Solving a Rubik Cube

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Solving a Rubik's cube Many 3×3×3 Rubik's Cube enthusiasts use a notation developed by David Singmaster to denote a sequence of moves, referred to as "Singmaster notation". [21] Its relative nature allows algorithms to be written in such a way that they can be applied regardless of which side is designated the top or how the colours are organised on a particular cube. F (Front): the side currently facing you B (Back): the side opposite the front U (Up): the side above or on top of the front side D (Down): the side opposite the top, underneath the Cube L (Left): the side directly to the left of the front R (Right): the side directly to the right of the front ƒ (Front two layers): the side facing you and the corresponding middle layer b (Back two layers): the side opposite the front and the corresponding middle layer u (Up two layers) : the top side and the corresponding middle layer d (Down two layers) : the bottom layer and the corresponding middle layer l (Left two layers) : the side to the left of the front and the corresponding middle layer r (Right two layers) : the side to the right of the front and the corresponding middle layer x (rotate): rotate the entire Cube on R y (rotate): rotate the entire Cube on U z (rotate): rotate the entire Cube on F When a prime symbol ( ′ ) follows a letter, it denotes face counter-clockwise, while a letter without a prime symbol denotes a clockwise turn. A letter followed by a 2 (occasionally a superscript 2 ) denotes two turns, or a 180- degree turn. R is right side clockwise, but R' is right side counter-clockwise. The letters x, y, and z are used to indicate that the entire Cube should be turned about one of 1

Transcript of Solving a Rubik Cube

Page 1: Solving a Rubik Cube

Solving a Rubik's cube

Many 3×3×3 Rubik's Cube enthusiasts use a notation developed by David Singmaster to denote a sequence of moves, referred to as "Singmaster notation".[21] Its relative nature allows algorithms to be written in such a way that they can be applied regardless of which side is designated the top or how the colours are organised on a particular cube.

F (Front): the side currently facing you B (Back): the side opposite the front U (Up): the side above or on top of the front side D (Down): the side opposite the top, underneath the Cube L (Left): the side directly to the left of the front R (Right): the side directly to the right of the front ƒ (Front two layers): the side facing you and the corresponding middle layer b (Back two layers): the side opposite the front and the corresponding middle layer u (Up two layers) : the top side and the corresponding middle layer d (Down two layers) : the bottom layer and the corresponding middle layer l (Left two layers) : the side to the left of the front and the corresponding middle layer r (Right two layers) : the side to the right of the front and the corresponding middle layer x (rotate): rotate the entire Cube on R y (rotate): rotate the entire Cube on U z (rotate): rotate the entire Cube on F

When a prime symbol ( ′ ) follows a letter, it denotes face counter-clockwise, while a letter without a prime symbol denotes a clockwise turn. A letter followed by a 2 (occasionally a superscript 2) denotes two turns, or a 180-degree turn. R is right side clockwise, but R' is right side counter-clockwise. The letters x, y, and z are used to indicate that the entire Cube should be turned about one of its axes. When x, y or z are primed, it is an indication that the cube must be rotated in the opposite direction. When they are squared, the cube must be rotated twice.For methods using middle-layer turns (particularly corners-first methods) there is a generally accepted "MES" extension to the notation where letters M, E, and S denote middle layer turns. It was used e.g. in Marc Waterman's Algorithm.[22]

M (Middle): the layer between L and R, turn direction as L (top-down) E (Equator): the layer between U and D, turn direction as D (left-right) S (Standing): the layer between F and B, turn direction as F

The 4×4×4 and larger cubes use an extended notation to refer to the additional middle layers. Generally speaking, uppercase letters (F B U D L R) refer to the outermost portions of the cube (called faces). Lowercase letters (ƒ b u d ℓ r) refer to the inner portions of the cube (called slices). An asterisk (L*), a number in front of it (2L), or two layers in parenthesis (Lℓ), means to turn the two layers at the same time (both the inner

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and the outer left faces) For example: (Rr)' ℓ2 ƒ' means to turn the two rightmost layers counterclockwise, then the left inner layer twice, and then the inner front layer counterclockwise.

