Thursday, May 23, 2024

Goblin Quest

Goblin Quest
by Jim C. Hines
Recommended Ages: 13+

Jig is a cowardly, weak-eyed little goblin who has never been outside his cave. Even by goblin standards, he doesn't have a lot going for him. As fighters go, goblins seem designed to die at the drop of an adventurer's mailed helmet, and their chances aren't much better with the hobgoblins who live deeper down, or the lizard fish with their poisonous spines, or whatever lives beyond them – a necromancer, some say. Maybe even a dragon. All Jig has on his side are a few more wits, a bit of luck, an independent streak and a pet fire spider.

One day, Jig cowers while his entire squad of goblin guards is wiped out by a party of treasure seekers. They're searching for the Rod of Creation, an object of inconceivable power that was hidden somewhere in Jig's underworld by the wizard-god that created it, because the prince feels like proving himself to his royal parents and surviving older brothers (adventurers all). It's the kind of MacGuffin that radiates plot twists the way cobalt-60 emits gamma rays. The invaders take Jig hostage and force him to act as their guide. "Act" is the right word for it, too, because the places this group wants to go are beyond the point past which no goblin has ever returned, so he's basically faking it. So off they go: a prince with a chip on his shoulder, his wizard brother whose magical exertions threaten to break his mind, their dwarf tutor whose deity gives him healing powers, and a young elf thief they have dragooned into their service. And Jig.

I won't drag this synopsis out any further. It's quite literally a "dungeons and dragons" story, only told from the point of view of the sort of non-player character that tends to perish wholesale. As Jig actually proves, increasingly, to be a real player, tensions only grow with the other members of the party. He spends the entire journey expecting, with good reason, to be killed sooner or later, and hoping it happens quickly. I think I can say, without spoiling anything you couldn't guess from the start, that it's the kind of ensemble whose members can't all survive. It's enough to make a goblin get religion – which Jig does, choosing a god well suited to the loser of all losers. But does he lose? Read it and see for yourself.

The trick is pretending it isn't a spoiler when I note that this is but the first book in a trilogy that continues with Goblin Hero and Goblin War. Michigan-based author Jim C. Hines is also the author of the "Princess" quartet (The Stepsister Scheme etc.), which Fantastic Fiction describes as a mash-up of Grimm's Fairy Tales and Charlie's Angels; the "Magic Ex Libris" series (Libromancer etc.), at least four novels featuring a librarian-turned-magician; the "Janitors of the Post-Apocalypse" trilogy (Terminal Alliance etc.), and several other novels and short story collections, including Goblin Tales.

Monday, May 20, 2024

IF

I eagerly anticipated seeing this movie. I guess it's how life goes. I didn't really premeditate going to see The Ministry of Ungentlemanly Warfare or The Fall Guy, but I was looking forward to this movie for weeks. I had an unqualified blast at those other two movies, but I didn't enjoy IF as much as I expected to. It was all right. It made me laugh and, a few times, get choked up. But it was definitely a case of the trailers making a movie look better than it really is. I suppose that's what they're supposed to do.

I'd like to mention, while I remember, that the trailers that I saw before the feature started included one for The Wild Robot, and I'm excited to see that. Which, based on this movie-going experience, perhaps isn't a sign of emotional wisdom in me. I could tell what was being advertised from almost the first shot in the trailer, and I was pumped. There was also a trailer for Sight, a movie about a surgeon trying to restore a little girl's vision. It was the second trailer I've seen for it, and I appreciated it because it was brief and left a lot to the imagination, whereas the first trailer was basically the whole movie. So, obviously, not all trailers do their job equally well.

All right. IF stands for Imaginary Friend, and in this movie, a 12-year-old girl named Bea (Cailey Fleming) can see other kids' Imaginary Friends. While she's staying in her grandma's apartment building to await the results of her widowed dad's heart surgery, she encounters an upstairs neighbor who is trying, without much success, to match IFs forgotten by their original kids with new kids. Bea joins the effort, getting to know the wacky residents of a retirement home for IFs and learning to explore the world of pure imagination. (And while that phrase is in your memory cache, doesn't the musical theme that runs through this movie remind you of "The Candy-Man Can"?)

