magichypercube.4n: Magic hypercubes of order 4n
In magic: Create and Investigate Magic Squares
Description
Usage
Arguments
Details
Author(s)
Examples
Description
Returns magic hypercubes of order 4n and any dimension.
Usage
1
magichypercube.4n(m, d = 3)
Arguments
m
Magic hypercube produced of order n=4m
d
Dimensionality of cube
Details
Uses a rather kludgy (but vectorized) method. I am not 100% sure that
the method does in fact produce magic squares for all orders and dimensions.
Author(s)
Robin K. S. Hankin
Examples
1
2
magichypercube.4n(1,d=4)
magichypercube.4n(2,d=3)
Example output
Loading required package: abind
, , 1, 1
[,1] [,2] [,3] [,4]
[1,] 1 252 248 13
[2,] 255 6 10 243
[3,] 254 7 11 242
[4,] 4 249 245 16
, , 2, 1
[,1] [,2] [,3] [,4]
[1,] 240 21 25 228
[2,] 18 235 231 30
[3,] 19 234 230 31
[4,] 237 24 28 225
, , 3, 1
[,1] [,2] [,3] [,4]
[1,] 224 37 41 212
[2,] 34 219 215 46
[3,] 35 218 214 47
[4,] 221 40 44 209
, , 4, 1
[,1] [,2] [,3] [,4]
[1,] 49 204 200 61
[2,] 207 54 58 195
[3,] 206 55 59 194
[4,] 52 201 197 64
, , 1, 2
[,1] [,2] [,3] [,4]
[1,] 192 69 73 180
[2,] 66 187 183 78
[3,] 67 186 182 79
[4,] 189 72 76 177
, , 2, 2
[,1] [,2] [,3] [,4]
[1,] 81 172 168 93
[2,] 175 86 90 163
[3,] 174 87 91 162
[4,] 84 169 165 96
, , 3, 2
[,1] [,2] [,3] [,4]
[1,] 97 156 152 109
[2,] 159 102 106 147
[3,] 158 103 107 146
[4,] 100 153 149 112
, , 4, 2
[,1] [,2] [,3] [,4]
[1,] 144 117 121 132
[2,] 114 139 135 126
[3,] 115 138 134 127
[4,] 141 120 124 129
, , 1, 3
[,1] [,2] [,3] [,4]
[1,] 128 133 137 116
[2,] 130 123 119 142
[3,] 131 122 118 143
[4,] 125 136 140 113
, , 2, 3
[,1] [,2] [,3] [,4]
[1,] 145 108 104 157
[2,] 111 150 154 99
[3,] 110 151 155 98
[4,] 148 105 101 160
, , 3, 3
[,1] [,2] [,3] [,4]
[1,] 161 92 88 173
[2,] 95 166 170 83
[3,] 94 167 171 82
[4,] 164 89 85 176
, , 4, 3
[,1] [,2] [,3] [,4]
[1,] 80 181 185 68
[2,] 178 75 71 190
[3,] 179 74 70 191
[4,] 77 184 188 65
, , 1, 4
[,1] [,2] [,3] [,4]
[1,] 193 60 56 205
[2,] 63 198 202 51
[3,] 62 199 203 50
[4,] 196 57 53 208
, , 2, 4
[,1] [,2] [,3] [,4]
[1,] 48 213 217 36
[2,] 210 43 39 222
[3,] 211 42 38 223
[4,] 45 216 220 33
, , 3, 4
[,1] [,2] [,3] [,4]
[1,] 32 229 233 20
[2,] 226 27 23 238
[3,] 227 26 22 239
[4,] 29 232 236 17
, , 4, 4
[,1] [,2] [,3] [,4]
[1,] 241 12 8 253
[2,] 15 246 250 3
[3,] 14 247 251 2
[4,] 244 9 5 256
, , 1
[,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8]
[1,] 512 9 17 488 480 41 49 456
[2,] 2 503 495 26 34 471 463 58
[3,] 3 502 494 27 35 470 462 59
[4,] 509 12 20 485 477 44 52 453
[5,] 508 13 21 484 476 45 53 452
[6,] 6 499 491 30 38 467 459 62
[7,] 7 498 490 31 39 466 458 63
[8,] 505 16 24 481 473 48 56 449
, , 2
[,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8]
[1,] 65 440 432 89 97 408 400 121
[2,] 447 74 82 423 415 106 114 391
[3,] 446 75 83 422 414 107 115 390
[4,] 68 437 429 92 100 405 397 124
[5,] 69 436 428 93 101 404 396 125
[6,] 443 78 86 419 411 110 118 387
[7,] 442 79 87 418 410 111 119 386
[8,] 72 433 425 96 104 401 393 128
, , 3
[,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8]
[1,] 129 376 368 153 161 344 336 185
[2,] 383 138 146 359 351 170 178 327
[3,] 382 139 147 358 350 171 179 326
[4,] 132 373 365 156 164 341 333 188
[5,] 133 372 364 157 165 340 332 189
[6,] 379 142 150 355 347 174 182 323
[7,] 378 143 151 354 346 175 183 322
[8,] 136 369 361 160 168 337 329 192
, , 4
[,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8]
[1,] 320 201 209 296 288 233 241 264
[2,] 194 311 303 218 226 279 271 250
