Dino Cube Tutorial

Behold, the Dino Cube, at front and center, supported by its fellow "Skewb-adjacent" puzzles, the Ivy Cube (left) and the Redi Cube. More on them later.

It isn't just a unique variant of the Rubik's Cube; it's the start of a whole new branch of 3-D scrambling puzzles, which include (among others) a Curvy Dino Cube (with zig-zag cuts between corners and edge pieces), a 4x4 Curvy Dino cube (with smooth curves), a Clover Dino Cube, a Dino Skewb, which is easily confused with the Master Skewb and the 3x3x3 Dino Cube, the Raptured Dino Cube and the Rex Cube. And I'm not even going into the Ivy Cube, the Redi Cube and variants thereof; I'm saving them for future tutorials. Here are pictures of those variants if you're interested:

But enough about that. The Dino Cube is a clever variant of the Rubik's Cube, or perhaps closer to the 2x2x2 Mini Cube, in which each of the cube's sides is divided into four edge pieces – no centers or corners. And these edges turn together, in groups of three, around the cube's vertices, meaning that each twist moves approximately one-fourth of the cube. It's a really clever shape whose unusual method of turning may take you a minute to wrap your head around it. I mean, think about it; it has four axes of rotation (each running through two vertices diagonally opposite each other) and, every way you turn it, three layers. Observe:

Neither of the two puzzle scramblers I have bookmarked has a scramble generator for the Dino Cube. However, if you don't mind the fact that the results won't look quite the same, you could use the Redi Cube scrambler at Cubing-dot-net. Here's a sample scramble pattern and the result when executed, to the best of my ability, on a Dino Cube.

To get there, however, it behooves you to learn what that scrambling notation means. It wasn't obvious to me at first, and for a while I had to look at every single step to make sure I was pivoting around the right vertex at each twist. Then I learned to apply the Skewb principle that the notation makes more sense when you look at the cube edge-on (starting with white up, green to the left of front and red to the right of front), while bearing in mind that the graphics on the scramble generator assume green starts out facing front. So here are examples of the clockwise moves (add a "prime" sign for counterclockwise moves). Here's the vertex to pivot around for an F (as in "front") move:

Directly below it is the center point of the D (as in "down") move:

Down here at the bottom, to the right of D, is the focal vertex of the R move:

Also at the bottom, to the left of D, is the L vertex:

On the top layer, above L and to the left of F, is what the scramble generator calls UL ("up-left"):

Directly across the top from it, as you can now probably guess, is UR ("up-right"):

The B (as in "back") vertex is directly behind the D vertex on the back corner of the bottom layer:

And U (as in "up") is here at the top, directly behind F:

A bit counterintuitive, innit. F above D; U above B. And after you went to the trouble of learning "BR" and "BL" for the Kilominx, here they go throwing in "UR" and "UL." But here again, to refresh your memory, is that completed scramble pattern, adapted from the Redi Cube scrambler.

Of course, you can save yourself the trouble of learning all this notation by just shuffling the puzzle to the best of your ability without a scramble generator. I ordinarily don't go for this kind of thing, because I recognize how difficult it is for people to do randomness, but in cases like this puzzle, I sometimes do take the easy way out and just try to make a unique series of turns until all sides of the cube seem sufficiently broken up. And if you regularly do that, you can forget about all this notation because my approach to this puzzle doesn't use it. STEP 1: Start by solving the white side. It helps to train your brain to think in terms of three-piece vertices – putting them together and dialing them into place. Like, for example, this white-red-green corner, made of three adjacent edge pieces.

Now, recall the BOGR mnemonic for the order of the side colors, as you rotate the cube in ascending order with white at the left. A unique quirk of this puzzle is that you can actually solve it with the colors going in the opposite direction; something I actually did by accident, once. That's fixable, though, in like eight to 12 moves. Either way, though, this yellow-orange edge will eventually need to go on the side opposite to the red-white edge.