Some of Bea's successes and failures really are poignant. Some of the emotional patches she goes through are quite powerful. The imagery is brilliant, and Ryan Reynolds (as the neighbor from upstairs) supplies a certain sarcastic wit that lightens the tone when needed. The imagery is spectacular, and certain scenes are achingly beautiful, like the one where grandma reconnects with her memories of being a ballet dancer. The cast is also pretty good, with director John Krasinski playing Bea's dad, Fiona Shaw (lately Harry Potter's Aunt Petunia) as the grandma and a cast of voice actors (as IFs) that includes Steve Carell, Phoebe Waller-Bridge, Louis Gossett Jr., Awkwafina, Emily Blunt, George Clooney, Bradley Cooper, Matt Damon, Bill Hader, Richard Jenkins, Keegan-Michael Key, Blake Lively, Christopher Meloni, Sam Rockwell, Maya Rudolph, Amy Schumer and Jon Stewart. There's also a whimsical "and introducing" credit in the closing titles that'll reward those who stay to watch the cast scroll by with a mild chuckle.

Three Scenes That Made It For Me: (1) Bea lets her imagination run wild at the IF retirement home. (2) Grandma relives a moment of her girlhood dreams of being a ballerina. (3) Bea's dad tries to prank her with knotted sheets going out his hospital window.

I'm not a starred-type reviewer. I've openly admitted that when I do book reviews, I consider myself more of a book booster than a critic; if I have to assign a star rating, a book almost has to disappoint me on some level to get less than four stars, and I think I'm pretty liberal in my distribution of five-star ratings even though I try to reserve that last star for books that I'm super thrilled about. Even less do I know how to rate movies, but I wouldn't give this one the full five stars and I'm not sure how many stars I'd take away, or really, why. I guess it was well made and deeply felt, but it didn't fully give me joy. Sometimes I was a little uncomfortable with it, maybe because of the amount of time Bea spends with the grown-up guy upstairs; and though there's a plot twist toward the end that make me feel stupid to admit that (and if you're a smart cat, you probably know what it is without my needing to tell you), it still leaves me feeling a little weird. Ultimately, I just don't know what position this movie is taking on the fate of IFs who outlive their kids' memory of them. I guess I was expecting the story to go in a different direction, and so the movie didn't quite live up to my imagination. Also, it has some structural issues that left me squirming at the end. Issues like not knowing when it's really over and just ending there. Bottom line: It was pretty good, and I enjoyed it, but although I was ready to fall in love with it, I didn't.

Wednesday, May 8, 2024

The Fall Guy

This past weekend, I took a shot at this movie, and it did not disappoint. It's the story of a Hollywood stuntman who comes out of exile after being injured in an on-set accident, thinking the director (an ex-girlfriend he still cares about) specifically asked for him, only to find out that she knew nothing about it and doesn't want him anywhere near her movie. Meanwhile, the producer secretly calls on him to find their missing star, whose personal stunt double our hero was before his, um, fall from grace. Pretty soon he's mixed up in a deadly adventure that provides plenty of opportunity for stunts, while being framed for murder and having bad guys out to kill him. It's a plot to hang a spectacular series of stunts on, so I won't trouble you with any further synopsis.

According to a pre-show "welcome to our movie" video, director David Leitch used to be a stuntman. So, you know where his priorities lie. This movie abounds in chase scenes, fight scenes, plunges, leaps, car rolls, car jumps, speedboat jumps, helicopter hijinks, pyrotechnics and every conceivable combination thereof. It features a French-speaking dog trained to go for the gonads, a romantic subplot that'll get you in the feels, some hard-hitting action that'll get you in other body parts (sympathetically), big laughs and an over-the-top climax.

Ryan Gosling, late of Barbie, heads the cast as Colt Seavers, with Emily Blunt as his gal pal and Aaron Taylor-Johnson as the missing movie star. Also in the cast are Stephanie Hsu (Oscar-nominated for Everything Everywhere All At Once), Winston Duke (Black Panther) and Hannah Waddingham (Ted Lasso), along with some superstar cameos including one very special guest whose name you'll see in the closing credits before he ever shows up onscreen. Which reminds me to remind you: Stay for the mid-credits bonus scene. It won't be hard. There's an outtakes reel to keep you amused until it comes along.

