Rubik's Cube with Pictures

Here is a diabolical 3x3x3 Rubik's Cube with ALL centers exactly the same, and pictures that require correct orientation. I was able to identify the six side colors and their relationship to each other by noticing there was ONE edge piece with Eyes on both sides (Purple/Black), ONE with a Chin on both sides (Orange/Blue), TWO with Eyes and Chin (Orange/Purple and Blue/Black), TWO with Eyes and Cheek (Green/Purple and Red/Purple), TWO with Chin and Cheek (Green/Blue and Red/Blue), and FOUR with Cheek and Cheek (four middle slice edges). This allowed me to determine the color arrangement shown below. Even when you can identify the proper centers, you have to maintain the proper alignment of the "teeth" in each picture.

Here is a picture of the cube showing the top and two sides.

The top is Purple, and the two sides that are showing are Orange and Green. The bottom is Blue, and the other two sides are Black and Red, with Red next to Orange, and Black next to Green. But let me warn you, YOUR Basketball Cube might have its faces and colors arranged differently. You need to use the twelve edge pieces, and their colors, to determine the arrangement of the basketball faces on your cube. One "eyes", one "chin", and two "cheeks" should all be colored the same on each face.

Notational Convention:

There are six faces, determined by the center square on each face. However you hold the cube, these six faces are the Up (U), Down (D), Front (F), Back (B), Left (L), Right (R). Up and Down are frequently called Top and Bottom, but don't get (B) for Back confused with Bottom. We use (D) for the Bottom. Up is also sometimes called Upper (U).

There also are three center slices. These slices run through the center of the cube, and each center slice is identified by C (Center) and one of the two neighboring faces. For example, L-C is the Left face and Center slice adjacent to the Left face. -RC would be the same Center slice. The other two slices are associated with U,D and F,B.

A "single turn" of a face is a 90-degree turn, or quarter-turn, around that face's center. Turns are also called moves or movements.

Turns are listed by showing the face letter, or minus letter. For example, L or -L means the Left face. L is a clockwise turn, and -L is a counter-clockwise turn, with respect to the center square of the face. So for the Back face, B is a clockwise turn LOOKING at the Back face. But if you are looking at the Front face, B appears to be counter-clockwise from your perspective. D appears to be -U when viewed from the Upper face. If you consider the top corners, L is a movement with your left hand of the Left face so that the top-front corner moves down to the bottom-front corner. A movement like F2 or L2 or U2 means your turn the face two consecutive clockwise or counter-clockwise single turns. A move like U2C2 means to turn the Upper face two single turns and then turn the Upper and associated Center slice two single turns TOGETHER. The result will be the Upper face back to its original position, and the Center slice will be turned twice. This idea of togetherness is always involved with Center moves. L-C is a clockwise turn of Left, then a counter-clockwise turn of both Left and the associated Center slice TOGETHER. This also returns Left to its original position, but does a counter-clockwise turn on the Center from Left's perspective. -LC is a counter-clockwise turn of Left and then a clockwise turn of both Left and the associated Center. Again, Left is restored. An equivalent slice move would be R-C. There are only three Center slices: one directly below Upper, one between Left and Right, and one directly behind Front. For simplicity, only U, F, and L or R are associated with C. You don't ever need to turn Bottom or Back to do a slice move.

The edges are identified by the two sides which make them up. So UF is an Upper-Front edge piece. The corners are identified by the three sides that make them up. URF is the Upper-Right-Front corner. As pieces move about, their faces change positions. For example, FU->DF means the Front-Upper edges have moved the the Down-Front positions. That means F moved to D, and U moved to F. That's very important because UF->DF means the same original piece moved to the same destination, but the orientation of the original faces got flipped. U moved to D, and F stayed on the F face. Of course, each piece has colors associated with them, so something like UF->DF would mean a Blue/Orange edge piece with Blue on the Upper face moved to the Down face with Blue on the Down face. Orange stayed on the Front. Corners can twist counter-clockwise or clockwise. These are denoted by a single or double apostrophes, respectively. So (URF)' means the colors on the three faces of the corner move through this progression: U->R->F->U. That is clockwise. So, URF has become RFU in the same position. Just like edges, corners can change position AND orientation. For example: UFL -> RUB indicates a change in position AND orientation.

Given a scrambled cube, you need to locate the six center squares and orient them so the "teeth" point in the proper direction. Since the centers are colorless, it is their orientation that matters first. We'll assign colors to them later. Pick a Top, and opposing Bottom. The four sides are then Front, Left, Back, and Right. You want the "teeth" in the center square of those four sides to all be pointing down at the Bottom. For more details, see the section below entitled: "Orientation of the centers".

To maintain proper orientation of the side teeth requires some intricate maneuvers. Let me reiterate the notation for turning faces. All clockwise turns assume you are looking directly at that face, and are shown by the single letters: L, R, U, D, F, B (while viewing the Front face). Remember, a clockwise turn of the Back looks counter-clockwise when viewed from the Front. Moves like L2 or U2 mean to turn that face 180-degrees, so clockwise or counter-clockwise turns are equivalent, like two single turns in one direction. A complete rotation on a face would be 4X where X represents any face's letter. So -X is equivalent to 3X. If you have a sticky cube, sometimes you can turn a face easier in one direction, so something like 3X may be easier than -X.

