Lozenge method of John Horton Conway
With the Lozenge method of John Horton Conway you get a magic square of odd order and you find all odd numbers in the (white) 'diamond' and all even numbers outside the diamond (in the dark area). See for detailed explanation: Lozenge 5x5 magic square.
Take 1x number from row grid +1
| 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | 24 | 25 | 26 | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 |
| 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | 24 | 25 | 26 | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 |
| 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | 24 | 25 | 26 | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
| 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | 24 | 25 | 26 | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |
| 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | 24 | 25 | 26 | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
| 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | 24 | 25 | 26 | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 |
| 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | 24 | 25 | 26 | 0 | 1 | 2 | 3 | 4 | 5 | 6 |
| 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | 24 | 25 | 26 | 0 | 1 | 2 | 3 | 4 | 5 |
| 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | 24 | 25 | 26 | 0 | 1 | 2 | 3 | 4 |
| 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | 24 | 25 | 26 | 0 | 1 | 2 | 3 |
| 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | 24 | 25 | 26 | 0 | 1 | 2 |
| 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | 24 | 25 | 26 | 0 | 1 |
| 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | 24 | 25 | 26 | 0 |
| 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | 24 | 25 | 26 |
| 26 | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | 24 | 25 |
| 25 | 26 | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | 24 |
| 24 | 25 | 26 | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 |
| 23 | 24 | 25 | 26 | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 |
| 22 | 23 | 24 | 25 | 26 | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 |
| 21 | 22 | 23 | 24 | 25 | 26 | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 |
| 20 | 21 | 22 | 23 | 24 | 25 | 26 | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 |
| 19 | 20 | 21 | 22 | 23 | 24 | 25 | 26 | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 |
| 18 | 19 | 20 | 21 | 22 | 23 | 24 | 25 | 26 | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 |
| 17 | 18 | 19 | 20 | 21 | 22 | 23 | 24 | 25 | 26 | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 |
| 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | 24 | 25 | 26 | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 |
| 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | 24 | 25 | 26 | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 |
| 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | 24 | 25 | 26 | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 |
+ 27x number from column grid
| 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | 24 | 25 | 26 | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 |
| 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | 24 | 25 | 26 | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 |
| 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | 24 | 25 | 26 | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 |
