Pandiagonal magic & symmetric 7x7x7 cube (shift method)

 

Use the same method to construct the panmagic 5x5 square (shift) to construct a symmetric & panmagic 7x7x7 cube.
 
Choose as first row of the first grid in the first level: 3-4-5-6-0-1-2. Construct row 2 up to 7 of the first grid of the first level by shifting the first row each time 4 places to the left. Construct the first grid of level 2 up to 7 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: 6-0-1-2-3-4-5. Construct row 2 up to 7 of the second grid of the first level by shifting the first row each time 4 places to the right. Construct the second grid of level 2 up to 7 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 are put in reversed order (7 up to 1 instead of 1 up to 7).
 
Take 1x number from first grid + 7x number from second grid + 49x number from third grid to get a symmetric & panmagic 7x7x7 cube.

  

 

1x number +1 [level 1]      +   7x number [Level 1]          +    49x number [Level 1]

3

4

5

6

0

1

2

   

6

0

1

2

3

4

5

   

4

5

6

0

1

2

3

0

1

2

3

4

5

6

   

2

3

4

5

6

0

1

   

0

1

2

3

4

5

6

4

5

6

0

1

2

3

   

5

6

0

1

2

3

4

   

3

4

5

6

0

1

2

1

2

3

4

5

6

0

   

1

2

3

4

5

6

0

   

6

0

1

2

3

4

5

5

6

0

1

2

3

4

   

4

5

6

0

1

2

3

   

2

3

4

5

6

0

1

2

3

4

5

6

0

1

   

0

1

2

3

4

5

6

   

5

6

0

1

2

3

4

6

0

1

2

3

4

5

   

3

4

5

6

0

1

2

   

1

2

3

4

5

6

0

 

 

 

 1x number +1 [level 2]     +   7x number [Level 2]          +    49x number [Level 2]

5

6

0

1

2

3

4

   

1

2

3

4

5

6

0

   

2

3

4

5

6

0

1

2

3

4

5

6

0

1

   

4

5

6

0

1

2

3

   

5

6

0

1

2

3

4

6

0

1

2

3

4

5

   

0

1

2

3

4

5

6

   

1

2

3

4

5

6

0

3

4

5

6

0

1

2

   

3

4

5

6

0

1

2

   

4

5

6

0

1

2

3

0

1

2

3

4

5

6

   

6

0

1

2

3

4

5

   

0

1

2

3

4

5

6

4

5

6

0

1

2

3

   

2

3

4

5

6

0

1

   

3

4

5

6

0

1

2

1

2

3

4

5

6

0

   

5

6

0

1

2

3

4

   

6

0

1

2

3

4

5

 

 

 

 1x number +1 [level 3]     +   7x number [Level 3]          +    49x number [Level 3]

0

1

2

3

4

5

6

   

3

4

5

6

0

1

2

   

0

1

2

3

4

5

6

4

5

6

0

1

2

3

   

6

0

1

2

3

4

5

   

3

4

5

6

0

1

2

1

2

3

4

5

6

0

   

2

3

4

5

6

0

1

   

6

0

1

2

3

4

5

5

6

0

1

2

3

4

   

5

6

0

1

2

3

4

   

2

3

4

5

6

0

1

2

3

4

5

6

0

1

   

1

2

3

4

5

6

0

   

5

6

0

1

2

3

4

6

0

1

2

3

4

5

   

4

5

6

0

1

2

3

   

1

2

3

4

5

6

0

3

4

5

6

0

1

2

   

0

1

2

3

4

5

6

   

4

5

6

0

1

2

3

 

 

 

 1x number +1 [level 4]     +   7x number [Level 4]          +    49x number [Level 4]

2

3

4

5

6

0

1

   

5

6

0

1

2

3

4

   

5

6

0

1

2

3

4

6

0

1

2

3

4

5

   

1

2

3

4

5

6

0

   

1

2

3

4

5

6

0

3

4

5

6

0

1

2

   

4

5

6

0

1

2

3

   

4

5

6

0

1

2

3

0

1

2

3

4

5

6

   

0

1

2

3

4

5

6

   

0

1

2

3

4

5

6

4

5

6

0

1

2

3

   

3

4

5

6

0

1

2

   

3

4

5

6

0

1

2

1

2

3

4

5

6

0

   

6

0

1

2

3

4

5

   

6

0

1

2

3

4

5

5

6

0

1

2

3

4

   

2

3

4

5

6

0

1

   

2

3

4

5

6

0

1

 

 

 

 1x number +1 [level 5]     +   7x number [Level 5]          +    49x number [Level 5]

4

5

6

0

1

2

3

   

0

1

2

3

4

5

6

   

3

4

5

6

0

1

2

1

2

3

4

5

6

0

   

3

4

5

6

0

1

2

   

6

0

1

2

3

4

5

5

6

0

1

2

3

4

   

6

0

1

2

3

4

5

   

2

3

4

5

6

0

1

2

3

4

5

6

0

1

   

2

3

4

5

6

0

1

   

5

6

0

1

2

3

4

6

0

1

2

3

4

5

   

5

6

0

1

2

3

4

   

1

2

3

4

5

6

0

3

4

5

6

0

1

2

   

