# Intuitive Cubing Resources

#### dudefaceguy

##### Member
What is intuitive Cubing and why would you want to do it?

Intuitive cubing is solving without using memorized algorithms. If you want to solve with world-class speed, you need to memorize algorithms. But if speed is not your main goal, then there are several reasons to solve intuitively:

1. If you take a break from cubing, you will forget most of your memorized algorithms. If you want life-long skills, learning intuitive concepts will serve you better.
2. You may find that memorizing algorithms is tedious and unappealing.
3. You will learn some cool concepts about how the cube works.
4. Solving intuitively is a lot of fun, and presents a constant challenge since you don't have a memorized solution for each case.

If you want to have a lot of fun developing skills that will last a lifetime and learning about all of the cool puzzles that exist, I recommend intuitive solving. This collection of resources includes beginner, intermediate, and advanced techniques.

Intuitive Solving for Absolute Beginners

Heise Method

Heise Method is a completely intuitive method for solving the 3x3 cube. It was the first method I learned, and I recommend it as a beginner method with some modifications. Since this is an intuitive solution, you will need a bit more patience and curiosity compared to beginner solutions that solve algorithmically.

I made a video tutorial of the beginner Heise method, for people who have never solved a cube before:

Since the first steps of Heise are too complicated for a beginner, I follow Petrus Method until step 4a, then finish the last layer with Heise Method beginning at Heise step 3 and using the “edges first” technique. Here is a short summary of this beginner method:
• Solve a 2x2x3 block
• Orient edges
• Solve another 1x2x2 square, to make the first 2 layers minus one corner-edge pair
• Use the unsolved “keyhole” pair to solve the last 5 edges
• Solve the last 5 corners using commutators (more about commutators below)
Ryan Heise’s guide to fundamental solving techniques is also very helpful: https://www.ryanheise.com/cube/fundamental_techniques.html

You may get stuck on step 3 of the Heise method (step 4 in my summary above). Here is a simple heuristic to make it easier. In order to finish solving edges in 3 moves, you need to have exactly 3 unsolved edges: 2 in the top layer, and 1 in the keyhole. If you have 2 or 4 unsolved edges, here is a trick to convert to 3 unsolved edges every time:
• Make sure that you have a top-layer edge piece in the keyhole, and all edges are correctly oriented (i.e. the top-face color is on top).
• Note the color of the side sticker on the edge that is in the keyhole spot. For example, if the top face is blue, then the side sticker is the sticker that is not blue.
• Find the edge on the top layer that has the opposite-color side sticker. Red is opposite orange, blue is opposite green, and white is opposite yellow.
• Move the edge in the keyhole to the top layer adjacent to its opposite piece, then move the opposite piece into the keyhole.
• Adjust the top layer until you see 2 solved edges in the top layer.
You can then proceed to solve the top-layer edges in 3 moves by replacing the unsolved top-layer edge with the edge in the keyhole, and putting the keyhole edge (i.e. the edge that does not belong on the top layer) into the keyhole spot.

Commutators

Commutators are essential for intuitive solvers - they move sets of 3 pieces, or flip 2 pieces in place, without disturbing the rest of the cube. Once you learn how to design commutators, you will be able to solve almost any case on any cube. Luckily there are many excellent resources for commutators, including the following:

Parity

Parity is an interesting concept from group theory, referring to the number of swaps required to sort a permutation (i.e. a puzzle or other mess). If you can put all of the pieces in the right place with an even number of swaps (3 unsolved pieces are solved with 2 swaps), the puzzle has even parity, and if you need an odd number of swaps (2 unsolved pieces are solved with 1 swap), it has odd parity. Odd parity cases cannot be solved directly with pure commutators. Heise method fixes parity so cleverly that you can ignore it; if all you want to do is solve a 3x3, you don't really need to know about parity. But if you want to solve some other types of puzzles, or do other events like blindfolded solving, you will need to be able to convert between even and odd parity. I cover specific parity cases in my intuitive methods for 4x4 and blindfolded 3x3 solving. The main thing to know about parity on the 3x3 is that any single quarter-turn of any face will convert the cube between even and odd parity.