To remember these more easily, I've described them in relation to corners.

Left( L) = Move front-top-left corner down to the bottom-front-left position.

Right (R) = Move front-bottom-right corner up to the top-front-right position.

Top (U)= Move the front-top-right corner left to the left-top-front position.

Bottom (D) = Move the front-bottom-left corner right to the right-bottom-front position.

Front (F) = Move the front-top-left corner up and over to the front-right-top position.

Back (B) = Move the back-top-right corner up and over to the back-left-top position.

All of these moves are clockwise for the face while looking at the Front. Notice the edge of the corner described by the name of the move remains unchanged, and the other two faces change positions. Thus Left (L) does: front->bottom; top->front; and left remains left.

Each of these moves has a counter-move, signified by placing a minus sign in front of the letter:

-L, -R, -U, -D, -F, -B.

These counter-moves in terms of corners are just a rewrite of "Move A.corner direction to the B.corner" as "Move B.corner -direction to the A.corner", where -direction is the opposite direction, except for "up and over" which remains unchanged. So directions "up, down, left, right" become -directions "down, up, right, left".

Back (B) is rarely used in a maneuver. Most sequences move Left, Right, Front, and Upper.

Bottom (D) is used for some twisting sequences and Center Rotations.

There are also "slice" moves like this: -LC or L-C, or L2C2 or R2C2 (these last two give the same result).

Something like U2C2 could be done as two consecutive slice moves: 2(U-C) or 2(-UC).

You should keep the Top on Top, which means the Bottom stays on the Bottom. It also means the four side faces remain on the sides. When asked to "Turn the entire cube" you are turning the side faces around the vertical axis of the cube. Each side face rotates to the Front while the others go around to the other sides. You can rotate in either direction: Right-to-Front or Left-to-Front. For a Right-to-Front quarter-turn rotation, faces move: Right-to-Front-to-Left-to-Back-to-Right.

Some people like a pictorial representation of the moves. Below is a table of the most frequently applied moves.

This table makes use of pictograms courtesy of James Yates at www.chessandpoker.com from their Rubik's Cube Solution page.

Orientation of the centers:

Because the centers are all the same, and the cube is presumed to be scrambled, you need to determine the location of the colored faces. That means assigning colors to the colorless centers. Pick any center and define it as being the Top center. Place a removable sticker on this center to remember it. You can use a paper punch to cut out a small sticker from the sticky portion of a Post-It note. Once the Top center is assigned, the Bottom center is on the opposite face. Hold the Top and Bottom between your thumb and index finger, like holding the poles of a globe, with the Top on Top. The sides are now the other four faces. Turn the Front face to orient the center so the "teeth" are pointing down. The teeth should at be the lower edge of the center square. Turn the entire cube to bring another face to the Front. Orient its center with its teeth pointing down. Continue this until all four sides have centers with teeth pointing down. Now look at the teeth on the Top face, and turn the entire cube until the teeth are pointing at the Front face. That's the Orange face. The Red face is on the Left, the Green face is on the Right, and the Black face is in Back. Top is Purple, and Bottom is Blue. We know this because of the colors of the edge pieces, and what portion of a basketball's image is on them. Finally, turn the Bottom face so its "teeth" are also pointing at the Front face. If you think it would help, apply Post-It note stickers to all centers, and use color marker pens of Green, Orange, Blue, Red, and Black to color the stickers on their corresponding center.

Now let's begin by placing the Bottom edges in position. None of these sequences will disturb the orientation of the Bottom center or the four centers on the sides. Only the Top center will rotate. First, we have to find the four edge pieces. They all have a Blue facet (Bottom color). Some could be on Top, some could be at the four edges of the middle slice, and some could be on the Bottom. The first piece you want to position is the Orange/Blue edge that has TWO Chins. It's the only edge piece on the cube that has two Chins. That's the Orange/Blue edge piece. Find the Orange face. Remember that's the side face pointed to by the teeth of the Bottom face's center. It is best to start with the Orange/Blue edge piece using whichever sequence below positions it properly. With that in place, the other three sides can easily be done. If it's on the Bottom, but in the wrong position, or twisted, use Step 1 to move it to the Top, then use Step 3 to position it properly on the Bottom. If it's in the middle layer, use Step 2 to move it to the Top, and then use Step 3 to position it properly on the Bottom. If any edge pieces are already in correct position with correct orientation (not twisted), then LEAVE THEM ALONE. They are already correct. Otherwise, you can do steps 1,2,3 in different orders depending upon the location of the Bottom layer edge pieces on the cube. Typically, you can do Step 1 and then Step 3, or Step 2 and then Step 3, for any Bottom layer edge piece. These steps are written as though you repeat each, then go on to the next. Always check Step 3 before continuing on to Step 4.

