homogeneous_solutions

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 (sⁿ % 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