So, in quick order, here are the Three Scenes That Made It For Me: (1) Blunt almost hands Gosling's keister to him when he surprises her in his trailer. (2) The running melee in the speeding garbage truck. (3) The insane final battle in which the bad guys take on the entire stunt department. There are so many ways I could spoil these scenes for you. See me refraining from doing so? You're welcome. Now, go see it and have a ball!

Tuesday, April 23, 2024

The Ministry of Ungentlemanly Warfare

"Darkest Hour" this ain't. I went to see this movie Sunday afternoon at the mall cinema in Detroit Lakes, Minn. and my enjoyment was untouched by lump-in-the-throat sentimentality. It was a non-stop thrill ride of action, comedy, suspense and sex appeal, featuring four-time Bond film actor Rory Kinnear in prosthetic jowls as a Winston Churchill who is about to have his brief taken from him and who risks it all on a daring (not to say daft), secret mission to destroy the supply chain to Hitler's U-boats, open up the Atlantic to break the Nazis' blockade of the U.K. and land U.S. troops in the European theater of World War II. Allegedly (according to a title card in the opening scenes of Guy Ritchie's latest movie) it's all based on a file that was only declassified about a decade ago. Hitler and his top men – a Brigadier significantly known as "M" and his aide, future James Bond creator Ian Fleming – choose a gaol-bird named Gus March-Phillips (a later title card claims he was the inspiration for Bond) to head this mission, which is not only secret but entirely disavowed. So, as they say not once but twice in the movie, if they're caught by the British, it's prison for sure; if they're caught by the Germans, it's torture and death. Why Gus? Because, although he is a rascal, rule-breaker and allergic to following chain of command, men will follow him. And he chooses some pretty wild and crazy guys to follow him.

I won't bore you with the biographies of the other members of the team, other than to say in general that they constitute one stupendously beautiful woman (who, apparently, gets married to Gus in later days) and a rogues' gallery of male sex appeal. Besides sometime Superman and ex-witcher Henry Cavill as March-Phillips, they include muscle-god Alan Ritchson (of "Reacher" and "Titans" fame), Nigerian-American actor Babs Olusanmokun (Dr. M'Benga on Star Trek: Strange New Worlds), Mexican beauty Eiza González (Baby Driver, Alita: Battle Angel), Alex Pettyfer (a sometime Alex Rider, also of I Am Number Four and Magic Mike), Henry Golding (Crazy Rich Asians, Snake Eyes), Hero Fiennes Tiffin (who once played a very young Lord Voldemort, and more recently starred in the steamy After films), the androgynous Freddie Fox (Worried About the Boy, Cucumber) as Fleming, Brazilian actor Henrique/Henry Zaga (Teen Wolf) as a Spanish officer, German actor Til Schweiger (Inglourious Basterds) as the main heavy, and best of all, Cary Elwes (Twister, The Princess Bride) as M.

Since I let that "best of all" slip, I might as well get straight to the Three Scenes That Made It For Me: (1) The opening scene in which M recruits March-Phillips. Cary Elwes's eye-rolling is actually what makes the scene for me, as M gamely puts up with Gus's blatant misbehavior. It also helps set the tone for a story in which civilization hangs on the actions of a group of very uncivilized people who, where Nazis are concerned, cheerfully commit acts of extreme violence at an incredible rate. (2) You get a goodly eyeful of this violence during the cutting-out expedition on the Atlantic island of La Palma, where the Germans are interrogating Pettyfer's character. Ritchson's character goes especially savage, shooting arrows that go right through one guy to kill another and finally ripping the heart out of a Nazi's chest while Pettyfer calmly looks on, patiently awaiting his liberation from a torture device. (3) The insane, yet brilliant, plan by which Gus's tiny team, augmented by a handful of burly islanders, takes on a garrison of 200-plus Nazis, plus the crew of an Italian ship and two tugboats, plus the allegedly neutral Spanish forces that nominally control the island, all at the same time. It's a complicated caper and, of course, not all of it goes to plan. In fact, everything goes absolutely insane, as befits a movie by the director (and in most cases, writer) of Lock, Stock and Two Smoking Barrels, Snatch, Sherlock Holmes, Sherlock Holmes: A Game of Shadows, The Man from U.N.C.L.E., Wrath of Man and The Gentlemen, for some illustrative examples.