Sequences for moving Bottom-edge pieces on the Bottom to the Top (Step 1):

Some Bottom edges may be in correct position with correct orientation (not twisted). If so, LEAVE THEM ALONE. They are already correct. To be correct, the Bottom facet must be on the Bottom face, and the side facet must match the color of the Center above it. Otherwise, you need to move the misplaced Bottom-edge from the Bottom to the Top. Turn the entire cube so the piece you want to move to the Top is at the Bottom of the Front face (DF). Next, we have to choose an edge piece on Top to place at the Upper-Left position. If the Front facet of the edge piece at the Bottom isn't the Bottom color and isn't the color of the Center above it, then try to find an edge piece on Top with the Bottom's color on Top, AND the Center's color on the Side. If there is such a piece, choose that edge piece; otherwise choose ANY other edge piece on Top that doesn't have the Bottom color on either facet. Turn the Top face, if necessary, so the chosen edge piece ends up at the Upper-Left (UL) position. Then, do this:

F2 -U F2 (DF -> UR) replaced by (UL -> DF)

This moves the Bottom-edge piece to the Top, moves it over the the Right side, and then restores the Front face orientation. The Top Left edge piece moves to the Bottom. This is IMPORTANT to maintain the orientation of the side teeth (all pointing down). You'll note that the Top center gets rotated. Don't worry, that's going to happen often. It may come back to proper orientation as we finish solving the cube. If there are other misplaced or "twisted" Bottom-edge pieces on the Bottom, repeat Step 1. Otherwise, continue to Step 2.

Sequences for moving middle layer Bottom-edge pieces to the Top (Step 2):

If there are no Bottom-edge pieces in the middle layer (slice), then continue to Step 3. Otherwise, turn the entire cube until a middle layer Bottom-edge piece is at the Front-Left position (FL). It either has the Bottom color on the Front face, or on the Left face. Choose any Top edge piece that doesn't have a Bottom color on it to place at the Upper-Left position. Turn the Top face, if necessary, so the chosen edge piece ends up at the Upper-Left (UL) position. Then do this sequence:

F -U -F (LF -> UR) replaced by (UL -> LF)

It is important to put a non-Bottom edge in the proper position on the Top (UL) so the sequence can replace it by the middle layer Bottom-edge piece (FL), and NOT disturb any other Bottom-edge pieces already on the Top or Bottom. Repeat Step 2.

Sequences for moving Bottom-edge pieces from Top to Bottom (Step 3):

Locate any Bottom-edge piece in the Top layer. If none are there, continue to Step 4. Otherwise, turn the entire cube to make the Front face color match that piece's non-Bottom side color. In other words, turn the entire cube until the center color of the Front face matches one color of the edge piece on Top. Then turn the Top until that edge piece is directly over the Left side (Upper-Left). Apply the appropriate sequence below depending where the Bottom facet is located on the Upper-Left edge piece (UL):

Bottom color on the Top: F2 -U F2 (UL -> DF)

Bottom color on the Left: F L -F -L (LU -> DF)

Repeat Step 3 until all Bottom-edge pieces are at the Bottom. At this point, the picture on the Bottom should have its Eyes, Chin, and both Cheeks. Along the sides, these four edge pieces should be the Chins under their correctly aligned teeth on the matching color sides. The Bottom corners are probably not correct. We'll tackle them next.

Sequences for moving misplaced Bottom corners to the Top (Step 4):

Some Bottom corners may be in correct position with correct orientation (not twisted). If so, LEAVE THEM ALONE. They are already correct. To be correct, the Bottom facet must be on the Bottom face, and the side facets must match the color of the neighboring Bottom edge piece on each side. Otherwise, you need to move the misplaced Bottom corner from the Bottom to the Top. The easiest way to do that is to turn the entire cube until the misplaced corner is in the Bottom-Left-Front (DLF) position. Turn the Top face to position any non-Bottom corner directly over that Bottom corner, at Top-Left-Front (ULF). Then do the following:

-L -U L (DLF -> RFU) replaced by (LUF -> DLF)

This puts the Bottom corner on Top, and the non-Bottom corner on the Bottom. Repeat this for every misplaced Bottom corner on the Bottom.

Sequences for moving Bottom corners from Top to Bottom (Step 5):

You now have Bottom corners on Top. Move them to the Bottom as follows:

Turn the entire cube until a non-Bottom corner is at Bottom-Left-Front (DLF). Turn the Top face until the Bottom corner with the two matching sides is directly over that Bottom corner, at Top-Left-Front (ULF). That corner will be oriented in one of three ways. You want to apply the sequence that places the Bottom color on the Bottom face. In the following sequences, each facet of the Top corner moves to the destination facet on the Bottom corner in the order the facets are listed.

(FLU->DLF) = -U -L U L (LUF->DLF) = -L -U L or U F -U -F

(UFL->DLF) = -L U L F U2 -F or -L U2 L U -L -U L

Notice that D is the Bottom facet at each destination, so use the formula that moves the Bottom facet at F or L or U down to D. For example, (FLU->DLF) moves the F facet to the D facet (Blue). Likewise, (UFL->DLF) moves the U facet to the D facet (Blue). Repeat this process until all Bottom corners on Top are correctly positioned on the Bottom.

