Robbie's 6-Cube Tutorial

This is further to my series of Rubik's-type 3D puzzle tutorials, which so far have covered the 2-cube, 3-cube, 4-cube, 5-cube (up to a point) and the Megaminx. At that point, I had only recently started playing with the 6- and 7-cubes, and had a lot of improving to do. Improved I have, I would say, from the fact that I've gone from calling the 4-cube my "comfort cube" to rather leaning toward the 5-cube. I will have to come back to that one, one of these days, to improve on my unfulfilled promise to clarify how to solve the last two centers and last two edges. I also have some more puzzles to discuss, but these tutorials are time-consuming to create, so be patient with me.

The 6x6x6 version of the Rubik's Cube is sometimes known as V-Cube 6, at least in the original design patented in 2002 by Greek game designer Panagiotis Verdes, who innovated in making puzzle cubes all the way up to the 11-cube. With six rows and six columns of colored squares on each side, the device consists of 152 "cubies," including 96 center pieces (one color each), 48 edge pieces (two colors each) and eight corner pieces (three colors each). So, you have to put together 4x4 centers and 1x4 edges before you can proceed to solve the puzzle (more or less) like a 3-cube. Like the 4-cube, but unlike the 3- and 5-cubes, its sides do not have fixed center pieces, so it is crucial that the player assemble the 4x4 centers for each side in the proper order (with white at the left and yellow at the right, B-O-G-R [blue, orange, green, red] in ascending order).

The number of ways a 6-cube can be scrambled totals up to approximately 1.57 times 10 to the 116th power. Recall that the estimated number of particles in the observable universe is something on the order of 10 to the 80th power. There are several methods to solve the 6-cube; I'm pretty much running with a variant of the beginner method, an extension of how I solve the 4-cube and 5-cube. I'm no speed cuber, so I don't come anywhere near the world record, currently held by good old Max Park at 59.74 seconds – I said seconds. That's less than a minute, people. Then there's a Korean guy who, just this year, set the record for the mean of three solves at 1 minute, 6.46 seconds. Even if I don't screw anything up, my sedate pace tends to clock in at something more like a quarter of an hour. It's the journey, not the destination, you know.

Nevertheless, and despite a few stumbles in the solve I photographed (do as I say, not as I do), here's what I can share about solving the 6-cube. First, scramble it. Here's a screenshot of the website I've linked to previous posts, which has a puzzle scrambler for cubes up to 11x11x11 and a few other 3D puzzles.

It's time to cave in to the scramble site's annoying notation for slice moves, since I can now no longer think of a serviceable alternative. Those subscript numbers stand for slice layer moves. So, an R₂ would be the move I've signified, in my 4- and 5-cube posts, as a lowercase r: i.e., turning the second layer from the right in the R direction. (It's not 100% clear to me whether the author of the puzzle scrambler actually means a two-layer wide move here, but I've always erred on the side of turning only the slice layer, or doing a wide move and then turning the outer layer back. Doing the latter increasingly becomes the easier option as cube sizes go up.) Well, that lowercase-letter notation goes right out the window now that there's a slice-3 layer (e.g., R₃, third from the right). So, with apologies, I'm switching to the scrambler's notation from here on. It now becomes important that you distinguish the big 2s (for a double move, or half-turn) from the little 2s (and 3s) specifying these inner layers, which are going to be turning a lot.

Making things even more confusing is that everybody seems to have their own notation for things. Another website, that I've often consulted for a few none-too-helpful hints about what to do with some tricky last-two-centers (L2C) and last-two-edges (L2E) cases, sometimes throws me for a loop when it uses notation like 3R to mean turning just the third layer from the right, 2R for just the second layer from the right, 2-3Rw for turning both inner layers on the right, and 1-3Rw for three-layer-wide moves. I'm not sure which is worse: having big numerals on both sides of the letters, or having to squint at subscript numerals and distinguish them from big numerals, all to the right of the letters. But because I use the scrambler a lot and I only try that 6x6 hints page once in a while (less and less often), I'm going to follow the subscript notation in the steps below.

