Related papers: Educational Challenges of Rubik's Cube
Thirty original and collected problems, puzzles, and paradoxes in mathematics and physics are explained in this paper, taught by the author to the elementary and high school teachers at the University of New Mexico - Gallup in 1997-8 and…
By using two different invariants for the Rubik's Magic puzzle, one of metric type, the other of topological type, we can dramatically reduce the universe of constructible configurations of the puzzle. Finding the set of actually…
Progress in understanding expert performance is limited by the scarcity of quantitative data on long-term knowledge acquisition and deployment. Here we use the Rubik's Cube as a cognitive model system existing at the intersection of puzzle…
The Rubik's Cube is the most popular puzzle in the world. Two of its studied aspects are God's Number, the minimum number of turns necessary to solve any state, and the first law of cubology, a solvability criterion. We modify previous…
The paper proposes a novel machine learning-based approach to the pathfinding problem on extremely large graphs. This method leverages diffusion distance estimation via a neural network and uses beam search for pathfinding. We demonstrate…
Puzzles based on coloured cubes and other coloured geometrical figures have a long history in the recreational mathematical literature. One of the most commercially famous of these puzzles is the Instant Insanity that consists of four…
This paper details our winning submission to Phase 1 of the 2021 Real Robot Challenge; a challenge in which a three-fingered robot must carry a cube along specified goal trajectories. To solve Phase 1, we use a pure reinforcement learning…
The prediction of the final state probabilities of a general cuboid randomly thrown onto a surface is a problem that naturally arises in the minds of men and women familiar with regular cubic dice and the basic concepts of probability.…
Rush Hour Logic was introduced in [Flake&Baum99] as a model of computation inspired by the ``Rush Hour'' toy puzzle, in which cars can move horizontally or vertically within a parking lot. The authors show how the model supports polynomial…
Tetravex is a widely played one person computer game in which you are given $n^2$ unit tiles, each edge of which is labelled with a number. The objective is to place each tile within a $n$ by $n$ square such that all neighbouring edges are…
Search algorithms are a foundational topic in artificial intelligence education, yet even simple domains can generate large state spaces that challenge learners' ability to form accurate mental models. This paper presents an interactive…
How many moves does it take to solve Rubik's Cube? Positions are known that require 20 moves, and it has already been shown that there are no positions that require 27 or more moves; this is a surprisingly large gap. This paper describes a…
We examine quadratic surfaces in 3-space that are tangent to nine given figures. These figures can be points, lines, planes or quadrics. The numbers of tangent quadrics were determined by Hermann Schubert in 1879. We study the associated…
Robotics sets have been successfully used in elementary and secondary schools in conformance with the 'learning through play' philosophy fostered by LEGO Education, while utilizing the Constructionism didactic approach. Learners discover…
We consider a puzzle such that a set of colored cubes is given as an instance. Each cube has unit length on each edge and its surface is colored so that what we call the Surface Color Condition is satisfied. Given a palette of six colors,…
Teaching Robotics is about empowering students to create and configure robotics devices and program computers to nurture in students the skill sets necessary to play an active role in society. The robot in Figure 1 focuses on the design of…
A great number of robotics applications demand the rearrangement of many mobile objects, e.g., organizing products on shelves, shuffling containers at shipping ports, reconfiguring fleets of mobile robots, and so on. To boost the throughput…
We present some fragments of a teaching experiment realized in a first grade classroom, to sow the seeds for a mathematical definition of rectangles that includes squares. Within the paradigm of semiotic mediation, we studied the emergence…
Artificial intelligence (AI) has the potential to transform education with its power of uncovering insights from massive data about student learning patterns. However, ethical and trustworthy concerns of AI have been raised but are…
A crucial skill for primary school teachers is maintaining efficient classroom management. Teachers use classroom seating arrangements to help maintain this efficiency. However, developing classroom seating arrangements is both…