This is a small collection of operations for the 3x3 Rubik's Cube that more or less reflect the way I solve the cube. I tried to keep it minimal, so it assumes that you already know how to get one entire face solved; this means not only having all of one color on one side, but also having those 8 pieces in the proper position with respect to the other sides.

The basic approach to my solution is to get one face (the "top")
solved, then get the middle slice solved, then get the bottom solved.
Some of the operations below (e.g., the first) assume that parts of
the cube have not yet been solved, so they may affect
already-disturbed pieces other than the particular ones being
manipulated. Other operations, on the other hand (e.g., the last),
affect *only* the pieces being manipulated; these operations
(and many others) are often useful in other situations.

**Note**: Since I've put this up on the Web, I occasionally get
queries for more online information about the cube. I have a small
list of cube-related URLs, and a list of
possible sources for cube-related puzzles.
I don't really know anything else.

- Cubelet
- There are 27 of these, one of which is hidden in the middle of the cube, and 6 more of which (the centers of the faces) are probably never referred to at all. The rest of them move about the cube freely, to our great consternation.
- Corner
- A cubelet at the intersection of three faces. May be referred to
by the names of the three faces that meet there. For example,
**UFR**and**DBL**are corners. - Direction
- (of a turn). There are 3 directions.
**+**means a quarter-turn clockwise,**-**means a quarter-turn counterclockwise, and*****means a half-turn. If the turn is not specified in a move, it means a quarter-turn clockwise. - Edge
- The three cubelets comprising the intersection of two faces. May
be called by the names of the two intersecting faces; for example,
**UF**and**FR**are edges. May also refer to the edge cubelet. - Edge cubelet
- The middle cubelet of the three on an edge. May also be called the edge.
- Face
- One of the six surfaces of the cube. The faces are called
**U**(top),**D**(down),**R**(right),**L**(left),**F**(front), and**B**(back), relative to the orientation of the cube in your hand. - Flip
- Turn a single cubelet -- usually an edge cubelet -- in place.
See also
**rotate**. Do not confuse with**swap**. - Inverse
- (of an operation). The
operation that exactly reverses
the moves involved in the operation. Take each turn backwards, and
take all of the turns in reverse order. For example, the inverse of
`(R2- D R2 D* R2- D R2)`is`(R2- D- R2 D* R2- D- R2)`. - Move
- A single turn of one or more slices of the cube together. A
move consists of a
**face**, a set of**slices**(usually just one for the 3x3 cube, but often more for bigger ones), and a**direction**. - Operation
- A sequence of moves.
- Orientation
- The way a cubelet is situated in its position. Corner cubelets may have 3 different orientations; edge cubelets may have 2.
- Position
- Where a cubelet is located.
- Rotate
- Turn a single cubelet, probably a corner, in place. See also
**flip**. Do not confuse with**swap**. - Slice
- Also
**layer**or**slab**. Nine cubelets. The 3x3 cube is 3 slices deep any way you look at it. The slices are numbered**1**,**2**and**3**,*relative*to a face. If slice(s) are not specified in a move, it means slice 1, i.e., the face itself. - Swap
- Switch the positions of 2 or 3 cubelets. Do not confuse with
**rotate**.

- Hold the cube so that the
*destination*spot is at FR (front right). - Turn the bottom so that the edge cubelet that is to be moved up is at FD.
- If the color showing on the front of the about-to-be-moved edge
cubelet matches the color on the (center of the) front face, do:
D- R- D R D F D- F-

Otherwise, do:U123 D* L D- L- D- F- D F

Note that that step 3b is really just "turn the cube sideways and do the mirror image of step 3a".

- It is always possible to turn the bottom face so that there are two corner cubelets in the right place. Do this.
- If the two out-of-place corners are adjacent to each other, hold
the cube with them at DFL and DFR, and do:
R- D- R F D F- R- D R D*

Otherwise, hold one of the out-of-place ones at DFR (and the other one at DBL) and do:R- D- R F D* F- R- D R D-

- See how many cubelets need to be rotated. An easy way is to look at the bottom of the cube and see how many corners' colors match the center cubelet.
- If two corners need fixing, use the operation to rotate two corner cubelets.
- If three corners need fixing, hold the one that is already fixed
at DFL and do:
R- D- R D- R- D* R D*

or its inverse. Which one you do depends on whether the corners need to be rotated clockwise or counterclockwise. In practice, I can never remember which is which, but it turns out that doing the above operation*twice*is the same as doing its inverse. So in practice I just apply the above operation, and if they're still not fixed, I do it again. - If all four corners need fixing, hold the cube so that none of the "bottom color" is showing on the front face. (There will be either one or two such sides.) Now do the operation given in the previous paragraph. This will fix one corner. Now do that operation again as described in that paragraph.

- If the corners are not adjacent, do a single turn to make them so. Remember which face you turned, so you can do its reverse later.
- Hold the two adjacent corners so that the one needing to be turned
clockwise is at UFR and the other is at UFL, and do:
R- D R F D F- U- F D- F- R- D- R U

- Undo the move you did in step 1.

R2- D R2 D* R2- D R2(or its inverse). This operation moves the three edge cubelets at DL, DB, and DR around each other clockwise. (Its inverse moves them counterclockwise.)

- If there is one edge cubelet in place, put it at DF and do either the above operation or its inverse, as appropriate.
- Otherwise, all four edge cubelets are disturbed. It doesn't matter which one is in front. The above operation or its inverse will make it so that one cubelet is in place. Do that, then go to the previous step.

- If the two cubelets are on adjacent edges, hold them at UF and UR
and do:
R- D2- R* D2* R- U- R D2* R* D2 R U

- If the two cubelets are on edges across from each other but on the
same face, hold them at UR and UL and do:
R- D2- R* D2* R- U* R D2* R* D2 R U*

- If the two edges are not on the same face, put them there with a single turn (remembering it), then go to one of the first two steps as appropriate. After that, undo the single turn you did.

Note: Despite my clarification of what "D2-" means, I still get occasional emails asking for an explanation of this operation, which I have now finally written.

Tom Magliery

tom@magliery.com