That just leaves this gap, with the orange-yellow edge, where the white-blue edge belongs:

Here I've maneuvered the white-blue edge into the slot directly above that orange-yellow edge. Then I dial orange-yellow up and to the right; replace it by dialing white-blue down and to the right; and twist the now completed red-white-blue edge into place.

Most of your solve is going to involve doing pretty much exactly this type of swap, more or less intuitively. When in doubt how to pull it off, slow down and give it a little thought before you rush into a series of moves. Or don't. Because maybe that's how you learn – by experimentation.

STEP 2. Now work on the yellow layer. Conceptually, at least, white will face "down" and yellow "up" for this part of the puzzle – though, of course, you can turn it any way you need to, as one move leads to another. So here (you can see from the bottom edges) are the green, orange and yellow sides of the cube. You could twist the top front vertex to put the yellow-green and green-orange edges exactly where they belong.

But remember, you want to have the whole, three-piece corner ready to dial into place, and that still leaves one piece (yellow-red) out of whack. Here it is, on the other side of the cube.

So, I dialed that front-right corner around to bring that yellow-orange edge in between yellow-green and orange green ...

... and then I rotated that whole, three-piece corner to solve the rest of the puzzle.

STEP 2.5: It doesn't always come out this easily. Often, you find yourself with pieces that need to be swapped across the cube from each other, requiring some relatively complex maneuvers. Usually, you can figure these out intuitively, just using the principles I've laid out above. However, a little experimentation with a solved Dino Cube has taught me that you can also use variations of the "down-down-up-up" gambit to cycle three pieces in various ways. Here's what happens when you "down-down-up-up" a solved cube, alternately twisting around the up-front-right and up-front-left vertices:

Of course, since each edge has three pieces, if you repeat the same pattern, you'll cycle those same three pieces a second time, before returning to the initial state on the third cycle. Or, you can reverse the cycle by alternating from left to right.

Beginning from the same starting state (yellow up, red at front), you get these results when you do "down-down-up-up" from right to left on the two bottom front edges:

Again, if you repeat the same pattern, you put the same three edges through another cycle, before arriving back at the start on the third cycle. Or, again, you can reverse the cycle by starting on the left.

Finally (for now; experiment further on your own), here's what happens when you do a "down-down-up-up" cycle from the top-front-right to the bottom-front-right. The same palaver applies regarding repeating the cycle or reversing it.

So, consider these patterns, or ones like them, if you spot these cycles toward the end of a solve and you want a quick, no-brainer solution to finish the puzzle.

This is one of the first Rubik's Cube-based puzzles that I picked up and solved without first consulting a solution guide or tutorial. I'd like to say a little deep thought led me to figure out the solution, but honestly, I started playing with it and before I really understood what I was doing, I accidentally solved it. That still happens from time to time; I think I'm three moves away from a solution and then, surprise! One move later it's solved. You can make the puzzle last a little longer by blundering ignorantly from one move to the next, but you do so at the risk of stumbling on a solution while you're still trying to learn how the moves work. I'm not saying it's impossible to struggle with this puzzle longer than you expect it to go unsolved; but it's definitely more satisfying to solve it when you really mean it. And it also has the attraction of moving in a unique way, feeling different in the hands from any other puzzle, and being put together in a fascinating manner. Truly a marvelous invention, for such a deceptively simple toy!

County names in the U.S. revisited

Way back in 2007, I wrote a post about my fascination with U.S. counties, focusing on ones that shared the same names. More recently, I did a another post or two on the shapes and sizes of counties in each state, suggesting that some of them shouldn't even exist. For the newspaper at which I work, I even published a column a few years ago about some confusing quirks of Minnesota counties in which (for instance) one county often shares its name with a town or city in another county. And of course I'm always amusing myself by making note of what county I'm passing through wherever I travel. So, of course, being an obsessive type, I recently put a lot of time and effort into creating a spreadsheet counting how many times each county name occurs within the 50 United States of America. And let me tell you the results. Hold still. This will only hurt a bit.

