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According to our practical experiments and literature search - computer algebra system GAP cannot "solve" Rubik's cube 4x4x4 and higher. … PS Here is an example from GAP tutorial to handle the standard 3x3x3 Rubik's cube: https://www.math.rwth-aachen.de/homes/GAP/WWW2/Doc/Examples/rubik.html …

The diameter of the Rubik's cube group for $n=4$ won't be high. My guesstimate would be that a typical random element would have an expression with $<100$, or at least in the order of magnitude. … But that's not at all needed to solve the cube, which is what you are asking about. …

Finding OPTIMAL (i.e. the shortest length) is known to be hard problem, even for some particular choices of generators: "Solving the Rubik's Cube Optimally is NP-complete" (see also: TCS783), "Bill Gates …

cube by a (possibly infinite) sequence of twists (without the Solver watching), presents the scrambled cube to the Solver, and the Solver attempts to unscramble it by a sequence of twists. … The cube Let $L$ be a linear order with no greatest element, write its reverse as $-L$. …

However, it seems that there is not a complete, comprehensive algorithm that uses the Schreier-Sims method to solve the Rubik's Cube. … Is there any simple introduction of using the Schreier-Sims method to solve the Rubik's Cube? …

I guess, by "solving the Rubik's cube" you mean expressing arbitrary words in the group as words in the six defining generators. … I tried doing this with ten random elements of the Rubik cube group in Magma. …

A Mathematica notebook that implements the algorithm is at Solving Rubik's Cube using the Schreier-Sims Algorithm. The Schreier-Sims algorithm is highly inefficient, as explained here. …

Rubik's cube are exactly the same task, see also Mark Sapir's MO, and so on. …

Which explains how one can come to $N^2log(N)$ estimate of the diameter of the N-dimensional Rubik cube. (See also MO77836). … Which are related to globe ("Masterball"), not cube puzzles. The detailed definition of that family of groups can be found here MSE4848434. …

The groups include N-dimensional Rubik's cube and other puzzle motivated groups like "Globe". … For example even the diameters of the N-dimensional Rubik's cube are still unknown, so computational experiments may shed light on these questions. …

//www.kaggle.com/competitions/santa-2023/discussion/470799#2622617 : Computational experiment not sure I am interpreting the outcomes correctly - but it seems that for some Cayley graphs for Rubik's cube …

Consider higher (NxNxN) Rubik's cube group, with specific set of generators described below. What is important - that there are huge COMMUTING subsets of generators. … The diameter for N-Rubik cube group seems still to be unknown. And that open problem seems which might be tackled by AI methods (to some extent), moreover it can be seen like "toy-model". …

For example ongoing (December 2023 - January 2024: "Santa 2023 - The Polytope Permutation Puzzle") is challenge to propose algorithms/solutions for Rubik's cube like puzzles for a given list of configurations … Mathematically speaking it means - we are asked to find the shortest path(s) between two given nodes of the Cayley graph of the Rubik's cube group (or coset, or some of its modifications). …

A neural network can, given a scrambled cube, suggest the next action toward solving it. … Their neural network-guided tree search, once trained, can perfectly solve a scrambled cube. …

The Cube was solved by reducing the total problem size to "only" 2,217,093,120 distinct tests, which could be run in parallel. … search the rest, if the problem size is on the order of the Cube search? (Maybe too much to hope for that someone knows this....) Any partial information in this vein? …