Notation

There are several notations; please refer to this notation guide.Briefly:

There are six sides to the cube, presented as Front, Back, Left, Right, Up and Down. They are usually referred to by their one-letter abbreviations. In the isometric diagrams below, where a corner points out at you, you see the F, R and U sides. The F faces to the left. Movements are presented as one quarter rotation (90 degrees) of an external face per movement. This means that the center tile colors are not changed. In our diagrams, F is blue, R is red and U is yellow. The other three colors are typically orange opposite red, green opposite blue and white opposite yellow Quarter-rotations of that face's layer default to clockwise. Counter-clockwise rotations are often referred to as "inverted" and indicated by ′, for instance, R′. (The ′ is commonly read as "prime", "apostrophe", "tick mark", "anti-clockwise", "anti" or "i" for inverted). Half-rotations (180 degrees) are indicated by the digit "2", for instance, R2 (meaning 2 quarter-rotations following the one-letter abbreviation). In order to display what is happening on the sides of the other three colors, the cube will be rotated as a whole described as rotating along the x, y, z space axis, all pointing out of the page. x is R, y is U and z is F, but since this sort of move also changes the colors of the center-tiles, it is used sparingly.

Example solveAs an example, let's consider a complete solve. 25 move scrambles are used to mix up the cube. Our sample scramble is:

U B′ R2 D′ U′ R U2 B R′ B2 L2 R F2 R2 U2 R B U2 F2 L2 F2 D R B2 R2 The solve is:

R′ B R D2 F2 L U′ F U R′ D R F D F′ F′ D′ F U2 R′ D′ R U2 U′ F′ D′ F U U B′ D′ B U′ y2 F D2 F2 R F R′ B′ D F D′ B D F′ F2 D M D2 M′ D F2 (54 moves,)

Step 1: Top edge pieces (cross)

The cube is assumed to be scrambled. The first thing to do is to choose a color, say white (it tends to stand out from the other colors on the cube). It's also a very good idea to always do a specific color first, since you will remember which colors are adjacent, which speeds things up considerably.How to read cubie positions: a cubie is either a corner or an edge piece. The UL piece, for instance, is an edge piece because it has only two colors. It is the edge piece with a sticker on the U face and a sticker on the L face. Similarly, the URF piece is a corner (it

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has three stickers), and it has a sticker on the U, R and F faces. The piece that is referred to depends on the orientation of the cube, which is why most solutions tell you to keep the cube with a certain color on top and a certain color in front (looking at the center sticker, since that one never moves).When talking about a white-other color edge, this is an edge with one white sticker and one other color, which on a standard cube could be red, orange, blue or green.The first step is to form a cross on the top face of the cube. Orient the cube so that the white center piece is on top. The aim is to get the correct pieces in the UL, UB, UR and UF locations. If you started with white, these pieces will be colored white-red, white-orange, white-yellow and white-green (using a Rubik's brand cube). So, some of the following moves are needed (be sure to do those in the first step first):

If a white-other color edge piece is on the U face: If white is in the U position, simply rotate the U face until the edge is lined up with its center. You should now see four stickers connected, e.g., white (center), white (edge), red (edge), red (center). If the piece is flipped in the up layer, then place the edge in the front layer and perform F U′ R U .

If the piece is in the middle slice of the cube (the second layer): Hold the cube so that white is still on the U face and your piece is in the FR location. Find the spot where the piece should go. Rotate U until either F′ or R can be applied to move the piece in the correct spot, so that the white face will move to the top. Make sure that the order of the edges in the top layer will still be correct. On a Rubik's brand cube, the order would be blue, red, green, orange. After placing the piece in the top layer, you can turn the U face until all correctly placed edges connect to their centers . An alternative to this method is to move the white sticker to D face (if possible without disturbing the current cross pieces) and move on to the next step.

If the white is on the D face, simply rotate D (or D′) until the piece is directly underneath its center, and apply F2 (assuming the piece is at the FD position) to put it in the correct location.

If the other color is on the D face (the flipped version of the previous state), keep the piece in the F layer. Rotate D so that the piece is in the RD position, and apply R F′ R′ . (R′ is not needed if the UR piece has not been placed correctly yet.)

There should now be a white cross formed on the top of the cube. By now, it will be possible to think how the edge pieces are located relativeto one another, which should speed things up.

