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Talk:Sicherman dice

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84: 74: 53: 22: 745: 604: 463: 752: 340: 140: 747:, thus producing the labelings 1,2,3,3,4,4,5,6 and 1,2,5,5,6,6,9,10. Other non-traditional arrangements lead to 1,2,2,3,5,6,6,7 and 1,3,3,5,5,7,7,9 or 1,2,2,3,3,4,4,5 and 1,3,5,5,7,7,9,11. 248: 780: 130: 775: 162:
The mathematical justification tells that it's also possible to extend it into other Dices. So what are the other Sicherman Dices? for D8 for D20
106: 609: 468: 756: 97: 58: 345: 33: 253: 21: 182: 39: 83: 167: 105:
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89: 73: 52: 163: 769: 102: 79: 760: 171: 740:{\displaystyle x(x+1)(x^{4}+1)^{2}=x+x^{2}+2x^{5}+2x^{6}+x^{9}+x^{10}} 599:{\displaystyle x(x+1)(x^{2}+1)^{2}=x+x^{2}+2x^{3}+2x^{4}+x^{5}+x^{6}} 15: 458:{\displaystyle (x(x+1)(x^{2}+1)^{2})(x(x+1)(x^{4}+1)^{2})} 612: 471: 348: 256: 185: 158:
Are there any Sicherman Dices for Other N-Side Dices?
101:, a collaborative effort to improve the coverage of 739: 598: 457: 334: 242: 335:{\displaystyle (x(x+1)(x^{2}+1)(x^{4}+1))^{2}} 8: 19: 342:and arrange these non-traditionally, e.g. 47: 731: 718: 705: 689: 673: 654: 638: 611: 590: 577: 564: 548: 532: 513: 497: 470: 446: 430: 393: 377: 347: 326: 307: 285: 255: 234: 224: 199: 184: 243:{\displaystyle (x+x^{2}+...+x^{8})^{2}} 49: 753:2003:DF:770D:1D00:41D1:3C1F:9358:DB4D 7: 95:This article is within the scope of 38:It is of interest to the following 14: 781:Low-priority mathematics articles 115:Knowledge:WikiProject Mathematics 776:Start-Class mathematics articles 118:Template:WikiProject Mathematics 82: 72: 51: 20: 135:This article has been rated as 651: 631: 628: 616: 510: 490: 487: 475: 452: 443: 423: 420: 408: 402: 399: 390: 370: 367: 355: 349: 323: 319: 300: 297: 278: 275: 263: 257: 231: 186: 172:09:42, 27 September 2023 (UTC) 1: 109:and see a list of open tasks. 761:13:24, 15 August 2024 (UTC) 797: 134: 67: 46: 141:project's priority scale 98:WikiProject Mathematics 741: 600: 459: 336: 244: 28:This article is rated 742: 601: 460: 337: 245: 610: 469: 346: 254: 183: 121:mathematics articles 737: 596: 455: 332: 240: 90:Mathematics portal 34:content assessment 155: 154: 151: 150: 147: 146: 788: 746: 744: 743: 738: 736: 735: 723: 722: 710: 709: 694: 693: 678: 677: 659: 658: 643: 642: 605: 603: 602: 597: 595: 594: 582: 581: 569: 568: 553: 552: 537: 536: 518: 517: 502: 501: 464: 462: 461: 456: 451: 450: 435: 434: 398: 397: 382: 381: 341: 339: 338: 333: 331: 330: 312: 311: 290: 289: 249: 247: 246: 241: 239: 238: 229: 228: 204: 203: 123: 122: 119: 116: 113: 92: 87: 86: 76: 69: 68: 63: 55: 48: 31: 25: 24: 16: 796: 795: 791: 790: 789: 787: 786: 785: 766: 765: 727: 714: 701: 685: 669: 650: 634: 608: 607: 586: 573: 560: 544: 528: 509: 493: 467: 466: 442: 426: 