Here are some resources explaining parity in general as a concept:

Ryan Heise’s parity explanation:

https://www.ryanheise.com/cube/parity.html

A cool video about group theory and the concept of permutation parity in general:

A long essay about 4x4 parity:

https://hlavolam.maweb.eu/parity-problem
But what if I want to be fast and intuitive?

If you want a speed cubing method that is both fast and intuitive, I recommend Roux. The entire method is intuitive except for solving the corners of the last layer. Most Roux solvers will use an algorithm set called CMLL to solve corners, but you can solve corners using only commutators. It’s not particularly fast though – I got to about 50 seconds using Roux with this corner method, before switching to the semi-intuitive method I describe further down the page.

How to solve corners on any cubic puzzle with only commutators

The Heise method forces corners to have even parity by solving edges first. If all edges are solved on an odd-layer puzzle (e.g. 3x3, 5x5, 7x7) then corners will always have even parity and you can just use commutators exactly as you would in Heise. But if you want to solve corners without solving edges first (as in the Roux method), or solve corners on even-layered puzzles in which corner and edge parity are not linked (e.g. 2x2, 4x4, 6x6), they you will need to learn a little bit about parity.

First, determine corner parity like so:
1. Place one corner in its solved position so that it is correctly permuted.
2. Examine the other 3 corners. If exactly 2 are out of place and the last is twisted in place or solved, the corners have odd parity. All other states have even parity.
Even parity cases can be solved directly with 1 or 2 commutators.

Odd-parity cases cannot be solved directly with commutators, but every quarter-turn of any face changes corner parity between odd and even (180-degree turns like U2 count as 2 quarter turns and do not change parity). This gives us two basic options for solving odd parity cases:
1. Turn the top face one quarter-turn, then solve using one or two commutators.
2. Solve a different corner using an odd number of quarter-turns, then solve with one commutator.
You can sometimes solve a different corner in one quarter-turn, but if not, then you will need 7 quarter turns (e.g. a conjugated 4-move commutator such as [F:[R,U]] plus one quarter-turn, or an 8-move commutator minus one move). A conjugated 4-move commutator is also useful for solving a single corner quickly if you have even parity and 4 corners unsolved.

Semi-intuitive corner method

If you can stomach learning just 2 algorithms, these two will make your life a lot easier: Niklas and Sune. Niklas is just a commutator with the last move left out, and is useful for converting a cube between even and odd parity. Sune twists 3 corners in place quickly and easily, solving an otherwise annoying case. These two algorithms, combined with corner twist commutators and a 4-move commutator, can solve corners quickly.

Sune: R U R' U R U2 R

Niklas: R U' L' U R' U' L

Expressed as a commutator, Niklas is [R, U’ L’ U]. But if you leave out the last U move, then you end up swapping the two corners that were on the left side of the cube. You can then adjust the top layer to put the corners back into position.

Here is a flowchart of the semi-intuitive corner method I use for Roux:

This is based on Lars Perus’s corner method, which contains a good explanation of how to use Niklas and Sune together to solve corners: https://lar5.com/cube/fas5.html

My method does not care about edge orientation, so I use a conjugated 4-move commutator (for example [F:R,U]) to swap diagonal corners, instead of his Eve algorithm. Since the move R U R’ U’ is also known as “Sexy Move,” this conjugation is known as FsexyF, which is how I refer to it in the flowchart.

Again, if your main goal is speed, just learn algorithms. But you can get respectable times with this method – my PB is 24 seconds, and I average about 35 seconds with Roux right now. I’ve probably done less than 1000 solves, so I could get much faster if I practiced (and if I were not an old man). There are a few tricks you can use to force a second-look skip, or force a good Sune case in the second look – Lars Petrus’s tutorial explains many of these.

If you ever decide that you want to set some speed records, you can easily learn the 42 CMLL algorithms to solve corners in one look.

Last-layer Edge Permutation

If you want to experiment with other methods such as ZZ, Petrus, or CFOP, you might need to solve last-layer edges after corners. If all edges are oriented, you can solve 3 unsolved edges as a conjugated 4-move commutator, for example: [M2 U: M’,U2]. Move cancellations will make this a 7-move sequence. For other cases, you can variations on Roux LSE (last six edges) or 8-move commutators.

