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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.

Most of these numbers were calculated by Landon Kryger and Brandon Enright. Exceptions to this are noted in the footnotes.

===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  | ? / 1382404516 [1] / 789730223053611000  | ? / ? / 5.55723240354287E+31  | x  | x  |
|  30  | 77558760 / 77558760 / 536870912  | ? / ? / 3.68456532867889E+22  | ? / ? / 1.06200365064067E+40  | ? / 0 / 1.9781359483314E+60  | ? / 0 / 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  |

[1] found by Kayla Toll
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