NOTE: I hope Drew Durnil doesn't mind me using his map of the instances of Washington County in the U.S., which I found on his Reddit. I have enjoyed quite a few of his videos on YouTube. Apparently we both have a bit of the same sickness. Another note: I'm including Louisiana parishes, Alaska boroughs and independent cities (of which Virginia has quite a few) in this list, since they're county-equivalent, second-level divisions after the states themselves.

So here's the damage. Counting variant spellings, and allowing for a margin for error in my vast task, I found 1,809 distinct county names in the U.S. The majority by far – 1,379 of them – are one-offs, which I'm obviously not going to list in full even though some of them are quite interesting. They range alphabetically from Abbeville (SC) to Ziebach (SD). There are 225 pairs of two counties with the same name, alphabetically from Albany (NY, WY) to Yuma (AZ, CO). There are 85 triples, from Baker to Wyoming; 138 foursomes, from Adair to Wood; 19 groups of five counties sharing names from Allen to York; 16 groups of six counties with names from Custer to Webster; only four groups of seven (Howard, Lewis, Pulaski and Richland); 11 groups of eight, from Boone to Randolph; and seven groups of nine counties sharing names from Benton to Shelby.

Breaking into two digits, we find six names shared by 10 counties: Hamilton, Hancock, Henry, Logan, Perry and Pike. If you're playing one of those Sporcle puzzles where you have to name all the counties in a state, these are all very good guesses; they'll be right one-fifth of the time. They get better from here. There are six names shared by 11 counties each: Calhoun, Crawford, Fayette, Lawrence, Morgan and Scott. (The variant Lafayette accounts for another six counties.) The seven names shared by 12 counties each are Adams, Clark (with no e; Clarke is in the five-county bracket), Douglas, Lake, Lee, Marshall and Polk. Only three names are distributed among 13 counties each: Carroll, Johnson and Warren. Greene (with an e) is the only name shared by exactly 14 counties. At 15, there are only two: Grant and Wayne. There are no 16-county name groups. The three names for groups of 17 counties are Marion, Monroe and Union. There are two names representing just 18 counties: Clay and Montgomery. And no 19-county groups.

At exactly 20 counties we have just one name: Madison. There's a wee gap, then two names with 24 counties each: Jackson and Lincoln. Tied for third place at 26 countiess each are Franklin and Jefferson; though Franklin is one of those cases where Virginia has a county and an independent city by the same name. But of course, and this can't be a surprise given my previous essay on this subject, holding the top spot is Washington at 30 states. Count 'em: Alaska, Arizona, Colorado, Florida, Illinois, Indiana, iowa, Kansas, Kentucky, Louisiana, Maine, Maryland, Minnesota, Mississippi, Missouri, Nebraska, New York, North Carolina, Ohio, Oklahoma, Pennsylvania, Rhode Island, Tennessee, Texas, Utah, Vermont, Virginia and Wisconsin. I should have listed the states that don't have a Washington County, but it's too late now!

I glanced at the derivation of many of the names in passing, and there are some surprises, such as a whole group of counties in Michigan whose names were made up by Henry Schoolcraft on purpose to be unique, and perhaps also to pass them off as Native American lingo. He's the same guy who gave us "Itasca" for the headwaters of the Mississippi River, based on the Latin phrase "veritas caput," though to this day there are people who cite it as a Native American word.

Many of the unique county names are genuine Native American words, though, or at least corruptions of them, which along with misspellings or corruptions of French and Spanish terms and even anglo names just show how fallible human beings are, especially in large groups such as a state legislature. And there are several instances where tiny differences of spelling separate essentially the same name into separate entries on this list, such as Cheboygan (MI) vs. Sheboygan (WI). There are Allegan (MI), Allegany (MD, NY), Allegheny (PA) and Alleghany (NC, VA); Andrew (MO) and Andrews (TX); Burnet (TX) and Burnett (WI); Callaway (MO) and Calloway (KY); Cook (GA, IL, MN) and Cooke (TX); Glascock (GA) and Glasscock (TX); Hayes (NE) and Hays (TX); Highland (OH, VA) and Highlands (FL); Hot Spring (AR) and Hot Springs (WY); Kearney (NE) and Kearny (KS); Leflore (MS) and LeFlore (OK); Loudon (TN) and Loudoun (VA); Storey (NV) and Story (IA); Uinta (WY) and Uintah (UT).

