Mag's 3x3 Rubik's Cube Solution
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.
- 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.
- 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.
- (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.
- 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
- Edge cubelet
- The middle cubelet of the three on an edge. May also be called
- 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.
- Turn a single cubelet -- usually an edge cubelet -- in place.
See also rotate. Do not confuse with swap.
- (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).
- 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
- A sequence of moves.
- The way a cubelet is situated in its position. Corner cubelets
may have 3 different orientations; edge cubelets may have 2.
- Where a cubelet is located.
- Turn a single cubelet, probably a corner, in place. See also
flip. Do not confuse with swap.
- 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
- Switch the positions of 2 or 3 cubelets. Do not confuse with
Operations (My Solution)
Move an edge cubelet from the bottom slice onto the middle slice
without disturbing the top slice
- Hold the cube so that the destination spot is at FR (front
- Turn the bottom so that the edge cubelet that is to be moved up is
- 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-
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".
Get bottom corner cubelets in place, ignoring their rotation in
place, without disturbing the top two slices
- 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-
Rotate bottom corner cubelets in place, without disturbing the top
- 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
- 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.
Put bottom edge cubelets in place, ignoring their orientation
The key operation is:
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
Flip two edge cubelets in place
- If the two cubelets are on adjacent edges, hold them at UF and UR
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.