Step 2: Top corner pieces

The second step is to correctly position three of the U face corner pieces. The reason that only three and not four will be put into place is that this method uses a "working space" which greatly simplifies the later steps. There are three basic possibilities for putting corner pieces into place:

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The piece is on the D slice, with the white side not on the D side. In this case, rotate the D face so that it is directly underneath the location that it should go to. Now, hold the cube so that the piece is in the DRF spot, and the intended location is the UFR spot.

If white is on the R side of the corner piece in DRF, apply R′ D′ R . If white is on the F side of the corner piece in DRF, apply F D F′ .

The corner piece is on the D slice, but the white face is on the D side. Rotate the D face so that the corner piece is in the DRF spot, and the intended location is the URF spot.Now apply R′ D2 R D R′ D′ R : Note that what is being done is R′ D2 R to move the white side off the bottom of the cube, so that one of the moves in the previous section can be used.Also note that equivalent to this is: F D2 F′ D′ F D F′ : for left-handed people this might make things easier. A right-handed person would probably do the "R′ D2 R …" move, without thinking about it.

The corner piece in question is in the right spot but incorrectly rotated. Therefore, it must be rotated. Hold the cube so that it is in the URF location. Now,

If the white side is on the R face, apply R′ D′ R D R′ D′ R . If the white side is on the F face, apply F D F′ D′ F D F′ .

So now one side should be done, except for one corner piece. This location will be used to swap corner pieces in and out, greatly simplifying later processes. The moves in the first two steps are really quite intuitive. After only a few repetitions, they will be simple and that's what you do.

Step 3: Middle edge pieces

This step involves correctly placing three of the four edge pieces on the "middle" layer of the cube.For these moves hold the cube so that the white face is on the bottom. The only middle layer edge piece that is not to be positioned is the one right above the corner piece that was not positioned correctly in step 2.Before you begin positioning edge pieces, you should rotate the middle layer so that all of the center pieces are correctly positioned.First of all, make sure the white side is on the bottom, and the "empty" (i.e., incorrect) corner piece on the white side is in the DRF location. The middle layer edge pieces will all be positioned in this step, except for the FR one.To move a piece into position, rotate the cube about its vertical axis, so that the intended location is the FR location. (For example, the FL piece is to be put in place. Rotate the cube a quarter turn counter-clockwise.) Now rotate the bottom slice so that the incorrect corner piece is in the DRF location. (So in the previous example – for the FL piece – first turn the cube, then apply D′.)Now all is prepared for the move. The move to put the new edge piece into place can only be done if it is on the U slice. If it is, note which side is NOT on the U face. Either F′ or R will need to be applied, depending on the orientation of the edge piece to be moved. Now, apply U until the piece to be moved is in the UF or UR (depending on the previous move)

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location, and then F or R′, to get it back to normal.Here is an example: Yellow is the F center. Orange is the R center. The Yellow-Orange edge piece is to be positioned, to the FR position. The D face has already been rotated so that the DRF location does not contain a white corner piece. The Yellow-Orange piece is in the UB location. The Orange is the U side, and Yellow is the B side. Thus, apply F′ U2 F (demo).To continue, simply keep rotating D or D′ and moving the cube to set up the same position, with an "empty" corner in DRF, the intended location at RF, and the piece to move in the U slice. Note that in some cases the piece may already be in the correct location, but oriented incorrectly. In this case take it out first (i.e., put any edge piece with the color whose center is opposite white on the cube into that location) and then put it back in that spot. In other words, with the DRF corner "empty" and the offending piece in the FR spot, apply F′ U′ F U R U′ R′ .Now two thirds of the cube should be done, less two pieces: a middle layer edge piece and its adjacent corner piece, that appears to take a chunk out of the bottom (white) layer. Note that it is possible for the "empty" corner piece on the bottom layer to get solved by accident. If so, just ignore it, and pretend that it is unsolved.

