Archive for the Algorithms Category
7 Axis Puzzle Algorithms
Posted in Algorithms, Blog, Cubing on June 13, 2025 by slatemanThis puzzle is a simple, light, addition to my collection. Sengso is putting out a lot of these lately and I’m quite enjoying them. While the first steps of this solve are simple (it just requires 3x3x2 algorithms), the last layer needs some more finesse. So, here’s what you need to know to solve the 7 Axis, pentagonal-shaped puzzle.
Step 1: Solve first-two layers
- This works just like a 3x3x2. Get the center layer completed intuitively.
- Then match bottom-layer edges
- Then position bottom-layer corners (R2, U, R2, U’, R2)
Step 2: Solve Last-Layer Edges (Three-Cycle)
With a flat side facing you, this swaps the L, R and BL edges. This retains the F and BR edges.
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Clockwise:
Counter-Clockwise:
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If you have adjacent edges correct, place one of those in the BR position. This ensures you’ll have one correctly-placed piece and means you’ll be doing this algorithm twice. Figure out which piece needs to move so that the second time you do this, it’ll solve all edges.
Step 3: Solve Last-Layer Corners
This is also a three-cycle. There are two different forms, however:
Case 1: FL, FR, B corners (Triangle) | |
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Clockwise: * BR, R, L, U, L, U’ * R, U, L, U’, L, BR Counter-Clockwise: |
Case 2: FL, FR and BL corners (B & BR safe) | |
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Clockwise:
Counter-Clockwise:
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Maple Leaf Skewb Tutorial
Posted in Algorithms, Blog, Cubing on January 5, 2025 by slatemanThis puzzle is a mostly-straightforward solve, but I got quite stuck at one certain point. It is similar to the Polaris Cube or Skewb Mixup in that you can’t do much without performing half-turns. That plus the fact that it’s a Skewb made the Skewb Mixup one of my lesser-liked puzzles, but this one is a bit more challenging. Here’s how I solved it, addressing the concern when we get to it.
Step One
For me, I got each center individually, but that became an issue with the final two centers. So, next time, I may instead just get the four triangles of each center. This would leave the petals to solve later. Remember, you can always see which side is which due to the colored plastic underneath.
Step Two
Solve those petals. In this case, there’s an algorithm which will do a three-cycle. This maneuver will move the red petal –> green petal –> white petal – so a counter-clockwise of those positioned petals.
- Move white up adjacent green
- Swap and return centers
- Move red down adjacent green
- Swap and return centers
- Repeat the same steps again (R/R’/L/L’ (x2))
Of course, this can be done in reverse (L/L’/R/R’ (x2)) to do a counter clockwise swap.
As you get to the very end, you may need commutators to move things around.
Step Three
Solve a Skewb. Have you forgotten how?
- Solve the white face intuitively
- Get yellow top corners
- Try to get headlights on yellow top
- If so, put them on right and do this:
- If not, do this once to get headlights and then do this:
- R’/L/R/L’ (usual down/up/down/up)
- Then aim to move opposite colors with the same algorithm but…
- R’/L/R/L’ – then turn 180° and repeat
Shengshou Pentahedron Guide
Posted in Algorithms, Blog, Cubing on June 9, 2024 by slatemanEDIT: I had a far-too-complex solution here, but it turns out that for the two and three-layered versions, things are quite simple. I solved the four-layered and haven’t tried the five yet. For now, a quick refresher – which works just like a 3x3x2. (Tutorial help if you need it) Also, here’s the link to the Four-layered tutorial
- Get White corners
- Insert centers (3x3x3 alg: R, U, R, U’, R)
- Swap centers or corners
- R, U, R, U’, R (rotate cube CCW), R, U’, R, U, R
- Depending on what you start with (corner or edge), it’ll cycle accordingly.
Helicopter Dodecahedron Algorithms
Posted in Algorithms, Blog, Cubing on May 27, 2024 by slatemanAt 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.
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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.
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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 slatemanFor 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 slatemanThis 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 slatemanI 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 slatemanThis 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!
- Solve centers (like a 4×4)
- Solve edges (like a 4×4)
- Return to Cuboid (like a 3×3)
- Make sure your two middle layers are all perfect
- Solve inner-edge pieces (I struggle here)
- Position inner-lower layer ‘cross’ segment (LL is not necessary yet)
- Then solve inner-lower layer edges (like a 3x3x2): R2 / U / R2 / U’ / R2
- 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
- Middle-Layer Parity (If necessary): Uu2 / R2 / F2 (Uu2 / U2) F2 / R2 / Uu2 / F2
- Now bottom cross (intuitive)
- Bottom edges (just like step #7)
- Repeat Headlights & inner edges steps (#8)
- 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!