[3,] 195 310 302 219 227 278 270 251
[4,] 317 204 212 293 285 236 244 261
[5,] 316 205 213 292 284 237 245 260
[6,] 198 307 299 222 230 275 267 254
[7,] 199 306 298 223 231 274 266 255
[8,] 313 208 216 289 281 240 248 257
, , 5
[,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8]
[1,] 256 265 273 232 224 297 305 200
[2,] 258 247 239 282 290 215 207 314
[3,] 259 246 238 283 291 214 206 315
[4,] 253 268 276 229 221 300 308 197
[5,] 252 269 277 228 220 301 309 196
[6,] 262 243 235 286 294 211 203 318
[7,] 263 242 234 287 295 210 202 319
[8,] 249 272 280 225 217 304 312 193
, , 6
[,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8]
[1,] 321 184 176 345 353 152 144 377
[2,] 191 330 338 167 159 362 370 135
[3,] 190 331 339 166 158 363 371 134
[4,] 324 181 173 348 356 149 141 380
[5,] 325 180 172 349 357 148 140 381
[6,] 187 334 342 163 155 366 374 131
[7,] 186 335 343 162 154 367 375 130
[8,] 328 177 169 352 360 145 137 384
, , 7
[,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8]
[1,] 385 120 112 409 417 88 80 441
[2,] 127 394 402 103 95 426 434 71
[3,] 126 395 403 102 94 427 435 70
[4,] 388 117 109 412 420 85 77 444
[5,] 389 116 108 413 421 84 76 445
[6,] 123 398 406 99 91 430 438 67
[7,] 122 399 407 98 90 431 439 66
[8,] 392 113 105 416 424 81 73 448
, , 8
[,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8]
[1,] 64 457 465 40 32 489 497 8
[2,] 450 55 47 474 482 23 15 506
[3,] 451 54 46 475 483 22 14 507
[4,] 61 460 468 37 29 492 500 5
[5,] 60 461 469 36 28 493 501 4
[6,] 454 51 43 478 486 19 11 510
[7,] 455 50 42 479 487 18 10 511
[8,] 57 464 472 33 25 496 504 1
magic documentation built on May 2, 2019, 12:21 p.m.
R Package Documentation
Browse R Packages
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Note that we can't provide technical support on individual packages. You should contact the package authors for that.
Description Usage Arguments Details Author(s) Examples
Description
Returns magic hypercubes of order 4n and any dimension.
Usage
1 | magichypercube.4n(m, d = 3)
|
Arguments
m |
Magic hypercube produced of order n=4m |
d |
Dimensionality of cube |
Details
Uses a rather kludgy (but vectorized) method. I am not 100% sure that the method does in fact produce magic squares for all orders and dimensions.
Author(s)
Robin K. S. Hankin
Examples
1 2 | magichypercube.4n(1,d=4)
magichypercube.4n(2,d=3)
|
Example output
Loading required package: abind
, , 1, 1
[,1] [,2] [,3] [,4]
[1,] 1 252 248 13
[2,] 255 6 10 243
[3,] 254 7 11 242
[4,] 4 249 245 16
, , 2, 1
[,1] [,2] [,3] [,4]
[1,] 240 21 25 228
[2,] 18 235 231 30
[3,] 19 234 230 31
[4,] 237 24 28 225
, , 3, 1
[,1] [,2] [,3] [,4]
[1,] 224 37 41 212
[2,] 34 219 215 46
[3,] 35 218 214 47
[4,] 221 40 44 209
, , 4, 1
[,1] [,2] [,3] [,4]
[1,] 49 204 200 61
[2,] 207 54 58 195
[3,] 206 55 59 194
[4,] 52 201 197 64
, , 1, 2
[,1] [,2] [,3] [,4]
[1,] 192 69 73 180
[2,] 66 187 183 78
[3,] 67 186 182 79
[4,] 189 72 76 177
, , 2, 2
[,1] [,2] [,3] [,4]
[1,] 81 172 168 93
[2,] 175 86 90 163
[3,] 174 87 91 162
[4,] 84 169 165 96
, , 3, 2
[,1] [,2] [,3] [,4]
[1,] 97 156 152 109
[2,] 159 102 106 147
[3,] 158 103 107 146
[4,] 100 153 149 112
, , 4, 2
[,1] [,2] [,3] [,4]
[1,] 144 117 121 132
[2,] 114 139 135 126
[3,] 115 138 134 127
[4,] 141 120 124 129
, , 1, 3
[,1] [,2] [,3] [,4]
[1,] 128 133 137 116
[2,] 130 123 119 142
[3,] 131 122 118 143
[4,] 125 136 140 113
, , 2, 3
[,1] [,2] [,3] [,4]
[1,] 145 108 104 157
[2,] 111 150 154 99
[3,] 110 151 155 98
