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====Solution Counts For Homogeneous Sets====
These counts avoid equivalent sets where the dice are simply relabeled. In other words, these counts assume that in the string representation of a solution the first “a” appears before the first “b” which appears before the first “c”, and so on.

===Legend===
|  | Players  |
|  Sides  | Unique pairwise subsets in solutions / Solutions / Search Space  |

  * ? = Unknown
  * x = Mathematically Impossible (s<sup>n</sup> % s! != 0)

===No Restrictions===
|  | 2  | 3  | 4  | 5  | 6  |
|  6  |29 / 29 / 462  |7 / 11 / 2858856  |0 / 0 / 96197645544  | x  | x  |
|  12  |30554 / 30554 / 1352078  |12986 / 3304324 / 564121960420200  |133 / 3374 / 9.82538756092255E+24  | x  |x   |
|  18  |56546511 / 56546511 / 4537567650  |? / ? / 1.46603287914294E+23  |? / ? / 1.51852014619867E+39  | x  | x  |
|  24  |? / 131377492010 / 16123801841550  |? / ? / 4.27294812093299E+31  |? / ? / 2.78828220975061E+53  | x  | x  |
|  30  |? / ? / 59132290782429200  |? / ? / 1.32679649279208E+40  |? / ? / 5.63043962364763E+67  |? / ? / 3.62586633628878E+98  |? / ? / 8.010847767853E+131  |
|  60  |? / ? / 4.83074544201835E+34  |? / ? / 5.81159881097334E+82  |? / ? / 3.5355588160268E+139  |? / ? / 6.3936307475257E+202  |? / ? / 1.6666596220405E+271  |


===Mirrored===
|  | 2  | 3  | 4  | 5  | 6  |
|  6  | 10 / 10 / 10   | 0 / 0 / 280  | 0 / 0 / 15400  | x  | x  |
|  12  | 462 / 462 / 462  | 135 / 916 / 2858856  | 20 / 187 / 96197645544  | x  | x  |
|  18  | 24310 / 24310 / 24310  | 6521 / 767975 / 37978905250  | 1278 / 84588 / 893864677761053000  | x  | x  |
|  24  | 1352078 / 1352078 / 1352078  | ? / 3163085576 / 564121960420200  | ? / ? / 9.82538756092255E+24  | x  | x  |
|  30  | 77558760 / 77558760 / 77558760  | ? / 15050285682919 / 8915829964229030000  | ? / ? / 1.1856736358608E+32 | ? / ? / 5.40670186413478E+46  | ? / ? / 4.12672592988253E+62  |
|  60  | 59132290782429200 / 59132290782429200 / 59132290782429200  | ? / ? / 1.32679649279208E+40  | ? / ? / 5.63043962364763E+67  | ? / ? / 3.62586633628878E+98  | ? / ? / 8.010847767853E+131  |

===Column Grouped===
|  | 2  | 3  | 4  | 5  | 6  |
|  6  | 10 / 10 / 32  | 6 / 10 / 7776  | 0 / 0 / 7962624  | x  | x  |
|  12  | 462 / 462 / 2048  | 317 / 11572 / 362797056  | 10 / 128 / 1521681143169020  | x  | x  |
|  18  | 24310 / 24310 / 131072  | 18889 / 74646644 / 16926659444736  | 105 / 3828 / 2.90797794982684E+23  | x  | x  |
|  24  | 1352078 / 1352078 / 8388608  | ? / ? / 789730223053611000  | ? / ? / 5.55723240354287E+31  | x  | x  |
|  30  | 77558760 / 77558760 / 536870912  | ? / ? / 3.68456532867889E+22  | ? / ? / 1.06200365064067E+40  | ? / ? / 1.9781359483314E+60  | ? / ? / 7.28857113063509E+82  |
|  60  | ? / ? / 576460752303421000  | ? / ? / 8.14561299678166E+45  | ? / ? / 2.70684420953785E+81  | ? / ? / 4.6956261960971E+122  | ? / ? / 3.8248753770958E+168  |

===Mirrored + Column Grouped===
|  | 2  | 3  | 4  | 5  | 6  |
|  6  | 4 / 4 / 4  | 0 / 0 / 36  | 0 / 0 / 576  | -  | -  |
|  12  | 32 / 32 / 32  | 17 / 38 / 7776  | 4 / 16 / 7962624  | -  | -  |
|  18  | 256 / 256 / 256  | 154 / 1492 / 1679616  | 23 / 456 / 110075314176  | -  | -  |
|  24  | 2048 / 2048 / 2048  | 1403 / 163960 / 362797056  | 163 / 329984 / 1521681143169020  | -  | -  |
|  30  | 16384 / 16384 / 16384  | 12202 / 17966790 / 78364164096  | 1131 / 246985190 / 21035720123168500000  | 0 / 0 / 1.28391846454886E+29  | 0 / 0 / 1.00613197241791E+40  |
|  60  | 536870912 / 536870912 / 536870912  | ? / ? / 3.68456532867889E+22  | ? / ? / 1.06200365064067E+40  | ? / ? / 1.9781359483314E+60  | ? / ? / 7.28857113063509E+82  |

===Column Paired===
|  | 2  | 3  | 4  | 5  | 6  |
|  6  | 4 / 4 / 4  | ? / 8 / 36  | 0 / 0 / 576  | -  | -  |
|  12  | 32 / 32 / 32  | ? / 960 / 7776  | ? / 64 / 7962624  | -  | -  |
|  18  | 256 / 256 / 256  | ? / 143360 / 1679616  | ? / 1024 / 110075314176  | -  | -  |
|  24  | 2048 / 2048 / 2048  | ? / 23654400 / 362797056  | ? / 1236992 / 1521681143169020  | -  | -  |
|  30  | 16384 / 16384 / 16384  | ? / 4132896768 / 78364164096  | ? / ? / 21035720123168500000  | ? / 0 / 1.28391846454886E+29  | ? / 0 / 1.00613197241791E+40  |
|  60  | 536870912 / 536870912 / 536870912  | ? / ? / 3.68456532867889E+22  | ? / ? / 1.06200365064067E+40  | ? / ? / 1.9781359483314E+60  | ? / ? / 7.28857113063509E+82  |

===Mirrored + Column Paired===
|  | 2  | 3  | 4  | 5  | 6  |
|  6  | 2 / 2 / 2  | ? / 0 / 6  | 0 / 0 / 24  | -  | -  |
|  12  | 4 / 4 / 4  | ? / 8 / 36  | ? / 8 / 576  | -  | -  |
|  18  | 16 / 16 / 16  | ? / 0 / 1296  | ? / 0 / 331776  | -  | -  |
|  24  | 32 / 32 / 32  | ? / 960 / 7776  | ? / 12480 / 7962624  | -  | -  |
|  30  | 128 / 128 / 128  | ? / 0 / 279936  | ? / 0 / 4586471424  | ? / 0 / 358318080000000  | ? / 0 / 1.0030613004288E+20  |
|  60  | 16384 / 16384 / 16384  | ? / 4132896768 / 78364164096  | ? / ? / 21035720123168500000  | ? / ? / 1.28391846454886E+29  | ? / ? / 1.00613197241791E+40  |
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