Pentultimate simulator and solver

Play a virtual Pentultimate in your browser, or enter the colors of your own Pentultimate and get a solution.

Info

Pieces

Type	Count	Stickers	Positions	Orientation (physical)	Orientation (visual)
6	12	1	12	5	1
6	20	3	20	3	3

One row per orbit. Orientation counts are per position; multiple values mean positions differ.

Stickers

72

Axes

66 cut planes across them

Solver

Available

Distinct-piece states

≈ 5.64 × 10³³338,614,404,853,905,491,534,363,492,352,000,000 arrangements of the stickers the moves reach (Schreier–Sims)÷ 60 turns of the whole puzzle= 5,643,573,414,231,758,192,239,391,539,200,000Tracks individual sticker identities, even on identical-looking pieces; whole-puzzle rotations are identified. Invisible rotations of a piece and internal pieces are not counted.

Visually distinct states

Not computedVisually distinct states = distinct-piece states ÷ reachable indistinguishable arrangements.Reachable indistinguishable arrangements = 1 × reachable fraction.No visually interchangeable sticker-bearing pieces were found.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 12 reaches the original sticker identities12!·1¹² · 20!·3²⁰ = 4,063,372,858,246,865,898,412,361,908,224,000,000 ways to put the pieces in: per type of piece, its pieces in any order and each in any orientation that looks different÷ 338,614,404,853,905,491,534,363,492,352,000,000 arrangements the moves reach = 12This uses distinct piece identities; the chance of reaching a visually solved state may be higher.

Moves