At this point, the entire Bottom face should be complete, with correctly oriented teeth in the center. The bottom edges are also complete for all the sides, each with a Chin under its corresponding teeth.

Positioning the four middle layer edge pieces (Step 6):

We now need to position the four edge pieces of the middle layer. These have a pair of colors that match neighboring sides (not the Top or Bottom). Remember, in this version of the cube, Top edge pieces have a Purple facet, and Bottom edge pieces have a Blue facet.. Also remember, this cube has Cheeks on each facet of a middle layer edge piece.

If any of the middle layer edges are in a position with both sides exactly matching the corner below them, LEAVE THEM ALONE. They are already correct. If some of the middle layer edges are on Top, determine which of the two neighboring side colors is on Top. Turn the entire cube to place that center's color in Front, then turn the Top layer until that edge piece is positioned at UB in Back (U matching the Front color). Use the appropriate sequence below depending upon which side, Left or Right, matches the Back color.

If any others in the middle layer belong in the middle layer, but at some other position, or are "twisted", then move them to the Top as follows:

Rotate the entire cube until the misplaced middle layer edge is positioned at the LF or RF. Turn the Top layer until a Top edge piece (one with a Top color facet) moves to the UB position. Now depending upon the middle layer edge being on the Left or Right on the Front face, apply the sequence that affects the Left or Right:

Left: (UB->FL) = F -U -F -U -L U L U (Also causes: LF->UF, UF->UL, UL->RU) Right: (UB->FR) = -F U F U R -U -R -U (Also causes: RF->UF, UF->UR, UR->FU)

Note how every sequence restore F, L, R, and U centers. Now, having rid the middle layer of misplaced or twisted edge pieces, substituting Top edge pieces for them, you apply the same sequences to move the edges on Top into the middle layer at their appropriate position. Just determine the two colors of the neighboring sides in the middle layer. Find the matching edge piece in the Top layer. Turn the entire cube until the Front face matches the Upper facet of the Top layer piece. Turn the Top until that one piece is at the Upper-Back position with the Upper facet matching the Front. Move it to the Left or Right, as appropriate. Note that the Upper facet should always match the Front side, so turn the cube until that side is in Front, and turn the Top to place the edge piece at UB.

You should now have a cube with everything in place except the top layer. In other words, the lower two-thirds of the cube are completely done. We'll now finish the process by doing the Top corners, and finally the Top edges. So let's begin with the Top four corners.

Positioning the four Top corners (Step 7):

Each of the Top corners has one facet that matches the Top color (Purple), and a pair of neighboring sides. If there are any corners with the Top color on Top, turn the Upper face to see if you can get it to line up with its matching sides. Sometimes you'll find two corners that have the Top color on Top, and when you line one up, the other also lines up, and the other two (with the Top color on a side) need to swap positions.

The four corner positions are named: UFL, ULB, UBR, URF. Each starts with the Top color (U) and then goes clockwise around the corner. But the Top color may be off to the side of a corner. That's OK. Don't worry about orientation of the colors on the corner, just worry about getting the three colored corners over the sides with two matching colors (obviously not the Top color). The first step is to position the four corners properly. Turn the Top layer until at least one corner rests over its matching side. If one or more corners have the Top color on top, try one of those first.

There are several possibilities:

1) All four corners are in proper position, but possibly "twisted", meaning the Top color isn't on Top for all of them. Go to "Twisting corners".

It isn't possible to have all four misplaced. Just turn the Top until one of the four corners is in proper position, but possibly twisted (Top color on a side facet).

The cubes are labeled such that UFL describes a cube in the UFL position, but the colors on the three facets of that corner cube may belong someplace else. As corners move, they frequently twist. UFL -> RUB means the Upper facet moves to Right, Front moves to Upper, and Left moves to Back. Therefore, UFL -> RUB is a shorthand for the individual face movements: U->R, F->U, L->B. The notation not only indicates where a corner moves (from->to), but it's facet orientations as well.

2) If two corners are in position, and two are not, skip to step #3 below. Otherwise, ONE corner is in position, and the other three are NOT in position. If you turn the entire cube to put the in-place corner at the Upper-Left-Back position (ULB), then the others form a triangle with one at the Front-Left and the other two on the Right. Check to see if Front-Left needs to move to Back-Right (UFL->RUB), or Back-Right needs to move to Front-Left (RUB->UFL). Use one of the following sequences, depending upon the direction:

-R U L -U R U -L -U (clockwise: UFL -> RUB -> RFU -> UFL) U L -U -R U -L -U R (counter-clockwise: RUB -> UFL -> RFU -> RUB)

The terms "clockwise" and "counter-clockwise" are used to describe the direction those three corners move relative to the Top center. Note that those corners "twist" as they move. The twists are also either clockwise or counter-clockwise, matching the movements. This is evident in the facet notation for each piece as it moves. The directed graph of these three corners shows three arrows indicating the three pieces on the left move one position to the right to occupy the three positions on the right. So the left-most and right-most are the same position in a continuous circulating motion.

