Robbie's 3-Cube Tutorial

A few months ago, I got it in my head to learn how to solve a Rubik's Cube. I bought one, brought it home, looked up a tutorial on YouTube and began practicing the eight-step Beginners' Method to solve any scramble whatsoever of a 3x3x3 cube. The more I mastered it, the more I hungered to develop my new obsession even further, which meant buying a bunch of other puzzles, watching a bunch of other tutorial videos and looking up pages and pages of algorithms and solutions for special cases. However, after that initial video that started me on this journey, the process became increasingly frustrating. I would pick up bits of what I needed to learn from here, pieces from there and have to put them together in my own way before I found success with higher-level, 3D position puzzles.

So here, minus the video (I tried to shoot one, but it turns out I'm terrible at it), is the first part of the series of cubing tutorials I wish I had found all in one place. I'll open with a disclaimer: I'm not a speed cuber or a champion puzzle solver or anything. I'm just a guy who enjoys doing these puzzles. My family thinks I'm weird. When I'm struggling with a tricky case, my stepmom will wonder aloud why I put myself through that. Whenever my brother is around, he'll manage to mention that his ideal strategy for solving a scrambled cube is to pop the pieces off and put them back together in the correct order. Me, I enjoy the puzzles, the challenge, the feeling of accomplishment when I solve them, the sense that the more I practice the better I get at it, and the overall impression that playing with toys like this exercises and sharpens my mind.

Benefits of Rubik's Cube, and related puzzles, include (in my opinion) building eye-hand coordination, spacial reasoning and pattern recognition, critical thinking and problem solving. Learning cube algorithms (i.e. sets of instructions to move from an initial state to some desired outcome) may also strengthen one's mathematical reasoning and memorization skills. And as you adapt and apply strategies learned in one puzzle to problems with another puzzle, you may also develop your powers of deduction.

Let's start with a basic introduction. Today, you can buy Rubik's cube under multiple brand names, made by different companies, some of them specifically designed for speed cubing competitions. Originally, the 3x3x3 was invented by Ernő Rubik of Hungary in 1974 and marketed as the Magic Cube. By whatever name, it's a 3D puzzle with six sides stickered, or otherwise colored, with a different color for each side — typically white opposite yellow, red opposite orange and blue opposite green. Each side is divided into nine squares in three rows and three columns, and all the sides can be twisted, or rotated, around their fixed centers. Pieces include eight corners with three colors each, 12 edges with two colors each, and six centers with only one color each. Keeping the centers where they belong is no issue; the only way to put them out of order is to disassemble the puzzle and reassemble it wrong, or to swap the stickers. The challenge is to scramble the puzzle, then put all the edges and corners together around their matching centers. There's a notation for the sides of the cube and how to move them, and it goes like this:

R—a quarter turn (90 degrees) of the right side of the cube, clockwise as viewed face-on. R' (R-prime) is the counter-clockwise move (again, and always, from the viewpoint of looking straight at that side), and R2 is the 180-degree, half-turn move.

L—a quarter turn of the left side of the cube, clockwise (again, as viewed from the left). L' is the counter-clockwise twist, and L2 is the half-turn.

F, F' and F2—the same moves, respectively, on the "front" side of the cube, facing toward you.

B, B' and B2—the same moves (as viewed from behind) on the "back" side of the cube, facing away from you.

U, U' and U2—the same moves on the "up" side of the cube, or the top as you're holding it.

D, D' and D2—the same moves (as viewed from below) on the "down" side, or bottom as you're holding the cube.

It's assumed that when you do these moves, you'll hold the other layers in place and only twist the indicated layer. But for what it's worth, there is also notation for turning the whole cube, without holding any layers in place. Using lower case letters, x means a 1/4 turn in the R direction (up and away) and x' is a whole-cube turn similar to R'; y goes in the U direction with y' corresponding to U'; and z rotates the cube in the F direction, with z' turning it like F'.