However, let's not also forget that Ritchie also brought us the horrendous Swept Away, Revolver, King Arthur: Legend of the Sword, the so-so live-action Aladdin and the only modestly successful RocknRolla. When he's on his game, he's on. When he's not, the results are dreadful. So, going to one of his movies is a crap-shoot. In my opinion, however, The Ministry of Ungentlemanly Warfare is a winner.

Thursday, April 11, 2024

Robbie's Megaminx Tutorial

I'm going to hold off for the moment on writing a 6-cube and 7-cube tutorial because I'm no expert yet. I've only solved each of them four or five times now, but (at the risk of putting out spoilers) I've found 5-cube algorithms to be very helpful, with some creative adaptation—proving my assertion, earlier in this series of posts, that solving this kind of puzzle promotes deductive thinking. I also realize that I have yet to fulfill my promise to make the 5x5x5 "last two centers" (L2C) and "last two edges" (L2E) cases more intuitive, something that I feel will help me as well. Give me some time!

But meanwhile, let's talk about another one of my favorite 3D position puzzles, which I rank right up next to the 4-cube as one of my comfort cubes: The Megaminx.
Obviously, it isn't a cube, strictly speaking. It's a dodecahedron. That is to say, it has 12 sides, all of which happen to be identical, regular pentagons. Identical, that is, if you ignore the colors. (On my stickerless Megaminx, the colors of opposite pairs of sides are white-gray, yellow-cream, dark blue-light blue, red-orange, purple-pink and dark green-light green. Substitute words like "beige" or "cyan" if that flips your minnow.)

This is another way interest in Rubik's Cube-type puzzles overlaps with an interest in mathematics, especially of the recreational variety. There's a small set of three-dimensional figures called Platonic Solids, including the cube and the regular dodecahedron. They're all convex polyhedra (meaning 3-D figures whose edges and vertices all project outward from a common center), and they're all perfectly regular (i.e. their faces are identical, regular polygons with identical sides and angles, all coming together at identical vertices and edges). And only five of them are possible. Besides the cube and the dodecahedron, the other Platonic solids are the tetrahedron (a pyramid with a triangular base, all made of equilateral triangles, three meeting at each vertex), the octahedron (a diamond shape with eight sides, all equilateral triangles, with four sides meeting at each vertex), and the icosahedron (a figure made of 20 equilateral triangles with five of them grouped around each vertex). And that's it.

Basically, we're talking the shapes you'd find in a set of polyhedral dice, used for roleplay games. Except one of them (the 10-sided die) isn't Platonic. And you'll also find Rubik's-type puzzles in all five Platonic solid categories, although some of them are harder to get. I have yet to score an icosahedral one, and it seems like any that I find offered for sale are either worth a mint or bait for an online scam. Also, there are non-Platonic-solid 3-D puzzles, including a pentahedron that I'll tell you all about one of these days. So, as I said, there seems to be a connection between an interest in these fascinating geometries and the twisty, turny puzzles that evolved from Rubik's Cube.

There are several other dodecahedral puzzles (some with more moving pieces, some with less), but the Megaminx is kind of the standard, the way the 3-cube holds the front line of six-sided puzzles. I think the thing was invented by a German guy named Uwe Meffert, but I've also read that multiple people invented it independently. Each side is divided into five corners with three colors, five edges with two colors—viewed face-on, they seem to form a five-pointed star—and one pentagonal center piece that only has one color, and doesn't move in relation to the other centers. Each face is a separate layer that rotates in 72-degree, or 1/5-turn, increments. With 50 movable pieces, it has over 1.01x1068 possible permutations (a few less for the six-color variant, which has some duplicate pieces), and yet the current world record for the fastest single solve is 24.12 seconds.

