# Algorithms for Solving Rubik's Cubes

@article{Demaine2011AlgorithmsFS, title={Algorithms for Solving Rubik's Cubes}, author={Erik D. Demaine and Martin L. Demaine and Sarah Eisenstat and Anna Lubiw and Andrew Winslow}, journal={ArXiv}, year={2011}, volume={abs/1106.5736} }

The Rubik's Cube is perhaps the world's most famous and iconic puzzle, well-known to have a rich underlying mathematical structure (group theory). In this paper, we show that the Rubik's Cube also has a rich underlying algorithmic structure. Specifically, we show that the n×n×n Rubik's Cube, as well as the n×n× 1 variant, has a "God's Number" (diameter of the configuration space) of Θ(n2/ log n). The upper bound comes from effectively parallelizing standard Θ(n2) solution algorithms, while the…

## 37 Citations

Solving the Rubik's Cube Optimally is NP-complete

- Mathematics, Computer ScienceSTACS
- 2018

In this paper, we prove that optimally solving an $n \times n \times n$ Rubik's Cube is NP-complete by reducing from the Hamiltonian Cycle problem in square grid graphs. This improves the previous…

On Algorithms for Solving the Rubik's Cube

- Computer ScienceArXiv
- 2020

A novel algorithm and its three variations for solving the Rubik's cube more efficiently and its algorithmic complexity of $O(n^2)$ is presented.

Advanced Rubik's Cube Algorithmic Solver

- Computer Science2021 7th International Conference on Automation, Robotics and Applications (ICARA)
- 2021

A technical solution for building an Advanced Rubik's Cube Algorithmic Solver (ARCAS), that uses a PC and an Arduino Due board as processing units and an implementation of Kociemba's algorithm and blindfolded method to solve the cube.

Zero Knowledge with Rubik's Cubes and Non-abelian Groups

- Mathematics, Computer ScienceCANS
- 2013

A public key identification scheme based on the problem of the Rubik's cube when the number of moves is fixed to a given value, which includes an interactive protocol which is zero-knowledge argument of knowledge under the assumption of the existence of a commitment scheme.

Comparison of Rubik’s Cube Solving Methods Made for Humans

- Computer Science
- 2015

The conclusion is that the CFOP, Roux, and ZZ method are fairly equivalent when it comes to move span, but CFOP has the lowest average number of moves used to solve a Rubik’s Cube.

Manu Will Unfold The Rubik’s Manifold: 42 Easy Steps To Solving The Cube

- Physics
- 2021

We have provided a simple step by step guide to solving the Rubik’s cube. We have aimed for this document to be completely self contained and yet easy to follow. We have described all the required…

Solving Rubik’s cube via quantum mechanics and deep reinforcement learning

- PhysicsJournal of Physics A: Mathematical and Theoretical
- 2021

Rubik’s cube is one of the most famous combinatorial puzzles involving nearly 4.3 × 1019 possible configurations. Its mathematical description is expressed by the Rubik’s group, whose elements define…

Rubik's for cryptographers

- Mathematics, Computer ScienceIACR Cryptol. ePrint Arch.
- 2011

This study studies mathematical generalizations of the famous Rubik’s cube puzzle, namely the factorization, representation and balance problems in non-Abelian groups and demonstrates that Cayley hash functions deserve further interest by the cryptography community.

Hamiltonian cycle and related problems : vertex-breaking, grid graphs, and Rubik's Cubes

- Mathematics
- 2017

In this thesis, we analyze the computational complexity of several problems related to the Hamiltonian Cycle problem. We begin by introducing a new problem, which we call Tree-Residue Vertex-Breaking…

Layers Method Implementation for Rubik’s Cube Solution

- Computer Science, Education
- 2017

This article will be presented step by step how to solve Rubik’s cube 3x3 by using layers method and show each detail side of Rubik's cube to facilitate new users to use and learn an application made by applying layers method.

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