Since you can turn each side either a quarter-turn clockwise, a quarter-turn counterclockwise, a half-turn or all the way around, there are over 43 quintillion possible arrangements of this cube. But despair not; there are also many methods for solving it, including the relatively easy-to-learn Beginner's Method that I'm going to share below. Speed cubers have been breaking each other's records on it right, left, up, down, front and back (pun intended) with the latest world record time for a single solve, at the time of this writing, standing at 3.13 seconds. Many of the current records are held by a profoundly disabled, non-verbal, autistic kid named Max Park. It's amazing what this puzzle can do for the brain, unlocking this kid's manual dexterity and even socializing him a bit (to the extent of being able to stand on the winners' podium).

Mathematicians spent years, and a colossal amount of computer time, cracking what they called the "God number," sort of a maximum minimum, if you will. They were looking to find the upper limit of the minimum number of moves in which any scramble of Rubik's Cube could be solved. Eventually, that number proved to be 20. Yes, the most efficient path from any configuration of the cube to fully solved can have no more than 20 moves, i.e. quarter or half turns of any side. While it would take a supercomputer ages to find the most efficient solution to a cube scramble, it's comforting to know that an expert like Max Park can still do it in seconds (albeit in more than 20 moves) and an average person like you or I, with a bit of practice, can solve it in a few minutes. If you mess up (which you'll do less and less often), consider it an additional opportunity to practice. Having a good attitude and self-discipline about practice is a key trait of people who become skilled at things other folks consider unreasonably difficult. It's a trait you can work on, too.

This puzzle's popularity led to the introduction of many, many, many spinoff puzzles. The most closely related ones, which are all sanctioned for international competition, are the 2x2x2, 4x4x4, 5x5x5, 6x6x6 and 7x7x7 cubes. I'll go into more depth with them in future installments of this series, but let me assure you, they're all sufficiently challenging, yet doable, to be fun to solve. If you're a glutton for punishment, cube puzzles that are mass produced go all the way up to 21x21x21.

Now to the basic steps for solving the 3x3x3. This procedure (or whatever procedure you know and prefer) will apply to all the bigger cubes, and with variations to 3D puzzles of other shapes, which we'll also get to in future segments. So my advice is to note down these steps, keep them handy until you know them by heart, and practice them until you can do it without peeking at your notes. Then continue to improve as you keep practicing and enjoying the endlessly varying permutations of this puzzle.

To start, you'd better scramble the puzzle somehow. You could try to just do a bunch of random moves until you're convinced it's sufficiently scrambled. Personally, I don't trust my ability to do randomness. So, I keep a puzzle scramble generator bookmarked on my cellphone. To do a regulation scramble, start with the white side at "up" and the green side at "front," or whatever colors are closest. You might notice that I like to arrange my cubes that way when they're solved. Here's a scramble I pulled off that website:

STEP 1: The Daisy. Using your own critical thinking skills, arrange all four white edge pieces around the yellow center. Typically, from this point on in the Beginner Method, yellow will always be "up" and white will be "down." Of course, you can choose any two sides to serve as "up" and "down" and adjust these steps accordingly.

STEP 2: Put on Sox. Rotate the top layer so that each white edge lines up with the center of its side color, like the white-red edge here.

Then, twist that side a half-turn to put the white edge on the bottom. Repeat until all four white edges are on the bottom, with their sides matching their centers like "sox" going up the middle of all four sides. At the end of this step, if you look at the bottom, you'll see a white cross, possibly with one or more white corner pieces in place as well.

STEP 3: Solve the Bottom Layer. This means that not only will the whole white side be complete, but the bottom corners will be correctly lined up with their neighboring sides. To get there, you may have to use several possible moves in the following order of priority.

First, look for a white corner piece facing sideways on the top layer. Twist the top layer so the corner's other sideways-facing color is on the same side as its matching center piece. In other words, find its center. Put that side toward you, at front. Then what you do will depend on whether that corner piece is on the right or left. Using the hand that the white side of the corner is facing, twist that side layer up 1/4, then give the top layer 1/4 turn with the corner in question moving toward you, then twist the side down. Think "Up, twist, down." If that corner is on the right, it'll look something like this, with the orange piece and its center at front; the move notation is R U R'.