NEW MOVES: You may have noticed that a dodecahedron is not a cube. Therefore, the available types of moves aren't quite the same. Viewing the Megaminx face-on, with one side lying flat on top, you could of course do an F move (rotating the front layer, facing toward you, 1/5 turn clockwise), kinda like this:
If you go 1/5 turn counterclockwise, that's F' (eff-prime). No surprises so far. However, with five possible positions, the face could go 2/5 turn both clockwise (F2) and counterclockwise (F2'), which adds a new wrinkle, and not the last one. And here, naturally, is the U move, which is also susceptible to U', U2 and U2' variants:
Still looking at the 'minx face-on, turn this side 1/5 clockwise (as if facing that side directly) and it's an R move.
No surprise there. And of course, 1/5 turn counterclockwise is R'. And you guessed it, both R2 and R2' are also possible. Without repeating all those permutations, which apply across the board, here's an L move:
Now, I'm sure you noticed, the top layer has five sides. This means there are two other sides you can turn just in the top half of the puzzle. Let's call this one BR as in "back right":
And this one, as you can probably guess, is BL:
Still in the face-on regime, there are two more moves you'll need to know: DR ("down right") and its counterclockwise version, DR', meaning this layer below the puzzle's waistline:
Don't worry about DL or any of the other lower-layer sides hidden around the back, because you won't need to turn them—at least, when you do, they'll be facing toward the front.

With me so far? OK, suppose you have to do a step that assumes you're looking at the puzzle edge-on; that is to say, with the edge between two faces at front, facing toward you. Early warning: This is gonna happen. And it flips the directions of the turns around. U is still up, of course, but now this is an R move:
And this is L:
Then we shall call this B, as in "back":
And since the front is now split between right and left, we'll call this FR for "front right":
And this, naturally, will be FL:
Theoretically, a D ("down") move is always possible, rotating the bottom layer, but in practice you never need it. Starting the scramble, white goes up and green to the front; during the solve, white generally goes down, but you're free to turn the puzzle every-which-way and, as you solve it step-by-step, you'll be looking at it from a different angle at every step.

