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Results for rubik cube
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17
votes
GAP cannot solve Rubik's cube 4x4x4 and higher ? (Practical limits of Schreier–Sims algorithm)
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. …
- 5,654
8
votes
1
answer
1k
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GAP cannot solve Rubik's cube 4x4x4 and higher ? (Practical limits of Schreier–Sims algorithm)
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 …
- 24.9k
4
votes
0
answers
79
views
Complexity to find "short" (e.g. polynomial in diameter) decomposition of the permutation in...
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 …
- 24.9k
6
votes
0
answers
150
views
Who wins the Scrambler-Solver game for infinitary Rubik's cubes?
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 $-L$. …
14
votes
Accepted
Schreier-Sims algorithm for solving 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. …
- 37.4k
8
votes
Schreier-Sims algorithm for solving Rubik's cube
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. …
- 188k
8
votes
2
answers
1k
views
Schreier-Sims algorithm for solving Rubik's cube
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? …
- 83
3
votes
0
answers
119
views
Short path problem on Cayley graphs as language translation task (from "Permutlandski" to "C...
Rubik's cube are exactly the same task, see also Mark Sapir's MO, and so on. …
- 24.9k
1
vote
0
answers
163
views
Locally "unshortable" paths in graphs
//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 …
- 24.9k
22
votes
4
answers
2k
views
Open problems which might benefit from computational experiments
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. …
4
votes
1
answer
240
views
Diameter of the "Masterball-puzzle" permutation groups by a kind of Cartier-Foata enumeration?
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. …
- 24.9k
1
vote
0
answers
166
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Random walk on N-Rubik cube group is going like sqrt(number of moves) or linear (number of m...
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". …
- 24.9k
2
votes
Open problems with monetary rewards
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). …
5
votes
0
answers
208
views
(How) does the spectral gap of the $n\times n$ Rubik's cube close with $n$?
This gap controls the mixing properties of the cube - i.e., how fast the cube can be scrambled. A larger gap may correspond to a faster mixing. … In both the QMBS problems and the Rubik's cube, finding the gap as $n$ go off to infinity corresponds to finding the thermodynamic limit. …
- 2,185
0
votes
1
answer
284
views
How many combinations of magic square on a white Rubik's cube?
A white Rubik's cube has 6 sides. There are 9 spaces on each side for numbers from 1 to 9, without color. … If we fill each side of a white Rubik's cube with a magic square, how many combinations can be filled on this Rubik's Cube? …