3) TWO corners are in position, and the other two need to swap places. Be careful and don't mistake a twisted corner for a misplaced corner. There are two possibilities: opposite corners need to swap places, or adjacent corners need to swap places.

To deal with opposite corners, do the following:

Turn the entire cube until one of the misplaced corners is at ULB and the other is at URF. Then apply the "counter-clockwise" sequence shown in #2 above. When done, all four corners should be correctly positioned. If not, you may have one that can be properly positioned and three that are NOT in position. In that case, go to #2 above. Otherwise, you should now have two adjacent corners that need to be swapped. Continue...

To deal with adjacent corners that need to be swapped:

Turn the entire cube to place the two that need to be swapped in Back. The two that are correctly positioned should be in Front (Left and Right). Apply the "counter-clockwise" sequence shown in #2 above. When done, if necessary, turn the Top layer to reposition the Top corners to get at least one in proper position.

If they are not all in position, repeat #2 or #3 again. Eventually, you should be able to turn the Top layer to position all corners. It is not possible to have three corners in position without forcing the fourth to its position. If that happens, look for color errors, like confusing Red and Orange, or Purple and Black.

Twisting corners (Steps 8 and 9):

At this point all your corners should be in position, but some Top corners may need twisting to get their Top color on Top. Properly oriented corners have their Top color on Top. Twisted corners have their Top color on one of the sides. There are several possibilities:

a) If all four corners are correctly positioned AND correctly oriented, Great -- go on to dealing with the four Top edge pieces (Steps 10 and 11).

If you have only one corner that is correctly oriented, and the other three need twisting, go to c).

Otherwise, two corners are correctly oriented, and two corners are twisted; OR all four corners are twisted; continue with b).

b) You will need these sequences, along with U, -U, or U2:

A = (-R D R F D -F)

-A = (F -D -F -R -D R) [the reverse of A]

For all of these sequences using A and -A, be VERY CAREFUL when doing D and -D, or R and -R. Usually F, -F, U, -U are easier. Use the pictogram as a guide.

If all four corners are twisted, you really have two PAIRS of corners that are twisted. Otherwise, you have a single PAIR of corners that are twisted. Each PAIR consists of a clockwise twisted corner (CW), and a counter-clockwise twisted corner (CCW). You can identify a CW corner by turning the entire cube placing each corner in the Upper-Right-Front (URF) position. If the Top color is on the Front face, that's a CW corner. If the Top corner is on the Right face, that's a CCW corner. If all four are twisted, there will be two CCW and two CW corners, making two PAIRS. Make a note of them. They could be adjacent, both on the Front, or both on the Right, or they could be on opposite sides of the center. Work separately on each PAIR (or the only PAIR you have).

With a CW corner at URF having the Top color on the F-facet, apply the A sequence. Then, using U, -U, or U2, turn the Top face to place the CCW corner at URF, and apply the -A sequence. Finally, return the top to the proper position for these two corners. They should now be untwisted.

Go back to a).

c) Only one corner is correctly oriented, and the other three need twisting. This can come in two flavors, either clockwise twist or counter-clockwise. For either of those cases, turn the entire cube until the correctly oriented corner is at the UBR position (Upper-Back-RIGHT). The other three should now be at URF, UFL, ULB, but with U not being the Top color.

If URF has the Top color on the Front, apply this sequence:

L U -L U L U2 -L U2 (twist clockwise: URF' UFL' ULB')

If URF has the Top color on the Right, apply the following sequence:

U2 L U2 -L -U L -U -L (twist counter-clockwise: URF" UFL" ULB")

Go back to a).

Dealing with the four Top edge pieces:

All that's left is positioning and orienting the four edge pieces on the Top layer. You need to have the Top color center on Top.

But if any Top edges are in the wrong positions or are twisted, you've got more work to do using steps 10 through 12.

Positioning Top edge pieces (Steps 10 and 11):

If necessary, turn the Top layer to position the four corners properly. Now examine the Top edge pieces. Are they all in "proper position"? "Proper position" means the edge piece has the Top color AND the side color positioned on the matching side. The side color may be on the U-facet, and the Top color on the side-facet, which means that piece is in proper position, but needs a twist.

There are three possible arrangements of the four edges in relation to their matching side colors. First, they are ALL in the correct positions, but possibly twisted. Second, pairs of edges need to swap positions. They are either neighboring edges, or opposite edges (across the center). Third, ONE is in proper position and the other three form a Triangle that needs to be be circulated either clockwise or counter-clockwise.

1) If ALL are in correct positions, but possibly twisted, then continue on to "twisting edges" (Step 12). Otherwise... [NOTE: Read the CAUTION at the end of this section.]

The images below illustrate the various arrangements for Top edge pieces that are misplaced.

You are looking down on the Top face (U). The Front is where the captions appear below the images.

Before doing moves, remember to hold the cube with the Top on Top, and the Front in Front of you.