SCRAMBLE: Getting this thing scrambled is another thing altogether. When you pull down the puzzle-type selector at this puzzle scrambler, you'll see a different notation again. For scrambling purposes, please don't ask me why, you only need six possible moves. D++ means you hold the top layer and twist the rest of the 'minx 2/5 of the way around, clockwise (as viewed from below). D-- is its counterclockwise counterpart. R++ and R-- mean you grab the left layer and do a 2/5 turn of the rest of the cube, clockwise and counterclockwise respectively. And U and U' are what they usually mean, a 1/5 turn only. Apparently a sequence of these turns, and only these turns, is sufficient to randomly scramble this puzzle, leading to a result like this:
STEP 1: White star. Actually, you could start with any color, but I make white my first layer every time. After this step, white will generally be facing down and gray will be facing up, with five sides on the lower tier (red, dark green, purple, yellow and dark blue) all pointy-end up, alternating with five points-down sides on the upper tier (orange, light green, pink, cream and light blue). To start—this bit is all intuitive, do-it-yourself-stuff—dial in the white edges (they look like triangles, viewed face-on) around the white center, making sure each edge's other color aligns with its matching center. I trust your problem-solving abilities to manage this, starting with one edge like white-yellow here:
...and continuing all the way around until you see a white star, like this:
STEP 2: Solve first layer. Which, again, generally means white. Find a corner piece that goes between two of the white star edges. Putting white at the lower front and viewing the upper tier edge on, put the edge piece directly above the spot where it belongs—like the purple, yellow and white corner here:
Now there are three cases for how to move this corner down to the slot between the purple-white and yellow-white edges. Notice in the case above that purple is on top of the piece in question, and the purple side is to the left. So you'll use the left corner algorithm: U R U' R'. In other words, you rotate the corner piece out of the way in the direction of its top color's center, dial the incorrect piece up and out of the corner, rotate your corner back in and dial it down into place: out, up, in, down. Result: Purple-yellow-white finds its spot, oriented correcty and all.
You can use that same mnemonic in the event the top color of your corner matches the center to the right, like in the case of purple-green-white in this example:
The move is U' L' U L but the reasoning is the same, as is the result:
For the third case, suppose the corner piece comes into that staging position with the white side up, like this red-green-white corner. What do you do then?
Well, you do the algorithm R U R' U' x2. The "x2" means you do those four moves twice, which is easier than memorizing an 8-move algorithm. That'll flip the corner around so one of the other colors is facing up, and then you can do whichever algorithm applies. I feel like it's usually the right-corner one, but don't quote me on that.
After you've worked your way around the white star, you'll not only have a solid white side, but all its corners and edges will line up with the correct lower-tier centers.
STEP 3: Lower-tier edges. This is about putting the correct, two-colored edge pieces between the sides on the lower tier. Pay attention, because you're going to use this algorithm a lot, and it has both right-handed and left-handed versions. First, find an edge piece somewhere on the 'minx and hustle it around so that it's standing upright, above and to the right or left of the edge where it belongs. Holding the puzzle with white in the lower front and where the piece belongs at front, position your piece above the center that matches its lower color—like this purple and yellow edge at the left:
Then do this rather long algorithm, which (as I said) you'll be doing a lot, so expect to learn it well: U R U' R' U' L' U L. This is the left edge algorithm, and you can think of it as dialing the correct edge out of the way (away from its top-color center), moving incorrect edge up in the other direction, pulling the correct edge back in and dialing the other side back down, then dialing the correct piece across to the other side of the target edge, pulling that edge out in the other direction again, moving the edge back to where it was before (but now with the correct corner moving with it) and then dialing both pieces down into place. Away, up, in, down, across, up, in, down. Result: your edge is now snug against the corner piece it belongs above.
Again, you can use the same reasoning to explain and remember the right edge algorithm. So, take the blue-yellow edge at the upper right:
Again, stage the piece above the center that matches its bottom color and start the move by twisting it out of the way, away from its top-color center, doing U' L' U L U R U' R', or away-up-in-down-across-up-in-down. Result:
When you've gone all the way around the lower tier, you'll see something like this (viewed from the bottom):
STEP 4: Middle-layer valleys. A video tutorial I watched when I was setting out on my Megaminx journey called these pieces "bunny ears," but that's silly. With the white side facing down, this step is about color-matching the two edges and one corner piece in each of the five, V-shaped angles where the upper-tier sides point down between the lower-tier sides. You have to be careful while doing this to avoid scrambling parts of the puzzle you've already solved, which makes this step a little tricky. However, you can do this either left-handed or right-handed, by which I mean the direction you're going around the cube, and in my opinion it's good practice to switch directions from one puzzle-solve to another, to keep your technique tuned up going both ways. For the sake of simplicity, the example solve for the pictures below will go around the puzzle toward the right.

First, dial in an edge piece that goes between an upper-tier side and a lower-tier one, like the cream-red edge at right.
Then, turning the puzzle so the next edge to the right is at front, bring the corner piece that belongs in the valley to the top front, above where it belongs. Apply the left, right or center corner algorithm from Step 2, as the case requires. For example, this green-red-cream corner...
calls for the right corner algorithm (U' L' U L). Then the cream-green edge, staged here above the cream center, will get the left-edge treatment from Step 3.
The result (in this example) is the three-piece, cream-red-green, edge-center-edge set all put together.
Now continue building these three-piece valley assemblies, moving from one side to the next, until only one side is left undone—I'm calling that a whole separate step, because it has a slight (cough) twist. Meanwhile, anytime you have to rotate a side whose valley-piece you've already assembled to free up a corner or an edge that you need elsewhere, don't forget to dial the valley back down to where it belongs. This will save you the maddening chore of having to re-solve something you previously solved.

