Learn How to Solve the Rubik's Cube

HOW TO SOLVE THE RUBIK’S CUBE INTRODUCTION There are many different methods for solving the Rubik's cube. They can be divided into two broad categories: LAYER METHODS AND CORNERS FIRST METHODS (and there are subcategories within these broad categories). Here we will discuss a layer based method. More specifically, the method we will learn is {Cross, F2L, LL}.

STRUCTURE OF THE CUBE We all know that 3x3x3=27, however, rather than thinking about the cube as 27 little "cubies", think about it as 6 fixed centres (that can rotate on their own axis) with 8 corners and 12 edges which rotate around it. As the centres are fixed, the centre colour defines the colour for the face. It's important to remember this, otherwise, you'll end up trying to do illogical (mechanically impossible!) things like wondering why you can't work out how to put a corner piece in an edge position, or assuming that you're looking at the blue face merely because 8 of the 9 cubies on it are blue (if the centre is white then it's the white face).

STANDARD CUBE NOTATION We will use algorithms to solve the three layers of the cube. These algorithms will be expressed using STANDARD CUBE NOTATION, which describes how you should manipulate the cube to obtain certain results. Here’s what you need to know: • • • • • •

F = front face B = back face R = right face L = left face U = up face D = down face

In addition to a letter, each move may be accompanied by an apostrophe or the number two: • • •

A letter by itself means turn that face 90 degrees clockwise (e.g. F). A letter followed by an apostrophe means turn that face 90 degrees anti-clockwise (e.g. F'). A letter followed by the number 2 means turn that face 180 degrees (direction is irrelevant), (e.g. F2).

So R U’ L2 is shorthand for "TURN THE RIGHT FACE 90 DEGREES CLOCKWISE, THEN TURN THE UP FACE 90 DEGREES ANTI-CLOCKWISE, THEN TURN THE LEFT FACE 180 DEGREES". When thinking whether to turn clockwise/anti-clockwise, imagine that you are looking directly at the particular face you are turning. For each algorithm, the notation is written with the assumption that the core of the cube remains fixed throughout the whole algorithm, andthe faces just turn around it. This means that you also need to know how to position the cube to start the algorithm.

THE SOLUTION THE FIRST LAYER The first layer is solved in two stages: 1. Form the cross 2. Insert the 4 first layer corners (each corner is inserted individually) You should do the first layer intuitively, that way you will understand how the cube works and you will be able to understand the algorithms better. Spend some time playing with the cube and moving the pieces around to familiarize yourself with it.

1 THE CROSS The first step to solve a cube is to make a cross on one of the faces. I prefer to start with the white cross because I find white easier to quickly identifyon a completely scrambled cube. You can, of course, use any colour you like, but once you choose a colour, stick to it and get used to it. This will avoid confusion and let you solve the cube faster. There are 4 edge pieces with white (i.e. the 4 arms of the cross) which have specific positions. You can't put any white edge piece in an arm of the cross because the other colour on the edge cubie must match up with its centre on the middle layer.

Here is what a correctly formed cross looks like. Here denotes is what an incorrectly Grey cubies that are formed cross looks like. irrelevant to the cross. Looking thewhite/red white face we Note thatatthe edge see a white cross, however the cubie matches up with the white white/red edge cubie doesSo not centre and the red centre. match up with the red centre do the white/blue cubie. just as the white/blue edge doesn’t match with the blue centre.

2 THE FIRST LAYER CORNERS STEP 1 The blue/red/white corner is sitting in the bottom layer (The blue part is facing the bottom so we can't see it in this picture). Turn the blue face 90 degrees anticlockwise.

STEP 2 Now your cube should look like this. Move the D face 90 degrees anticlockwise to line up the blue/white edge with the blue/white/red corner.

STEP 3 Now that the blue/white edge and the blue/white/red corner have been lined up, re-form the white cross by turning the blue face 90 degrees clockwise.

STEP 4 Now the blue/white/red corner is in its correct place.

THE 2 N D LAYER (OR THE MIDDLE LAYER) INSERTING THE 4 MIDDLE LAYER EDGES There is one algorithm plus one mirror algorithm for inserting the middle layer edges. To perform this algorithm you should find an edge that is currently sitting in the last layer. The example that follows shows the blue/red edge.

THIS BLUE EDGE CUBIE IN THE LAST LAYER IS THE BLUE/RED EDGE CUBIE.

In this picture, U=white, L=red and F=blue. We can't see the other three faces, but obviously the R face is the one opposite the L face, the D face is opposite the U face and the B face is opposite the F face. Now, position the blue/red edge piece so that the colour on the side of the cube (blue in this case) lines up with its centre. Now perform the following algorithm: D L D' L' - D' F' D F If the blue/red edge piece was flipped the other way so that the blue was on the bottom rather than the red, you would position the cubie under the red centre and perform the following algorithm: D' F' D F - D L D' L' (The blue face is still the F face). This is the mirror of the previous algorithm (You can see that the parts on either side of the dash are reversed). The axis of symmetry lies diagonally across the white face, and along the line which divides the blue face and the red face.

WHAT IF THE EDGE PIECE IS NOT IN THE LAST LAYER? The instructions above assume that the middle layer edge piece you are inserting is sitting somewhere in the last layer. If some middle edges are in the last layer and some are in the middle layer in the wrong spot, always start working with the edge pieces that are in the last layer. After you've done this, sometimes (but not too often) you'll be left with a middle layer edge piece that's in the middle layer The red/blue middle layer but in the wrong spot. In this situation, you can use the same edge piece is in the middle middle layer algorithms from above (D L D' L' D' F' D F or D' layer but not oriented F' D F D L D' L') to insert another edge piece into the middle correctly. It needs to be layer edge position, thereby knocking the middle layer edge moved to the last layer piece out of its spot and into the last layer. Once you've done then put back into the this, the middle layer edge piece is in the last layer and you middle layer in the right can deal with it in the usual way.