Step 4: Solve remaining edge pieces

Solve first three remaining edge pieces (UF, UL, UB)There are two basic parts to this step, as follows:The goal of the whole step is to solve all of the 5 remaining edge pieces. The first part is to solve three of these (UF, UL, UB), and the second part is to solve the other two together.First of all, hold the cube so that the "empty" edge piece is in the BR position, and thus the "empty" corner piece is in the RDB position. To do moves in this part, first of all move a piece into the BR location, then move it to the U face, to one of those UF, UL, or UB positions.The move is as follows. First, optionally rotate U. Then, apply R′ or B. Then rotate U the desired amount. Then do R or B′ (to undo the first part of this move).An example: Say the Blue-Yellow piece is in the BR location. Furthermore, Blue is the U color, and Yellow is the L color. The order would be: U (to put the UL location – the destination – in the right spot), B U′ B′.However, when actually trying to solve the cube quickly, instead of applying U′ in the previous move, look to find the next edge piece that is required to put in the right location.So rotate U until it is in the UB location, and then by applying B′ return the cube to a stable position. Then, rotate U some amount to get the UL piece (Blue-Yellow in the example) back to the right place.There is a tremendous amount of freedom in this sequence of moves. In fact, there is no need to return the edge pieces to the correct spots in between repetitions of this move.Simply realize how the pieces go with respect to one another, and then finally align them, when all three (UF, UL, UB) are done.[edit]Remaining two edge pieces (BR, UR)This is the only step that requires any actual memorization. The moves from the other

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steps should become very natural after a short time.There are four possibilities. The remaining edge pieces are the BR piece and the UR piece. Do the following:

Luckily, the pieces are correct. Move to the next step. The pieces are in the correct locations, but incorrectly oriented. Apply B U′ B′ U R′ U R U′ (demo). Both edge pieces (BR and UR) have the same color on the R side of the piece, which is the same color as the R center. Apply U′ R′ U′ R U′ R′ U′ R U′ (demo). The other case (the UR piece has the R color on its U side, and B color on its R side, and the BR piece has the U color on its R side, and the R color on its B side). Apply B U B′ U B U B′ U2 (demo).

To reduce memorization at the expense of some speed, two of these moves suffice. In other words, apply all three of these moves in any sequence to an all-edges correct cube, and the result will be an all-edges correct cube.[edit]Step 5: Position corner piecesThis step will move the remaining 4 unsolved corner pieces to their correct positions, irrespective of orientation. The basic strategy is to move the "empty" corner piece to DRB and the corner piece to be moved to UFL. A move (L D2 L′) is used to swap the two corners (as well as temporarily jumble up the cube). Then U slice is rotated such that the correct position for the corner (now in DRB) is in UFL. Then the move (L D2 L′) is applied again to undo the cube jumbling as well as move the corner to the correct position.This shouldn't need to be done more than 3 times (since there are only 4 corners to move and the last two will swap with each other to their correct positions).This step can be a little confusing at first. First of all, make sure the DRB piece is that "empty" (unsolved … not missing!) corner piece.Say the UFL piece is Blue-Yellow-Orange. But that piece should go in the URB position. Do the following moves: L D2 L′ (move the piece in question out of the way – to the DRB position), U2 (move the correct position to the UFL spot), L D2 L′ (move the piece in question back to the U slice), U2 (undo the U twist done earlier).One thing to note when doing this move, make sure the original UFL piece does not contain the color of the bottom face (white in the ongoing example).Also note that it is satisfactory to rotate the U face before the move so that a particular corner piece can be moved into the UFL position so that it can be worked on. The only (slight) difference will be a need to rotate U at the end to make up for that.Note that these U-rotations should be very obvious. Simply line up the top-layer edge pieces with their respective centers.[edit]Step 6: Orient corner pieces correctlyCorner pieces must be rotated in pairs – one clockwise and one counter-clockwise. If you combine two clockwise or counter-clockwise rotations, the rest of your cube will be compromised.Find two incorrectly rotated corner pieces that are on the same slice. Hold the cube so that one of the pieces in the UFL position and the other is somewhere on the U slice.

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To rotate a piece clockwise, apply L D2 L′ F′ D2 F (demo). To rotate a piece counter-clockwise, apply F′ D2 F L D2 L′ (demo).