STEP 5: The last valley. This is when you only have one middle-layer valley to fill in. Attach the first inverted bunny-ear (if you will) the same way as usual, making sure you right any other side that you have to twist out of alignment to do so. Like this light blue-dark green edge, for example. (I apologize for the overexposure in the photos that follow.)
Now, give that last side a 1/5 turn to bring the corner at the bottom of the valley one twist closer to the top. This is important, because it will enable you to put that purple-dark green-light blue corner (on top in the previous picture) where it belongs without scrambling the adjacent side. And ditto with the light blue-purple edge at the upper left in this picture, which will become the final bunny ear.
STEP 6: Middle-layer peaks. This is where you color-match the corner piece at the top of each lower-tier side, as well as the edge piece that sits on top of it like a floppy hat. It doesn't matter whether you do each corner and its neighboring edge before moving on to the next, or all the corners first and then all the edges. You're just going to use the same center and edge algorithms you've already learned, for example, to put this red-pink-cream corner in its proper spot...
...as well as this almost undetectably pink-cream edge (sorry again):
The result is everything solved except the top layer of the puzzle.
Yay! That means there are only four steps left! Four tricky, easy-to-mess-up steps that are, by themselves, half the challenge of solving the Megaminx. If you have the right attitude, you'll enjoy them ... and you won't begrudge the extra practice you get if/when you screw them up.

STEP 7: Gray star. Otherwise known as "orient last layer edges," meaning the object is to arrange all the two-colored edge pieces gray-side-up around the gray center, like the points of a star. If you reach the end of Step 6 and you don't already have a gray star (and I never have), you'll see one of three cases. Either you'll have one, lonely gray edge piece pointing away from its center; if so, point it toward the back left, viewing the puzzle face-on, like so:
Or you'll have three gray edges all bunched together, like the points of a crown; again, put the middle point toward the back left:
Or, finally, you may have three gray edges with two of them separated from the third, like an arrow. Let the tip of the arrow point to the right (or, again, the middle point to the back left):
And now do the algorithm—it's the same algorithm regardless—F R U R' U' F'. Seem familiar? Yes, it's a slight variation of the "yellow cross" move on the cube-shaped puzzles, and it does basically the same thing, only pentagonally. Like F U R U' R' F' on the cube, you may have to do it multiple times to get the desired gray star.
Also like that move, I find it crucially important to say the notation aloud so that I don't mess it up. Because I seriously want to do the cube/yellow cross algorithm, every time, and that's no good here. If it helps, say "fur urf" to yourself on the cube and "fru ruf" (froo roof) on the 'minx.

STEP 8: Gray-side up. I guess you could call this "orient last layer," in the sense that when this step is complete, all the pieces on the top laye will be oriented correctly, even if they are jumbled around in the wrong order. This is a deceptively simple yet dangerously tricky step. Screw up Step 7 and you'll only have to fix a couple pieces. Screw this up, and you'll be redoing practically the whole puzzle. So pay close attention now. (1) Holding the puzzle so you're viewing it face-on with an unsolved corner (i.e. not gray-side-up) at front right. (2) Do R' DR' R DR either x2 or x4, depending on which way the piece is oriented. I find it helpful to chant "down-down-up-up" during this move. DO NOT FORGET to complete that last DR ("up") move even after that corner moves into place gray-up. I mean it. Unless you need a lot of practice and fancy starting the puzzle over almost from the star. (3) Holding the puzzle in place and turning only the top layer, put another unsolved corner at front right and repeat step 8-2. (4) Trying not to break into a cold sweat as each move seems to be scrambling the puzzle, continue in this way until all five top-layer corners are gray-side-up. As a bonus, and as if by a miracle, all the lower layers will be restored to their previous, solved condition. Like this:
STEP 9: Permute top edges. Now that everything on the top layer is gray-up, you'll probably notice that the colors around the side are still scrambled. Don't worry about the corners for now; this step is about the edges. Again, there are a couple of cases but only one algorithm. In Case 1, you no more than one top edge aligns matches its side-color's center at a time, no matter how you turn the top layer. Put a side where the top edge matches its center at front (viewing the puzzle face-on). In Case 2, you can turn the top layer so that two adjacent edges line up with their side-color's center. In this case, you'll also find another adjacent pair of correctly aligned sides, but the fifth side will be the odd color out. Turn the top layer so that edge finds its center, and put that center at front. In Case 3, two non-adjacent sides have edges that line up with their side colors. Hold the puzzle with one of those colors at front and one at back right. Then, regardless of the case, do the following moves: R2 U2 R2' U R2 U2 R2'. It's very likely that you'll have to do this step multiple times, particularly if you have to cycle through Cases 1, 2 and 3. So, get used to seeing something like the following during this step:
Result: top edges permuted.
STEP 10: Permute top corners. This is the final solve, people! It's also a pretty intuitive step, by which I mean it isn't a simple formula; you have to think and use good judgment, and one of the cases conceals a pitfall that can also lead to (cough) additional practice. And it's another move where you need to hold the puzzle in one position throughout (viewed face-on), twisting only the top layer as you move from solved corner to unsolved corner. (1) Put an unsolved corner at front right, then dial it down and out of the way, and dial a dummy corner up into its place. For example, do R' DR' R. (2) Look at the gray corner you just pulled down and out. Determine the colors of the other two sides, which will tell you which edge pieces this corner belongs between. Then turn the top layer (only!) to put the corner between those two edges at front right. Dial that (wrong) corner piece down and out of the way, turning the DR layer in the opposite direction from before; this puts the "wrong" gray corner out of the way and pulls the "right" corner into position to dial up into place. Example: R' DR R. (3) Repeat 10-2 (changing the direction of the DR move each time) until either all five corners are correctly aligned, or you get stuck.

