Robbie's 5-Cube Tutorial

The 3D puzzle craze continues with the 5x5x5 cube, a.k.a. the 5-cube, a.k.a. the "Professor's Cube," which was invented by someone named Udo Krell in 1981. With five layers moving in each of six directions, it could (in theory) be scrambled into approximately 2.82x10⁷⁴ possible configurations. Significantly, the number of atoms in the observable universe is estimated to be between 10⁷⁸ and 10⁸². And yet the world record for the fastest single solve is 32.08 seconds, times 10 to the power of nothing. Aren't people amazing?

It's just like the 4-cube, except that it has 5 rows and columns of cubies on each side, and so the centers you need to build are 3x3 squares, and the edges you need to "pair" have three pieces (you can still bring an edge together in a single move, though), and there could be a new parity case that you'd never see on the 4-cube, and oh yes by the way that never-fails method for solving the last two edges on the 4-cube now never works, instead! And there are other examples of what we have been calling "new wrinkles," which is why I downloaded and keep on my phone a two-page diagram of "L2E" (last two edges) cases with the steps to solve them, as well as "L2C" diagrams for the last two centers. I'm going to try to make that step simpler in the tutorial below. But I won't deny that having those sheets to cheat from has been helpful, for example, as a starting point to deduce moves that could apply to L2C cases on the 7-cube.

If you've gotten the impression that the 5-cube is a little more trouble to solve than the 4-, you've read me right. But it isn't so much more trouble that I haven't worked on it a lot. I've enjoyed my time with it and I've come to appreciate the little bit of extra time and effort that it takes to build those centers and edges. And after all, it follows pretty much the same solve pattern as the 4-cube, only with 1x3 bars now becoming building blocks for 3x3 centers, etc.

Let's start with a scramble, using the 5x5x5 scramble generator on that website I've linked to more than once, so you should have bookmarked it by now.

STEP ONE: Start working on the white center, putting together 1x3 bars one at a time and dialing them onto the same side.

You may experience some frustration in this before you learn to keep your existing white bars out of the way while matching up new ones; this can be as simple as rotating the existing edge to a different orientation. Bask in your sense of accomplishment when this first step is done.

You know by now what STEP TWO is. Enjoy this picture illustrating the strategy of chasing one yellow bar with another, after which you'll rotate the following bar and pull the leading one back into place, on the side opposite to the white center.

I won't bore you with pictures of the whole process. The only new thing about it is that you have to do three bars, and sometimes it's a little tricky to push a yellow piece off the top layer to join up with two other yellow pieces waiting for it to join their bar. Think strategically before you make a move so you don't end up breaking an existing white or yellow bar.

STEP THREE is, again, solving the other four centers. Here, to speed us a long, is just a picture of the last two centers (L2C) with just one piece to be swapped between each of them.

In this particular case, purely for example, there's one orange piece in a corner of the green center and vice versa. I put the green center on top and the orange center at front with the problem pieces at the lower right and upper right, respectively. Then I did the moves Rw U Rw' U Lw F2 Lw'. Here's that algorithm round about that Lw move—perhaps you can see how nearly intuitive it is, becoming the kind of move you'll do pretty much every time you build centers.

And the result:

STEP FOUR is, again, the edge "pairing," only with three edge pieces coming together.

Try to avoid cases of what we're going to call Edge Parity, where the middle of the three edge pieces is flipped the wrong way, by rotating it up, around and down on the other side of the other two edges to bring it in from the opposite direction. If you can't (because, say, two edge pieces are already paired together and one of them is flipped the wrong way), don't worry about it; we'll deal with that issue later. Anyway, once the three edge pieces are lined up, do what you know to do from the 4-cube: Rotate the edge up and out of the way, and rotate an unsolved edge into its place.

Then, don't forget to fix the centers that were broken when you put your edge together.

