Archive for the Algorithms Category

Shengshou Pentahedron Guide

Posted in Algorithms, Blog, Cubing on June 9, 2024 by slateman

I got a 4 and 5-layer Pentahedron and opted to grab 2 and 3-layer versions. Here are some algorithms for the smallest version to help before I move on to the higher-order puzzles.

Step #1: Get White & Yellow Centers

This puzzle is red-white-green clockwise unlike a standard puzzle, so get that on white on the bottom and move on to the top.

If you have two swapped, keep the correctly-placed center on the left. With a triangle pointing at you.

F/ U / F / D’ / F /

Step #2: Finish white Layer

Put the proper white piece above its correct location and do the standard 3x3x2 algorithm. R / U / R / U’ / R. This is an easy, familiar step.

Step #3: Last-Layer: Corners

We’re going to start our last layer with corners first. If you need to swap two of these, put the correctly-placed corner triangle pointing at you and:

R / F / U /
R / F / U / R / F

Step #4: Last-Layer Centers

If you end up with a pair of incorrectly-positioned centers, keep the solved side on your right and perform this lengthy algoritm.

L / R / U / R /
U’ / R / D / R /
U / R / U / R

Need to verify this all. Then I’m moving to the bigger puzzles.

Helicopter Dodecahedron Algorithms

Posted in Algorithms, Blog, Cubing on May 27, 2024 by slateman

At this stage of the game, more than 10 years into cubing, I collect based on looks and solves together. Some puzzles look great but I just know that a solve is a lot of work or that it’s not particularly fun. While helicopter puzzles look great, they aren’t often too difficult and so I figured I’d take the plunge with this one as part of a very-large purchase. The solve isn’t too bad, but I did need help on the later steps. Enter Twisty Puzzling’s tutorial. And here are the steps to solve this guy!

WIP: More To Come!

Step One: Solve the bottom face

This was intuitive and I got my white face situated pretty easily. Moving things around isn’t hard when you have plenty of free space to deposit things temporarily. This step situates the white face and the entire ‘layer’ above it all the way up to the long, edge pieces of each helicopter wing.

Step Two: Start building the bottom middle layer

This isn’t much of a layer, but here you’re going to want to maneuver these numbered pieces into place. I’ve numbered them in this photo in order of sequence. Some of these are intuitive, but keep moving around to the right of the puzzle. If you need to rotate one of the three-colored centers, just see the orientation on the top layer. If it needs to rotate clockwise, then spin it around the top layer counter-clockwise and vice versa. Move things out of the way as necessary here and as you get to the very end, use intuition to figure out the final pieces.

Step Three: Build the top middle layer

Now that you have the second layer done, your focus is the top-middle layer. This will include the higher three-colored pieces and the two petals to the left and right of them. You can do the centers (those three-colored pieces) first or build these all on the top layer and bring them down. So far, nothing too difficult.

Step Four: Position Petals

After orienting the lengthy center slices, now you move the petals around in a convenient three-cycle. In this photo, the pink on the right will swap with the off-white on top which will swap with the grey to the far left. The standard up, up, down, down here is intuitive and can be used to align all these nicely and swiftly.

Step Five: Position Corners

This three-cycle will move corners counter-clockwise from left to center to right. You will begin by moving the top-left piece to the left section, performing the algorithm and then undoing.

So, if we go left, front, left, front – then swap the right piece down – then front, left, front, left and fix the right.

I assume there’s a mirror version of this, but for now, that’ll do it. L / F / L / F / R / F / L / F / L / R is your three-cycle.

Step Six: Orient Corners

Unicorn Cube Tutorial

Posted in Algorithms, Blog, Cubing on September 9, 2023 by slateman

For the first half, I’m using Super Antonio Vivaldi’s tutorial as my basis. If I get stuck in my descriptions, just go watch the video. The later steps were guided by Bearded cubing 101’s guide.