[4,] 148 105 101 160
, , 3, 3
[,1] [,2] [,3] [,4]
[1,] 161 92 88 173
[2,] 95 166 170 83
[3,] 94 167 171 82
[4,] 164 89 85 176
, , 4, 3
[,1] [,2] [,3] [,4]
[1,] 80 181 185 68
[2,] 178 75 71 190
[3,] 179 74 70 191
[4,] 77 184 188 65
, , 1, 4
[,1] [,2] [,3] [,4]
[1,] 193 60 56 205
[2,] 63 198 202 51
[3,] 62 199 203 50
[4,] 196 57 53 208
, , 2, 4
[,1] [,2] [,3] [,4]
[1,] 48 213 217 36
[2,] 210 43 39 222
[3,] 211 42 38 223
[4,] 45 216 220 33
, , 3, 4
[,1] [,2] [,3] [,4]
[1,] 32 229 233 20
[2,] 226 27 23 238
[3,] 227 26 22 239
[4,] 29 232 236 17
, , 4, 4
[,1] [,2] [,3] [,4]
[1,] 241 12 8 253
[2,] 15 246 250 3
[3,] 14 247 251 2
[4,] 244 9 5 256
, , 1
[,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8]
[1,] 512 9 17 488 480 41 49 456
[2,] 2 503 495 26 34 471 463 58
[3,] 3 502 494 27 35 470 462 59
[4,] 509 12 20 485 477 44 52 453
[5,] 508 13 21 484 476 45 53 452
[6,] 6 499 491 30 38 467 459 62
[7,] 7 498 490 31 39 466 458 63
[8,] 505 16 24 481 473 48 56 449
, , 2
[,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8]
[1,] 65 440 432 89 97 408 400 121
[2,] 447 74 82 423 415 106 114 391
[3,] 446 75 83 422 414 107 115 390
[4,] 68 437 429 92 100 405 397 124
[5,] 69 436 428 93 101 404 396 125
[6,] 443 78 86 419 411 110 118 387
[7,] 442 79 87 418 410 111 119 386
[8,] 72 433 425 96 104 401 393 128
, , 3
[,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8]
[1,] 129 376 368 153 161 344 336 185
[2,] 383 138 146 359 351 170 178 327
[3,] 382 139 147 358 350 171 179 326
[4,] 132 373 365 156 164 341 333 188
[5,] 133 372 364 157 165 340 332 189
[6,] 379 142 150 355 347 174 182 323
[7,] 378 143 151 354 346 175 183 322
[8,] 136 369 361 160 168 337 329 192
, , 4
[,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8]
[1,] 320 201 209 296 288 233 241 264
[2,] 194 311 303 218 226 279 271 250
[3,] 195 310 302 219 227 278 270 251
[4,] 317 204 212 293 285 236 244 261
[5,] 316 205 213 292 284 237 245 260
[6,] 198 307 299 222 230 275 267 254
[7,] 199 306 298 223 231 274 266 255
[8,] 313 208 216 289 281 240 248 257
, , 5
[,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8]
[1,] 256 265 273 232 224 297 305 200
[2,] 258 247 239 282 290 215 207 314
[3,] 259 246 238 283 291 214 206 315
[4,] 253 268 276 229 221 300 308 197
[5,] 252 269 277 228 220 301 309 196
[6,] 262 243 235 286 294 211 203 318
[7,] 263 242 234 287 295 210 202 319
[8,] 249 272 280 225 217 304 312 193
, , 6
[,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8]
[1,] 321 184 176 345 353 152 144 377
[2,] 191 330 338 167 159 362 370 135
[3,] 190 331 339 166 158 363 371 134
[4,] 324 181 173 348 356 149 141 380
[5,] 325 180 172 349 357 148 140 381
[6,] 187 334 342 163 155 366 374 131
[7,] 186 335 343 162 154 367 375 130
[8,] 328 177 169 352 360 145 137 384
, , 7
[,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8]
[1,] 385 120 112 409 417 88 80 441
[2,] 127 394 402 103 95 426 434 71
[3,] 126 395 403 102 94 427 435 70
[4,] 388 117 109 412 420 85 77 444
[5,] 389 116 108 413 421 84 76 445
[6,] 123 398 406 99 91 430 438 67
[7,] 122 399 407 98 90 431 439 66
[8,] 392 113 105 416 424 81 73 448
, , 8
[,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8]
[1,] 64 457 465 40 32 489 497 8
[2,] 450 55 47 474 482 23 15 506
[3,] 451 54 46 475 483 22 14 507
[4,] 61 460 468 37 29 492 500 5
[5,] 60 461 469 36 28 493 501 4
[6,] 454 51 43 478 486 19 11 510
[7,] 455 50 42 479 487 18 10 511
[8,] 57 464 472 33 25 496 504 1
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