rules to play rubiks cube

Rotations are named by the name of the face. A rotation X rotates the face X clockwise by 90

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

These pages describe basic rules in designing algorithms to solve the Rubiks Cube. Based on these rules, a strategy (the Strategy of 8 Corners) is built. You would develop a new perspective of the cube, with which you can design algorithms and strategies on your own. Some prior experience on meddling with the cube and on using algorithms are needed.
The algorithms are demonstrated using Neil Rashbrooks java applet showing the Rubiks Cube. Learn how to use it before you start! Also, you should turn off the JIT compiler to order to use the applet.
If it is your first visit, start with the first link (Background and Naming of the Parts) below.

The essence of my solution is a new paradigm. A new way to look at the cube.The way you look at something affects how you think about it, and affects what you think you can do to it. If you see it as a cube with six faces that you can turn, you would very soon be frustrated by the wild number of interactions between the things you can do. Each of your rotation makes changes to the four adjacent faces, and soon you lose track of what is happening.

Alternatively, you may view the cube as three layers, and attempt to solve them one by one. You would have a hard time trying to move pieces around on the second and third layer without destroying the layer you have built.

In the theory below, we work on subsets of the cube in manageable bits. We look only at the subset and forget about the rest of the cube, so that the complexity will be contained in the subset. More important, we would ask what we want to do in the subset, and why we choose the particular movements to achieve our goals.

From Mathematics, a vector space of dimension N can be spanned by N basis vectors. It has been proven that two algorithms alone are sufficient to span the whole pattern space of the cube (and therefore can bring you to any pattern, including solving the cube). Unfortunately, these two sequences are very very long, and you need to combine them in the correct way to arrive at the desired target pattern.

On the other hand, it is obvious that the six basic face movements can solve the cube. This fact is hardly useful because the face movements themselves affect too many pieces each time. Therefore, they cannot help us to achieve meaningful goals.

Notice that corners always move to corners and edges to edges. You can never move a corner to an edge. Therefore, they are very different objects, and should be treated separately. The minimum basis vectors I have chosen are

CM3 moves 3 corners, preserving other corners
CT2 twists 2 corners, preserving other corners
EM3 moves 3 edges, preserving all other pieces
EF2 flips 2 edges, preserving all other pieces

Since the Strategy of 8 Corners settles corners first, corner algorithms can affect edges, but edge algorithms must preserve corners.

These basis algorithms, together with their mirror images and conjugates (see below), are sufficient to solve the cube. Notice that by looking at the cube as corners and edges, you have to handle only two scenarios how to work with corners, and how to work with edges. For each scenario, you have only two things to do move them around, or fliptwist them in place. That is all you need to solve the cube.

Three things are always conserved by any algorithm total number of twists (modulus 3), total number of flips (modulus 2), and total number of piece exchanges (modulus 2). This is a useful property when you are designing algorithms you do not have to worry that the cube might end up with one edge flipped, or two corners twisted in the same direction

When performing edge movements, view the eight corners as if it is an iron cage. Feel the strain when you twist them from their original positions. All algorithms end by relieving this strain, therefore preserving the corners. Remember the paradigm is more important than the sequences themselves.There will be more and more slice movements (M, C, S), because the three slices flows (like rivers) without affecting the corners. After all, every edge lies on a slice; while slices consist only of edges and centers, and no corners. On the other hand, there is no movement that move corners but not edges. This asymmetry leads to the observation that edges are easier to settle than corners, and the logical conclusion that we should settle all the corner before any of the edges.

Since EM1 affects FD, there will be one edge in U and one in D that cannot be settled by EM1. Solve them simultaneously as follows
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Move the edge required at FD to UF (using some form of EM1B), and the edge required at UF to BR using Mn; then
EM1BR will capture BR into UF, while at the same time moving UF to FD.
This assumes that at least one of the two required pieces is in the M slice. It does not work if FD and UF are occupying each others location. In that case, we consider it as an edge exchange (FD,FU) and settle them later.

At this stage, all U and D edges (except perhaps the exchange required at the end of last section) have been settled. Physically rotate the cube sideways to view the remaining four M edges as C edges.w that both the the R and L faces (ie the original U and D faces) have been (largely) settled, we shift to a new paradigm. Regard these two faces as two metal plates with the C slice in between. Only this C slice have edges to be solved. They can always be solved with either of the following algorithms with suitable conjugates of Cn.

Noting that C moves one C edge to another, EM3