# The Salvia method

by David J. Salvia

## Introduction

The first time I saw Rubik's cube was toward the end of 1980. I saw how it moved, and before I found one for sale several months later I thought about how to make such a thing work mechanically.
When I finally got one in 1981 I found that I liked the way it worked, and the problems it posed. By the time I finally swapped the last two corners to solve it completely for the first time, I was already trying to improve on how I solved each part. My second solve took an hour, my third took fifteen minutes.
At that time I wasn't in touch with others who were that interested in it.
At the preliminary American Championship round at Magic Mountain in the Fall of 1981 I saw many people who had solved the cube on their on, and their methods for solving were as varied as they were. That day I saw that people who believed they could solve the cube on their own did in fact figure it out.
I recommend that you try to solve the cube on your own. Take your time, be patient with yourself, and stick with it.
One man told me he solved it on paper before he had a cube. He may have had an advantage because he wrote it all down as he went along. If you write things down as you go along it may help you pay attention. The notation at the bottom of the page is the one I use for writing moves down.

If you are trying to solve the last level on your own, but you are stuck, here are two hints:
1. What you do to one piece you (may be able to) undo to another.
2. Take something out of place one way and put it back another way.

## The method

This is my method for solving the First Two Levels (F2L) of Rubik's Cube. I developed the strategy outlined on this page by looking for simple and efficient movement. The question was, "what can I solve first which leaves me the greatest freedom of movement to solve what follows?" Usually the cube can be solved this way within 33 to 54 moves.
A sequence of moves is called an algorithm, and an algorithm always has the same effect. If you repeat any algorithm enough times, the cube will return to the state you began with. That is to say, if you begin at the solved state, you will end at the solved state if you repeat any algorithm enough times. The number of repetitions needed to do this varies and depends on what the algorithm does.
The cube has 3 kinds of pieces, often called cubies. There are 12 edge pieces, 8 corner pieces, and 6 center pieces. The center pieces are firmly fixed in place and only rotate in place, they do not move with respect to one another.
There are lots of brilliant Last Level (LL) solving methods on the internet. I have included the beginner's version of my LL method because it is different from most.
This basic LL method solves the Last Level in 4 steps, so you only need to learn 4 algorithms. The first 2 steps solve the corners and the second 2 steps solve the edges. Even though it's for beginners, and you often need to apply an algorithm twice, it can solve the cube quickly.
The regular version of my Last Level method solves the LL in two steps, called CLL-ELL, that is, 44 algorithms solve the corner positions then 29 algorithms solve the edge positions.
Other than knowing how to move the pieces around efficiently, the most important technique for speedcubing is *looking ahead* for what's next. Once you are familiar with each step, the movements can become smooth and fast, and while performing them you can locate any piece(s) you wish to place next. I've included "Options" for when you are familiar with the pieces and how they move. By taking the steps labeled "Options," when you finish the F2L the LL is done as well.

### First 2 Levels

It helps if you choose which color will be the First Level when the cube is solved, and note what the opposite (Last Level) color is. I use Orange as the First Level and Red as the Last Level.
1.
Place two edge pieces, i.e. one across-the-center-of-one-side pair, on the middle level, like RF and LF (right front and left front) The four middle level edge pieces do not have the colors of the centers of the first and last levels. In my case these four edge pieces have neither Orange nor Red.
2.
Place four corners on the first level, (on top or the left)
3.
Place the other two edges on the middle level,
4.
Place the four edges of the first level; (first level now on bottom)

#### Some detail:

1. Place two middle level edge pieces - neighbors - like RF and LF (right front and left front)
Beginning with an average scramble where no edge pieces are in place, these can usually be placed at the same time in 3 or 4 moves, rarely 5.
Once in place I hold these two edge pieces (and the opposing centers they are next to) with the thumb and middle finger. I use my left hand. For the next step the First Level is on top or on the left.

2. Place four corners on the first level
If the first level in on the top, then place them using the top, bottom, and right side; if the first level in on the left, then place them using the left top, and right sides. Feeding the four corners into the first level, can sometimes be done two at a time. This varies greatly - 6 moves is common, so is 11 moves.
Notes:
The first two edges and the first two corners may be placed simultaneously.
If I switch my left hand's position while placing the corners I need to keep track of where the two in-place edge pieces are.
On occasion, where a few moves will place the first four corners, there is the option of doing step 2 first, that is: four corners first, then the four middle edge pieces. This can be very fast.
[Option] Sometimes it's easy to see and to solve the Last Level corners while placing the final First Level corner.

3. Place the other two edges on the middle level
These can usually be placed at the same time in about 7 or 8 moves.

4. Place the four edges of the first level
By now, usually the First Level is now on the bottom.
Notes:
I think there may be 1 chance in 4 that one first-level edge piece is already in place correctly.
This placement can usually be done two pieces at a time, i.e. one across-the-center edge pair at a time.
To flip over one edge piece in place takes 7 moves. To flip over two edge pieces takes 8 moves. I count a slice move as one move.
After the first across-the-center edge pair is placed there are a whole lot of good opportunities. For instance, I can usually flip over two Last Level edge pieces while placing the last two First Level edges.
[Option] If the Last Level corners are solved now, it is possible to solve the remaining First Level across-the-center edge pair and the four Last Level edges all in one go.