In other cases, similar county names are really unrelated, but though spelled differently, they're pronounced about the same, such as Aiken (SC) vs. Aitkin (MN), which has a silent t; Barber (KS) vs. Barbour (AL, WV); Barren (KS) and Barron (WI); Coffey (KS) vs. Coffee (AL, GA, TN); Coal (OK), Cole (MO) and Coles (IN); Coos (NH, OR) and Coosa (AL); Dickson (TN) and Dixon (NE); Foard (TX) and Ford (IL, KS); Forest (PA, WI) and Forrest (MS); Green (KY, WI) and Greene (14 states); Harford (MD) and Hartford (CT); Huntingdon (PA) and Huntington (IN), not to mention Hunterdon (NJ); Johnson (13 states) and Johnston (NC); Kewaunee (WI) and Keweenaw (MI); Kimball (NE) and Kimble (TX); Linn (IA, KS, MO, OR) and Lynn (TX); Stafford (KS, VA) and Strafford (NH); Tooele (UT) and Toole (MT).

On the other hand, there are also county names that are externally different but, secretly, named after the same things, such as Berks (PA) and Berkshire (MA); Buckingham (VA) and Bucks (PA); Charlotte (FL, VA) and Mecklenburg (NC, VA), etc. Several county names memorialize people by both their first and last name, such as Charles Mix (SD); Jo Daviess (IL), also the namesake of three Daviess counties (IN, KY, MO); Deaf Smith (TX); Jim Hogg (TX); Jim Wells (TX); and Tom Green (TX).

Louisiana has three pairs of parishes with the same name except either "East" or "West": East Baton Rouge and West Baton Rouge, East Carroll and West Carroll, East Feliciana and West Feliciana. Some of Virginia's independent cities have the same name as a Virginia county. Awkwardly, two or three of Virginia's actual counties have the word "City" in their name. Other independent cities, outside of Virginia, include St. Louis (MO), Carson City (NV) and Baltimore (MD); both Missouri and Maryland also have counties by the same name. Don't get me started on cities and counties with unified governments!

Quite a few counties share their names with a state of the U.S. Surprisingly few of them are within the state so named. They include Arkansas (AR), Colorado (TX), Delaware (IN, IA, NY, OH, OK, PA), Hawai'i (HI), Indiana (PA), Iowa (IA, WI), Mississippi (AR, MO), Nevada (AR, CA), New York (NY), Ohio (IN, KY, WV), Oklahoma (OK), Oregon (MO), Texas (MO, OK), Utah (UT) and Wyoming (NY, PA, WV). Arguably, you could also include Dakota (MN), Hampshire (MA, WV), Jersey (IL) and York (KY, NE, PA, SC, VA). And of course there are those 30 Washington counties across the country, right?