2) Pairs of edges need swapping.

You can transform Neighbors #2 into Neighbors #1 by turning the Top so either the Left or Right side becomes the Front.

You can transform Opposites or Neighbors #1 into a Triangle by applying the Clockwise Triangle sequence. That is:

L->R: -LC U L-C U2 -LC U L-C (Clockwise Triangle: UL -> UR -> FU -> UL)

If necessary, turn the Top layer to position the four corners properly. One of the Top edges should now be in position, but possibly twisted. Continue with step 3 (next).

3) One is correct and the other three form a Triangle. First turn the Top until that correctly positioned edge piece is at the Upper-Back edge (UB). The Triangle now has one piece in Front and the other two on the Left and Right edges. Apply one of the following sequences depending upon which piece needs to cross over the center to the opposite side, Left-to-Right, or Right-to-Left.

L->R: -LC U L-C U2 -LC U L-C (Clockwise Triangle: UL -> UR -> FU -> UL) R->L: -LC -U L-C U2 -LC -U L-C (Counter-Clockwise Triangle: UR -> UL -> FU -> UR)

If necessary, turn the Top layer to position the four corners properly. All pieces should now be in position, possibly with some twisted.

CAUTION: All of these Triangle sequences cause the Back center to rotate 180-degrees. That means you may have to apply Rotating Center sequences at the end. The alternative is to do a Clockwise Triangle motion by applying the Counter-Clockwise sequence TWICE, and likewise for Counter-Clockwise motion by doing the Clockwise sequence TWICE. It's your choice. NOTE: This caution also applies to 2) above when used to transform Opposites or Neighbors.

However, if you only turn the Top before doing a triangle-sequence, and you do an EVEN number of only one kind of triangle-sequence, or you do an EQUAL number of both CW and CCW triangle-sequences, then the Back center should be OK.

Lastly, if you're right-handed, you may use R-C as a substitute for -LC, and -RC as a substitute for L-C.

Twisting Top edge pieces (Step 12):

We are at the final phase, twisting Top edge pieces. There's a 1-in-4 chance everything is in place, properly oriented. If so, congratulations, you're done! Otherwise you have one of three configurations to handle, and then you'll be done. Either ALL four Top edge pieces are twisted, or a neighboring pair is twisted, or an opposite pair is twisted. Neighboring pairs have a corner between them, and opposite pairs have the center between them. You'll need the following sequences:

W = (L U-C L2 U2C2 L)

-W = (-L U2C2 L2 -UC -L)

1) If all four need twisting, do a W U -W -U sequence with the cube as it is, then continue below.

Note: see the "Opposites" and "Neighbors" images in the Positioning Top edge pieces (Step 10).

The arrows in those images point to the pairs that need twisting.

2) If a neighboring pair needs twisting, turn the entire cube until that pair is on the Left and Front faces of the Top layer. Then do this:

W U -W -U (twist: UL', UF')

3) If opposite edges need twisting, turn the entire cube until these two edges are on the Left and Right faces of the Top layer. Then do this:

W U2 -W U2 (twist: UL', UR')

Your cube should now be completely solved. Congratulations!

Rotating Centers (Step 13):

It shouldn't be necessary to rotate centers, but Positioning Top Edges can rotate the Back Center.

If you have only one center that needs rotation, hopefully it's a 180-degree rotation (two quarter turns).

The following rotates the Top center 180-degrees:

U R L U2 -R -L U R L U2 -R -L

Notice that the (U R L U2 -R -L) sequence is done twice.

Lastly, here's a sequence described by "How to Solve Rubik's Cube" (Wiki) that will rotate the

Top center counter-clockwise (ccw) and the Left center clockwise (cw), each n quarter turns:

(-L R -F B -U D) L[n] (-D U -B F -R L) -U[n]

The first part of the sequence isolates the Left center, which you then rotate n-times clockwise.

The second part restores, and -U is a counter-clockwise rotation done n-times.

This is the only sequence I've included that turns the Back face.

Look for pairs on faces with a common edge, and do those first by orienting the cube so those centers

are the Top and Left centers. Use the Top and Left center sequence to turn one into alignment, and the

other into alignment or to to where the 180-degree sequence can be applied. If the only remaining

pair are on opposite sides on the cube, then make them the Top and Bottom. Apply the Top and Left

sequence to orient the Top. Now, Left and Bottom need alignment. Orient the cube to make them the

Top and Left centers, and proceed using the Top and Left center sequence with an appropriate "n".

Eventually, you should get all centers aligned.

Other variations of Rubik's Cube:

If you have a standard cube with six solid colors, you don't have to worry about center orientation.

Just solve the cube starting with any color as the bottom layer (including the center).

If you have a cube with five solid colors, and one side with a single special center, like a logo, then

determine the colors of the other five centers, and the remaining color is the color associated with

the special center. Again, solve the cube starting with the bottom layer having the special center and

the color associated with that special center.

If you have a cube with five solid colors, and one side has a pattern or picture, treat this like the

special center described above. Solve the pattern or picture layer first, as the bottom layer.

