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| Solve the Cross | Example Cross Solves | Cross Training Page |
Solving the cross quickly and efficiently is a real art form, and can only be learnt through practice and experience. A beginner can not pick up the cube and expect to see the optimal solution to the cross straight away (a lot of experts have trouble with this too) let alone execute it in the best way.
On this page I hope to demonstrate some things you should look for when inspecting the cube, and some techniques which can be learnt. I will also give examples for various cases. But don't expect to master it in one day! :)
Analysis has shown that from every possible starting configuration, you can expect to solve the cross in 8 moves maximum.
| Number of Moves to solve | Number of cases (out of a possible 190080) | Percentage of total possible cases | calculating these figures |
| 1 | 0.00005% | ||
| 15 | 0.00789% | ||
| 158 | 0.08312% | ||
| 1394 | 0.73338% | ||
| 9809 | 5.16046% | ||
| 46381 | 24.4008% | ||
| 97254 | 51.1648% | ||
| 34966 | 18.3954% | ||
| 102 | 0.05366% |
Other salient points to note are that almost all (99.95%) cases can be solved in 7 moves maximum, and on average you would only require between 5 and 6 moves to solve the cross. So If you could see the shortest or near shortest cross solution every time, and execute it quickly, a cross in 1.5-2 seconds is perfectly reasonable.
My first and foremost recommendation is to always solve the cross on the bottom. If your current method is to solve a cross on the top face, and then turn upside down at some stage to solve the final layers, I would recommend that you get out of this habit immediately. Some solvers prefer to solve the cross on the left, which is just as good as solving the cross on the bottom, but for the purposes of this page I shall concentrate on "cross on bottom" solving, because this is the method I like best and find easiest to use.
Solving with the cross on the bottom is a good idea, it allows you to have the best view of the U layer, which means that you can easily look ahead and search for the F2L pieces while you solve the cross. It also means that you don't have to turn the cube upside down at some stage during your solve, which saves valuable seconds.
Secondly, know the colour scheme of your cube inside out. Make sure that with the cross on the bottom, you know which colours are opposites of each other (look at directly opposite centers), and you know the order of the colours all the way around the cube. On my cube, I know that Red is opposite Orange, Blue is opposite Green, and if I have Red facing me then Green is on the R face, Blue is on the L face, and Orange is on the B face. It is this knowledge that will allow you to concentrate on the other aspects of solving the cross. Learn your colour scheme and practice it until it becomes second nature.
Relative position is a concept which you must firmly fix in your mind before you can even hope to start seeing the shortest solutions to the cross for a given configuration.
If you think about it, it is not necessary to line up each edge with it's coloured center one at a time, and then place them one at a time in the D-layer. This is a fine method if you are a beginner, or even intermediate, but if you want to start speedcubing seriously you need to get out of this habit. This is where a good knowledge of your cube's colour scheme is needed. As long as you place (for example on my cube) the Red/White edge opposite the Orange/White edge, and the Blue/White opposite the Green/White edge, and you have made sure that the colours are correct all the way round, a D move will position the cross and fix all the pieces simultaneously every time. In other words, if you place the cross pieces incorrectly in the D-layer, but correctly relative to each other, you still get a solved cross.
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Using the concept of relative position, you can see that all these crosses are solved, only D moves need to be made to fix all the edges at the same time.When you are looking to solve the cross, you will of course concentrate on the cross edges only, and in your mind blank out the rest of the pieces altogether. Another useful thing to note about each cross edge as you inspect the cube is it's "flip". But what is "flip"?
A correctly flipped edge
An edge which has a correct flip only needs a maximum of one move to be inserted into the D-layer, in the correct way so that it forms a part of the cross. It may already be sitting in the D-layer, in which case it does not need to be moved at all.
An incorrectly flipped edge
An edge which is incorrectly flipped will always need two moves to be inserted into the D-layer, so that it forms part of the cross. One move is required to correct it's flip, and the other to insert it into the D-layer.
