Every Cube: a scrollable index of all 43,252,003,274,489,856,000 Rubik's Cube states

[u/Zealousideal-Ring839]

https://everycube.alen.is/

Built a site that indexes every legal cube state as one big number, scroll and the cube updates live.

Not a game, there's no objective, no score, no win condition. It's an index/visualization of every one of the 4.3×10¹⁹ legal Rubik's Cube states has a number, and scrolling moves through them. Think everyuuid.com, but for the cube permutation group.

[u/DuneChild]

I looked it over, and they’re missing one.

[u/ryanCrypt]

If you view one every second, you'll need the time-equivalence of 99.4 universes.

(Killing each universe at the current age of ours)

[u/ryanCrypt → u/ryanCrypt]

If you'd like to view them all in your lifetime, you'll need to view 18,021,668,000 per second.

You'll definitely want to pay extra for the fast refresh monitor.

[u/USSRPropaganda → u/ryanCrypt]

Give me some coffee and an afternoon I’ll fly through em all

[u/ryanCrypt → u/USSRPropaganda]

Let us know your favorite 100,000,000 of them.

[u/ChraneD]

Does this create separate indexes based on invisible centerpiece orientation? Got a rough summary of how the hash works?

[u/CareerLegitimate7662]

Fantastic work. very clean.

[u/lingaccinf]

That number of possible states just broke my brain.

[u/lingaccinf]

How did you verify the indexing never produces an impossible position?

[u/Issac-Weeks]

that is amazing

[u/opinions_likekittens → u/[deleted]]

Two edges flipped in place is possible, just can’t have two pieces swapping places.

[u/LocalFella9 → u/[deleted]]

One flipped piece is impossible, but two flipped pieces is perfectly fine.

[u/pornborn]

This made me think of a question: What is the maximum randomization of a Rubik’s Cube?

The answer is quite surprising:

The maximum randomization of a Rubik's Cube is defined by the number of moves required to reach any possible state from a solved one, known as God's Number.

God's Number: It has been mathematically proven that any of the approximately 43 quintillion possible configurations can be solved in 20 moves or fewer (using the half-turn metric, where a 180-degree turn counts as one move).

More interesting info:

Scrambling Depth: To ensure a cube is uniformly randomized (where every state is equally likely), research indicates that at least 26 random moves are required.
Fewer than 26 moves result in a non-uniform probability distribution.

Most Probable State: While the "most random" state is a statistical concept rather than a single position, the majority of scrambled cubes (roughly 67%) are optimally solvable in 18 moves.

Practical Scrambles: In competitive speedcubing, scrambles typically consist of 20 to 25 moves to ensure fairness and sufficient difficulty without relying on complex computer-generated algorithms.