Face by Face - 3x3x3 Tutorial

Introduction

If you've traveled in the broad world of twisty puzzles for some time, you might have heard other people say things like "I can solve one side on a 3x3!". In most cases, this side is indeed solved to be one color, but the pieces aren't permuted properly so that a further layer by layer solve isn't possible. A common reaction is saying that one ought to solve the puzzle layer by layer instead of face by face.

Nevertheless, it certainly is possible to solve a 3x3 side by side, and it isn't even that hard!

In this tutorial, I'll teach you how to solve a 3x3x3 face by face. I'm assuming you're familiar with the traditional way of the layer by layer solve, including the algorithms that come with it, and some common algorithms that occur in other standard twisty puzzles (e.g. the corner swap, adjacent edge swap...).

The first 2 faces

Traditionally, we'd start on the white face. Just to spice things up, I'll start my tutorial on the blue face.
You can solve the first face like you would solve the first layer, nothing challenging so far.

I'll chose white as my second face. I recommend choosing a face which shares an edge with the previous one. In my case: I won't chose the green face.

To solve the white-red and white-orange edges, you can use the standard algorithm which inserts an edge, just like in a layer by layer solve (with blue as your bottom face, this will be the case throughout the entire solve).

Inserting the final edge, which finds a place on the top, green, layer, isn't that difficult either. Just turn the U-face until it's in its place. In case it's somewhere in the second layer, just get it out with the previous algorithm and turn the U-face until it's where it's supposed to go on the white face.

In case it's flipped, you can just turn it upside down with the regular algorithm you might use with the final layer edges: F R U R' U' F'.

The 2 remaining corners which are needed to complete the white side are already in the top layer. Using the standard (or another) algorithm to shuffle corners around, you can easily put them in the white face. I used the standard (U R U' L') (U R' U' L).

When the two corners are on the white face, you can rotate them in the correct orientation with the commonly known algorithm (R' D' R D) (R' D' R D). You might have to rotate one of the other 2 corners in the top face in order to restore the bottom half of the puzzle, but this really doesn't matter at this point of the solve.

Now you see that you can quite easily solve 2 of the 6 faces on a 3x3 with nothing more than known algorithms!

The third face

I'll chose red as my third face. I recommend choosing a face which shares a corner with the two previous ones. In may case: I won't chose the yellow or green face, but the red or orange face.
You can see that there are at most 3 pieces which need to be inserted: 2 edges and 1 corner.

The first thing you want to do is put the 2 red edges on the green face, the opposite face of your first one, just like shown in the picture below. You can also chose the yellow face, the opposite face of the second solved face. As long as they are not in the orange face (assuming the 2 edges aren't solved). I'll put all of them on the green face. There are a couple of possibilities.

The yellow-orange edge is solved by coincidence

To get an edge out of the orange face (note that there's only 1 place on the orange face which can hold a red edge which is not already on the green face as well), I'll do an adjacent edge swap between this red edge and a random edge on the green face (not a red one!). Since this causes misplacement, I'll turn the red edge onto the green face first so that the misplaced edges, caused by the algorithm, aren't edges that are already solved.

To be more specific: If you turn the yellow face in order to put the red edge on top, you can swap it with the unsolved edge on the yellow face. With yellow as your U and green as your R, you can see that you can perform the algorithm with no problems caused by misplacement.

The adjacent edge swap algorithm, (2R U 2R U) (2R 2U 2R 2U) (2R U 2R U') 2R, puts the red edge on the green face and swaps 2 edges of the green face (which doesn't really matter). Don't forget to reverse your set-up move (putting the red edge on the green face before executing the algorithm).

In case your edge is in the red-yellow spot (and not solved) you can get it out onto the green face in a similar fashion.

The first edge

Now that both red edges are on the green face, we need to put them in their proper place. I recommend putting the non green edge in first, in this case: the yellow-red edge. This needs a little more thought and there was a lot of trail and error before I found an intuitive way to put the edges in.
First of all, make sure the yellow-red edge is in the yellow face, meaning you have red as an R. You can shuffle edges around by doing a U-perm. The algorithm I use is 2R U' R' U' R U R U R U' R (with 3 shuffled edges on the U-face and the solved one in the front).

Now that the yellow-red edge is in the yellow face (the F-face), make sure the yellow sticker is facing the top. If this orientation is not right, you can flip the edge with in the traditional way. Note that this requires to solve the 2 white corners in the back again. Now you can put the edge in its place by doing R U' R' U.