Quite a few counties share the same opening move, such as Grand Forks (ND), Grand Isle (VT) and Grand Traverse (MI); Green Lake (WI), Greenbrier (WV), Greenlee (AZ), Greenup (KY), Greenville (SC) and Greenwood (KS); King and Queen (VA), King George (VA), King William (VA), Kingfisher (OK), Kingman (KS) and Kingsbury (SD); La Crosse (WI), La Paz (AZ), La Plata (CO), Labette (KS), Laclede (MO), Lafourche (LA), LaGrange (IN), Lamoille (VT), LaMoure (ND), LaPorte (IN) and LaRue (KY); McClain (OK), McCone (MT), McCook (SD), McCormick (SC), McCracken (KY), McCreary (KY), McCulloch (TX), McCurtain (OK), McDonald (MO), McDonough (IL), McDowell (NC, WV), McDuffie (GA), McHenry (IL, ND), McIntosh (GA, ND, OK); McKean (PA), McKenzie (ND), McKinley (NM), McLean (IL, KY, ND), McLennan (TX), McLeod (MN), McMinn (TN), McMullen (TX), McNairy (TN) and McPherson (KS, NE, SD); San Augustine (TX), San Benito (CA), San Bernardino (CA), San Diego (CA), San Francisco (CA), San Jacinto (TX), San Joaquin (CA), San Juan (CO, NM, UT, WA), San Luis Obispo (CA), San Mateo (CA), San Miguel (CO, NM), San Patricio (TX) and San Saba (TX); St. Charles (LA, MO), St. Clair (AL, IL, MI, MO), Ste. Genevieve (MO), St. Joseph (IN, MI), St. Louis (MN and both a county and an independent city in MO), St. Bernard (LA), St. Croix (WI), St. Francis (AR), St. Francois (MO), St. Helena (LA), St. James (LA), St. John the Baptist (LA), St. Johns (FL), St. Landry (LA), St. Lawrence (NY), St. Lucie (FL), St. Martin (LA), St. Mary (LA), St. Mary's (MD) and St. Tammany (LA); Wood (OH, TX, WV, WI), Woodbury (IA), Woodford (IL, KY), Woodruff (AR), Woods (OK), Woodson (KS) and Woodward (OK); and a partridge in a pear tree!

If I've forgotten to mention anything remotely interesting, it's no fault of mine. I've worked hard enough and long enough on this to get on with my life now. Are you still here? If so, thanks for bearing with my insanity!

Skewb Ultimate Tutorial

Here, front and center, is the Skewb Ultimate, supported by its dodecahedral friends, the Kilominx and the Megaminx.

Like both of those puzzles, it's a Rubik's Cube-inspired 3D twisty puzzle based on the marvelous dodecahedron, the Platonic solid that has 12 identical, regular pentagons for sides. If you're a math geek, you gotta love a regular dodecahedron (and the regular pentagon, for that matter) because the Golden Ratio, φ, drips out of them every-which-way. No doubt that's connected to the fact that φ (phi), which is to 1 what 1+φ is to φ, is exactly equal to one plus the square root of five, all divided by two. Look it up for yourself. This isn't a math essay. We're talking about the Skewb Ultimate.

The other puzzles the Skewb Ultimate is related to are the Skewb and the Skewb Diamond, which I discussed in some prior tutorials. I mentioned that the Skewb family of puzzles basically take the shape of one of the regular, face-turning puzzles, like Rubik's Cube or the FTO, and change the direction of the cuts so that the pieces turn diagonally and each move twists half of the puzzle.

Instead of 12 faces that all turn around their own center, the Skewb Ultimate is cut in half four ways, with the cuts running across its faces in different directions and dividing each face into similar groups of pieces – three corners and an edge. But one of the corner pieces on each side is also an edge piece between two adjacent sides, so that two large pentagonal sides meet at each edge and two smaller rhombuses join them in a corner at each end; so, a four-colored piece. The other two corners on each side really are just corners, with three similar but rotated trapezoids coming together at each vertex. These funky shapes mean it's possible to get pieces of the right colors in the right places while having them rotated in the wrong direction. Isn't that fun?

However, solving it is only as difficult as remembering which way to hold the puzzle while executing a series of "down-down-up-up" moves, or (if you do a "y2," 180-degree equatorial rotation between two of those) the so-called Sledgehammer move. Well, almost only as difficult. The first step is a wrinkle unto itself. It kind of makes the puzzle, if you ask me.

Here are examples of the four different ways you can turn a Skewb Ultimate. I'm not bothering with notation on this one. So, either clockwise or counterclockwise, you could twist it along any of these axes:

Before we get into it, though, let's appreciate the unusual color scheme of this puzzle, with a sticker on it that won't let you forget it's manufactured by Mefferts. The colors are a little tricky to tell apart. Like in the sides pictured below, there's a white, gold, purple and blue side, but also a green side and a side that is neither quite light blue nor light green; I suppose you could call it cyan.

