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Thursday, March 14, 2013

How to Solve a Rubik's Cube (Easy Move Notation)

The Rubik's Cube can be very frustrating and may seem next to impossible to restore to its original configuration. However, once you know a few algorithms, it is very easy to solve. The method described in this article is the layer method: we first solve one face of the cube (first layer), then the middle layer, and finally the last layer.

Steps


First Layer

  1. 1
    Familiarize yourself with the Notations at the bottom of the page.
  2. 2
    Choose one face to start with. In the examples that will follow, the color for the first layer is white.
  3. 3
    Solve the cross.
    Solve the cross.
    Solve the cross. Set into 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 eight moves (five or six in general).
    • Place the cross at the bottom. Turn the cube over 180° so that the cross now on the bottom.
  4. 4
    Solve the four corners of the first layer, one by one. You should also be able to place the corners without needing algorithms. To get you started, here is an example of one corner being solved:
    Image:Rubik_example01_step1_246.png
    Image:VRU_128.png
    Image:Rubik_example01_step2_768.png
    Image:HUL_668.png
    Image:Rubik_example01_step3_219.png
    Image:VRD_231.png
    Image:Rubik_example01_step4_398.png
    • At the end of this step, the first layer should be complete, with a solid color (in this case, white) at the bottom.
  5. 5
    Verify your first layer is correct. You should now have the first layer complete and look like this (from the bottom side):
    Image:Rubik_FLcomplete_1_571.png
    Image:Rubik_FLcomplete_2_642.png
    Image:Rubik_FLcomplete_3_348.png

Middle Layer

  1. 1
    Place the four edges of the middle layer. 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 :
      Image:Rubik_ML_1_995.png
      Image:HUL_668.png
      Image:VRU_128.png
      Image:HUR_929.png
      Image:VRD_231.png
      Image:HUR_929.png
      Image:FCCW_690.png
      Image:HUL_668.png
      Image:FCW_465.png
      		(1.a)
      Image:Rubik_ML_2_778.png
      Image:HUR_929.png
      Image:VLU_765.png
      Image:HUL_668.png
      Image:VLD_114.png
      Image:HUL_668.png
      Image:FCW_465.png
      Image:HUR_929.png
      Image:FCCW_690.png
      		(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.
  2. 2
    Verify correct positioning. Your cube should now have the first two layers complete and look like this (from the bottom side) :
    Image:Rubik_F2Lcomplete_1_660.png
    Image:Rubik_F2Lcomplete_2_149.png
    Image:Rubik_F2Lcomplete_3_840.png

Last layer

  1. 1
    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.
    • Locate two adjacent corners that share a color other than the color of the top layer (other than yellow in our case).
    • 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 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 :
      Image:VLU_765.png
      Image:HUR_929.png
      Image:VLD_114.png
      Image:FCW_465.png
      Image:HUL_668.png
      Image:FCCW_690.png
      Image:VLU_765.png
      Image:HUL_668.png
      Image:VLD_114.png
      Image:HUL_668.png
      Image:HUL_668.png
      		(2.a)
    • 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 with 2 and 3 with 4 :
      Image:VLU_765.png
      Image:HUR_929.png
      Image:VLD_114.png
      Image:FCW_465.png
      Image:HUL_668.png
      Image:HUL_668.png
      Image:FCCW_690.png
      Image:VLU_765.png
      Image:HUL_668.png
      Image:VLD_114.png
      		(2.b)
  2. 2
    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:
    Image:Rubik_LL_Corners_Orient11_237.png
    Image:Rubik_LL_Corners_Orient12_951.png
    Image:VRU_128.png
    Image:HUL_668.png
    Image:VRD_231.png
    Image:HUL_668.png
    Image:VRU_128.png
    Image:HUL_668.png
    Image:HUL_668.png
    Image:VRD_231.png
    Image:HUL_668.png
    Image:HUL_668.png
    		(3.a)
    • The algorithm will rotate three corners on themselves at once (from the side to the top). The blue arrows show which three 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 :
      Image:Rubik_LL_corners_complete_112.png
      Image:Rubik_LL_corners_complete3D_156.png
    • It is also convenient to use the symmetrical algorithm (here the red arrows are counter-clockwise turns):
      Image:Rubik_LL_Corners_Orient21_209.png
      Image:Rubik_LL_Corners_Orient22_925.png
      Image:VLU_765.png
      Image:HUR_929.png
      Image:VLD_114.png
      Image:HUR_929.png
      Image:VLU_765.png
      Image:HUR_929.png
      Image:HUR_929.png
      Image:VLD_114.png
      Image:HUR_929.png
      Image:HUR_929.png
      		(3.b)
      Symmetrical to (3.a)
    • Note: performing one of these algorithms twice is equivalent to performing the other. In some cases, you will need to perform the algorithm more than once :
    • Two correctly oriented corners :
      Image:Rubik_LL_CO_11_540.png
      		=
      Image:Rubik_LL_CO_12_123.png
      		=
      Image:Rubik_LL_CO_13_185.png
      		+
      Image:Rubik_LL_CO_14_139.png
      Image:Rubik_LL_CO_21_332.png
      		=
      Image:Rubik_LL_CO_22_161.png
      		=
      Image:Rubik_LL_CO_23_935.png
      		+
      Image:Rubik_LL_CO_24_58.png
      Image:Rubik_LL_CO_51_809.png
      		=
      Image:Rubik_LL_CO_52_345.png
      		=
      Image:Rubik_LL_CO_53_343.png
      		+
      Image:Rubik_LL_CO_54_269.png
    • No correctly oriented corner :
      Image:Rubik_LL_CO_31_931.png
      		=
      Image:Rubik_LL_CO_32_753.png
      		=
      Image:Rubik_LL_CO_33_614.png
      		+
      Image:Rubik_LL_CO_34_739.png
      Image:Rubik_LL_CO_41_157.png
      		=
      Image:Rubik_LL_CO_42_249.png
      		=
      Image:Rubik_LL_CO_43_207.png
      		+
      Image:Rubik_LL_CO_44_611.png
    • More generally, apply (3.a) in those cases:
      Two correctly oriented corners :
      Image:Rubik_LL_OC_2c_116.png
      No correctly oriented corner :
      Image:Rubik_LL_OC_0c_870.png
  3. 3
    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 :
      Image:Rubik_LL_EP_11_863.png
      Image:Rubik_LL_EP_12_216.png
      Image:VMU_830.png
      Image:HUR_929.png
      Image:VMD_671.png
      Image:HUR_929.png
      Image:HUR_929.png
      Image:VMU_830.png
      Image:HUR_929.png
      Image:VMD_671.png
      		(4.a)
    • Or its symmetrical :
      Image:Rubik_LL_EP_21_608.png
      Image:Rubik_LL_EP_22_334.png
      Image:VMU_830.png
      Image:HUL_668.png
      Image:VMD_671.png
      Image:HUL_668.png
      Image:HUL_668.png
      Image:VMU_830.png
      Image:HUL_668.png
      Image:VMD_671.png
      		(4.b)
      Symmetrical to (4.a)

