Robbie's Kilominx Tutorial

My 3D twisty puzzle collection jumped to 30 toys this past week. Omitting two duplicates – the stickered FTO and my original 3x3x3 Rubik's Cube ‐ my puzzling repertoire in progress includes, front row from left: the Skewb, Square-1, Dino Cube, Ivy Cube, Redi Cube; row 2: FTO, CTO, ETO, Skewb Diamond, 3-, 4- and 5-Layer Pentahedron; row 3: 2-, 3-, 4-, 5-, 6- and 7-Cube, Master Pyraminx, Pyramorphix, Pyraminx and 2x2x4 Tower; back row: Kilominx, Megaminx, Skewb Ultimate, Master Kilominx, Gigaminx and the immovable object itself, Evgeniy's Icosahedron. I've been having a ball teaching myself how to solve the newest additions. I figured out Dino, Ivy and Redi with no trouble at all and spent a night and a day grappling with Square-1, despite pouring over a video tutorial and a solution guide. But that's not what we're here to talk about.

When I learned the Megaminx (below, at right), I reckoned I was mastering the basic, dodecahedral version of the Rubik's Cube. It's kind of a 3x3x3 puzzle, with each pentagonal side lined with iterations of two three-colored corner pieces and one two-colored edge piece, all the way around. The idea was to make the corners and edges of all 12 pentagons align with the non-moving center pieces of the same color, like on the 3-Cube. You were faced with pretty much the same problems in the same order: solving the first side, building rows of matching edges and corners layer by layer from there, then orienting and permuting the corners and edges of the last layer to clinch the solve. Labor intensive, a little strategic, a little intuitive, fraught with a few algorithms/procedures that take a minute (ha) to learn by heart, and best enjoyed by someone who doesn't mind practicing their moves over and over because they will screw up numerous times before they can reliably do it right, it's essentially the same experience only with 12 pentagons instead of six squares. And still, after months of practice, fun to do!

But then I found out about the Kilominx (at left), and I realized there was actually a simpler 12-sided twisty puzzle designed along the same principle. It's to the 3x3x3 Megaminx what the 2-Cube is to the 3-Cube: a face-turning dodecahedron with two corner pieces on each edge – in other words, no edge pieces as such. A step in the simpler direction from the Megaminx, the Kilominx also doesn't have colored centers – not that the Megaminx's centers moved or anything, but the centers of the Kilominx's sides are even more trivial, with a neutral color such as black or white throughout; or more basically, just some of the exposed guts of the puzzle showing between the moving pieces. It's the 2-cube of Minxes; it's a 2x2x2 dodecahedron. Funnily enough, this both liberates you and challenges you in a new way, as you move from Mega- to Kilominx: It allows you to build your first side wherever the heck you want; but as the sides still need to go together in a certain order, it forces you to arrange them without the helpful hint that the Megaminx's unmoving centers provide. Which way you need to twist the corner you're trying to slot into place depends on which direction its "top" color's side is in; but when there are no pieces, even a center, of that color to guide you, you often have to make a leap without a net under you. You could call it thrilling.

Now it turns out, both Minxes are at the bottom end of parallel series of puzzles with an increasing number of layers or axes of rotation. The even-numbered puzzles ascend from the Kilominx, such as the 4-layer Master Kilominx pictured below at the far left. The odd-numbered ones rise from the Megaminx, like the 5-layer Gigaminx below at the far right.

Actually, they're pretty much the same series of puzzles, apart from the bizarre manner in which they're named. It's just that, like the cube-shaped puzzles, the ones with even numbers of layers don't have fixed centers, requiring you to manage the color order of the sides for yourself, while the odd-layered puzzles offer just that little bit more help. (EDIT: Just noticed that the Master Kilominx in my photo does actually have colored centers. Oops.) For your information (and thank you, Wikipedia), the names of some higher-level variants include the 6-layer Elite Kilominx, the 7-layer Teraminx, the 8-layer Royal Kilominx, the 9-layer Petaminx, the 11-layer Examinx, the 13-layer Zettaminx, the 15-layer Yottaminx, the 19-layer Quettaminx and the 21-layer Minx of Madness, which like the 21-Cube is where mass production currently tops out. I don't know why, but the even-numbered sequence seems to end at the 8x8 level, at least as far as my sources go.

Digging a little deeper (and delaying getting to the tutorial part of this tutorial), the Kilominx was invented in 2008 by David Litwin. It has 20 corner pieces, and like, that's it. Early versions of the Kilominx were marketed as the Flowerminx, and it's apparently similar to the Impossiball puzzle of the 1980s. According to Grubiks.com, this puzzle can be scrambled almost 23.6 septillion ways – that's a 26-digit number. Nevertheless, it's not too hard to solve; easier than the Megaminx, really. I taught myself to solve it without looking at a solution guide or a tutorial, based on my prior experience with the Megaminx (one way the analogy to the 3-Cube vs. 2-Cube relationship breaks down). It's practically the same puzzle but with fewer steps, thanks to the omission of edge pieces. It isn't a sanctioned speed cubing event, but again pace Grubiks, the unofficial record for fastest solve is 9.17 seconds. Ready now? OK, let's go.

First, scramble the sucker. I recommend this scrambler, which is bookmarked on my phone. Here's a screenshot showing which silhouette to pick from the graphic menu (that little black dingus above the text). Note that, like cube-shaped puzzles, you're meant to start your scramble with the darker green side at front and white on top.

