Rubik's Cube Solution - with 7 Algorithms (i.e. series of steps to complete a particular cube manipulation)

* Preamble  *

'Rubik's Cube is a 3-D combination puzzle invented in 1974 by Hungarian sculptor and professor of 
architecture Ernő Rubik ... [with over] 350 million cubes sold ... worldwide making it ... the world's 
best-selling toy,' according to Wikipedia, and the cube has become an excellent means through the use of 
algorithms to retard the onset of Alzheimer's disease; although, admittedly some have accused this
infuriating little cube of causing dementia! (i.e. It has over 43 quintillion possible positions!) 
There may be other reasons to solve it as well.

Before attempting to solve the cube, one should play with it for a while to become familiar with 
how it works.  Within a little time, most beginners can solve one face intuitively, but it is from here 
on that things start to become quite difficult.  By now, however, one can make a number of important 
observations about the cube: i) it has "center" pieces which are fixed (i.e. they do not move) relative 
to each other (i.e. white is opposite yellow, blue is opposite green, and red is opposite orange; at 
least on most current models), and ii) it has eight "corner" and twelve "edge" pieces which move relative 
to each other. To solve multiple faces, one needs algorithms so let us get back to algorithms.

Algorithms are a set of steps to accomplish some task.  Solving a Rubik's cube requires following a number 
of steps that are called algorithms.  In the algorithms to describe a solution to Rubik's cube, it will be 
useful to use some shorthand notation: F=Front-side (i.e. face towards user), R=Right-side, L=Left-side, 
U=Upper-side (i.e. on top). Normally the steps to solve Rubik's Cube involve a series of quarter (1/4) 
turns in the clockwise direction when looking directly at the face (i.e. side of the cube) being rotated. 
When there is a need for counterclockwise quarter turn, the following symbol will follow the letter 
indicating the face to turn ` (i.e. R` will mean rotate the right-hand face, from the user's point of view, 
one quarter turn counterclockwise). Furthermore, when there is a need to rotate a face 180 degrees, it will 
be useful to follow the letter indicating the face to turn with the number 2 to indicate a double turn 
(i.e. 180 degrees) or two 1/4 turns in succession. N.B. Obviously the direction one turns a face 180 
degrees is unimportant, since the result is the same. Most of the Rubik's cube algorithms can be broken 
down into a three stage process: undo-reposition-redo, with each stage consisting of 1-4 turns.  It will 
be useful in solution algorithms to refer to three the horizontal cube levels as: upper-layer, middle-layer, 
bottom-layer.  Finally, unless told to rotate the cube itself, generally it is helpful to always keep 
the same face of the cube facing towards the user.

Finally, this text-based non-graphical write-up may not be the easiest to read nor the quickest to perform, 
as there are many other algorithms that complete multiple manipulations at the same time and are used by 
power-solvers of the cube (in fact, it has been proven that God would need no more than 20 moves at most 
to solve a Rubik's 3x3 cube).  These seven algorithms are, however, easy for a novice to memorise and 
enable a person to complete the cube in 3-5 minutes in about 100-130 turns if one has not learned 
speed-turning techniques.  They also document one of the first set of algorithms this author used to solve 
the cube.  (M. Wells - 2016 version 1.0) PS. I use the cube to delay the onset of alzheimers ;-}


* Complete the first-layer: (Solve this level using "intuitive moves".) *

1) With white-colored center-piece on the bottom-layer, create, using the edge pieces, a small-white-diamond 
on the upper-layer by just using your eyes to rotate the pieces into position (i.e. this is 
called using "intuitive moves"). Finally, flip the diamond to the bottom-layer by using your eyes 
intuitively to align each white-colored edge-piece's adjacent color with its corresponding 
same-colored center-piece and then immediately rotate the upper-edge-piece 180degrees (i.e. two 1/4 turns) 
to create, after doing this with all four white-edge-pieces, a white cross on the bottom-layer.
2) Using your eyes, intuitively move each white-colored corner-piece into its correct position on the 

Hint for the white-colored corner-pieces: an easy algorithm to aim for when the white corner piece is 
situated upper-front-right directly above the position where it needs to be inserted in the bottom-layer, 
and at the same time with the corner's white face facing out to the right, is as follows: 

R-U-R` (i.e. right-face 1/4 turn clockwise, upper face 1/4 turn clockwise, and right face 1/4 turn 

Alternatively, when the corner-piece is situated (by rotating the cube itself) upper-front-left directly 
above the position where it is to be inserted in the bottomlayer and at the same time with the corner's 
white-face facing out to the left, one mirrors the previous algorithm as follows: 

L`-U`-L (i.e. left-face counterclockwise 1/4 turn, upper-face counterclockwise 1/4 turn, and left-face 
clockwise 1/4 turn). 

One may have to intuitively manipulate the white-colored corner-pieces and rotate the cube itself to get 
them into one of these two starting positions for the algorithm: i) upper-front-right or 
ii) upper-front-left.

At this point one complete layer of the three layers of the cube to complete should be finished.


* Complete the second level: (Using one algorithm of 8 turns.) *

3) To begin this algorithm that moves upper-edge-pieces into their appropriate place on the middle-layer, 
align a upper-edge-piece's color with its corresponding center to allow it to be moved from the upper-layer 
into its correct place on the middle-layer. 
- if the edge-piece's upper-side color corresponds to the right-face center-piece's color then: 
- if the edge piece's upper-side color corresponds to the left-face center-piece's color then: 
U`L`U-LU-FU`F`  (i.e. these are mirror moves or mirror algorithms)
N.B. if a middle-layer's edge-piece is already in the middle-layer but positioned wrongly, use one of the 
above algorithms to move another incorrect top-layer-edge piece into the middle-layer-edge piece's 
position in the middle-layer and then redo one of the above algorithms to move the middle-layer-edge piece 
back into the correct position in the middle-layer.


