**Formula:**

Most 3×3×3 Rubik's Cube solution guides use the same notation, originated by David Sing master, to communicate sequences of moves. This is generally referred to as "cube notation" or in some literature "Sing master notation" (or variations thereof), or sometimes (but rarely) it is called "direction inferred notation" or "DIN". Its relative nature allows algorithms to be written in such a way that they can be applied regardless of which side is designated the top or how the colors are organized on a particular cube.

*F*(Front): the side currently facing you*B*(Back): the side opposite the front*U*(Up): the side above or on top of the front side*D*(Down): the side opposite the top, underneath the Cube*L*(Left): the side directly to the left of the front*R*(Right): the side directly to the right of the front*f*(Front two layers): the side facing you and the corresponding middle layer*b*(Back two layers): the side opposite the front and the corresponding middle layer*u*(Up two layers) : the top side and the corresponding middle layer*d*(Down two layers) : the bottom layer and the corresponding middle layer*l*(Left two layers) : the side to the left of the front and the corresponding middle layer*r*(Right two layers) : the side to the right of the front and the corresponding middle layer*x*(rotate): rotate the Cube up*y*(rotate): rotate the Cube to the left*z*(rotate): rotate the Cube on its side to the right

When an apostrophe follows a letter, it means to turn the face counter-clockwise a quarter-turn, while a letter without an apostrophe means to turn it a quarter-turn clockwise. Such an apostrophe mark is pronounced *prime*. A letter followed by a 2 (occasionally a superscript ²) means to turn the face a half-turn (the direction does not matter). So *R* is right side clockwise, but *R'* is right side counter-clockwise. When *x*, *y* or *z* are primed, simply rotate the cube in the opposite direction. When they are squared, rotate it twice. For 'z', you should still be viewing the same front face when rotating.

This notation can also be used on the Pocket Cube, the Revenge, and the Professor, with additional notation. They not only have the *F*, *B*, *L*, *R*, *U*, *D* notation but also *f*, *b*, *l*, *r*, *u*, *d*. For example: *(Rr)' l2 f'*

(Some solution guides, including Ideal's official publication, *The Ideal Solution*, use slightly different conventions. Top and Bottom are used rather than Up and Down for the top and bottom faces, with Back being replaced by Posterior. '+' indicates clockwise rotation and '-' counter-clockwise, with '++' representing a half-turn. However, alternative notations failed to catch on, and today the Sing master scheme is used universally by those interested in the puzzle.)

Less-often used moves include rotating the entire Cube or two-thirds of it. The letters *x*, *y*, and *z* are used to indicate that the entire Cube should be turned about one of its axes. The *x*-axis is the line that passes through the left and right faces, the *y*-axis is the line that passes through the up and down faces, and the *z*-axis is the line that passes through the front and back faces. (This type of move is used infrequently in most solutions, to the extent that some solutions simply say "stop and turn the whole cube upside-down" or something similar at the appropriate point.)

However there is another (less common) system of move notation. It is very similar to cube notation, but has a key difference that makes it less daunting to new cube solvers. It is called "direction displayed notation" or "DDN". Each move is represented by two letters. The first indicates which side is to be moved, the second indicates which direction that side is turned. from the *F* point of view.

*F*(Front): The side facing you. "R" means turn it right or clockwise. "L" means turn it left or counter-clockwise.*U*(Up): The side on top. "R" means turn it right (from the F perspective). "L" means turn it left (from the F perspective).*D*(Down): The side on the bottom. "R" means turn it right (from the F perspective). "L" means turn it left (from the F perspective).*R*(Right): The side to right. "D" means turn it downward (from the F perspective). "U" means turn it upward (from the F perspective).*L*(Left): "D" means turn it downward (from the F perspective). "U" means turn it upward (from the F perspective).

*B*(Back): The side opposite from the side facing you. This side is hardly ever used in algorithms of any notation let alone direction displayed notation. However if you need to know, first turn the entire cube so that the*B*side faces you then rotate it as if you were rotating the*F*side. "R" means turn it right or clockwise. "L" means turn it left or counter-clockwise.

To indicate a half move just put a 2 at the end of the first letter. To indicate rotation of the cube as a whole, use the same notation for direction displayed notation as one would for Sing master notation. (*x* *y* *z*)

Lowercase letters *f*, *b*, *u*, *d*, *l*, and *r* signify to move the first *two* layers of that face while keeping the remaining layer in place. This is of course equivalent to rotating the whole cube in that direction, then rotating the opposite face back the same amount in the opposite direction, but is useful notation to describe certain triggers for speed cubing. Furthermore, *M*, *E*, and *S* (and respectively their lowercase for larger sized cubes) are used for inner-slice movements. *M* signifies turning the layer that is between *L* and *R* downward (clockwise if looking from the left side). *E* signifies turning the layer between *U* and *D* towards the right (counter-clockwise if looking from the top). *S* signifies turning the layer between *F* and *B* clockwise.

For example, the algorithm (or operator, or sequence) *F2 U' R' L F2 R L' U' F2*, which cycles three edge cubes in the top layer without affecting any other part of the cube, means:

- Turn the Front face 180 degrees.
- Turn the Up face 90 degrees counter-clockwise.
- Turn the Right face 90 degrees counter-clockwise.
- Turn the Left face 90 degrees clockwise.
- Turn the Front face 180 degrees.
- Turn the Right face 90 degrees clockwise.
- Turn the Left face 90 degrees counter-clockwise.
- Turn the Up face 90 degrees counter-clockwise.
- Finally, turn the Front face 180 degrees.

For beginning students of the Cube, this notation can be daunting, and many solutions available online therefore incorporate animations that demonstrate the algorithms presented.

4×4×4 and larger cubes use slightly different notation to incorporate the middle layers. Generally speaking, uppercase letters (*F B U D L R*) refer to the outermost portions of the cube (called faces). Lowercase letters (*f b u d l r*) refer to the inner portions of the cube (called slices). Again Ideal breaks rank by describing their 4×4×4 solution in terms of layers (vertical slices that rotate about the *z*-axis), tables (horizontal slices), and books (vertical slices that rotate about the *x*-axis).

Source: http://en.wikipedia.org/wiki/Rubik%27s_Cube

Hope this formula can help you solve your Rubik’s Cube. Happy Cubing!!

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