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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 |
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 | | | | |
/ 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 |
