Archive for the Algorithms Category

6×6 Pyraminx Algorithms

Posted in Algorithms, Blog, Cubing on December 29, 2025 by slateman

I quite enjoyed the 5×5 Pyraminx so I thought the 6×6 might be fun. I wasn’t prepared for it to be such a different, unique solve. I’m going to try to break down how I did it, having bastardized some other suggestions. Still WIP.

Step One: Solve Centers

This can be a bit of a challenge for me. Getting two centers is fine, it’s those last two. Important to note: Make sure centers are proper. My first solve had swapped centers, so I couldn’t solve without breaking it all.

If you get one center edge swapped, here’s what you do. In this image it’s yellow and green. In this position, you could just bring the top yellow down to the green, but you don’t want to do that just yet. Move the front face with the yellow center clockwise or ccw so the wayward green piece is out of the way. We’re going to do a pair of D/D/U/U algs. In this pic, the yellow on the top face is on the left side, you’ll start on the left. Do a D/D/U/U moving the yellow down to a dummy/properly-placed front-faced yellow piece. Then move the front face back so the incorrect green piece is on the top (where it’s shown in the pic). Do the D/D/U/U again, but now start on the right. This will reverse the swap and you’re golden!

Step Two: Get Three Edges

For this, you’ll be matching these three red/yellow edges here.

Find your piece, position it on the right or left and bring three layers down to put it adjacent to the center edge. Next, move your entire top layer away from the tip you just turned. If you’re matching on the right, then move top layer left and out of the way (and vice versa). This is like a 4×4 edge-match, where you’ll replace it with another mismatched edge. You’ll eventually have to figure out what to do if you have only two edges left, but that’s for a different day. Keep matching these until you get them all sorted out. You could always do two at once, if you’re smart. 2025 me? Not so great. Oh, here’s a link to a video if you need.

Step Three: Get Inner Edges

There are four green/blue pieces shown in the pic above, but we’re talking about the inner pair. The outer pair can be matched by turning the tips after this step. Easy.

For the inner pair, this is a simple D/D/U/U algorithm, as these are not deeper cuts. Just do it properly to retain the center tips. It’s pretty simple.

Step Four: Final Edges

This is going to be the outer green/blue pieces shown above. This is just a wide D/D/U/U matching. Same as before.

Step Five: Pyraminx Time

Though this is reduced to a Jing’s Pyraminx, it’s just really regular Pyraminx algs. If you need to swap four centers, give it a D/D/U/U cycle three times.

If you have parity, I struggle here. For this section, use Super Antonio Vivaldi’s guide, linked by timestamp.

Hanoiminx / 3-Layer Magic Drum Algorithms

Posted in Algorithms, Blog, Cubing on December 16, 2025 by slateman

This is a relatively-simple and rather-fun puzzle that really only requires two steps and a little bit of intuition. Let’s look!

Step 1: Solve Small Edges

If two are flipped (correctly placed, but flipped)

  • Place on top layer, on L and R.
  • Small triangle facing you.
  • R’, L, R, L’
  • U, L’, U’, L

Link with timestamp

Step 2: Solve Triangle Edges

Mostly intuitive


Step 3: Solve corners

Three-cycle

You can do this starting on the right like this photo or on the left. Just a mirror algorithm. For this one:

  • R’, L, R, L’
  • (this positions the green layer piece on yellow)
  • Move the yellow triangle to the next spot (clockwise here)
  • L, R’, L’, R

5-Layer Pyraminx Algorithms

Posted in Algorithms, Best / Worst, Blog, Cubing on October 27, 2025 by slateman

5-Layer Pentahedron Guide

Posted in Algorithms, Blog, Cubing on June 22, 2025 by slateman

5-Layer Magic Drum Guide

Posted in Algorithms, Blog, Cubing on June 19, 2025 by slateman

Just images for now until I can figure it all out. This puzzle has perplexed me!

7 Axis Puzzle Algorithms

Posted in Algorithms, Blog, Cubing on June 13, 2025 by slateman

This 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.

Clockwise:

  • R2, U’2, R2, U’, R2, U’2, R2

Counter-Clockwise:

  • R2, U2, R2, U, R2, U2, R2

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)
Clockwise:
* BR, R, L, U, L, U’
* R, U, L, U’, L, BR

Counter-Clockwise:
* BL, L, R, U’, R, U
* L, U’, R, U, R, BL

Case 2: FL, FR and BL corners (B & BR safe)
Clockwise:

  • F, L, R, D, R, D’, L, D, R, D’, R, F

Counter-Clockwise:

  • F, R, D, R, D’, L, D, R, D’, R, L, F

Maple Leaf Skewb Tutorial

Posted in Algorithms, Blog, Cubing on January 5, 2025 by slateman

This 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 slateman

EDIT: 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

  1. Get White corners
  2. Insert centers (3x3x3 alg: R, U, R, U’, R)
  3. Swap centers or corners
    • R, U, R, U’, R (rotate cube CCW), R, U’, R, U, R
  4. 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 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.