So, here's the 6-cube, freshly scrambled. You might notice that the scrambling process gets longer with each new layer of cubies.

Like with the 4- and 5-cubes, the first thing you do is choose a side (typical choice: white) and assemble its 4x4 center, one 1x4 bar at a time. Easy-peasy:

Next, using the technique I described in the 4- and 5-cube tutorials, do the same with the appropriate color to position on the opposite side of the cube (i.e, yellow). Remember the key to putting together one center without messing up the center you already did? It's mostly about bars of the same color chasing each other around corners, giving the target side a half turn and twisting back. Bang:

Then you just pick one of the remaining colors and assemble its center on one of the remaining sides. Say, for example, orange:

That's easy enough. Then, choose an adjacent side (remembering the B-O-G-R sequence of colors) and build its center. You'll probably have to do more of that chase-and-twist maneuver to keep this second middle-layer color from mixing up the center you just did. But all in all, it isn't too hard. So, here we have green and orange solved.

If you're an eagle-eyed reader, you'll probably notice that in the moves that follow, I botch the B-O-G-R sequence and get red and blue reversed. However, there's an easy fix for that, basically a two-slice-at-a-time version of the chase-and-twist manuever, rinse and repeat. I actually didn't do this until after I completed the last two centers, and I don't show this step, so I'm saying it now before some smart-aleck points out that the colors are in the wrong order.

Anyway, here's the sitch in which the blue and red sides found themselves upon completing the green and orange centers. Bit of a jumble, no?

Using the chase-and-twist technique, I reduced the L2C problem to this state, with just three remaining center pieces on each side needing to be swapped.

And I'm proud to say that after much practice, critical thinking and experimentation, with a little help from one of those "how-to" websites (which more pushed me in the right direction than spoon-fed me this technique), I've figured out how to get from here to the last two centers solved without consulting a cheat-sheet. And this technique scales up and down, from the 5-cube up to at least the 7.

To prepare the ground, put the last two centers at top and front, and rotate the sides so that two pieces that need to exchange places are in the same spot on both sides. For example, the two odd pieces in the upper right corners of both centers, shown here:

Now, there isn't an exact formula for what you do next. It's more of a case-by-case thing, but the general principle holds no matter which pieces you're trying to swap. First, you turn the slice layer containing the target pieces "up," i.e. in the R or L' direction. In this case, we're doing an R₂ move.

Second, you turn the top layer either clockwise or counterclockwise – but generally, to put the odd piece (originally from the F side of the cube) on the other side of the top layer, so it's above a bar on the front layer that you can use to clean up the odd piece. For example, take this U' move:

Third, you dial that bar on the front up, as in this L₂' move. See how that creates a solid blue bar across the top row of the up-side?

Fourth, you turn the up-side back in the direction it came from, so the bar you've just repaired is above its proper slot on the front; e.g. this U move:

Fifth, like duh, return that bar to where it belongs, like with this R₂' move:

Sixth, reverse that up-side turn again, like with this U' move:

And finally, seventh, dial that second bar down into its proper place, like with this L₂ move:

So, in the case of the odd piece that was in the upper right corner of both centers, we made the swap using the algorithm R₂-U'-L₂'-U-R₂'-U'-L₂. But don't be in too much of a rush to memorize that algorithm, because the exact moves vary according to which pieces you're trying to swap. Here is another sequence of pictures to demonstrate the flexibiilty of this technique. Let's swap the two pieces in the top row, second from the left, of each center as shown here:

This time around, the sequence of moves as illustrated below is L₃'-U-R₂-U'-L₃-U-R₂':

And here, for a final example, I've flipped the cube around so we can swap the last two odd-center-pieces-out, in the top row, second-from-right position on both top and front:

To use the same exact technique, the moves this time are R₃-U'-L₂'-U-R₃'-U'-L₂. Thus:

It was between those steps and the following that I had to do that center-swap, since (as you eagle-eyes may have noticed) I had red and blue the wrong way around. But I swear, it took all of four moves to fix that. Nothing to panic about. And now, here we are, looking at putting together some 1x4 edges. Let's start with the yellow and orange edge pieces. Here you may see two of them already paired together at top, one at the left and (take my word for it) one at the right.

