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Info
Pieces
Type
Count
Stickers
Positions
Orientation (physical)
Orientation (visual)
1
2
1
2
6
1
2
12
1
12
1
1
3
12
1
12
1
1
4
12
1
12
1
1
4
12
1
12
1
1
4
6
2
6
2
2
4
6
1
6
2
1
5
12
3
12
1
1
5
12
2
12
1
1
One row per orbit. Orientation counts are per position; multiple values mean positions differ.
Stickers
128
Axes
414 cut planes across them
Solver
Available
Distinct-piece states
≈ 3.26 × 10⁵⁴39,135,131,252,060,644,840,305,371,365,368,294,895,779,840,000,000,000,000 arrangements of the stickers the moves reach (Schreier–Sims)÷ 12 turns of the whole puzzle= 3,261,260,937,671,720,403,358,780,947,114,024,574,648,320,000,000,000,000Tracks individual sticker identities, even on identical-looking pieces; whole-puzzle rotations are identified. Invisible rotations of a piece and internal pieces are not counted.
Indistinguishable arrangements
72,220,413,630,873,600,000,0006! × 6! × 6! × 6! × 6! × 6! × 6! × 6! = 72,220,413,630,873,600,000,0008 groups of visually interchangeable pieces within their movement orbits, using the original stickers.Counts all permutations within these groups, without checking which combinations are reachable. Internal pieces are excluded because the state count tracks stickers only.
Visually distinct states
Not computedVisually distinct states = distinct-piece states ÷ reachable indistinguishable arrangements.Reachable indistinguishable arrangements = 72,220,413,630,873,600,000,000 × reachable fraction.The reachable fraction accounts for restrictions such as permutation parity. Computing the correct fraction and the final visual state count is not yet implemented.
Put together at random
1 in 20,480 reaches the original sticker identities12!·1¹² · 12!·1¹² · 12!·1¹² · 12!·1¹² · 12!·1¹² · 12!·1¹² · 2!·1² · 6!·2⁶ · 6!·1⁶ = 801,487,488,042,202,006,329,454,005,562,742,679,465,571,123,200,000,000,000,000 ways to put the pieces in: per type of piece, its pieces in any order and each in any orientation that looks different÷ 39,135,131,252,060,644,840,305,371,365,368,294,895,779,840,000,000,000,000 arrangements the moves reach = 20,480This uses distinct piece identities; the chance of reaching a visually solved state may be higher.