Step 1: Align All Corners
This is the obvious first step. You can easily set up two or so, but as it goes on, it can get tricky. Once you have an edge piece flipped, hold the cube face on to yourself. Do a F2 turn to move the top edge piece down, swap it left or right to a piece that works (now on the bottom), do another F2 spin and your top layer should be complete.

I place the good side on the bottom now. To do middle layer edges, you can use a 3×3 algorithm to bring a piece from the top down. Or, you could just swap a front-right edge with a top-layer edge by bringing it up, swapping out and bringing the new piece down.

For the last layer, see how many incorrectly-placed pieces you have. If it’s all, do a standard 3×3 suni alg (r, u, r’, u, r, u2, r’). Now ideally you’ll have two in places/lined up and two not. Place those incorrectly-aligned edges on F and R and use a 3x3x2 edge-swap algorithm (R2, U, R2, U, R2, U2, R2, U2, R2, U, R2, U’, R2)

Sometimes I’ll get a bar of lined-up pieces instead of adjacent. In this situation, I do a l, u’, r’, u, l’, u to make them adjacent. Then I do the edge-swap alg above.

Step 2: Reduce Center
Find one center that you want to match up. Then flip the puzzle making this your bottom. Then we do the middle layers. You’ll use the top layer here as your free face to move around the pieces as you need. I think this is mostly intuitive, just don’t destroy your other middle-layer, correctly-placed pieces. If you get stuck, don’t forget: I can take my left (or right) center corner into my front face, then take a piece from the top and swing it down to the front, thus returning that newly-misplaced center corner back. There’s another method of doing this, but I think my solution will work fine.

Step 3: Reduce Edges
This will work something like 4×4 edge reduction. We are going to maintain one corner angular integrity and not worry about the rest of the puzzle. I usually choose the front-right corner. Your goal here is to slot an opposite piece (same colors – but a small/big to a big/small), do the angle turn, then restore. Ideally, when restoring, you’ll move another, properly-colored piece into place.

The trick here is maneuvering these other pieces into position while retaining the angular cut in the front-right spot. In addition, you’ve got to make sure the piece is slotted properly – i.e. with the big chunk on the left and the small to the right.

Step 4: Solve as a 3×3
The final step is intuitive. You may have to rotate centers, you may get adjacent edges flipped, but it should work out fine unless you get the dreaded one-corner-twisted parity. I haven’t even looked into that solution.

Master Icosamate Algorithms

Posted in Algorithms, Blog, Cubing on May 8, 2022 by slateman

This puzzle is kicking my ass. Fortunately, our hero Super Antonio Vivaldi made a tutorial (including another video with algorithms and another on the regular Icosamate.)

Step One: Get Corners On One Face

This should be done intuitively. Use a beginner’s method to move/rotate these as you go on.

Step Two: Permute Last-Layer Corners

This is a challenge and will be the most time-consuming part of your solve. First, flip the puzzle over and remember your bottom-layer colors (it’s easy to get mixed up and forget, particularly after putting the puzzle down!) Now, you’re going to find one corner to use as a basis for figuring out what the top piece must be.

You will do a DDUU algorithm as expected. This swaps the top with the front center piece and it also swaps the back left and back right. Doing the algorithm a second time returns all to their proper spots. However, it will also rotate them.

Starting on the left side, this will spin those centers clockwise. Counter-clockwise is done starting on the right.

Usually you won’t have this all land perfectly. Remember some cheats: you can move up the front L & R pieces to the back L & R. Since those back ones will swap/rotate and the front won’t, it’s an easy way to move around which pieces you want.

If you’re stuck with a pair of adjacent ones, do the algorithm once. This swaps the top and the center. Then rotate the second wrong piece to the front and do the alg again. This is how you do a three-cycle. Make sure you do the DDUU on the right to start and then return with the left to ensure the back sides don’t get messed up.

Step Three: Rotate Last-Layer Corners

Get the top center rotated properly while keeping at least one corner oriented properly. You’ll do your DDUU until the top center is right (and you keep one aligned perfectly so you know which is which).