STEP FIVE is, again, the L2E (last two edges) and I'm afraid the rumor that I started is true: Uw' + edge flipping algorithm + Uw no longer works like it did on the 4-cube. I recommend the "5x5 L2E Algorithms" page that I downloaded from here, and its corresponding cheat sheet for L2C algorithms as well. They live in my phone's otherwise uncluttered downloads folder in case I get stuck. I don't worry too much about finding exactly the right algorithm for which way each piece is flipped, because there's a way to fix an Edge Parity error if you get one. During my sample solve, I was confronted with this case:

The steps I followed to swap those two middle edge pieces, at front and back on the top layer, were Rw2 F2 U2 Rw2 U2 F2 Rw2, which is probably one of two or three L2E formulas worth getting down by heart. I'll spare you a picture of the outcome. Take my word for it, this formula solved the last two edges for me. Look up other cases for yourself; it's what I do.

STEP SIX: Before we move on to the old "Make Like It's a 3-Cube" step, check your edges. There's a chance that you've got some of those dreaded Edge Parity cases, where the middle piece of an edge is flipped the wrong way around.

Have you been practicing the OLL Parity algorithm that I gave you for the 4-cube? Good. Simply put the problem edge at top front and use that. I actually originally had a different algorithm for this (or maybe it went the other way around), but I found out by accident that the same algorithm works for both parity errors and that saved me having to memorize two complicated formulas. In case you've lost it, it's r' U2 l F2 l' F2 r2 U2 r U2 r' U2 F2 r2 F2, where (once again) those lower-case letters are pronounced "r-slice prime, l-sliece," etc., and mean moving the next layer in from the outer layer of the indicated side. While I didn't see fit to shoot a picture of this algorithm in action, here's what you see when you complete that final F2 move—which doesn't do anything, really, except bring the repaired edge back up for you to gaze upon with a feeling of proud accomplishment.

STEP SEVEN: Moving only the outer layers, do the eight-step cha-cha for solving a 3-cube, applying the OLL and/or PLL parity algorithms from the 4-cube if and as needed. I probably don't need to show these to you again, but here they are anyway. Lo, the Daisy:

and the white cross with sox:

and the bottom layer solved:

After solving the side edges, here are the unsolved sides of the yellow cross at 3 and 6 o'clock—though, remember, you won't always get this configuration. This just happened to be an ideal case.

So ideal, in fact, that when I completed the "F U R U' R' F'" step, I got to the PLL move (top corners) without having to do OLL (getting the whole top layer yellow-side-up). Remember to put the layer, if any, with matching top corners (like orange in this picture) at the back before doing R' F R' B2 R F' R' B2 R2.

And in another happy bonus, upon completing the OLL step, I had solved the cube without having to do the usual last step, and with none of those tricky parity cases from the 4x4x4. So that's that!

I may have given the impression that the 5-cube irritates me a bit. I actually had that impression, myself, when I was getting used to it. But I didn't give up. I kept trying and I got better at it, which I think is a net benefit for my reasoning skills and all those other areas that I think practicing these puzzles is good for. (Reread my 3-cube tutorial if you've forgotten.) I hardly ever go anywhere for an overnight stay without bringing this cube, along with a handful of others. While I readily admit that the 4-cube is special to me on a level only approached by the Megaminx, if at all—we'll get to that, don't worry—the added challenge of the 5-cube is sometimes just the mental stimulation that I need. And when I know I'm going to have hours to blow with a gobblebox yakking in my general direction (TV doesn't hold that much interest for me), I take ever growing satisfaction from scrambling all my cubes—from 2 to 7 now—and going down the line, solving one after another. I've even been working on trying to choose whatever puzzle will fill the time I need to fill, like yesterday when I played with my 7-cube during a long car ride and almost had it finished by the end of the trip. I'll never be a speed cuber, but I'll get faster at it after I've had more time with it. And for me, it's not about speed; it's about enjoying the puzzle and getting lost in the patterns.