(4) I didn't tell you about this before, but there's a case—when this step starts with exactly four corners out of alignment—where at some point, you run out of correct edges to swap with the next incorrect edge, and you have to start over. This is the perilous moment when, only three or four moves from having the whole puzzle solved, I sometimes botch the whole thing and have to make repairs all the way down to the bottom layer. The key is not to panic. Make the next "dial the 'wrong' top corner and out of the way" move, only be sure to turn the DR layer in the direction that restores the puzzle somewhat, and don't forget to dial a dummy corner up into the space vacated by the wrong corner you'd just pulled out. Then continue repeating 10-2 until the top corners are aligned; and if you haven't botched it, you may only need to twist the top layer a 1/5 turn or two to complete the solve. Here are some illustrations of this crucial but complex step: First, here's the gray-blue-orange corner being pulled down off the top. (Believe it or not, the color at front is light green. Again, sorry about the overexposure.)
And here's that same corner being pulled out of the way, to the lower left.
Next, the blue, pink and (I think) light-green "dummy" corner is rotated up into that slot—an important step because otherwise, the adjacent top edge and corner on the right layer would also be knocked out of place.
Then, after twisting the top layer so the corner between the blue and orange edges is at front right, you twist that corner down ...
And you swap the gray-orange-blue corner into its spot:
And dial it inup to the top layer where it belongs:
Here, without further commentary, are photos of the third corner being twisted into front right and pulled out of the top layer and the second corner being pushed back in where it belongs:
The last corner goes into the spot where you stuck a dummy corner, earlier:
And behold, as you dial the last top corner into its proper place, everything else goes with it (give or take a final top-twist):
In summary:
  1. White star
  2. First layer
  3. Lower-tier edges
  4. Side valleys
  5. Side peaks
  6. Orient top edges
  7. Orient top corners
  8. Permute top edges
  9. Permute top corners
. And you can do all those lower- and middle-layer edeges and corners with right- or left-handed moves that are probably better learned by understanding what you're doing than by memorizing algorithms (i.e. reasoning not rote). The only algorithms it really pays to get down by heart are the case where you have to rotate a corner piece (R U R' U' x2) and F R U R' U' F'. Even the formulas for Steps 8 and 9 are probably better remembered by muscle memory (or "down, down, up, up," etc.) than by strings of letters, and of course the denouement is a magnificent move in which you don't have to memorize any algorithm, instead using your reasoning skills and an understanding of how the puzzle works to complete a solution.

Steps 7-10 above are different from how I first learned to solve the Megaminx. I probably wouldn't like it as much, and might even have quit playing with it by now, if I hadn't come across a different method. What was presented to me as a beginner's method was so complex that I needed a cheat-sheet to remind me of which way to turn the dodecahedron at each step, and different algorithms for each case. I am so glad that I kept shopping around until I found a method that (for example) required only one algorithm for Steps 7 and 9 and that gave me an intuitive handle on Step 10. So my final advice on this wonderful toy is: Don't give up if my instructions, or anybody's instructions, don't work for you. Keep searching and you may find the answers your need.