Now you’re going to get the remaining corners. You can have two or three out – never one. This is a beginner’s method approach using R’/D’/R/D. You’ll count how many turns you need. You will be looking for a multiple of five (to keep your top oriented correctly). You do your R’/D’/R/D until one corner is set. Then, using a last-layer method from a 3×3, keep the lower-right piece in place (it’s rotated wrong now). Keep doing the algorithm a total of five times (or multiple of five). If it’s not a multiple of five, that’s OK, now use the one incorrectly-rotated center as your center.

If you’re unlucky and get parity, you’ll find yourself with everything done and an incorrectly-oriented top center as stated above. In order to fix this, place your top center how it’s supposed to be. This will mess with the other five corners. *sigh*. Yup. Now using intuition, move around these pieces to get the top layer perfect.

I’m guessing here, but you’ll likely swap a top and a front – then turn the puzzle and perform the opposite algorithm (starting on left vs right). You’ll likely need to fix the piece you just put in place. Feel free to do so (clockwise or ccw).

If you get all those pieces put in properly, you’ll likely have a few corners which need rotations. Count how many you need: hopefully you’ll end up with five rotations and go back to the R’/D’/R/D to figure it all out.

Step Four: Match Edges

This three-cycle will swap edges. This will go red/green/blue clockwise if you start on the right. Like the Face Turning Octahedron algorithm, this will require you to bring one slice down, then do a D/D/U – return slice – D/U/U algorithm.

Starting on the left will rotate them clockwise (R/G/B). You will use a face with a V in front of you (like the blue/green shown here). If you bring the left (red) piece down, then you do Right down, left down, right up – return slice – right down, left up, right up.

If you start on the right (move yellow down to the blue), then your algorithm will go left down, right down, left up – return slice – left down, right up, left up.

Now…what to do when a pair are inevitably flipped upside down? OK, so get them adjacent like you’ve been doing. You’ll be flipping these, so hopefully these are your last two edges that need fixing. If they’re the blue and green here, use a dummy piece (yellow) as a start. Now, you’re going to want to flip the green piece. Do this by the following:

You’re going to be working with the lower-right corner (LR – the green triangle) and bottom layer. Turn LR’, then D, D, and return LR LR. This will flip the piece that was originally there.

Now, do your algorithm. Then undo your flip, now by LR’, LR’ D’, D’ and LR – the opposite of your prior flipping alg. Finally, do your step-four algorithm two more times. If you need guidance, check out SAV’s tutorial (with timestamp).

Step Five: Match Petals

This algorithm is the opposite of the step-four alg. Here, however, you will move up the M slice layer, perform three moves, return the M slice and then do three more. It’s almost exactly the opposite of the one above. I need time to get to this part.

Start by moving that M slice up to put the pink petal where the yellow is. Then, using the colored center as your basis, do a Right down (x2), left down (x2), right up (x2) then restore the M slice to its original spot and do a Right down (x2), left up (x2), right up (x2).

Update: A solid week of dedicated work resulted in a full solve. One of my proudest solves. Not sure how eager I am to mix this up again. :D

Rex Cube/Super Ivy Cube Algorithms

Posted in Algorithms, Blog, Cubing on May 7, 2022 by slateman

I bought a Rex Cube ages ago but never really enjoyed solving it. The puzzle itself felt like it was going to fall apart at any minute and upon solving it, I shelved it and hardly ever touched it again.

Last year I purchased a Super Ivy Cube and despite being the exact same puzzle in a sense, it’s a lot more fun and a much more solid. However, as usual, I forgot the final step and had to look it up. Thus, the usual tutorial/algorithms for my own personal reference.

Step One: Align All Edges

This is an intuitive step and is essentially solving a Dino Cube. You should be able to get all of these solved pretty easily.

Step Two: Move Centers

This is the standard up/up/down/down algorithm and I do this intuitively as well. I try to get three mismatched centers oriented around one corner to easily swap them. If they’re all in a line, I just try to solve one before moving on.