Method for solving 4x4 and larger cubes intuitively

In an effort to avoid learning a parity algorithm, I created this fully-intuitive big cube method which requires no algorithms. It’s a lot of fun, and I average about 2:10 with it right now. It will solve any NxN cube intuitively.

Intuitive blindfolded solving

You may think that blindfolded solving is for savants or hardcore world-class solvers, and is too difficult for a casual solver like yourself. But blindfolded solving is actually perfect for an intuitive solver because you can solve the entire cube using only commutators. As an intuitive solver who is already familiar with commutators, you can start with the most “advanced” blind method, which is based around commutators: 3-Style. This may be “advanced” for a speedsolver who only knows how to solve using memorized algorithms, but for an intuitive solver, it is actually extremely simple. All you really need to learn is 1 interchange and 4 insertions each for edges and corners, making 8 types of commutators in all.

I made a separate post explaining how I learned 3-style intuitively, here:

Solving Other Puzzles Intuitively

You can solve many other puzzles using these principles. For example, you can solve the Megaminx using Heise with almost no modifications. Solving 3x3 shape mods using Heise is also very entertaining – this method makes it easy to deal with puzzles in which center orientation matters.

Some 3x3 modifications will have pieces that have false equivalency, which can seem to cause parity problems (e.g. the Penrose cube). You should be able to solve these cases easily using the knowledge above.

If you want to explore other types of twisty puzzles, I recommend Youtuber Superantoniovivaldi, who is an intuitive solver and enthusiastic collector of unusual puzzles. He often gives detailed explanations of his intuitive solves.

Go Have Fun

This by no means an authoritative or definitive guide – it’s just some resources that I’ve found or figured out. The main point is that you don’t have to be fast to have fun.

The vast majority of cubing resources are modeled on the top cubers in the world, and are focused on the relentless pursuit of speed. But it’s okay to just chill out and have fun – use sub-optimal techniques, figure things out as you go along, and build skills that will last a lifetime even if they won’t get you a podium finish. I hope that other intuitive cubers will share their techniques and tricks. That’s it so far – have fun!

#### WarriorCatCuber

##### Member
But... But... Squares and matching them while doing EO are Heise's easiest steps!

#### dudefaceguy

##### Member
But... But... Squares and matching them while doing EO are Heise's easiest steps!
That may be true, but Petrus is easier still. Unmatched squares are too complicated for a beginner who has never solved a cube before. Saving 8 moves or so is completely useless for a beginner - it’s more important to have an easy F2L. When they are ready they can explore the full beauty of Heise.

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#### guelda

##### Member
Hi Dudefaceguy, quite new to cubing, your last posts about intuitive 3-style and intuitive cubing are exactly what I was looking for! Thank you so much for this great job and for sharing it, much appreciated!

#### dudefaceguy

##### Member
Hi Dudefaceguy, quite new to cubing, your last posts about intuitive 3-style and intuitive cubing are exactly what I was looking for! Thank you so much for this great job and for sharing it, much appreciated!
That's great to hear - I'm so glad that you found them useful! I hope you have a lot of fun.

#### dudefaceguy

##### Member
I've been working on one-handed solving using ZZ, which has been a lot of fun. My times are terrible of course (over a minute), but I've come up with some really fun ways to do edge permutation. There are only 3 basic cases, all of which are solvable with combinations of simple commutators or entirely intuitive triggers, as in Roux 4c.

Since I usually do one-handed solving while standing up on the subway, I want to use techniques that don't use table abuse. So, I am using S' moves instead of M moves. The problem with this is that I can do S' easily (after some practice), but not S. So I had to get creative with the move set and introduce wide moves to avoid S moves.

After accounting for some move cancellations, I came up with these fun algorithms. I like them because two of them flip the cube orientation - you end up with a solved cube flipped upside down or backwards, which doesn't matter because it's always the last alg you do.

The most frequent case of 3 unsolved edges (conventionally called a U perrm) can always be solved with a conjugated 4 move commutators, in the form [R2 U: S', U2]. Taking advantage of cancellations, this becomes R2 U S' U2 S U R2. But I had to eliminate that S move, so I eventually figured out that I could do Dw2 instead of U2, which effectively converts the S into an S'. The alg would then finish with Rw2, making the following final alg: R2 U' S' Dw2 S' U' Rw2. The solved cube is flipped upside down.