Flipped the other way around, we find that there's another blue side, another green, a red, a pink and – what's this? another pink? I'm not sure what to call that unless we run with the "cyan" theme and call it magenta.

So a dark blue (indigo?), light blue and cyan; a dark red, light red (pink?) and magenta; a dark green and a light green; and also purple, gold, yellow and white. They're gorgeous colors, to be sure, but not exactly Mefferts' gift to the color-challenged. My ballot in the suggestion box would be to revise this color scheme with more easily distinguishable hues, such as (say) a straight-up black side, gray, and good old orange! Just sayin'.

According to Wiki, the Skewb Ultimate was initially called the Pyraminx Ball. Due to the limited number of pieces and the fact that, like the FTO, each turn takes you right past a side where you can't stop before you get to one where you can – and there are only two other positions where it can stop before coming back to where it started – the number of possible scrambled states is a measly 100,776,960. Grubiks tells us the Skewb Ultimate was invented in 2000 by Tony Fisher and that Meffert's first edition of it had only six colors, meaning opposite sides were colored the same, which I suppose made the puzzle even easier. Also, Mefferts initially misspelled the word "Ultimate," a misprint that probably makes the unopened OG model a valuable collectors' item. Finally, Grubiks informs us that while the Skewb Ultimate isn't a sanctioned speed-solving event, the record time for solving it is unofficially 4.67 seconds. For what it's worth.

Here we are, all scrambled. I just tried to make a random-ish series of turns among all different axes. If there's a scramble generator for this puzzle, I don't know about it; and I don't know what other puzzle's notation would apply so you could use that puzzle's scrambler. Just do your best not to accidentally solve the puzzle while you're trying to scramble it. Good luck.

STEP 1. Make a yellow and dark-blue cross. This is the step that isn't all about algorithms; you have to reason it out and intuitively apply a few general procedures. The goal here is to take this yellow and dark-blue edge and surround it, in the correct orientation, with the four three-sided corner pieces that feature those two colors. Also, pay attention to the two shades of red on the rhomboid corners at the ends of the edge piece; for the cross to be correct, the trapezoidal corners need to line up with those as well. Here, for example, there's a yellow-pink corner at bottom left and a yellow-red corner at the right. Unfortunately, they're both oriented the wrong way and, more concerningly, they're on the dark-blue side of the edge.

Here, you can see I twisted the lower hemisphere to bring that yellow-pink corner to the right, under the dark green-magenta edge. If you squint a bit, you can see that dark-blue edge at left.

Next, I twist the side of the puzzle that pivots around the yellow-pink corner in the direction that will put the yellow side in line to dial into place. And dial it I do.

Then I twist the red-yellow corner into position to dial into its place. And dial it I do.

Checking the blue side of the edge, I find the blue-red corner is already where it belongs, but oriented incorrectly.

Take note of which direction it needs to rotate to face the right direction – in this case, to the left. Naturally, this means you need to rotate that corner to the right on the bottom layer (always the opposite direction).

Then twist the side that pivots around that corner so that the red and blue sides will match up with the edge when you dial it back in; and dial it back in.

Again, if we dial the pink-blue corner into place, we find that it's oriented incorrectly.

So, we dial it out in the opposite direction to the way you'd rotate it for it to be oriented correctly; pivot a whole hemisphere around it; dial it back in to place; and then restore the corner that was displaced by that pivot move.

Voila! You have a yellow and blue (and pink and red) cross!

Now put the yellow-blue edge at the bottom of the puzzle and move on to ...

STEP 2. Solve the top corners. Eventually, the edge opposite yellow-dark blue will be white-light blue (shown here, obviously not in the correct spot).

