Related papers: Educational Challenges of Rubik's Cube
The Rubik's cube was invented in 1974 by Erno Rubik, who had no idea of the incredible popularity and mathematical fascinations his toy would bring. Through the years of study on the mathematical properties of the cube, the Rubik's Cube…
Learning to solve a Rubik's Cube requires the learners to repeatedly practice a skill component, e.g., identifying a misplaced square and putting it back. However, for 3D physical tasks such as this, generating sufficient repeated practice…
This work describes in detail how to learn and solve the Rubik's cube game (or puzzle) in the General Board Game (GBG) learning and playing framework. We cover the cube sizes 2x2x2 and 3x3x3. We describe in detail the cube's state…
Rubik's Cube is one of the most famous combinatorial puzzles involving nearly $4.3 \times 10^{19}$ possible configurations. Its mathematical description is expressed by the Rubik's group, whose elements define how its layers rotate. We…
The Rubix Cube is a 3-dimensional single-player combination puzzle attracting attention in the reinforcement learning community. A Rubix Cube has six faces and twelve possible actions, leading to a small and unconstrained action space and a…
A generally intelligent agent must be able to teach itself how to solve problems in complex domains with minimal human supervision. Recently, deep reinforcement learning algorithms combined with self-play have achieved superhuman…
Since its first appearance, transformers have been successfully used in wide ranging domains from computer vision to natural language processing. Application of transformers in Reinforcement Learning by reformulating it as a sequence…
We present a learning-based approach to solving a Rubik's cube with a multi-fingered dexterous hand. Despite the promising performance of dexterous in-hand manipulation, solving complex tasks which involve multiple steps and diverse…
The Rubiks Cube, with its vast state space and sparse reward structure, presents a significant challenge for reinforcement learning (RL) due to the difficulty of reaching rewarded states. Previous research addressed this by propagating…
We describe in details the nxnxn Rubik's Cube, namely a Rubik's Cube with n rotating slices in each face. Then we state and prove the "first law of Cubology", i.e. the solvability criterion, for it
We introduce higher-dimensional cubical sliding puzzles that are inspired by the classical 15 Puzzle from the 1880s. In our puzzles, on a $d$-dimensional cube, a labeled token can be slid from one vertex to another if it is topologically…
We present our game, Cube2Pipes, as an attempt to investigate a unique gameplay design where we use a tangible 3D spatial puzzle, in the form of a 2X2 Rubik's Cube, as an interface to a tabletop mobile augmented reality (AR) game. The game…
The Rubik's cube is a famous puzzle in which faces can be moved and the corresponding movement operations define a group. We consider here a generalization to any $3$-valent map. We prove an upper bound on the size of the corresponding…
Games and puzzles play important pedagogical roles in STEM learning. New AI algorithms that can solve complex problems offer opportunities for scaffolded instruction in puzzle solving. This paper presents the ALLURE system, which uses an AI…
In intuitive physics the process of stacking cubes has become a paradigmatic, canonical task. Even though it gets employed in various shades and complexities, the very fundamental setting with two cubes has not been thoroughly investigated.…
Rubik's Revenge, a 4x4x4 variant of the Rubik's puzzles, remains to date as an unsolved puzzle. That is to say, we do not have a method or successful categorization to optimally solve every one of its approximately $7.401 \times 10^{45}$…
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…
With a vast domain of applications and now having quantum computing hardware available for commercial use, an education challenge arises in getting people of various background to become quantum literate. Quantum Odyssey is a new piece of…
Existing combinatorial search methods are often complex and require some level of expertise. This work introduces a simple and efficient deep learning method for solving combinatorial problems with a predefined goal, represented by Rubik's…
We demonstrate that models trained only in simulation can be used to solve a manipulation problem of unprecedented complexity on a real robot. This is made possible by two key components: a novel algorithm, which we call automatic domain…