### Last level

This leaves only the last level (now on top). This part about the Last Level is mostly for beginners, with some intermediate stuff.
For the LL I generally do the corners then the edges. Some of my algorithms either permute or orient the corners, or both, while flipping over two edge pieces. Examples of these and other combos below.

5. Move the corners into position

6. Rotate the corners

7. Flip over edge pieces

8. Move the edge pieces into place

Generally I permute then orient corners; orient then permute edges.
There are positions which are mirror images and inversions of each other, so there are the practical and the possible. Though there are 6 possible out-of-place permutations, as a practical matter there are only two which need to be solved, that is, two ways.

#### Some detail:

5. move the LL corners into position (permute them) (two ways)
a.) swap two adjacent corners - (4 possibilities) - 7 moves
b.) swap two corners across the center - (2 possibilities) - 6 moves
Moving the corners without rotating them (changing their facing) 10 moves (9 moves and 14 moves)

6. rotate the LL corners (orient them) (six ways)
a.) one up, three rotated in the same direction - "one up, three down" - (8 possibilities) - 7 moves
b.) two up, two adjacent facing one direction - "headlights" - (4 possibilities) - 14 moves
c.) two up, two adjacent facing opposite directions - "sidelights" - (4 possibilities) - 14 moves
d.) two up, two across the center rotated in opposite directions - "oddlights" - (4 possibilities) - 14 moves
e.) none up, adjacent pairs facing away from each other - "wheels" - (2 possibilities) - 11 moves
f.) none up, two adjacent facing one direction, the other adjacent pair facing opposite directions - "barrow" - (4 possibilities) - 9 moves
Though there are 26 possibilities of rotated corners, as a practical matter there are really only 6 positions which need to be changed, that is, 6 ways.

The maximum moves needed to solve the corners this way is 21 (7 + 14).
Often the corners can be swapped in such a way as to leave them oriented, or only 7 moves from being oriented. In reality there are no corner positions which cannot be solved within 14 moves.
(plus 1 to orient the LL with the F2L.)
Often two edge pieces can be flipped over while the corners are placed and/or rotated.

7. flip over any LL edge pieces, never more than 12 moves
a.) two flipped across - two possibilites - 12 moves or 9 moves
b.) two flipped adjacent - four possibilies - 12 moves or 7 moves
c.) four flipped - one possibility- 12 moves.
Where these 12 moves are used to flip edges there is no change in position.

8. Move the LL edge pieces into place, never more than 7 moves:
a.) one in, three out  - eight possibilities - 7 moves
b.) two pair swapped adjacent - 2 possibilities - 7 moves
c.) two pair swapped across  the center - 1 possibility - 7 moves
The maximum moves needed to solve the edges this way is 19 (12 + 7).
So corner's maximum, plus edge's maximum, plus 1 move which may be needed to align the LL with the F2L, equals a maximum of 41 moves.
You can solve the LL using only four algorithms and/or their mirror images, though you sometimes need to apply the algorithm twice:
R U' L' U R' U' L (U)
R U R' U R U2 R' (U2)
r U r' U2 r U r'
F2 U r U2 r' U F2

#### Some useful algorithms:

5. Place (Permute) the corners:
R' U' F' U F R (swaps two corners across the center) [reverses them]
R U2 R' U' R U2 L' U R' U' L (swaps two corners and two edges)
R U' L U2 R' U R U2 R' L' (swaps two corners and two edges)(Better)
R U' L U2 R' U L' R U' L U2 R' U L' (swaps two corners across the center and four edges)

6. Orient the corners:
R U R' U R U2 R' (U2) - (Rotates three corners and exchanges three edges)

7. Orient the edges:
r U r' U2 r U r' (flips two exchanges three)

8. Place the edges:
a. One in place, three out: F2 U r U2 r' U F2
b. Swap two pair across: r2 U r2 U2 r2 U r2
c. Swap two pair adjacent: r2 D f2 D' f' r2 f

### Combos

Examples of doing more than one thing at a time:

5.
6. R U' L' U R' U' L (U) - (swaps two corners, rotates three corners)

5.
7. R2 B2 R' B' R B2 L' B R' B' r (swaps two corners and two edges)

5.
8. QR' R2 U2 R' U' R U2 L' U R' U' r'

6.
7. and 8. R r U R' U R U2 R' r' (U2)

Two steps in the right direction in the future:
First when placing the last FL corner(s) solve the last level corners;
Second when placing the last FL edge(s) solve the LL edges.

### Notation

U = Upper or top layer (or face)
u = middle layer or slice between U and D
D = Down or bottom layer
F = Front layer
f = middle layer or slice between F and B
B = back layer
R = Right layer or right side
r = middle layer or slice between R and L
L = Left layer or left side

All the lower case letters are middle layers, so "r" is the center slice between the "R" side and the "L" and it is turned in the same direction as the "R" side is turned.
The small case letters d, b and l may be used for convenience.
U = top turned clockwise 90 degrees
with a single quotation mark, like
L' = Left side turned counter-clockwise 90 degrees
or with a "2"
U2 = top turned 180 degrees
Q for cube, for example, QU2 means rotate the cube in your hand 180 degrees as you would turn the Up side.

I use a space between turns like R' F' U' F U R.

When labeling pieces I use the letters of the side where they are, or where they belong. The order of the letters usually doesn't matter.

The "Back Left" edges may be labeled Bl or LB. The "Right Up Front" corner may be labeled URF UFR FUR FRU RFU or RUF.

Good luck and enjoy yourself,

David James Salvia