If the white corner is at the left, it'll look something like this picture with the blue piece aligned with its center; the notation for the move I described above would then be L' U' L.

The result will be, that corner will find its correct place on the bottom layer.

Second, once you've exhausted all side-facing white corners, you can deal with any white corners that are facing up, like the one to the right in the picture above. Take a peek at the bottom (white) layer, and position that top corner above any unsolved corner. Then with that corner toward the front and using whichever hand is nearest, do an "up, twist, twist, down" move. That would be R U2 R' with your right hand or L' U2 L with your left. The result will be another side-facing white corner piece on the top layer for you to slot into place using the previous procedure.

Third, after you've put away all the top-layer white corners, there may be a white corner piece facing sideways on the bottom layer, like in this picture.

Sure, it's a bad example because there's still a white corner on top, but work with me here. In this case, twist the bottom layer (if necessary) so the other side piece on that corner finds its center; then do the old "up, twist, down" move from before. Then, and this is important, be sure to restore the bottom layer's "sox," so the bottom edges match their centers. The outcome will be another top-layer white corner to put away as previously described.

Once all the white corners are dialed into their proper places, the bottom layer should look like this—and what's more, it should stay that way as you move up the cube, solving each successive layer.

STEP 4: Solve the Middle Layer. To do this, you just need to put the side edge pieces where they belong. Start by looking at the top layer for any edges that have two colors other than yellow. That's because yellow is going to end up on top, right? For example, this picture shows a blue-red edge.

Twist the top layer as needed to align the side color with its center, and put that side at front. Then make the following two moves in succession: First, using the hand on the side whose center matches the edge piece's top color, twist the top layer 1/4 turn away from that center, and follow up with an "up, twist, down" move using the same hand. Notice that this brings a white corner piece up from the bottom. Immediately, then, switch hands and twist the top 1/4 turn back in the opposite direction, so the colored side of that white corner piece finds its center; rotate the entire cube to put that side at front; and do another "up, twist, down," effectively putting a white corner that you'd brought up from the bottom back where it belongs. Only, in that process of pulling that edge piece out of the way and then pulling it back in, you've also put it on the side where it belongs. Like so:

In the above example, the edge piece's top-color center was to the left, so the notation for this "Out-Up-Twist-Down, In-Up-Twist-Down" move was U' L' U' L - U y R U R'. Alternatively, you could see a situation like this, where the blue-orange edge is lined up with the orange center at front while the blue center is to the right.

This calls for the mirror move of U R U R' - U' y' L' U' L. Whew! Once all of the side edges have been solved, you can move on to the next step. However, a case may arise where there are no edges without a yellow side in the top layer, but the side edges still aren't correctly aligned. In this case, just choose a side where the side edge is out of whack and do this move on it, then repeat the move with the non-yellow edge that this move will bring to the top.

STEP 5: Orient Top Edges. By this point all the edge pieces in the top layer will have a yellow side. The objective of this step is to get all four of them facing yellow-side-up, like a yellow cross (regardless of corner pieces). It helps if two adjacent sides' edges are already yellow-side up. The tutorial where I learned this method said to orient the cube so those edges are at 9 and 12, or like the hands of a clock displaying 9:00. (It doesn't matter whether the corner between them is yellow-up or not.) For example:

Experience with larger cubes has taught me that it's probably more helpful to think about putting non-yellow edges at 3 and 6. If this isn't possible, don't worry about it. In any case, the notation for the move is F U R U' R' F' and I've always found it helpful to mutter the notation under my breath as I do it, to ensure that I don't screw it up. Anyway, you may have to do this step multiple times, checking after each repetition for either a 9 o'clock or a yellow cross. On the other hand, you may be able to skip this step altogether, if you come out of Step 4 with all four yellow edges face-up. It pays to be flexible and recognize, from the patterns, when you can skip a whole step, or even more than one!

