Is Rubix cube math?

Yes, the Rubik's Cube is absolutely related to math.

The relationship between the Rubik's Cube and mathematics is primarily found in the mathematical structure called a group, specifically group theory. The moves you can make on a Rubik's Cube form a group, and this mathematical structure is what allows for the development of algorithms to solve the cube. You can solve Rubik's cube using two basic ideas from group theory: commutators and conjugation.

Mathematical Concepts Involved:

• Group Theory: The set of possible moves on a Rubik's Cube, along with the operation of move composition (doing one move after another), forms a mathematical group.
• Algorithms: Solution strategies for the Rubik's Cube are essentially algorithms that utilize group theory principles to navigate the cube's possible states and reach the solved state.

How Group Theory Helps Solve the Cube:

1. Understanding Permutations: Each move on the Rubik's Cube can be thought of as a permutation of the cube's pieces. Group theory provides the tools to analyze and understand these permutations.
2. Finding Commutators: A commutator is a sequence of moves of the form A B A' B', where A' is the inverse of move A and B' is the inverse of move B. Commutators have the property that they often affect only a small number of pieces, leaving the rest of the cube unchanged. This makes them incredibly useful for solving the cube piece by piece.
3. Conjugation: Conjugation involves transforming one operation by another, usually to reposition or reorient cube pieces.