1

2

3

4

5

6

0

   

4

5

6

0

1

2

3

0

1

2

3

4

5

6

   

4

5

6

0

1

2

3

   

0

1

2

3

4

5

6

 

 

 

 1x number +1 [level 6]     +   7x number [Level 6]          +    49x number [Level 6]

6

0

1

2

3

4

5

   

2

3

4

5

6

0

1

   

1

2

3

4

5

6

0

3

4

5

6

0

1

2

   

5

6

0

1

2

3

4

   

4

5

6

0

1

2

3

0

1

2

3

4

5

6

   

1

2

3

4

5

6

0

   

0

1

2

3

4

5

6

4

5

6

0

1

2

3

   

4

5

6

0

1

2

3

   

3

4

5

6

0

1

2

1

2

3

4

5

6

0

   

0

1

2

3

4

5

6

   

6

0

1

2

3

4

5

5

6

0

1

2

3

4

   

3

4

5

6

0

1

2

   

2

3

4

5

6

0

1

2

3

4

5

6

0

1

   

6

0

1

2

3

4

5

   

5

6

0

1

2

3

4

 

 

 

 1x number +1 [level 7]     +   7x number [Level 7]          +    49x number [Level 7]

1

2

3

4

5

6

0

   

4

5

6

0

1

2

3

   

6

0

1

2

3

4

5

5

6

0

1

2

3

4

   

0

1

2

3

4

5

6

   

2

3

4

5

6

0

1

2

3

4

5

6

0

1

   

3

4

5

6

0

1

2

   

5

6

0

1

2

3

4

6

0

1

2

3

4

5

   

6

0

1

2

3

4

5

   

1

2

3

4

5

6

0

3

4

5

6

0

1

2

   

2

3

4

5

6

0

1

   

4

5

6

0

1

2

3

0

1

2

3

4

5

6

   

5

6

0

1

2

3

4

   

0

1

2

3

4

5

6

4

5

6

0

1

2

3

   

1

2

3

4

5

6

0

   

3

4

5

6

0

1

2

 

= 

Sym. & panm. 7x7x7 [Level 1]

242

250

307

21

71

128

185

15

72

129

186

243

251

308

187

244

252

302

16

73

130

303

17

74

131

188

245

246

132

189

239

247

304

18

75

248

305

19

76

133

183

240

77

127

184

241

249

306

20

             
             

Sym. & panm. 7x7x7 [Level 2]

111

168

218

275

332

46

54

276

333

47

55

112

162

219

56

106

163

220

277

334

48

221

278

335

49

50

107

164

43

51

108

165

222

279

336

166

223

280

330

44

52

109

331

45

53

110

167

224

274

             
             

Sym. & panm. 7x7x7 [Level 3]

22

79

136

193

201

258

315

194

202

259

309

23

80

137

310

24

81

138

195

203

253

139

196

197

254

311

25

82

255

312

26

83

140

190

198

84

134

191

199

256

313

27

200

257

314

28

78

135

192

             
             

Sym. & panm. 7x7x7 [Level 4]

283

340

5

62

119

169

226

63

113

170

227

284

341

6

228

285

342

7

57

114

171

1

58

115

172

229

286

343

173

230

287

337

2

59

116

338

3

60

117

174

231

281

118

175

225

282

339

4

61

             
             

Sym. & panm. 7x7x7 [Level 5]

152

209

266

316

30

87

144

317

31

88

145

153

210

260

146

154

204

261

318

32

89

262

319

33

90

147

148

205

91

141

149

206

263

320

34

207

264

321

35

85

142

150

29

86

143

151

208

265

322

             
             

Sym. & panm. 7x7x7 [Level 6]

70

120

177

234

291

299

13

235

292

300

14

64

121

178

8

65

122

179

236

293

301

180

237

294

295

9

66

123

296

10

67

124

181

238

288

125

182

232

289

297

11

68

290

298

12

69

126

176

233

             
             

Sym. & panm. 7x7x7 [Level 7]

324

38

95

103

160

217

267

104

161

211

268

325

39

96

269

326

40

97

105

155

212

98

99

156

213

270

327

41

214

271

328

42

92

100

157

36

93

101

158

215

272

329

159

216

273

323

37

94

102

 

 

Extra magic features:

  • The 7x7x7 cube is symmetric;
  • The 7x7x7 cube is panmagic in each level;
  • Thee 7x7x7 cube is pandiagonal magic through the levels

 

History
See on website http://www.multimagie.com/English/Perfectcubes.htm#FirstPerfect  that Rev. A.H. Frost constructed the first symmetric panmagic 7x7x7 cube in 1866!!! Probably he used the same construction method (but with alternate shifts).

 

 

Use the shift method to construct magic cubes of odd order and from 9x9x9 and up the result is Nasik. See on this website the shift method for:

5x5x57x7x79x9x911x11x1113x13x1315x15x1517x17x1719x19x1921x21x21,

23x23x2325x25x2527x27x2729x29x2931x31x31

 

Download
7x7x7, panmagic.xls
Microsoft Excel werkblad 163.0 KB
Download
7x7x7, Analysis Frost's 7x7x7 magic cube
Microsoft Excel werkblad 220.5 KB