STEP 6: Orient Top Corners. The objective here is to turn the yellow corners so they're yellow-side-up, though for the moment it doesn't matter if they're correctly permuted (i.e. in the corners where they belong). On the 3x3x3, there are basically two cases of this step. First, it helps if there's exactly one yellow corner oriented yellow-side-up, as shown here.

If that's the case, turn the whole cube so that one yellow-up corner is at front and left (sorry, I didn't take a picture of this). Then, strictly using your right hand, do the move you can think of as "up, twist, down, twist, up, twist-twist, down," notated as R U R' U R U2 R'. If this doesn't bring all the top corners yellow-side-up, repeat this step (including the bit about putting that one yellow-up corner at front and left). Then there's the case when either zero or two of the top corners have yellow facing up, like so:

In this case, you'll want to orient the cube so a corner with a side-facing yellow piece is at the front left corner, then do the exact same algorithm and repeat as necessary. Interesting to note (well, I think it's interesting), you'll never see three top corners yellow-side-up on a 3x3x3 cube. Or if you do, it's a sure sign that somebody has twisted one of your corners out of true and you'll never be able to solve the cube without first twisting it back. Don't laugh. I've known it to happen.

STEP 7: Permute Top Corners. By now, all the top corners are yellow-side-up, but the last layer most likely isn't solved yet. Although there are times when you'll be able to skip this step, most often you'll come out of the previous step with at least some of the top corners swapped around. If there's a side with two top corners of the same color, make sure they find their center (like the red side shown here).

Then, put that side at the back (facing away from you). If there's no such side, don't worry which side is facing where. Either way, learn this algorithm and put it to use: R' F R' B2 - R F' R' B2 - R2 U'. I'm sorry it's long but it's really important, so commit it to memory. I put those hyphens in there as an aid to memory. Funnily enough, even though I still have to chant "F U R U' R' F'" when I do Step 5, I don't have to do that now with this step; it's just become something my hands do. Isn't that weird? Anyway, after you do this step, check whether you have to do it again (and you might). When all the top corners are where they belong, you'll see something like this:

STEP 8: Permute Top Edges. Again, this is a step you can sometimes skip—meaning that you come out of Step 7 and the whole cube is solved. I've even seen this happen after Step 6. And though there's a special thrill when that happens, you may also feel a bit of a let-down because this is a fun step, and also one that you may get to do multiple times. If at any point you have one side (other than yellow and white) that's fully solved, put it at the back before doing this step. If not, no worries. The move is F2 U R’ L - F2 R L’ - U F2—again, with hyphens for memory-aiding purposes only. Thinking of it another way, you're dialing the front layer around to put a strip of white at the top; then twist the top to put the white strip at your left; then dial both sides down to put a yellow and a white strip at front; rotate the front so those strips swap sides; dial them back up on top; twist the top so the white strip lies across the front again; and dial it down to the bottom. In brief, "Dial around, twist, both sides down, dial around, both sides up, twist, dial around." Whatever aids your memory. The outcome of this move, after maybe a repeat or two, will be that all the top edges will find their side-color centers. Which means the cube is completely solved. How do you like that?

There's more to come another time about the 2-, 4-, 5-, 6- and 7- cubes. But there won't be as much, because apart from the 2-cube (which has its own challenges) they all end up being solved like a 3-cube after a certain point. Only with added wrinkles which, with the right attitude, can be part of the fun of solving these wonderful puzzles.

In summary, the 3-cube solution in eight easy(ish) steps is as follows; and you can scribble this down on a notepad and keep it at your elbow while you're learning these steps:

1. Daisy
2. White Cross/Sox
3. White Corners (R U R' etc.)
4. Side Edges (U R U R' U' y' L' U' L etc.)
5. Yellow Cross (F U R U' R' F')
6. Orient Last Layer ("OLL": R U R' U R U2 R')
7. Permute Last Layer ("PLL": R' F R' B2 R F' R' B2 R2 U')
8. Coup de grâce (F2 U R’ L F2 R L’ U F2)