Summary of move sequences:

When tracking movements, always remember facets move one-to-one.

Thus for DF -> UR, the D facet moves to U, and the F facet moves to R.

1. Move Down-Front bottom edge to top.

F2 -U F2 (DF -> UR) replaced by (UL -> DF) UL should be non-bottom edge

2. Move Left-Front middle layer edge to top.

F -U -F (LF -> UR) replaced by (UL -> LF) UL should be non-bottom edge

3. Move bottom edges from top to bottom.

F2 -U F2 (UL -> DF) Left color to Front

F L -F -L (LU -> DF) Upper color to Front

4. Move misplaced bottom corners from bottom to top.

-L -U L (DLF -> RFU) replaced by (LUF -> DLF) LUF should be non-bottom

5. Move top corners to bottom.

-U -L U L (FLU -> DLF)

-L -U L (LUF -> DLF)

-L U L F U2 -F (UFL -> DLF)

6a. Move middle layer edges on top to middle.

6b. Move misplaced middle layer edges to top.

Try to do 6a first, then 6b and 6a until done.

-F U F U R -U -R -U (UB -> FR) and (RF -> UF)

F -U -F -U -L U L U (UB -> FL) and (LF -> UF)

7. Position top corners.

a) Two corners can be placed in correct position, although possibly "twisted".

To swap the other corners, opposite or adjacent, turn the entire cube to place

one of them at ULB, do ccw move and reposition. Then try the triangular move.

b) Only one corner can be placed in correct position. (Not the other three).

For a triangular move, turn the entire cube to place the positioned

corner at ULB. Then, do appropriate clockwise or ccw move.

Repeat steps a) or b) as needed until all four corners are positioned.

-R U L -U R U -L -U (clockwise: UFL -> RUB -> RFU -> UFL)

U L -U -R U -L -U R (ccw: RUB -> UFL -> RFU -> RUB)

8. Twist three corners; correct corner at URB.

L U -L U L U2 -L U2 (twist clockwise: URF' UFL' ULB')

U2 L U2 -L -U L -U -L (twist ccw: URF'' UFL'' ULB'')

9. Twist only two corners.

A = (-R D R F D -F)

-A = (F -D -F -R -D R)

Neighboring corners at URF, URB.

A U -A -U (twist Front clockwise: URF' UBR'')

U A -U -A (twist Front ccw: URF'' UBR')

Opposite corners at URF, ULB.

A U2 -A U2 (twist Front clockwise: URF' ULB'')

U2 A U2 -A (twist Front ccw: URF'' ULB')

10. Position pairs of top edge pieces.

For two pairs of edges, opposites or neighbors.

For a pair of neighbors, place one pair at UL, UF.

-LC U L-C U2 -LC U L-C (clockwise: UL -> UR -> FU -> UL)

11. Position three edges (one is already correct at UB).

-LC U L-C U2 -LC U L-C (clockwise: UL -> UR -> FU -> UL)

-LC -U L-C U2 -LC -U L-C (ccw: UR -> UL -> FU -> UR)

Note: 10 & 11 twist the back center. You can avoid that by

doing ccw as 2(clockwise), and clockwise as 2(ccw).

12. Twisting top edges.

W = (L U-C L2 U2C2 L)

-W = (-L U2C2 L2 -UC -L)

All four need twisting: do W U -W -U once.

A neighboring pair at UL, UF needs twisting:

W U -W -U (twist: UL' UF')

An opposite pairs at UL, UR needs twisting:

W U2 -W U2 (twist: UL' UR')

13. Rotate centers.

Quarter-turns needed for Left center (cw) and Top center (ccw):

(-L R -F B -U D) L[n] (-D U -B F -R L) -U[n]

where [n] is the number of quarter turns.

Top center needs a 180-degree turn:

U R L U2 -R -L U R L U2 -R -L

If a pair of centers both need cw or ccw turns, use the

quarter-turn sequence, and then the 180-degree turn.

Conclusion:

This solution method should work on ANY 3x3x3 Rubik's Cube where you can properly identify the six centers.

It is designed to maintain center alignment, so it should work for the Rubenking Cube.

Shown above is a six-color Rubenking Cube. My colors are Red, Green, White, Blue, Yellow and Orange represented by the letters: R,G,W,B,Y,O. Note that the image on the left (Rubenking 1) shows three faces with Yellow and Orange on the top face, Yellow in back and Orange in front, with a dividing line running horizontally between them. The image on the right (Rubenking 2) is Rubenking 1 flipped over along the plane of that line and the two side edges. As you can see in Rubenking 2, Yellow is now on the left and Orange is on the right with a dividing lines running vertically in the image. This was the bottom of Rubenking 1. The three faces visible in Rubenking 1 are not visible in Rubenking 2, and are "opposite" their same-color pair faces that are visible. So for Rubenking 2, considering Top as Yellow/Orange, Front as While\Blue, and Left as Green/Red, then Yellow runs between Red and Blue along the Bottom, White runs between Yellow and Green in Back, and Red runs between Orange and White on the Right. The six-color corner facing you in Runenking 2 is the invisible corner not showing in Rubenking 1.