| 17 | 18 | 19 | 20 | 21 | 22 | 23 | 24 | 25 | 26 | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 |
| 18 | 19 | 20 | 21 | 22 | 23 | 24 | 25 | 26 | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 |
| 19 | 20 | 21 | 22 | 23 | 24 | 25 | 26 | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 |
| 20 | 21 | 22 | 23 | 24 | 25 | 26 | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 |
| 21 | 22 | 23 | 24 | 25 | 26 | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 |
| 22 | 23 | 24 | 25 | 26 | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 |
| 23 | 24 | 25 | 26 | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 |
| 24 | 25 | 26 | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 |
| 25 | 26 | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | 24 |
| 26 | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | 24 | 25 |
| 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | 24 | 25 | 26 |
| 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | 24 | 25 | 26 | 0 |
| 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | 24 | 25 | 26 | 0 | 1 |
| 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | 24 | 25 | 26 | 0 | 1 | 2 |
| 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | 24 | 25 | 26 | 0 | 1 | 2 | 3 |
| 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | 24 | 25 | 26 | 0 | 1 | 2 | 3 | 4 |
| 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | 24 | 25 | 26 | 0 | 1 | 2 | 3 | 4 | 5 |
| 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | 24 | 25 | 26 | 0 | 1 | 2 | 3 | 4 | 5 | 6 |
| 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | 24 | 25 | 26 | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 |
| 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | 24 | 25 | 26 | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
| 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | 24 | 25 | 26 | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |
| 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | 24 | 25 | 26 | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
| 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | 24 | 25 | 26 | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 |
| 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | 24 | 25 | 26 | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 |
= 27x27 Lozenge magic square
| 392 | 420 | 448 | 476 | 504 | 532 | 560 | 588 | 616 | 644 | 672 | 700 | 728 | 27 | 28 | 56 | 84 | 112 | 140 | 168 | 196 | 224 | 252 | 280 | 308 | 336 | 364 |
| 418 | 446 | 474 | 502 | 530 | 558 | 586 | 614 | 642 | 670 | 698 | 726 | 25 | 53 | 81 | 82 | 110 | 138 | 166 | 194 | 222 | 250 | 278 | 306 | 334 | 362 | 390 |
| 444 | 472 | 500 | 528 | 556 | 584 | 612 | 640 | 668 | 696 | 724 | 23 | 51 | 79 | 107 | 135 | 136 | 164 | 192 | 220 | 248 | 276 | 304 | 332 | 360 | 388 | 416 |
| 470 | 498 | 526 | 554 | 582 | 610 | 638 | 666 | 694 | 722 | 21 | 49 | 77 | 105 | 133 | 161 | 189 | 190 | 218 | 246 | 274 | 302 | 330 | 358 | 386 | 414 | 442 |
| 496 | 524 | 552 | 580 | 608 | 636 | 664 | 692 | 720 | 19 | 47 | 75 | 103 | 131 | 159 | 187 | 215 | 243 | 244 | 272 | 300 | 328 | 356 | 384 | 412 | 440 | 468 |
| 522 | 550 | 578 | 606 | 634 | 662 | 690 | 718 | 17 | 45 | 73 | 101 | 129 | 157 | 185 | 213 | 241 | 269 | 297 | 298 | 326 | 354 | 382 | 410 | 438 | 466 | 494 |
| 548 | 576 | 604 | 632 | 660 | 688 | 716 | 15 | 43 | 71 | 99 | 127 | 155 | 183 | 211 | 239 | 267 | 295 | 323 | 351 | 352 | 380 | 408 | 436 | 464 | 492 | 520 |