Note that after orienting the first corner piece, apply U until the other corner piece goes in the UFL location. When the second corner piece has been oriented, turn U to undo the previous twisting (this should be fairly obvious).Here's an explicit example – the UFL piece needs rotating counter-clockwise, and the UFR piece needs rotating clockwise. The full sequence would be as follows: F′ D2 F L D2 L′ (orient UFL piece), U (position other corner), L D2 L′ F′ D2 F (orient original UFR piece), U′ (undoes rotation of U that was done earlier). (Demo.)This pattern may need to be applied up to three times. Note that with this method only one clockwise and one counter-clockwise twist can be done; other methods twist 3 corners but have side-effects on edges.If the two remaining corner pieces are diametrically opposed (e.g., at UFL and DRB), then apply R2 (in this case) to bring both of them onto the U slice. Then, do the sequence. Then apply R2 again to get to the original configuration (demo).Congratulations, your cube should now be solved!

[edit]Rotating the center facesSome cubes have multi-color designs on each face rather than a single color, in which case the orientation of the center faces is an issue. Usually, solving the cube with the center faces oriented correctly is possible, and the fastest method; but there exists a (very slow) way to rotate two of the center faces at a time without affecting the rest of the cube. If you want to rotate the F and R center faces (both clockwise), simply repeat F R a full 105 times after each other. If you want to rotate F clockwise and R counter-clockwise, do F R′, etc. This method can be very time-consuming, however, so planning ahead while solving the rest of the cube is preferred – that is, match the side center faces to the top edges, and hope the bottom turns out correctly. This less time-consuming sequence will rotate the top center face counter-clockwise (ccw) and the left center face clockwise (cw), each n quarter turns:

(L′ R F′B U′ D) Ln (D′ U B′ F R′ L) U′n

With different notation, the sequence (n = 1) can be abbreviated (demo):(M E M′) U (M E′ M′) U′

The result is the same when combined with a sequence to rotate the top center face two quarter turns:

(U R L U2 R′ L′)2

Left and top center faces are turned one quarter in same sense.[edit]Faster methodsWhile the above method may be good for a beginner, it is too slow to be used in speedcubing. The most popular method for speedcubers is very similar to the method above, except steps 2 and 3 are combined, and the last layer is solved in two steps instead of three. The inventor of this common method is Jessica Fridrich. With this method, speedcubers with good dexterity and memory can average under 20 seconds after a few months of hard practice. However, to learn the method you must learn 78 algorithms. There are methods just as fast that require far fewer algorithms to be memorized. Here is a brief synopsis of several popular speedcubing methods:

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[edit]Layer by Layer methodsFridrich Method: A very fast First 2 Layers (or F2L) method, start by solving a cross on one face, then proceeding to solve the First 2 Layers pairing up edge and corner combinations and putting them into their slot. This is followed by solving the Last Layer in two steps, first orienting all pieces (one color on the last layer), then permuting them (solving the ring around the last layer). The basic method has 78 algorithms (without the inverse of them), and is recognized as one of the fastest methods currently in use. [1]F2L Alternatives: Methods that follow the same principle as Fridrich's method, but using different algorithms. Many of the algorithms are shared but there are a few differences, so there should be one to suit your fingers:

Bob Burton: Shotaro 'Macky' Makisumi: Speedcubing.com Collection: speedcubinglovers.com

ZB method: This method was developed independently by Ron van Bruchem and Zbigniew Zborowski in 2003. After solving the cross and three c/e pairs, the final F2L pair is solved while orienting LL edges. This is known as ZBF2L. The last layer can then be solved in one algorithm, known as ZBLL. The ultimate method requires several hundred algorithms. To date, no one has learned the entire method. Lars Vandenbergh's site has ZBF2L algorithms, used in his VH system. ZBLL algorithms can be found on Doug Li's webpage.ZZ method: This method was created in 2006 by Zbigniew Zborowski, the co-creator of the ZB method. It has three basic steps: EOLine, F2L, and LL. EOLine stands for Edge Orientation Line. The orientation of edges is defined as either good or bad. Good meaning the edge can be placed into the correct position with a combination of R, L, U, D, F2, or B2, moves. Bad meaning it would require an F, F′, B, or B′ move to be moved into its correct position. Any F, F′, B, or B′ move will cause the four edges on that slice to change from its current state, good or bad, to the opposite state. The Line portion of EOLine is forming a line on the bottom of the cube that consists of the DB edge and the DF edge in their correct positions. The next step is F2L, First 2 Layers. This process is similar to the F2L of the other three Layer By Layer methods with two variations. The first being that blocking building techniques similar to those in the Petrus, Roux, and Heise methods can be used to solve the c/e pairs. The second variation is the ability to solve the entire F2L using only R, U, and L moves. This allows for very quick solving of F2L as it does not require cube rotation. The final step of the ZZ method is LL, Last Layer, and it can be broken into multiple steps or maintained as one depending on the algorithms used. There are two main approaches to this method OLL [7] and PLL [8], Orientation of LL and Permutation of LL, and COLL and EPLL, Corner OLL and Edge PLL. The first, OLL and PLL, is to use one of 7 algorithms to solve the top layer (OLL) and then permute the the edge and corners into their correct positions (PLL), this requires 21 algorithms. The total algorithms required for the first approach of solving LL is 28. The second approach to solving LL is to solve the top and the corners in one algorithm (COLL) and then solve the edges (EPLL). COLL requires 40 algorithms and EPLL requires 4, making the total 44 algorithms. The second approach is faster due the ease of recognition and speed of execution of EPLL.