THE LAST LAYER Before trying to solve the last layer, turn the cube around so that the white face which was previously the U face is now the D face and the yellow face is now the U face. All algorithms discussed from here are written considering that the yellow face is the U face.

1 ORIENTING THE LAST LAYER EDGES The first step is to orient the last layer edges so that the yellow side of these edges is in the yellow U face. You need to create a yellow cross on the U layer; except this time, the edges’ colours do not have to match with the colours of the centres. Your yellow face might look like one of the states described below. I’ve described each state and what you need to do. STATE 1: Your LL edges are correctly oriented and you need not do anything. Move on to the next stage.

STATE 2: Adjacent edges are correctly matched. Perform the following algorithm: F U R U’ R’ F’. You must hold the cube so that the U face appears this way to you.

STATE 3: Opposite edges are correctly matched. Perform the following algorithm: F R U R’ U’ F’. You must hold the cube so that the U face appears this way to you.

STATE 4: No edges are correctly matched and you need to perform both the algorithms, to be precise, you should do F U R U’ R’ F - U2 - F R U R’ U’ F’.

2 PERMUTING THE LL EDGES At this point you should have a solved First2Layers and a Cross on your Top face. The Last Layer edges will not necessarily be in their solved positions at this time, so the next step is to position the edges correctly. The first thing to do is to check that this step is necessary! If you can align your U-layer so that all of the edge colours around the side are matched up with their respective centre colours, then the edges are already correctly permuted, and you can move on to the next step. There is a 1 in 12 chance that this may happen, so look out for it. However, if this is not the case, try to align your U layer so that only 1 edge is solved (the colour around the side matching with the corresponding centre colour). Hold the cube so that the solved edge is on the Front face, and then identify which case you have from below. Use the corresponding algorithm to permute the edges.

Edges need to be permuted ANTICLOCKWISE the algorithm is R U R’ U R U2 R’.

Edges need to be permuted CLOCKWISE the algorithm is R U2 R’ U’ R U’ R’.

3 ORIENT THE LL CORNERS At this stage all that remains is to solve the Top Layer Corners. We will attack this in two stages, very much in the same manner as fixing the edges. First of all, we will twist (orient) the corners correctly, which will result in a completely solved top face. Note that, similarly to the step where we oriented the Top Layer Edges, we don't care about the colours around the side of the U-layer just yet, it is only the U-face we are concerned with solving. So first, identify the corners that need to be oriented, It is possible to have to twist 2, 3, or even all 4 corners, but if you have to only twist 1 corner there is something wrong with your cube and you will have to take it apart and put it back together correctly in order to be able to solve it! A corner which needs to be oriented is one which doesn't yet have the top layer colour (Yellow in this case) on the top face. Once you have identified the corner you want to work on, you should: 1. Turn the U layer so that the corner you are working on is at the Back-Right position (i.e. North-East as you look at it). 2. Identify whether the top layer colour (Yellow) sticker on the corner sits on the Right face or the Back face. 3. Using that information, apply the correct move from below to twist the corner so that the top layer colour (Yellow) is moved to the top.

Yellow face to the right: R D R’ D’ – R D R’ D’

Yellow face to the back: D R D’ R’ – D R D’ R’

4. STOP. Now it looks like you have messed up your First 2 Layers. But don't worry; it's supposed to be like this! DON'T ROTATE THE CUBE IN YOUR HANDS, but turn the U layer to bring the next corner that you want to work on into the BackRight position. Go back to Step 2. Once you have twisted all the corners that

needed to be twisted, your top face should be solved, AND your First 2 Layers will have magically restored itself!

SPECIAL CASE You will be able to permute the edges using the above algorithms in 3/4 of your solves on average. Sometimes however it will not be possible to position the U-layer so that only one edge is solved. In this instance simply execute one of the algorithms given above (your favorite one), and the result will be that you end up with a position that is solvable by using one of the algorithms given above.

4 PERMUTE THE LL CORNERS The final step towards solving the Last Layer Corners is to permute them, and by doing so you will have solved the entire cube. The first thing to do is to identify which corner is already in the "correct position". You can easily find this corner; it will be the only one where all the stickers around it match up perfectly with it, like they would do when the cube is completely solved. It is possible that there isn't a solved corner, for these cases please read further down the page. If you do have a solved corner, turn the cube in your hands so that you hold it with the solved corner at the Front-Left position (i.e. South-West as you look at it). Then identify whether you need to move the remaining 3 corners around clockwise or anti-clockwise, much like you did in a previous step with the edges. Once you have identified all of this, use one of the following moves to complete the cube.

R2 B2 – R F R’ – B2 – R F’ R

R’ F R’ – B2 – R F’ R’ – B2 R2

WHAT IF THERE ISN'T A SOLVED CORNER? The method for dealing with this special case is analagous to the way we dealt with the case of not being able to align the U-layer to solve only 1 edge during the Permute Last Layer Edges step. We can solve this case in exactly the same way, just execute one of the moves above (your favourite one), and the result will be that you end up with a position where there is one solved corner. You can then go on and solve that by using the table above.

Practice these moves over and over, practice solving the whole cube from scratch, and once you can use these moves confidently and by heart, you will be able to solve any randomly scrambled Rubik's Cube!