119

71

79

44

150

158

166

27

35

36

142

101

109

117

125

84

85

1

156

164

172

33

41

49

99

107

115

123

131

90

98

14

162

170

178

39

47

6

112

113

121

129

137

96

55

20

175

176

184

45

4

12

118

126

127

135

143

53

61

26

34

42

43

149

157

165

124

132

140

141

100

59

67

179

187

195

154

8

16

24

81

89

97

56

57

114

122

185

46

5

13

168

169

177

87

95

54

62

70

120

128

191

3

11

19

174

182

183

93

52

60

68

76

133

134

148

9

17

25

180

188

196

50

58

66

74

82

139

147

161

15

23

31

186

194

153

63

64

72

80

88

145

104

167

28

29

37

192

151

159

69

77

78

86

94

102

110

173

181

189

190

2

10

18

75

83

91

92

51

108

116

 

 

Use the method of Strachey to construct magic squares of order is double odd. See 6x610x1014x1418x1822x2226x26 en 30x30

 

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14x14, Method of Strachey.xls
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