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VH method: Created by Lars Vandenbergh and Dan Harris, as a stepping stone from Fridrich to ZB. First, F2L without one c/e-pair is solved with Fridrich or some other method. Then the last pair is paired up, but not inserted. Then it's inserted to F2L and LL edges are oriented in one go. Then, using COLL, corners of LL are solved while preserving edge orientation. Then edges are permuted.

Block methodsPetrus System: Created by Lars Petrus. One of the shortest methods in terms of face turns per solve, the Petrus method is often used in fewest moves contests. Petrus reasoned that as you construct layers, further organization of the cube's remaining pieces is restricted by what you have already done. In order for a layer-based solution to continue after the first layer had been constructed, the solved portion of the cube would have to be temporarily disassembled while the desired moves were made, then reassembled afterward. Petrus sought to get around thisquagmire by solving the cube outwards from one corner, leaving him with unrestricted movement on several sides of the cube as he progressed. There are not as many algorithms to learn compared to the other F2L methods, but it takes a lot of dedication to master. The basis of the method is to create a 2 × 2 × 3 block on the cube, then proceed to solve a 3 × 3 × 2 block, but also flipping the edges on the Last Layer. Then the Last Layer is solved in two steps, first corners and then edges. Heise method: Created by Ryan Heise, this method doesn't require any algorithms. First, one inner square and three outer squares are built intuitively. Then they are placed correctly while orienting remaining edges. After that you create two c/e-pairs, and solve the remaining edges. The last 3 corners are solved using a commutator.Gilles Roux Method: Another unique method, but works in blocks like the Petrus method. You start by solving a 1 × 2 × 3 block and then solve another 1 × 2 × 3 block on the other side of the cube. Next you solve the last 4 corners and finally the edges and centers. Has only 24 algorithms to learn.[edit]Corners first methodsWaterman Method: Created by Mark Waterman. Advanced corners first method, with about 90 algorithms to learn. Solve a face on L, do the corners on R and then solve the edges. An extremely fast method.Jelinek Method: Created by Josef Jelinek. This method is very similar to Waterman's. Create a solved 4 × 4 × 4 cube on one corner and rotate the remaining blocks (it may take a while but you will eventually solve it).

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1 Familiarize yourself with the Notations.

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2 Choose one face to start with. In the examples that will follow, the color for the first layer is white. Remember the first part is the hardest

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3 First Layer

3 Solve the cross : place in their correct position the four edge pieces that contain white. You should be able to do this by yourself without needing algorithms. All four edge pieces can be placed in a maximum of 8 moves (5 or 6 in general).3 Place the cross at the bottom.

Solve the four corners of the first layer, one by one. At the end of this step, the first layer should be complete, with a solid color (in this case, white) at the bottom. You should also be able to place the corners without needing

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algorithms. To get you started, here is an example of one corner being solved:

Your cube should now have the first layer complete and look like this (from the bottom side) :

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o Middle Layer

Place the four edges of the middle layer, one by one. Those edge pieces are the ones that do not contain yellow in our example. You need to know only one algorithm to solve the middle layer. The second algorithm is symmetrical to the first.

If the edge piece is located in the last layer :

(1.a)

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(1.b)symmetrical to (1.a)

If the edge piece is in the middle layer but in the wrong place or with the wrong orientation, simply use the same algorithm to place any other edge piece in its position. Your edge piece will then be in the last layer, and you just have to use the algorithm again to position it properly in the middle layer.