* Complete the third level: (Using four algorithms of 6 to 12 turns.)  *

i) orientate upper-layer-edge pieces to complete a cross using the upper-layer center-piece's color, 
ii) orientate upper-layer corner pieces with the correct color facing upwards,
iii) correctly position the upper-layer-edge-pieces, 
iv) correcly position the upper-layer-corner-pieces.

4) To complete a cross on the top layer, four top layer shapes are possible, all of which are formed using 
the color of the top center piece: i) a unicolor bar exists in the top layer, ii) a unicolor backward's L 
exists on the top layer positioned on the top-back-left (one may have to turn to cube to get it into the 
back left position), iii) a cross is already formed, or iv) none of the previous three shapes exist.
i) if one has a single color bar shape, using the upper center piece's color, horizontal to the user, then: 
ii) if you have a backwards L formed with the center piece's color and positioned on the upper-back-left 
corner, then: 
iii) do nothing, it is already complete. (Luck!)
iv) use either of moves i) or ii) and then one of the first two shapes will appear and then repeat 
i) or ii). (N.B. Repeating either of these algorithms from 1 to 3 times will complete this pattern.)

There should be a single-color cross on the top now.

5) To flip the corner pieces so that the whole top layer is now the same color (albeit probably in the 
wrong positions), use combination of the following two algorithms. First we must name the corner pieces. 
When looking at the four upper layer corner pieces and starting with the upper-back-left corner piece, 
it will be called '1', the upper-back-right corner piece called '2', the upper-front-right corner piece 
called '3', and the upper-front-left corner piece called '4'. 
i) to rotate corner's 1, 3, and 4 clockwise while leaving corner 2 unchanged, use: 
LUL`U-LU2L` (called Zune, named by its swedish inventer.)
ii) to rotate corner's 2, 3, and 4 counter-clockwise while leaving corner 1 unchanged, use: 
R`U`RU-`RU2R` (called Anti-Zune)
The idea is for the first use of one of the above algorithms to leave only one upper corner piece's 
upper face color correct and for the other three upper corner piece's upper color to be on a side and 
then for the second use of one of the above algorithms, after having moved the upper corner piece with 
the upper face's color correct to either upper corner piece's position 1 or 2 depending on whether the 
other corner pieces need to be rotated clockwise, and hence use algorithm i) or on the contrary the three 
other corner pieces need rotating counter-clockwise, and hence use algorithm ii) to complete the upper 
layer with all the upper layer pieces showing the correct color on the upper face.

6) Move the upper corner pieces to their correct position on the top layer.  Three possibilities exist: 
i) none or one upper corner piece is in its correct position, ii) two upper corner pieces are in their 
correct position, iii) all four upper corner pieces are in their correct position. 
This algorithm moves, in a trangular fashion, corner piece 2 to 3, and 3 to 4, and 4 to 2, leaving 1 
i) do: 
ii) position the two correctly placed upper corner pieces with their other color facing the use 
(tailight position): use the same algorithm as i).
iii) do nothing, Luck!

7) Move the upper-edge-pieces to their correct position in the upper layer. Three posibilities exist: 
i) none of the upper-edge-pieces is in its correct place with regards to their corresponding upper-corner- 
piece's color, 
ii) one of the upper-edge-pieces is in its correct place with regards to its corresponding upper corner 
pieces' color, 
iii) all four upper-edge-pieces are in their correct position. Luck!

The solution algorithms for each of these possibilities are as follows:
i) do: 
it doesn't matter which as they are mirror algorithms (i.e. the same moves in the opposite direction).
ii) Move the correct upper-edge-piece to the front side by rotating the cube. Next if the other three 
upper-edge-pieces need to move in a clockwise triangular way (i.e. from upper-left to upper-back, 
from upper-back to upper-right and from upper-right to upper-left) then do: 
from 1), or otherwise, if the upper-edge pieces need to move in a counter-clockwise triangular way 
(i.e. from upper-right to upper-back, from upper-back to upper-left, and upper-left to upper-right) then do: 
(NB: at a minimum, one might memorize only one of these two mirror algorithms and repeat it from 1-3 times 
to complete the upper-layer.)
iii) Puzzle solved! Smile and pat yourself on the back.


* In a nutshell *

1st layer 1) create a small diamond on top and flip upper-layer-edge pieces to the bottom, intuitively.
          2) insert correctly the bottom-layer-corner pieces: R-U-R` or L`-U`-L
2nd layer 3) move upper-edge-pieces to middle layer (to the right) UR`U`-R`U`-FUF or (left) U`L`U-LU-FU`F`
3rd layer 4) orientate upper-layer-edge pieces into a cross: FRU-R`U`F` or FUR-U`R`F` (1-3 times) 
          5) orientate upper-layer-corner pieces: LUL`U-LU2L` Zune and/or R`U`RU-`RU2R` Antizune (1-2 times)
          6) position the upper-layer-corner pieces: F2R2-FLF`R2-FL`F (1-3 times) 
          7) position the upper-layer-edge pieces: R`UR`-U`R`U`R`-URUR2 or LU`L-ULUL-U`L`U`L2 (1-3 times).