Step Three: Move Petals Around

This algorithm is the only reason for this post, really. This will swap petals on your front faces as seen here. You will start with Right up, left up, right down, left down, then turn the puzzle clockwise on the corner you’re looking at and reverse it. Left up, right up, left down, right down. This should flip those two sets of petals. Now, it’s just a matter of coordinating those swaps and you’re gold!

4x4x6 Algorithms

Posted in Algorithms, Blog, Cubing on July 30, 2021 by slateman

This was my favorite puzzle and when it fell and got destroyed in Sweden, I was heartbroken. However, a few years later, whilst living in Italy, I replaced it and – to my dismay – realized I had forgotten some crucial steps into solving it!

Things are really quite simple and matching those inner-edge pieces remains my toughest challenge. I figure I should catalogue this stuff for future reference, rather than relying on old YouTube videos to help me through. OK, let’s see!

  1. Solve centers (like a 4×4)
  2. Solve edges (like a 4×4)
  3. Return to Cuboid (like a 3×3)
  4. Make sure your two middle layers are all perfect
  5. Solve inner-edge pieces (I struggle here)
  6. Position inner-lower layer ‘cross’ segment (LL is not necessary yet)
  7. Then solve inner-lower layer edges (like a 3x3x2): R2 / U / R2 / U’ / R2
  8. Now inner-upper layer edges (headlights)
    • Headlights on Left (or do this 2x): R2 / U / R2 / U’ / R2 — u’ / d — R2 / U’ / R2 / U / R2
    • Inner-edge swap (Opposite): R2 / U2 / R2 / U2 / R2
    • Inner-edge swap (Adjacent): R2 / U / R2 / U — R2 / U2 / R2 / U2 — R2 / U / R2 / U’ / R2
  9. Middle-Layer Parity (If necessary): Uu2 / R2 / F2 (Uu2 / U2) F2 / R2 / Uu2 / F2
  10. Now bottom cross (intuitive)
  11. Bottom edges (just like step #7)
  12. Repeat Headlights & inner edges steps (#8)
  13. Middle-Layer Parity Redux (if necessary)

See if that makes sense the next time I need it!!!

Update 2023: Fixed for clarity and remedied errors – this puzzle is still my favorite!

Mixup Cube Algorithms

Posted in Algorithms, Blog, Cubing on January 17, 2021 by slateman

This puzzle was a curious one and I required a helpful tutorial to solve it. Just some quick algorithms to help me solve this cool cube.

Step 1: Return to a cube

First, you’ll get offset centers lined up with an edge piece sloped downward above it. Here, you move the center piece 45° to the right, then perform a R, U’, R’ before returning the center. You then keep repeating this process. If you’re stuck with a flipped edge, just bring it down to make it a center and repeat.

Step 2: Restore centers

Just prep centers. This will swap front and right centers. When you have a pair to exchange, move your center 45° to the right, then R2 and return. Super easy.

Step 3: Solve F2L

Solve the first two layers are you would on a normal 3×3.

Step 4: Last-Layer Parities

If you get the classic 4×4 parity, you can bring down your front edge 45° (an M slice). Then F2, an E (turn left as you look at it), F2, and return the E and return M’.

This will mess up three layer 2 edges which can be fixed easily apparently. Place the proper piece on bottom/back and whip out a: B2 M B2 M. This should fix it.

If you get a parity where your final two edges are swapped, place the flipped edge in front. A M’ here is a 45° upward.

M’, R, U, R’, U’
M’, U, R, U’, R’

I’m finding a problem where this doesn’t necessarily solve it all. But for now, it’s a good start. Perhaps I’ll edit this again in the future.

Clover Pyraminx Algorithms

Posted in Algorithms, Blog, Cubing on January 15, 2021 by slateman

This puzzle looks cool, turns wonderfully and appears simple enough. While it’s effectively just a 3×3 shape mod, I simply cannot visualize it as such. This tutorial helped me whittle the whole thing down to something digestible.

Step 1: Solve two-colored edges

These act like corners, so just find the proper plane and solve all three two-colored edges. This is an easy step and no image is necessary.