Your cube should now have the first two layers complete and look like this (from the bottom side) :

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Last layer

3 Permute the corners. At this step, our goal is to place the corners of the last layer in their correct position, regardless of their orientation.

3 Locate two adjacent corners that share a color other than the color of the top layer (other than yellow in our case).

3 Turn the top layer until these two corners are on the correct color side, facing you. For instance, if the two adjacent corners both contain red, turn the top layer until those two corners are on the red side of the cube. Note that on the other

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side, the two corners of the top layer will both contain the color of that side as well (orange in our example).

Determine whether the two corners of the front side are in their correct position, and swap them if needed. In our example, the right side is green, and the left side is blue. Therefore the front corner on the right must contain green, and the front corner on the left must contain blue. If it is not the case, you will need to swap those two corners with the following algorithm:

Swap 1 and 2 :

(2.a)

3 Do the same with the two corners at the back. Turn the cube around to place the other side (orange) in front of you. Swap the two front corners if needed.

As an alternative, if you notice that both the front pair and the back pair of corners need to be swapped, you can do it with only one algorithm (note the huge similarity with the previous algorithm):

Swap 1 and 3 :

(2.b)

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Orient the corners. Locate each top color facelet of the corners (yellow in our case). You need to know only one algorithm to orient the corners :

(3.a)

The algorithm will rotate 3 corners on themselves at once (from the side to the top). The blue arrows show which 3 corners you are turning, and in which direction (clockwise). If the yellow stickers are the way shown on the pictures and you perform the algorithm once, you should end up with the four yellow stickers on top :

It is also convenient to use the symmetrical algorithm (here the red arrows are

(3.b)

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counter-clockwise turns):

Symmetrical to (3.a)

Note : performing twice one of these algorithms is equivalent to performing the other.

In some cases, you will need to perform the algorithm more than once :2 correctly oriented corners :

= = +

= = +

= = +

no correctly oriented corner :

= = +

= = +

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Or more generally, apply (3.a) in those cases :Two correctly oriented corners :

No correctly oriented corner :

Permute the edges. You will need to know only one algorithm for this step. Check whether one or several edges are already in the correct position (the orientation does not matter at this point).

If all the edges are in their correct positions, you are done for this step.

If one edge only is correctly positioned, use the following algorithm :

(4.a)

or its symmetrical :

Symmetrical to (4.a)

(4.b)

Note : performing twice one of these algorithms is equivalent to performing the other. If all four edges are incorrectly positioned, perform one of the two algorithms once from any side. You will then have only one edge correctly positioned.

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Orient the edges. You will need to know two algorithms for that last step :

Dedmore "H" Pattern

(5)Dedmore "Fish" Pattern

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(6)

Note the DOWN, LEFT, UP, RIGHT, sequence to most of the Dedmore "H" and "Fish" algorithms.

Note you really have only one algorithm to remember since :(6) =

+ (5) +

If all four edges are flipped, perform the "H" pattern algorithm from any side, and you will have to perform that algorithm one more time to solve the cube.

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6

Congratulations! Your cube should now be solved.

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Tips

Know the colors of your cube. You must know which color is opposite which, and the order of the colors around each face. For instance, if white is on top and red in front, then you must know that blue is on the right, orange in the back, green on the left and yellow at the bottom. For the color to start with, you can either always start with the same color to help you with knowing where each color goes, or try to be efficient by choosing a color for which it is easier to solve the cross. Practice! Spend some time with your cube to learn how to move pieces around. This is especially important when you are learning to solve the first layer. To solve the cross efficiently, first locate all four edges and try to think ahead about how to move them into position without actually doing it. With practice and experience, this will teach you ways to solve it in fewer moves. And in a competition, participants are given 15 seconds to inspect their cube before the timer starts. Try to figure out how the algorithms work. While executing the algorithm, try to follow key pieces around to see where they go. Try to find pattern in the algorithms. For instance :