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are all examples of positions where the cross edge is correctly flipped. They can be moved correctly into the cross layer by turning the face that the blue sticker is on.
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are examples of positions where the cross edge is incorrectly flipped. They need two moves to be inserted into the cross layer correctly.Even when you have mastered the concept of relative position (if you've not yet heard of or grasped this concept please read further up this page), it can seem very difficult to see at a glance whether certain cross pieces are going in the right places relative to each other. A useful rule to know is the 3-colour rule, which is a rule based upon the colours of two edge pieces and the two center pieces they are connected to, and is best demonstrated using examples. The following cases should demonstrate the full suite of cases for which this rule can be applied.
| Case | How to apply the "3-colour" rule |
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The question is: If I move R', will the cross edges be in the correct relative positions to one another? In this case, you can easily see that this is not true. The Green/White edge piece is matching with the Red center, and the Red/White piece is connected to the Green center. Since White is the cross colour, it can be ignored. So we are only looking at two colours, Green and Red, which means that moving R' would not place the cross pieces in the correct relative positions. Two colours = wrong. |
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The question is: If I move F2, will the cross edges be in the correct relative positions to one another? This time, it's not quite so easy to see. So we apply the 3-colour rule. Other than White (the cross colour which can be ignored) we have, a Blue/White edge connected to the Red center, and a Red/White edge connected to the Green center. So the colours we are concerned with are Blue, Red, and Green, 3 colours. 3 colours = correct and so by the 3-colour rule we can say that by moving F2 the cross edges are in the correct positions relative to one another. |
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The question is: If I move R' followed by F2, will both cross edges be in the correct positions relative to one another? At a glance, this question is not easily answered, unless you know the 3-colour rule. Looking at the case, we can see that the Blue/White edge is connected to the Red center, and the Orange/White edge is connected to the Green center. This time we are looking at all 4 colours, Blue, Red, Orange and Green. 4 colours = wrong so by the 3-colour rule we can see that R' followed by F2 would not place these edges in the correct relative positions. We can see however that by doing F2 followed by L we move the Orange/White edge over to match the Blue center, eliminating the colour Green and leaving us with 3 colours, Blue, Red and Orange. This indicates that the cross edges are now in the correct relative positions. |
The 3-colour rule breaks down if one or both of the connected edge/center pairs are the same colour, or opposite colours. But in these cases, it is much easier to see whether the edges will place in the correct relative positions or not.
| Case | See how the "3-colour" rule breaks down |
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In this case, we can see 4 colours, but we can also see that both edge/center pairs are oppositely coloured. So although we see 4 colours, we can more easily see that they are in the correct relative positions since a D2 move would fix them both. |
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Here, we can only see 2 colours, but since both edge/center pairs are matching colours they are obviously in the correct relative positions! |
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This time, we can see 3 colours, so if we were to use the 3-colour rule we would believe that these cross edges are in the correct positions. But one of the cross edges is the same colour as the center it is connected to, and the other cross edge is the opposite colour of the centre it is connected to, so the 3-colour rule breaks down. Even so, we can easily see that these edges are not in the correct relative positions. |
For each cube, you only get one chance at the cross. By learning the techniques above you can make the most of your 15 seconds pre-inspection time. It is important to see how each technique helps the other, and how they overlap. However the second component which helps you to see the shortest solution to each cross can not be taught, for it is mastering the ability to see what happens to the cube as you apply 6 or 7 or 8 moves to it, in your head. In the examples which can be found by clicking the link below, I try to demonstrate as many of the tricks for solving or seeing ahead as I can, and I give a detailed description of the thought processes which go on in my head as I take 15 seconds to look at the cube. If you follow each example carefully, it should reinforce everything that I have said on this page, and put it into a visual context. I hope you find them useful.
| Solve the Cross | Example Cross Solves | Cross Training Page |
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