Consequently, the adjacent corners need to end up with their light-blue and white sides up. But to start, those four corners could be aimed in any direction. With the yellow-dark-blue edge oriented down and and a pentagonal face at front, check whether you have a pair of either white or light-blue "headlights" at either right or left. If not, aim one "headlight" to the right, like the one on the green-white corner below:

Then repeat the "down-down-up-up" algorithm, alternating from right to left, and pivoting around the corners closest to top front on each side.

While I didn't immediately reach a state that had light-blue or white headlights, I eventually got there by repeating this pattern. See below, with the two light-blue "headlights" shown here.

Putting the headlights to the right, then, repeat that down-down-up-up pattern one more time. Result (viewed from above): all four white and light-blue corners correctly oriented and facing up.

STEP 3. Move that white and light-blue center to the top. Still with the yellow and dark-blue edge facing down, find the edge that should end up at the opposite end; here it is, at front.

Put it at the back and do the Sledgehammer pattern – that's the same old down-down-up-up, followed by a y2 move (a 180-degree, equatorial turn), and repeated from the other side. What this move does is cycles three edges, from back to top, from top to front and from front to back. At the same time, it rotates each of those edges 90 degrees counterclockwise. The initial result, viewed from above:

Well, that's the blue-white edge on top, all right. Unfortunately, the counterclockwise-rotation part of the Sledgehammer algorithm flipped it the wrong way around. To fix that, you need to do another Sledgehammer to get the blue-white edge off the top again, then rotate it to the back and do one more Sledgehammer to put blue-white on top, the right way around:

Gosh, that's beautiful. And now we hit STEP 4: Solve the remaining centers. Strange but true, at this point all the corners are correct, and you should have maybe four, but ideally three edges to cycle into place using – you guessed it! – the Sledgehammer pattern. Start by putting the first two centers (yellow-dark blue and white-light blue) at right and left; that way, nothing that happens from here forward can touch them. Also, if one of the other centers is solved, put it at the bottom, edge-down. Again, the Sledgehammer pattern, complete with that equatorial rotation in the middle, will leave the bottom edge untouched. But it will cycle the back, top and front edges from back to top, top to front and front to back, while also rotating them counterclockwise. So you might have to repeat the Sledgehammer a few times to get them where you want them, the way you want them. Just don't do a "y2" between Slegehammers; only as part of the algorithm itself. Got it?

So here's "before and after" my first Slegehammer cycle, starting with yellow at left, white at right, and ending vicey-versey:

One result was an additional solved edge, which I then put at bottom to keep it safe while continuing to work on the remaining three edges:

After some number of Sledgehammer moves – I can't remember how many; my photography is somehow failing to remind me) I realized I had solved the third-to-last edge, but the two remaining edges were flipped around backwards – one of two possible parity cases that may require special attention.

As these were adjacent centers, the solution was to put the parity edges at the back and the top (solved centers at bottom and front) and do two Sledgehammer moves – again, being careful not to do a y2 rotation between them! – and this was the result:

To solve the parity case where the two rotated edges are on opposite sides of the Skewb, just do two Sledgehammer moves (again, without a y2 rotation between them; only as part of the pattern itself!) to get into the adjacent-edges parity case, then do what I did above. It doesn't matter how the puzzle is oriented as long as yellow and white stay at left and right.

So there it is. And again, I'm helping myself as much as you (if not more) by making a record of this solution method, but one of several for this puzzle and the "beginners' method" at that, because of the same reasons I shared in my Skewb Diamond tutorial. It's an attractive puzzle. It feels nice in the hands. It turns with a satisfying clicking sound. It doesn't put up much of a fight when you set your mind to solving it. The hardest thing about coming to grips with it is keeping track of which corners your "down-down-up-up" moves are meant to pivot around. Once you've drilled that into your mind, the only parts that require deep thought are solving the initial cross and deciding how best to cycle the last few centers. When you mess up, you get more practice. And more practice is definitely needed when, the longer I spend away from this puzzle, the more likely I am to need to relearn how to solve it. Keep the brain supple and flexible. Strive for variety in your puzzling exercises!