All twelve edge pieces are unique pairs of colors. There is only one Orange|White edge and it must touch Orange and White centers. You can clearly see this in Rubenking 2 on the top-right. Likewise, Yellow|Green is visible on the top-left. Four corners have all six colors, and four corners have three solid colors, like the Orange-Green-Blue corner at the front of Rubenking 1. There are two corners of each type on both the top and bottom faces. These eight corners and the twelve edge pieces help organize the centers, especially the four six-color corners. The Rubenking Pattern on the far right also shows the orientation of the centers. You see the Y/O top with B\W front below the top, and G/R left side, all of which are visible in Rubenking 2. The Y/O at the bottom, and B\W and R/G side panels are invisible in Rubenking 2, but visible in Rubenking 1, "up-side-down" in the Pattern where O-G-B come together at one corner. If you hold the cube with the upper-left and lower-right facets being solid colors, then rotating the entire cube 180-degrees forward or backward shows you the opposite face looks exactly the same. You can see that in the Y/O faces in the pattern. That also true of the B/W and R/G faces. You may have to turn the top 90-degrees to get solid colors in the upper-left and lower-right positions. That's why the R/G faces look wrong in the pattern.

The secret to solving a scrambled Rubenking Cube is to properly orient the six centers. Each center has a pair of colors, and opposite centers should have those same colors. For example, the Y/O centers are on opposite faces. Likewise the G/R and W\B centers. If you hold the Y/O centers between your thumb and index finger, you can rotate the entire cube with your other hand. Each of the four side faces should present themselves as you rotate the cube. The centers have two alternate color pairs, like G/R, then W\B, then G/R again, and finally W\B again. The use of "\" or "/" indicates the slant of the division between the two colors, with the top color first and then the bottom color. To create the Rubenking Pattern, rotate the cube to a W/B center and turn the face so the division between them looks like W\B. Rotate the cube to the neighboring G/R center and orient it that way. Then rotate to the other W/B center and orient it, and finally rotate to the final G/R center and orient it. Now neighboring sides have slants that "point" to a corner at the top or bottom of the cube. Those are the four six-color corners. The other pair of corners on each face are solid colors. There are only four solid-color corners. Only one has red AND blue, and the other color should be yellow. That is the bottom corner in Rubenking 2. The other two bottom corners you can see are six-color corners. Find the neighboring sides with red and blue center triangles pointing down toward a bottom corner. That's where the red-blue-yellow corner will go. The bottom center must have yellow pointing at this same corner. Turn the Bottom layer so the center has yellow pointing to this corner, and orange pointing away from this corner. Turn the Top layer so its center has yellow pointing to the red-side of this corner, and orange pointing to the blue-side of this corner. You now have a properly oriented set of centers, AND you know where solid corners and six-color corners must go. When dealing with the Top layer, don't let the orientation of the center fool you. It can be twisted. Rely on the sides for colors and patterns. In fact, each edge has a unique pair of colors, so you should be able to find the four edges of the Bottom layer. They are: R|Y, B|Y, G|O, and B|O. Y/O are the colors of the Bottom and Top faces. The pair of solid-colored corners on the Bottom layer are YRB and OGB. The pair of six-color corners are YO/BW/GR and OY/BW/RG. The six-color corners on the Top are YO/WB/RG and OY/WB/GR. All corners of each type (solid or six color) are diagonally opposite each other on a face. Of course, your Rubenking cube could have a different color scheme. You'll have to translate my color scheme to yours.

Addendum

• ||===|===|===|| || 3 | 8 | 7 || || 2 | 1 | 9 || || 5 | 6 | 4 || ||===|===|===||===|===|===||===|===|===||===|===|===|| || 9 | 7 | 1 || 3 | 9 | 7 || 1 | 4 | 2 || 4 | 3 | 6 || || 2 | 4 | 8 || 6 | 1 | 5 || 8 | 7 | 3 || 7 | 6 | 1 || || 5 | 3 | 6 || 8 | 2 | 4 || 6 | 9 | 5 || 9 | 2 | 8 || ||===|===|===||===|===|===||===|===|===||===|===|===|| || 1 | 5 | 2 || || 4 | 6 | 3 || || 7 | 8 | 9 || ||===|===|===||

The outline you see above is called "Sudoku on a puzzle cube". It's a pattern of six sides folded so the four squares in the middle wrap around. The top and bottom panels then fold back to form the top and bottom of the cube. Each face of the cube is an arrangement of the digits 1-9 as you might see them on a Sudoku puzzle. What makes this cube difficult, if is moves like a Rubik Cube, is that all the tiles are the same color, and all the digits are another color. I'll point out four corners for you, all associated with the panel between to top and bottom panels. Clockwise from 10 o'clock: 1-3-5, 4-7-1, 2-4-6, 6-8-1. Once scrambled, it's very difficult, but notice there are two panels with "1" in their center. You need to get those centers lined up with their 6-9 edge piece. Good luck.

Dick Guertin's Google Home Page