| 574 | 602 | 630 | 658 | 686 | 714 | 13 | 41 | 69 | 97 | 125 | 153 | 181 | 209 | 237 | 265 | 293 | 321 | 349 | 377 | 405 | 406 | 434 | 462 | 490 | 518 | 546 |
| 600 | 628 | 656 | 684 | 712 | 11 | 39 | 67 | 95 | 123 | 151 | 179 | 207 | 235 | 263 | 291 | 319 | 347 | 375 | 403 | 431 | 459 | 460 | 488 | 516 | 544 | 572 |
| 626 | 654 | 682 | 710 | 9 | 37 | 65 | 93 | 121 | 149 | 177 | 205 | 233 | 261 | 289 | 317 | 345 | 373 | 401 | 429 | 457 | 485 | 513 | 514 | 542 | 570 | 598 |
| 652 | 680 | 708 | 7 | 35 | 63 | 91 | 119 | 147 | 175 | 203 | 231 | 259 | 287 | 315 | 343 | 371 | 399 | 427 | 455 | 483 | 511 | 539 | 567 | 568 | 596 | 624 |
| 678 | 706 | 5 | 33 | 61 | 89 | 117 | 145 | 173 | 201 | 229 | 257 | 285 | 313 | 341 | 369 | 397 | 425 | 453 | 481 | 509 | 537 | 565 | 593 | 621 | 622 | 650 |
| 704 | 3 | 31 | 59 | 87 | 115 | 143 | 171 | 199 | 227 | 255 | 283 | 311 | 339 | 367 | 395 | 423 | 451 | 479 | 507 | 535 | 563 | 591 | 619 | 647 | 675 | 676 |
| 1 | 29 | 57 | 85 | 113 | 141 | 169 | 197 | 225 | 253 | 281 | 309 | 337 | 365 | 393 | 421 | 449 | 477 | 505 | 533 | 561 | 589 | 617 | 645 | 673 | 701 | 729 |
| 54 | 55 | 83 | 111 | 139 | 167 | 195 | 223 | 251 | 279 | 307 | 335 | 363 | 391 | 419 | 447 | 475 | 503 | 531 | 559 | 587 | 615 | 643 | 671 | 699 | 727 | 26 |
| 80 | 108 | 109 | 137 | 165 | 193 | 221 | 249 | 277 | 305 | 333 | 361 | 389 | 417 | 445 | 473 | 501 | 529 | 557 | 585 | 613 | 641 | 669 | 697 | 725 | 24 | 52 |
| 106 | 134 | 162 | 163 | 191 | 219 | 247 | 275 | 303 | 331 | 359 | 387 | 415 | 443 | 471 | 499 | 527 | 555 | 583 | 611 | 639 | 667 | 695 | 723 | 22 | 50 | 78 |
| 132 | 160 | 188 | 216 | 217 | 245 | 273 | 301 | 329 | 357 | 385 | 413 | 441 | 469 | 497 | 525 | 553 | 581 | 609 | 637 | 665 | 693 | 721 | 20 | 48 | 76 | 104 |
| 158 | 186 | 214 | 242 | 270 | 271 | 299 | 327 | 355 | 383 | 411 | 439 | 467 | 495 | 523 | 551 | 579 | 607 | 635 | 663 | 691 | 719 | 18 | 46 | 74 | 102 | 130 |
| 184 | 212 | 240 | 268 | 296 | 324 | 325 | 353 | 381 | 409 | 437 | 465 | 493 | 521 | 549 | 577 | 605 | 633 | 661 | 689 | 717 | 16 | 44 | 72 | 100 | 128 | 156 |
| 210 | 238 | 266 | 294 | 322 | 350 | 378 | 379 | 407 | 435 | 463 | 491 | 519 | 547 | 575 | 603 | 631 | 659 | 687 | 715 | 14 | 42 | 70 | 98 | 126 | 154 | 182 |
| 236 | 264 | 292 | 320 | 348 | 376 | 404 | 432 | 433 | 461 | 489 | 517 | 545 | 573 | 601 | 629 | 657 | 685 | 713 | 12 | 40 | 68 | 96 | 124 | 152 | 180 | 208 |
| 262 | 290 | 318 | 346 | 374 | 402 | 430 | 458 | 486 | 487 | 515 | 543 | 571 | 599 | 627 | 655 | 683 | 711 | 10 | 38 | 66 | 94 | 122 | 150 | 178 | 206 | 234 |
| 288 | 316 | 344 | 372 | 400 | 428 | 456 | 484 | 512 | 540 | 541 | 569 | 597 | 625 | 653 | 681 | 709 | 8 | 36 | 64 | 92 | 120 | 148 | 176 | 204 | 232 | 260 |
| 314 | 342 | 370 | 398 | 426 | 454 | 482 | 510 | 538 | 566 | 594 | 595 | 623 | 651 | 679 | 707 | 6 | 34 | 62 | 90 | 118 | 146 | 174 | 202 | 230 | 258 | 286 |
| 340 | 368 | 396 | 424 | 452 | 480 | 508 | 536 | 564 | 592 | 620 | 648 | 649 | 677 | 705 | 4 | 32 | 60 | 88 | 116 | 144 | 172 | 200 | 228 | 256 | 284 | 312 |
| 366 | 394 | 422 | 450 | 478 | 506 | 534 | 562 | 590 | 618 | 646 | 674 | 702 | 703 | 2 | 30 | 58 | 86 | 114 | 142 | 170 | 198 | 226 | 254 | 282 | 310 | 338 |
Use this method to construct magic squares of odd order (= 3x3, 5x5, 7x7, ... magic square).
See 3x3, 5x5, 7x7, 9x9, 11x11, 13x13, 15x15, 17x17, 19x19, 21x21, 23x23, 25x25, 27x27, 29x29 and 31x31