389: 373: 344: 343: 322: 303: 281: 252: 251: 230: 220: 195: 181: 180: 160: 120: 117: 114: 111: 110: 88: 81: 61: 32:on Knowledge's 29: 12: 11: 5: 794: 792: 784: 783: 778: 768: 767: 764: 763: 750: 749: 748: 734: 730: 726: 721: 717: 713: 708: 704: 700: 697: 692: 688: 684: 681: 676: 672: 668: 665: 662: 657: 653: 649: 646: 641: 637: 633: 630: 627: 624: 621: 618: 615: 593: 589: 585: 580: 576: 572: 567: 563: 559: 556: 551: 547: 543: 540: 535: 531: 527: 524: 521: 516: 512: 508: 505: 500: 496: 492: 489: 486: 483: 480: 477: 474: 454: 449: 445: 441: 438: 433: 429: 425: 422: 419: 416: 413: 410: 407: 404: 401: 396: 392: 388: 385: 380: 376: 372: 369: 366: 363: 360: 357: 354: 351: 329: 325: 321: 318: 315: 310: 306: 302: 299: 296: 293: 288: 284: 280: 277: 274: 271: 268: 265: 262: 259: 237: 233: 227: 223: 219: 216: 213: 210: 207: 202: 198: 194: 191: 188: 179:You can split 159: 156: 153: 152: 149: 148: 145: 144: 133: 127: 126: 124: 107:the discussion 94: 93: 77: 65: 64: 56: 44: 43: 37: 26: 13: 10: 9: 6: 4: 3: 2: 793: 782: 779: 777: 774: 773: 771: 762: 758: 754: 751: 732: 728: 724: 719: 715: 711: 706: 702: 698: 695: 690: 686: 682: 679: 674: 670: 666: 663: 660: 655: 647: 644: 639: 635: 625: 622: 619: 613: 591: 587: 583: 578: 574: 570: 565: 561: 557: 554: 549: 545: 541: 538: 533: 529: 525: 522: 519: 514: 506: 503: 498: 494: 484: 481: 478: 472: 447: 439: 436: 431: 427: 417: 414: 411: 405: 394: 386: 383: 378: 374: 364: 361: 358: 352: 327: 316: 313: 308: 304: 294: 291: 286: 282: 272: 269: 266: 260: 250:into factors 235: 225: 221: 217: 214: 211: 208: 205: 200: 196: 192: 189: 178: 177: 176: 175: 174: 173: 169: 165: 157: 142: 138: 132: 129: 128: 125: 108: 104: 100: 99: 91: 85: 80: 78: 75: 71: 70: 66: 60: 57: 54: 50: 45: 41: 35: 27: 23: 18: 17: 161: 137:Low-priority 136: 96: 62:Low‑priority 40:WikiProjects 112:Mathematics 103:mathematics 59:Mathematics 30:Start-class 770:Categories 164:Supyovalk 139:on the 36:scale. 465:with 757:talk 606:and 168:talk 131:Low 772:: 759:) 733:10 170:) 755:( 729:x 725:+ 720:9 716:x 712:+ 707:6 703:x 699:2 696:+ 691:5 687:x 683:2 680:+ 675:2 671:x 667:+ 664:x 661:= 656:2 652:) 648:1 645:+ 640:4 636:x 632:( 629:) 626:1 623:+ 620:x 617:( 614:x 592:6 588:x 584:+ 579:5 575:x 571:+ 566:4 562:x 558:2 555:+ 550:3 546:x 542:2 539:+ 534:2 530:x 526:+ 523:x 520:= 515:2 511:) 507:1 504:+ 499:2 495:x 491:( 488:) 485:1 482:+ 479:x 476:( 473:x 453:) 448:2 444:) 440:1 437:+ 432:4 428:x 424:( 421:) 418:1 415:+ 412:x 409:( 406:x 403:( 400:) 395:2 391:) 387:1 384:+ 379:2 375:x 371:( 368:) 365:1 362:+ 359:x 356:( 353:x 350:( 328:2 324:) 320:) 317:1 314:+ 309:4 305:x 301:( 298:) 295:1 292:+ 287:2 283:x 279:( 276:) 273:1 270:+ 267:x 264:( 261:x 258:( 236:2 232:) 226:8 222:x 218:+ 215:. 212:. 209:. 206:+ 201:2 197:x 193:+ 190:x 187:( 166:( 143:. 42::

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