Solving the Rubik's Cube Systematically

The Strategy of 8 Corners was first developed by one of my classmate, Mr. Edward Leung. The basic rules of his original design include:

- edges are easier to move corners
- edges on the middle slice (planes without corners) are the easiest to move
- the symmetry of the cube should be exploited

More basic rules have been discovered, and are used to reselect the algorithms used.

This section deals with how to name things.

We usually start the cube in a random configuration.
The aim is to **solve** the cube.
That is, to restore it back to the configuration where each face shows only one colour.

A **strategy** is a system of algorithms solving the cube.
It specifies the sequence of sub-goal to be attained, and the algorithm to be used in each situation.
Strategies and algorithms need not have an one to one correspondence: a strategy references many algorithms, and an algorithm can be used in many strategies.
The strategy presented here is **the Strategy of 8 Corners**.

Names are assigned to parts of the cube. All names are relative to the spatial directions irrespective of colour of the faces.

The six faces are called Right, Left, Up, Down, Front, and Back. Although they are perfectly symmetric, algorithms concentrates their movements on the R/D/U/F faces (in descending priority). Observation are nearly always made on F/U faces. Thus, the algorithms usually move faces easiest to move and observations are on faces easiest to observe.

The twelve edges are called by the name of the two faces forming the edge: e.g. UR. When calling a single edge, UR can be called RU also.

The eight corners are called by the name of the three faces forming the corner: e.g. URF.

Rotations are named by the name of the face.
A rotation X rotates the face X clockwise by 90°, viewed from the exterior of the cube towards the face X.
Therefore, R moves RF to RU, but L moves LF to LD.
R^{-1} moves the R face in the opposite direction: it is the inverse of R.

We move the slices (the six central planes without corners) as well.

- The slice between R and L is called Center. C moves in the same direction as R: e.g., Centre moves FD to UF.
- The slice between U and D is called Middle. M moves in the same direction as U: e.g., M moves FR to LF.
- The slice between F and B is called S (nameless slice). S moves in the same direction as F: e.g., S moves LU to UR. S is rarely used because this slice is very difficult to access.

Demonstrating the following moves: R C L, U M D, F S B in this order. Notice that R and L actually rotates in opposite directions because of the way they are defined. Click the triangular arrow to see each move in turn.
In |

A corner at a certain place can have three states. Algorithms that take a corner from one state to another twists a corner. For pratical reasons, twisting is considered undefined when a corner does not stay at the same place. Mathematically, twisting can still be defined, but only in a less intuitive way of little concern to us.

When viewed from the exterior toward the corner,
a clockwise twist of 120° is called positive (e.g. URF →
RFU, or simply X → X_{+}).
Twisting in the opposite direction is called negative (e.g. URF → FUR, or
simply X → X_{-}).
Note that X_{++} º X_{-}, and X_{+++} º X.

An edge at a certain place can have two states.
Algorithms that take an edge from one state to another flips an edge.
Flipping is considered undefined when an edge is moved to another place.
An example of flipping is UR → RU,
or simply X → X_{+}.
Note that X_{++} º X.

If X is an algorithm, then X^{-1} applies X backwards, and making all face movements in the opposite direction.

If X = YÅZ (i.e. Y followed by Z), X^{-1} = Z^{-1}ÅY^{-1}

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