Step 2: Flatten Petals

Now you will be faced with one of three situations. If the two pieces are beside one another like shown here, place them on the right plane. Move this right side down, then move the bottom/left layer (here, the other green petal) down, then back up and up (R’, L, R, L’)

The second scenario is when the two incorrectly-placed pieces are on adjacent faces. Hold the tip of the triangle at you and the upright petals on the top-left and top-right. With the one stickered side facing you positioned on the left, turn this layer down 90°, then the right layer a full 180° and return the first face. I’ve included a video here for easier reference.

A third scenario exists where they’re on adjacent layers but on the same pivot. In this case, move one side away so it mirrors scenario #2. I believe this will be an easy fix.

Step 3: Solve all Petals

This step will involve either a two or a three-cycle. For the latter, hold pyramid tip at you, this swaps far left, top center and far right. Shown here, it’ll exchange the left red piece, the top yellow and the right blue. Do 180° flips between the two layers (DDUU – L2, R2, L2, R2). This is kind of intuitive and while it may involve commutators, for your basic purposes, it’s not difficult.

Now, sometimes you will encounter three that you can’t easily swap. You have two options here. A three-cycle may work (for instance, swapping two blues at once). But if you’re lost, which I often get, you may benefit from some two-cycles instead. Here, bring a face down with a 90° turn. This will look like a person wearing glasses looking at you (see pic). Now, your three-cycle maneuver (clockwise or CCW based on your needs) will cycle these just as you’d hope. This is a really-quick fix as, like before, you can swap the same-colored pieces to maneuver what you want without much thinking.

Step 4: Solve Centers/Corners

Any inverted (jutting out) centers here signify a hidden piece under a pyramid tip. Find it! OK, now leave it hidden in the tip of the pyramid. You are now going to swap this hidden piece with one that is jutting out, making sure the inverted piece is on top, also shown here. You’ll reveal it w/ a 90° right turn upwards (like shown in this image), then the usual algorithm (R, L’, R, L) but you’ll do this three times. This will also swap the two lower-layer centers as well, FYI. Do this as many times as necessary. You may get lucky and solve the puzzle this way. If not, move on to step #5.

Step 5: Swap Centers

Now that everything is flat, we can swap centers. You’re going to use the same algorithm as in step 4, but you don’t want to kick out those inverted pieces. First, find two centers you want to swap. (If you have more, just choose two and then repeat this step). Place these in front of you on the bottom as shown here. In order to prevent bumping out those inverted pieces, turn the top layer 90°. This way, those inner pieces will harmlessly swap. Do the same algorithm as before (again, three times) and your two bottom centers will be exchanged.

Petal Pyraminx Guide

Posted in Algorithms, Blog, Cubing on January 1, 2021 by slateman

This little puzzle isn’t altogether too difficult, but it’s a good-enough challenge. As always, I need a little help to push myself through these and I will inevitably forget it all. For the sake of posterity, here are the instructions I’ve worked with, alongside some help from this tutorial.

There are only really four major steps to solving this puzzle: two on the Pyraminx portion and two on the inner circles. Step 1 is just matching the tips. This is easy. Step 2 gives me trouble sometimes because, unlike a Pyraminx, you can’t just rotate the tips when need be. Here’s what I do:

Get one face. Once done, you will have either all edges solved, 2 wrong (flipped) or 3 wrong. Usually it’s the latter.

Move the 3rd side to the bottom (requiring two turns) / Then do a standard d/d/u/u / Move the 3rd side back.

If you did it right, all will be properly positioned. However, many times you’ll have two edges flipped. Holding them on the left and right, do L/R’/L’/R – then U’/R/U/R’. This is the normal Pyraminx alg.

  1. Situate tri-color tips so they’re all aligned.
  2. Solve the 6 two-sided edges to match those tips.
  3. Solve small inner-circle triangles.
  4. Solve large inner-circle triangles.