I used a similar technique for the case of 4 unsolved edges permuted to adjacent rather than opposite positions (covnentionally called a Z perm). This can be solved intuitively with two 4-move commutators. The full process looks like this: [M2, U'] M2 [E2, M']. With one cancellation, it is the slightly more efficint M2 U' M2 U E2 M' E2 M'. The obvious problem with using this in one-handed solving is that E moves are very difficult to peform. Similarly to the algorithm above, I converted this to S moves instead of M moves, took advantage of cancellations, and added wide moves to avoid E moves. The resulting alg is S2 U' S2 U' D2 S' U2 Uw2 S'. The solved cube is flipped backwards.

The last case of 4 unsolved edges permuted to opposites sides is trivially solvable with [S2 U2 S2, U'].

Of course, these are all useless for competitive speed solving because it's easier to use M moves with table abuse. But it was a lot of fun to come up with some ways to solve these cases that work well for my own purposes.

#### newtonlkh

##### Member
Thank you!!! I am so grateful to be able to find you QTPI video and then this post!! I feel so alone in cubing groups because others only care about speed. ("Why commutators? Just do 4LL") ("Just do CFOP") ("Avoiding parity is possible but not worth it, just do the parity Alg"). Finally found someone who shares my passion!

Emotions aside, may you share some insights on how to solve 4a (EO) of Roux intuitively? I was told by many that it is intuitive, but I find myself spamming MUM moves and their primes. But I can't get a system to think what should I do. I tried sitting down with paper and pencil to write cases and find ways by I don't even know how to work on this step.

Also want to add that, to me, the beginner version of Heise, is 8355. I am currently solving with step 1-2 of CFOP, and step 3-4 of Heise.

#### WarriorCatCuber

##### Member
Thank you!!! I am so grateful to be able to find you QTPI video and then this post!! I feel so alone in cubing groups because others only care about speed. ("Why commutators? Just do 4LL") ("Just do CFOP") ("Avoiding parity is possible but not worth it, just do the parity Alg"). Finally found someone who shares my passion!

Emotions aside, may you share some insights on how to solve 4a (EO) of Roux intuitively? I was told by many that it is intuitive, but I find myself spamming MUM moves and their primes. But I can't get a system to think what should I do. I tried sitting down with paper and pencil to write cases and find ways by I don't even know how to work on this step.

This tutorial should help!

#### newtonlkh

##### Member

This tutorial should help!
It really helped!!! His explainations are ingenious!! So simple yet so effective. I've watched about 3-4 Roux 4a videos, some up to 4 times, but nobody teaches that as clear as Kian did!!! Thanks for pointing me to this!

#### WarriorCatCuber

##### Member
It really helped!!! His explainations are ingenious!! So simple yet so effective. I've watched about 3-4 Roux 4a videos, some up to 4 times, but nobody teaches that as clear as Kian did!!! Thanks for pointing me to this!
No problem!

#### dudefaceguy

##### Member

This tutorial should help!
It really helped!!! His explainations are ingenious!! So simple yet so effective. I've watched about 3-4 Roux 4a videos, some up to 4 times, but nobody teaches that as clear as Kian did!!! Thanks for pointing me to this!
I was about to link Kian's video but I see that WarriorCatCuber beat me to it. Once you understand the arrow case and the two triggers used to get there, it's very intuitive.

I'm very glad that you found my posts useful! I knew there was at least one other person out there like me. And thank you very much for your kind words - it means a lot to me. I hope you'll post more about your own cubing style.

Cool that you're doing CFOP+Heise - I also like to mix and match methods. I used to use ZZ+Hesie as my one handed method. Now I'm back to Roux for OH since I figured out how to do S moves (I start with my knuckle under the S layer). But I still do ZZ sometimes because it's fun.

#### newtonlkh

##### Member
But... But... Squares and matching them while doing EO are Heise's easiest steps!
I find that step SOOOO difficult!!

#### dudefaceguy

##### Member
I find that step SOOOO difficult!!
Heise actually says on his site that making matching blocks is usually the best choice, since that allows you more options for subsequent steps.

So, you can just do Petrus.