Sudoku method (1)

 

Use four grids with 4x4 Sudoku patterns to construct a 16x16 most perfect (Franklin pan)magic square. See for more detailed information, the 4x4 and 8x8 magic square.

 

 

Take 4x number from first grid +1                            + 1x number from second grid 

0

1

2

3

0

1

2

3

0

1

2

3

0

1

2

3

   

0

1

3

2

2

3

1

0

0

1

3

2

2

3

1

0

3

2

1

0

3

2

1

0

3

2

1

0

3

2

1

0

   

3

2

0

1

1

0

2

3

3

2

0

1

1

0

2

3

1

0

3

2

1

0

3

2

1

0

3

2

1

0

3

2

   

0

1

3

2

2

3

1

0

0

1

3

2

2

3

1

0

2

3

0

1

2

3

0

1

2

3

0

1

2

3

0

1

   

3

2

0

1

1

0

2

3

3

2

0

1

1

0

2

3

0

1

2

3

0

1

2

3

0

1

2

3

0

1

2

3

   

0

1

3

2

2

3

1

0

0

1

3

2

2

3

1

0

3

2

1

0

3

2

1

0

3

2

1

0

3

2

1

0

   

3

2

0

1

1

0

2

3

3

2

0

1

1

0

2

3

1

0

3

2

1

0

3

2

1

0

3

2

1

0

3

2

   

0

1

3

2

2

3

1

0

0

1

3

2

2

3

1

0

2

3

0

1

2

3

0

1

2

3

0

1

2

3

0

1

   

3

2

0

1

1

0

2

3

3

2

0

1

1

0

2

3

0

1

2

3

0

1

2

3

0

1

2

3

0

1

2

3

   

0

1

3

2

2

3

1

0

0

1

3

2

2

3

1

0

3

2

1

0

3

2

1

0

3

2

1

0

3

2

1

0

   

3

2

0

1

1

0

2

3

3

2

0

1

1

0

2

3

1

0

3

2

1

0

3

2

1

0

3

2

1

0

3

2

   

0

1

3

2

2

3

1

0

0

1

3

2

2

3

1

0

2

3

0

1

2

3

0

1

2

3

0

1

2

3

0

1

   

3

2

0

1

1

0

2

3

3

2

0

1

1

0

2

3

0

1

2

3

0

1

2

3

0

1

2

3

0

1

2

3

   

0

1

3

2

2

3

1

0

0

1

3

2

2

3

1

0

3

2

1

0

3

2

1

0

3

2

1

0

3

2

1

0

   

3

2

0

1

1

0

2

3

3

2

0

1

1

0

2

3

1

0

3

2

1

0

3

2

1

0

3

2

1

0

3

2

   

0

1

3

2

2

3

1

0

0

1

3

2

2

3

1

0

2

3

0

1

2

3

0

1

2

3

0

1

2

3

0

1

   

3

2

0

1

1

0

2

3

3

2

0

1

1

0

2

3

 

 

+ 16x number from third grid                                    + 64x number from fourth grid

2

3

0

1

2

3

0

1

0

1

2

3

0

1

2

3

   

0

3

0

3

0

3

0

3

0

3

0

3

0

3

0

3

0

1

2

3

0

1

2

3

2

3

0

1

2

3

0

1

   

0

3

0

3

0

3

0

3

0

3

0

3

0

3

0

3

3

2

1

0

3

2

1

0

1

0

3

2

1

0

3

2

   

3

0

3

0

3

0

3

0

3

0

3

0

3

0

3

0

1

0

3

2

1

0

3

2

3

2

1

0

3

2

1

0

   

3

0

3

0

3

0

3

0

3

0

3

0

3

0

3

0

3

2

1

0

3

2

1

0

1

0

3

2

1

0

3

2

   

0

3

0

3

0

3

0

3

0

3

0

3

0

3

0

3

1

0

3

2

1

0

3

2

3

2

1

0

3

2

1

0

   

0

3

0

3

0

3

0

3

0

3

0

3

0

3

0

3

2

3

0

1

2

3

0

1

0

1

2

3

0

1

2

3

   

3

0

3

0

3

0

3

0

3

0

3

0

3

0

3

0

0

1

2

3

0

1

2

3

2

3

0

1

2

3

0

1

   

3

0

3

0

3

0

3

0

3

0

3

0

3

0

3

0

2

3

0

1

2

3

0

1

0

1

2

3

0

1

2

3

   

1

2

1

2

1

2

1

2

1

2

1

2

1

2

1

2

0

1

2

3

0

1

2

3

2

3

0

1

2

3

0

1

   

1

2

1

2

1

2

1

2

1

2

1

2

1

2

1

2

3

2

1

0

3

2

1

0

1

0

3

2

1

0

3

2

   

2

1

2

1

2

1

2

1

2

1

2

1

2

1

2

1

1

0

3

2

1

0

3

2

3

2

1

0

3

2

1

0

   

2

1

2

1

2

1

2

1

2

1

2

1

2

1

2

1

3

2

1

0

3

2

1

0

1

0

3

2

1

0

3

2

   

1

2

1

2

1

2

1

2

1

2

1

2

1

2

1

2

1

0

3

2

1

0

3

2

3

2

1

0

3

2

1

0

   

1

2

1

2

1

2

1

2

1

2

1

2

1

2

1

2

2

3

0

1

2

3

0

1

0

1

2

3

0

1

2

3

   

2

1

2

1

2

1

2

1

2

1

2

1

2

1

2

1

0

1

2

3

0

1

2

3

2

3

0

1

2

3

0

1

   

2

1

2

1

2

1

2

1

2

1

2

1

2

1

2

1

 

 

= Most perfect (Franklin pan)magic 16x16 square

33

246

12

223

35

248

10

221

1

214

44

255

3

216

42

253

16

219

37

242

14

217

39

244

48

251

5

210

46

249

7

212

245

34

224

11

247

36

222

9

213

2

256

43

215

4

254

41

220

15

241

38

218

13

243

40

252

47

209

6

250

45

211

8

49

230

28

207

51

232

26

205

17

198

60

239

19

200

58

237

32

203

53

226

30

201

55

228

64

235

21

194

62

233

23

196

229

50

208

27

231

52

206

25

197

18

240

59

199

20

238

57

204

31

225

54

202

29

227

56

236

63

193

22

234

61

195

24

97

182

76

159

99

184

74

157

65

150

108

191

67

152

106

189

80

155

101

178

78

153

103

180

112

187

69

146

110

185

71

148

181

98

160

75

183

100

158

73

149

66

192

107

151

68

190

105

156

79

177

102

154

77

179

104

188

111

145

70

186

109

147

72

113

166

92

143

115

168

90

141

81

134

124

175

83

136

122

173

96

139

117

162

94

137

119

164

128

171

85

130

126

169

87

132

165

114

144

91

167

116

142

89

133

82

176

123

135

84

174

121

140

95

161

118

138

93

163

120

172

127

129

86

170

125

131

88

 

 

Use this method [Sudoku method (1)] to construct magic squares of order is 2^n (= 2x2, 2x2x2, 2x2x2x2, ...) from 4x4 to infinity. See 4x48x816x1632x32

 

Download
16x16, Sudoku method (1).xls
Microsoft Excel werkblad 443.0 KB