The tutorial shows how to swap those large triangles around. It’s not super intuitive for me and this is the hardest step for me. Here’s the timestamp in the video where he discusses this, but he places the swapped large triangles on the top of the front layer, and on the left of the top. You’ll perform this using the right layer of the side facing you. When you do it, this must bring the large triangle you want to swap up with it. If not, something is wrong and it won’t work. In this photo, the triangle is positioned properly.

Up, Circle Right
Down, Circle Left
Up, Circle Right
Down, Circle Right
Up, Circle Left, Down

All the circle rotations are done on the top layer, FYI. Good luck!!!

Skewb Ultimate Algorithms

Posted in Algorithms, Blog, Cubing on December 13, 2018 by slateman

I grabbed this little guy while in New York and, it being a Skewb variation, I quickly ran into troubles. Not quire sure what’s up with these friggin’ things, but my brain breaks a little bit, particularly this dumb dodecahedron. It didn’t help that after getting a few steps in, I kept getting confused by orientation and the tutorials out there leave a bit to be desired. Not knocking their content – but they’re not too organized. Anyhow, here’s my solution, which will likely require some tweaking before I forget how it’s all done. That’s kinda silly though, as it only really requires the same one algorithm all Skewbs need. R’, L, R, L’. You can reverse it (L, R’, L’, R) for step 2.

Step 1: Solve an X
This isn’t so bad, though sometimes moving an item out of the way takes a second. This should really be intuitive, but worst case, you might have the piece in the correct spot but not oriented.

If so, move it up to the opposite side. If moved to the right, rotate counter-clockwise, if on the left, CW. Then bring it down and fix the initial turn. Note, if the color you want is facing up when starting this, you’ll have to do this step twice. You can situate all four without breaking one another. This is the easiest step and even if you mess it up, it’s easy enough to fix before moving to step 2.

Step 2: Position remaining centers
This will swap the top and front centers as well as the left and the right. You’re going to use the X you’ve just solved as a starting point for the bottom layer: hold that with your thumb on the bottom. As these centers can have a vertical or horizontal black line (between stickers), it’s easy to get the orientation messed up. However, just keep that thumb on the bottom X as a starting point.

Now, if you’re smart enough, you can plan this out. I, on the other hand, just keep bringing the top piece down to its correct spot (and messing up the rest in the process) until everything is right. Don’t worry about orientation – just getting them in the right spot. You’ll know which algorithm to use based on its upper-level orientation. If the piece you need is on the left face, start with a R’ to bring it to its position. If on the right, start with L. This takes a few tries, but it’s easy.

Step 3: Orient top-layer X
Still using your bottom facing down, you now have 4 corners correctly positioned and oriented and now your goal is the remaining 4. This can be a pain. Figure out the top-layer colors (here they’re pink and green) and you want there to be two on one face. In this photo these stickers are close, but it could be on the other side where they are farther apart. (Close = they’re adjacent to a horizontal face, far is if they’re adjacent to a vertical face) These can be any combination of those colors too. G,G/P,P or how it is here, one of each. You’ll put these on the left side and rotate the puzzle clockwise (if looking from the right) so that the bottom piece (thumb still on it!) is now the crossroads for this algorigm.
Doubled algorithm this time: R’, L, R, L’ (x2).

If you have no doubles, which is likely, find one sticker you want. If it’s on the left, start with the R’ version of the algorithm and vice versa. I believe this should consistently give you a usable pair.

Step 4: Orient remaining centers
The very same algorithm will be used to rotate centers. This will flip four centers: U, F, L and R. If you only have two, you’ll be doing this algorithm twice – by fixing one and breaking three others (3+1=4).

Get the four centers U, F, L and R as mentioned and rotate up slightly. You will be performing this algorithm on a properly-oriented side as shown here. Make sure the top and front centers are part of the algorithm (sometimes I do this and my F layer is on the bottom – ensure that it’s part of your algorithm!) Do the same algorithm 6x. Every so often you will have four mis-oriented centers in a row and not a plus pattern. Despite having four, your goal, you still have to perform this step repeatedly. Use your intuition to figure out which to fix so to prep yourself for a proper final step.

Good luck!