      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.
  4. 4
    Orient the edges. You will need to know two algorithms for that last step :
    Image:Rubik_LL_EO_11_599.png
    Image:Rubik_LL_EO_12_218.png
    		Dedmore "H" Pattern
    Image:VRD_231.png
    Image:HML_291.png
    Image:VRU_128.png
    Image:VRU_128.png
    Image:HMR_429.png
    Image:HMR_429.png
    Image:VRD_231.png
    Image:HUL_668.png
    Image:HUL_668.png
    Image:VRU_128.png
    Image:HMR_429.png
    Image:HMR_429.png
    Image:VRD_231.png
    Image:VRD_231.png
    Image:HMR_429.png
    Image:VRU_128.png
    Image:HUL_668.png
    Image:HUL_668.png
    		(5)
    Image:Rubik_LL_EO_21_958.png
    Image:Rubik_LL_EO_22_808.png
    		Dedmore "Fish" Pattern
    Image:FCW_465.png
    Image:HML_291.png
    Image:VRU_128.png
    Image:VRU_128.png
    Image:HMR_429.png
    Image:HMR_429.png
    Image:VRD_231.png
    Image:HUL_668.png
    Image:HUL_668.png
    Image:VRU_128.png
    Image:HMR_429.png
    Image:HMR_429.png
    Image:VRD_231.png
    Image:VRD_231.png
    Image:HMR_429.png
    Image:VRU_128.png
    Image:HUL_668.png
    Image:HUL_668.png
    Image:VRD_231.png
    Image:FCCW_690.png
    		(6)
    • Note the DOWN, LEFT, UP, RIGHT, sequence to most of the Dedmore "H" and "Fish" algorithms. You really have only one algorithm to remember since :
      (6) =
      Image:FCW_465.png
      Image:VRU_128.png
      		+ (5) +
      Image:VRD_231.png
      Image:FCCW_690.png
    • 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.
  5. 5
    Congratulations! Your cube should now be solved.

Notations

  1. 1
    This is the key to the notations used.
    • 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:
      • The centers (or center pieces), at the center of each face of the Cube. There are six of them, each have one facelet
      • The corners (or corner pieces), at the corners of the Cube. There are eight of them, and each have three facelets
      • 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 the colors used for these illustrations is called BOY (because the Blue, Orange and Yellow faces are in clockwise order).
      • White opposes yellow;
      • Blue opposes green;
      • Orange opposes red;
  2. 2
    This article uses two different views for the Cube:
    • 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).

      3D View
    • The Top View, showing only the top of the cube (yellow). The front side is at the bottom (red).

      Top View
  3. 3
    For the top view, each bar indicates the location of the important facelet. In 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.

    Showing Yellow Facelets
  4. 4
    When a facelet is grey, it means that its color is not important at the moment.
  5. 5
    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.

    algorithm (3.a)
    • 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).
    • Blue arrows are used for clockwise turns (algorithm (3.a)).
    • Red arrows are used for counter-clockwise turns (algorithm (3.b), symmetrical to (3.a)).
  6. 6
    For the top view, the light blue facelets indicate that an edge is incorrectly oriented. In the picture, the edges on the left and right are both incorrectly oriented. This means that if the top face is yellow, the yellow facelets for those two edges are not on the top, but on the side.

    Showing Incorrectly Oriented Edges
  7. 7
    For the move notations it is important to always look at the cube from the front side.
    • Rotation of the front side.
      Image:FCW_465.png
      Image:FCCW_690.png
    • Rotation of one of the three vertical rows:
      Image:VLU_765.png
      Image:VLD_114.png
      Image:VMU_830.png
      Image:VMD_671.png
      Image:VRU_128.png
      Image:VRD_231.png
    • Rotation of one of the three horizontal rows:
      Image:HUR_929.png
      Image:HUL_668.png
      Image:HMR_429.png
      Image:HML_291.png
      Image:HDR_354.png
      Image:HDL_108.png
    • A few examples of moves:
      START
      Image:FCW_465.png
      Image:VMU_830.png
      Image:VRD_231.png
      Image:HUR_929.png
      Image:Rubik_Initial_537.png
      Image:Rubik_after_FCW_53.png
      Image:Rubik_after_VMU_719.png
      Image:Rubik_after_VRD_341.png
      Image:Rubik_after_HUR_368.png
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