To a mathematician, cryptography means public-key encryption using a one-way trapdoor
function. We often teach it as an elegant application of results in number theory, such as the …

We give an expository account of our computational proof that every position of the Rubik's
Cube can be solved in 20 moves or fewer, where a move is defined as any twist of any face …

Recently, methods such as DeepCubeA have used deep reinforcement learning to learn
domain-specific heuristic functions in a largely domain-independent fashion. However, such …

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 …

Recently, Approximate Policy Iteration (API) algorithms have achieved superhuman
proficiency in two-player zero-sum games such as Go, Chess, and Shogi without human …

Handbook of Cubik Math is a book about problem solving and some of the fundamental
techniques used in problem solving throughout mathematics and science. Both the …

Rubik's cube is a famous mathematical puzzle invented by Ern Rubik in 1974. The goal of
the puzzle is to restore the cube from a scrambled state to its original state, where each face …

Tis are lecture notes I prepared for a course on Computational Group Teory which I taught in
the Springs of 2006, 2010, and 2024 at Colorado State University. Te audience consisted …

This article presents a design proposal for a socially engaging, architecturally dynamic, and
adaptable pavilion that fosters interaction among individuals. The pavilion aims to bridge the …

The most common application of graph theory is search problems. Using graph theory, this
project aims to solve one such NP-hard problem, ie, finding a path for a Rubik's cube to …