o In the algorithms (2.a) and (2.b) used to permute corners of the last/top layer, you execute 4 moves (at the end of which all first/bottom layer and middle layer cubies are back in the first/bottom and middle layers), then turn the upper layer, and then execute the reverse of the first four moves. therefore this algorithm does not affect the first/bottom and middle layers.o For the algorithms (4.a) and (4.b), note you are turning the top layer in the same direction that you need to turn the three edges.o For the algorithm (5), Dedmore "H" Pattern, a way to remember the algorithm is to follow the path of the flipped edge on the top right and the pair of corners around it for the first half of the algorithm. And then for the other half of the algorithm, follow the other flipped edge and pair of corners. You'll notice that you perform 5 moves (7 moves if counting half turns as 2 moves), then half turn the top layer, then reverse those first five moves, and finally half turn the top layer again.o Progress further. Once you know all the algorithms, you may want to find faster ways to solve the Rubik's:

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Solve the first layer corner along with its middle layer edge in one move.[1]

o Learn algorithms to orient the last layer corners in the five cases where two (3.a/b) algorithms are necessary.o Learn algorithms to permute the last layer edges in the two cases where no edge is correctly positioned.o Learn the algorithm for the case where all last layer edges are flipped.

Progress even further. For the last layer, if you want to solve the cube fast, you will need to do the last four steps two by two. For instance, permute and orient the corners in one step, then permute and orient the edges in one step. Or you can choose to orient all corners and edges in one step, then permute all corners and edges in one step.[2]

The layer method is just one of many methods out there. For instance, the Petrus method, which solves the cube in fewer moves, consists in building a 2×2×2 block, then expanding it to a 2×2×3, correcting edge orientation, building a 2×3×3 (two layers solved), positioning the remaining corners, orienting those corners, and finally positioning the remaining edges.[3]

For those interested in speed cubing, or those who simply don't like how hard it is to turn pieces, it is a good idea to buy a DIY kit. The pieces of speedcubes have rounder inner corners and DIY kits allow you to adjust the tension, making it a lot easier to move pieces. Consider also lubricating your cube with a silicon based lubricant.

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Notations

The pieces that compose the Rubik's Cube are called Cubies, and the color stickers on the Cubies are called Facelets. There are three types of Cubies :

o the centers (or center pieces), at the center of each face of the Cube. There are 6 of

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them, each have 1 Facelet.o the corners (or corner pieces), at the corners of the Cube. There are 8 of them, and each have 3 Facelets.o the edges (or edge pieces), between each pair of adjacent corners. There are 12 of them and each have 2 Facelets.

Not all cubes have the same color schemes. The cube used for the illustrations is such that :

o White opposes yellow;o Blue opposes green;o Orange opposes red;o Color scheme is BOY (because the Blue, Orange and Yellow faces are in clockwise order).

This article uses two different views for the Cube :

3D Viewo The 3D View, showing three sides of the Cube : The front (red), the top (yellow) and the right side (green). In step 4, the algorithm (1.b) is illustrated with a picture showing the left side of the cube (blue), the front (red) and top (yellow).

Top Viewo The Top View, showing only the top of the cube (yellow). The front side is at the bottom (red).

Showing Yellow Facelets For the top view, each bar indicates on which side the important facelet is located. On the picture, the yellow facelets of the top back corners are on the top (yellow) side, while the yellow facelets of the top front corners are both located on the front side of the cube. When a facelet is grey, it means that its color is not important for the situation considered.

algorithm (3.a)

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The arrows (blue or red), show what the algorithm will do. In the case of the algorithm (3.a) for instance, it will rotate the three corners on themselves as shown. If the yellow facelets are as drawn on the picture, at the end of the algorithm they will be on top.

o The axis of the rotation is the big diagonal of the cube (from one corner to the corner all the way on the other side of the cube).o Blue arrows are used for clockwise turns (algorithm (3.a)).o Red arrows are used for counter-clockwise turns (algorithm (3.b), symmetrical to (3.a)).

Showing Incorrectly Oriented Edges For the top view, the light blue facelets indicate that an edge is incorrectly oriented. On the picture, the edges on the left and right are both incorrectly oriented. Which means that if the top face is yellow, the yellow facelets for those two edges are not on the top, but on the side. For the move notations, it is important to always look at the cube from the front side.

o : Rotation of the front side.

o : Rotation of one of the three vertical rows.

: Rotation of one of the three horizontal

rows.

A few examples of moves :START

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