You might have to twist some sides around to get them facing the right direction, then line them up around the middle layer so you can twist them together, slice by slice, until they're all lined up on one edge:

Dial that edge up to the top layer:

Twist the solved edge out of the way (here it's at the back):

Dial an unsolved edge down into the now-solved edge's previous place:

And restore the centers that you temporarily broke along the way:

I've already bored you enough by repeating procedures I previously explained in my 4- and 5-tutorial. There's just one new wrinkle that comes into play in cubes 6 and up: You sometimes can't solve a whole edge in one go. It's nice when two matching edge pieces travel together, but when they're on four different edges to start with, it can be more trouble than it's worth to position them correctly around the middle layers, all at one time. There's no shame in solving only three-fourths of an edge in one go, like with these green and orange pieces:

...and then addressing the last piece separately:

This creates a bit of extra work, but it's especially good to know when you're down to the last few edges and it starts to get tricky to line up all your edge pieces and still have an unsolved edge to exchange them with.

The last two edges, of course, are (and remain, from the 5-cube on up) a pain in the ass. Like these green-red and blue-white edges:

I frankly struggle with this. Unlike with the 5-cube, however, the L2E algorithm that works on the 4-cube (U₂'-R-U-R'-F-R'-F'-R-U₂) isn't completely useless on the 6-cube. You just have to adapt it and mess around with it, by trial and error, repeating the algorithm to undo it if you don't get the desired result, and maybe flipping one of the edges around so different pieces are opposite each other before trying again, or twisting a different slice in that U-slice-prime move & its opposite number that bookend the algorithm. I didn't shoot pictures as I did this, because it's a little embarrassing, but I did eventually brute-force my way through it and solve the last two edges (here shown at front-left and -right):

And now, the cube is ready to solve like a 3-cube, give or take our good friends, the OLL and PLL parity errors and the formulae for correcting them, which I gave you in the 4- and 5-cube tutorials. Here, for example, I was confronted by OLL parity:

And here is a picture of me screwing up the first move of the OLL parity algorithm, which I share as an instructive example that you sometimes have to do a double-slice version of the algorithm (R_2-3, etc.).

Never mind the fact that I stupidly did an R_2-32 move at the outset, with the result that I then had to re-swap some centers that got out of order and then re-solve two or three edges before I could move on with the solve. Like I said, do as I say, not as I do. Again, allowing for the subscript in the OLL algorithm featuring either a two or a three, or both, as the case may require, the correct formula is R₂'-U2-L₂-F2-L₂'-F2-R₂2-U2-R₂-U2-R₂'-U2-F2-R₂2-F2. It looks different from before only because I'm using this new subscript notation now, but it's still the same formula – except if you need to use the ₃ or _2-3 version. And remember, this is also the "edge parity" algorithm, for when the edge pieces are correctly matched but some of them are turned the wrong way around; then you just apply the maneuver to the slices with the pieces that need to be swapped. And the same principle holds with the PLL parity algorithm, which I didn't have to do this time around; just bear in mind that these formulae are adaptable to different cases, and so the puzzle continues to reward players who think critically and creatively.

I'm not going to end with a list of algorithms, as I did in some of my previous tutorials. After all, the only thing that's really different with the 6-cube is the scale of the problem you're given to solve. It's still fun to solve, and I'm finding it increasingly doable with less help from cheat sheets and often no help whatsoever. In fact, with that L2E algorithm back in play, which still doesn't help at all on the 5-cube, there's a sense in which the 6-cube is easier than the next cube down. And at risk of spoilers, I've always felt the 7-cube was a bit easier still. More work, but more fun with it. I hope you try them out and find this out for yourself.