Related papers: Educational Challenges of Rubik's Cube
We develop infinitary analogues of the $N\times N\times N$ Rubik's cube. We'll be pushed to consider the possibility of transfinitely many twists and the foremost question we shall study is whether or not all infinite scrambles are…
We encounter mathematical problems in various forms in our lives, thus making mathematical thinking an important human ability. In this paper, we present Bublz!, a simple, click-driven game for children to engage in and develop mathematical…
Due to their pedagogical advantages, large final projects in information visualization courses have become standard practice. Students take on a client--real or simulated--a dataset, and a vague set of goals to create a complete…
Several articles deal with tilings with squares and dominoes on 2-dimensional boards, but only a few on boards in 3-dimensional space. We examine a tiling problem with colored cubes and bricks of $(2\times2\times n)$-board in three…
Reinforcement Learning is a mature technology, often suggested as a potential route towards Artificial General Intelligence, with the ambitious goal of replicating the wide range of abilities found in natural and artificial intelligence,…
Fun acts as a catalyst for learning by enhancing motivation, active engagement and knowledge retention. As social robots gain traction as educational tools, understanding how their unique affordances can be leveraged to cultivate fun…
This paper presents results from the design and testing of an educational version of Quantum Moves, a Scientific Discovery Game that allows players to help solve authentic scientific challenges in the effort to develop a quantum computer.…
The diameter of the Cayley graph of the Rubik's Cube group is the fewest number of turns needed to solve the Cube from the hardest initial configuration. For the 2$\times$2$\times$2 Cube, the diameter is 11 in the half-turn metric, 14 in…
The core mechanical system is built around three stepper motors for physical manipulation, a microcontroller for hardware control, a camera and YOLO detection model for real-time cube state detection. A significant software component is the…
This thesis captures the ongoing development of twisted cubes, which is a modification of cubes (in a topological sense) where its homotopy type theory does not require paths or higher paths to be invertible. My original motivation to…
This paper extends the work started in 2002 by Demaine, Demaine and Verill (DDV) on coin-moving puzzles. These puzzles have a long history in the recreational literature, but were first systematically analyzed by DDV, who gave a full…
Tangible interfaces in mixed reality (MR) environments allow for intuitive data interactions. Tangible cubes, with their rich interaction affordances, high maneuverability, and stable structure, are particularly well-suited for exploring…
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 result that optimally solving an $n \times…
This paper intends to introduce a game-based 3D Virtual Learning Environment (VLE) to second graders. The impetus arose from the need to make learning in mathematics more effective and interesting through multimedia. Applied in a game, the…
In this lecture I will talk about three mathematical puzzles involving mathematics and computation that have preoccupied me over the years. The first puzzle is to understand the amazing success of the simplex algorithm for linear…
Based on the rules of magic cubes, a game of two-dimensional magic cube was deliberately designed. This essay will explore its properties with the assistance of group theory and computer programming. It will first elaborate the rules of…
Mathematical reasoning with algebraic and graphical representations is essential for success in physics courses. Many problems require students to fluently move between algebraic and graphical representations. We developed a freely…
In the evolving landscape of education, robotics has emerged as a powerful tool for fostering creativity, critical thinking, and problem-solving skills among students of all ages. This innovative approach to learning seamlessly integrates…
This article proposes and discusses qualitatively the use of a didactic board game in Science Education for high school students. The game contemplates in an interdisciplinary way the areas of Physics, Biology, Chemistry and Astronomy and…
The design of a serious game is presented that served as an instrument to motivate and aid to Physics education using active and ludic learning, specifically the topic of free fall of objects, with diverse educational purposes, first to…