Now that your yellow-red edge is in its place, you can see that 2 pairs of corners are swapped (try this on a solved cube). You can unswap them by doing the algorithm in reverse. Since you don't want to get your edge back out, you can put another unsolved edge in its place by doing an E-turn (this means turning the middle layer in the same direction as a U'-turn). Now you can do the algorithm in reverse, U' R U R', undo the middle move, E', and you'll see that the red-yellow edge is in its proper place and properly oriented while the already solved pieces remain intact.

This strategy shuffles 3 edges around.

The final edge

To put the final red edge in, you can follow a similar strategy. Put your red edge in the yellow-green place (the same way we did with the previous one, using the U-perm). Make sure the red sticker of your edge is on the green face as shown in the image below. You can do this just like in the previous step. Now you can see that we have the exact same situation as before if you take green as your F and yellow as your U. Hold your cube in this orientation to solve this final edge.

Since the approach I came up with shuffles 3 edges around, we need to get the solved red-yellow edge out of the way first. I did an S'-move, which puts the red-yellow edge on the bottom (white) face and puts an unsolved edge in its spot. This allows us to use the same strategy by shuffling 3 unsolved edges around. This time, we perform the algorithm on the left side: L' U L U' shuffles the edges around and puts the red-green edge in its proper spot, an E'-turn puts an unsolved edge in its place. Reversing the algorithm by doing U L' U' L and reversing the middle move, E, does the job. The only thing left to do is reversing the set-up move, S, and you'll see that all the red edges are in their proper positions and properly oriented, while the other 2 solved faces are still solved.

The corner

The only piece left on the red side is the red-yellow-green corner. There are 2 places this corner can be, in the right spot or in a spot adjacent to the first.

If it's not in the right spot, we must first put it there. Since there a only 2 unsolved corners left, this can be done with the standard corner swap algorithm: (2R U 2R U' 2R) U' D (2R U' 2R U 2R) D'.

This algorithm also swaps 2 edges. In the current configuration, 1 of these edges will already be solved (the white one), so we have to replace it by an unsolved one. The way to do this, is having green as your U and orange as your F (so that the red corner is in front of you to the right and the unsolved one in the back on the right face). Now the corners are in the proper configuration to perform the corner swap algorithm. Replacing the solved edge with an unsolved one can easily be done by doing an E'-turn followed by an L'-turn. You'll see that you're now ready to perform the algorithm. When you're done and you've reversed the set-up moves, the corner is now in its proper position.

Now that the corner is in the proper position, it needs to be rotated correctly (assuming it's not already). This can easily be done with the standard corner rotation algorithm with green as your U, (R' D' R D) (R' D' R D), using the last unsolved corner as a buffer to restore the bottom half of the puzzle.

After rotating the corner, and thus solving the red face, you'll see that the last corner (green-yellow-orange) is also properly rotated!

The final 3 faces

Since the last corner is already solved, the only thing left on the puzzle are 3 unsolved edges.

I'll chose orange as my fourth face, holding it in front of me as my F and green as my U. The other 2 unsolved edges are on the R-face. To shuffle the edges around, I came up with a simple algorithm which is made up of a commutator and a middle move: (R' F R F') M (F R' F' R) M'. This algorithm shuffles the 2 unsolved edges in front of you with the edge at the back on the U-face (green).

To use this algorithm in our situation, we need to put the edge on the right side of the U face at the back. This can be done by the set-up moves R B R'. In other words: the algorithm to solve one of the remaining edges is: R B R' (R' F R F') M (F R' F' R) M' R B' R'.

It might happen that you need a variation of this algorithm or that you have to do it twice, but using this strategy will make sure you can solve at least 1 of the 3 edges.

All that's left are 2 unsolved edges. Due to the rules which a 3x3 obeys, the puzzle can't have 1 unsolved edge. So in order to solve the fourth face, you must solve the fifth and the sixth face at the same time!

Keeping this in mind, it's easy to find that you can solve the fourth, fifth and sixth face simultaneously using your favorite method to solve the last layer in a layer by layer solve.

Conclusion

You see that, with a little creativity, we were able to solve a 3x3 face by face, instead of the common layer by layer approach. Now nothing is holding us back to solve a 4x4, 5x5... the same way! I'll definitely make more tutorials on this strategy. If you have any questions or suggestions, make sure to leave them in the comments.