It takes an oddly long time for it to generate a scramble, compared to some of the other puzzles. Also interesting to note, the Kilominx scramble uses standard(-ish) cubing notation instead of the R++/D-- stuff developed for scrambling the Megaminx. Look at this scramble, for instance:

Notice that there are some notational oddities that you don't see on cube-shaped puzzles. For example, you can do either a U2 or a U2' move, because two 72-degree turns only twist the "up" layer 2/5 of the way around, clockwise or counterclockwise; whereas on the cube, a U2 move turns the top layer 180 degrees regardless of which direction you go. Also, those BL and BR moves, as distinguished from L and R, assume that you're holding a face (not an edge) toward you; L and R are the sides immediately to the left and right of F (front), while BL and BR are toward the back. And finally, see that x2 move in the middle of the scramble? Yeah, you get at least one of those every time. And to save you having to look up what an x2 move is, I'll tell you right here that it means flip the whole puzzle over 180 degrees, turning in the direction of a standard cube R move (i.e., around an axis of rotation running horizontally from left to right). Trust me, I clicked on the x2 on the scrambler and it was apparent from the where the animation froze at that point, compared to the prevous step, that this is what x2 means. Or check it out for yourself. It's neat. Don't worry, the scrambler won't make you do any y or z moves, so you only need to remember what whole-puzzle rotation x stands for.

So, I attempted to do that exact scramble, shown above, and got the result below. It doesn't look quite right, but that might be because I bought a puzzle with the "bright" color theme. Or maybe I goofed it up. No matter, a scramble is a scramble unless you're competing at a sanctioned event, and the Kilominx isn't a sanctioned event anyway.

Here is a series of pictures showing how I put the first layer together (solving the white side, which we'll think about as the bottom of the puzzle even when it sometimes isn't). First, I lign up one white-orange edge to dial in next to the other, using a U'-R-U-R' move that assumes the dark blue side will go to the right. Missing those centers yet?

Looks like that worked (below). If it didn't (and believe me, my first guess didn't always work), there's always backing up and doing over.

Now I'm dialing in the other blue-white corner, using the same algorithm because red, which is at the top of the corner piece, belongs to the right (see below).

You might sometimes have to dial a corner piece around a bit to get the color you want at the top. Or there's always that corner-flip algorithm to fall back on: R-U'-R'-U-R-U'-R'-U. (Can't abbreviate that with an "x2" anymore, for reasons you now know.) For example, the fourth white corner (below) came in with the white side at the top, which needs to end up at the bottom:

After doing that corner-flip algorithm, it's now ready for the U'-R-U-R', slotting the green side toward the right. Remember, though, if the top color goes to the left, the move is U-R-U'-R'. Megaminx basics.

That just leaves one corner out of the bottom layer:

Which, of course, was completed in a trice.

You then just keep applying those same algorithms to complete the sides going around the lower half of the puzzle, as shown (without further comment) in the series of photos below. Just be alert to the fact that without center pieces, getting these corners in the right order will require some spatial reasoning, critical thinking and strategy. Either that or a bunch of trial and error, or a flawless memory for the order in which the colors go around the sides of the puzzle.

Finally, you're left with the top layer, which most likely, won't have all five gray sides facing up.

The first thing to do is the Megaminx procedure for orienting the top corners – the one where you put an unsolved corner at top-front-right, chant "down, down, up, up" to yourself while alternately turning the R and DR layers, and repeat until the gray side is up, then twist the top layer to the next unsolved corner and do it again, etc. Result:

The last step, then, is permuting the top corners, which was the last Megaminx step as well. That's where you dial one of the corners out of the way, replace it with a dummy piece, and very carefully twist the top layer to put the corner where it belongs above it, then swap it with whatever piece is there, etc. What makes this step extra spooky, right on the point of solving the puzzle, is that you don't have any edge pieces to help you figure out which corner you're shooting for. This way you kind of miss those edge pieces despite the steps saved by not having to solve them. What I suggest is picking at least one to coner to be "solved" and starting this step with that corner right where it belongs. Then dial a corner that belongs next to it out of the way, twist the top layer and swap it into where it belongs, and continue from there, reasoning out where each corner should go. It gets easier the more solved the top layer is, until:

It's quite satisfying to see it all come together, innit.

I reckon I'll keep going back to the Megaminx when I want to occupy myself with a puzzle for a while. I repeat once again, I'm no speed cuber. I'm in this to enjoy solving puzzles, not to set speed records. So I'll embrace all those fiddly edge pieces and their long-ass algorithms, and the extra steps they bring to solving the last layer, for the sake of passing time and stimulating my brain. But I can also see myself doing the Kilominx quite often when I can only snatch a few moments here and there from other stuff going on, or maybe to relax my mind at the end of a long day. It has just a few wrinkles that need one's full attention – like deciding whether or not the last corner or two in the middle layers need to be solved on the top layer, to avoid re-scrambling something you've already solved. I'm not sure that's necessary in all cases, on the Kilominx — but it sometimes seems to help. It's a puzzle that you'll get through quickly, during one of those fits where you scramble every puzzle you have and then solve them one at a time. That isn't just me, is it? Or an easy, but not too easy, solve to clear your mind when you're banging your head against that d****d Square-1, about which more another time. I like it. It's a keeper.