dudefaceguy
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- Feb 17, 2019
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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
Update: 8355 is easier than Heise for beginners. It's related, so you can easily transition to Heise later on.
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:
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:
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:
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:
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:
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 guide for the semi-intuitive corner method I use for Roux:
EDIT: Graphic updated
Update: as of 2024 I'm using the above 2-look CMLL system that uses 7 algs and averages about 15 moves.
www.speedsolving.com
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.
https://www.speedsolving.com/threads/intuitive-4x4-method-with-parity-avoidance.73049/
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:
www.speedsolving.com
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!
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
Update: 8355 is easier than Heise for beginners. It's related, so you can easily transition to Heise later on.
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)
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.
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
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
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:
- Place one corner in its solved position so that it is correctly permuted.
- 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.
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:
- Turn the top face one quarter-turn, then solve using one or two commutators.
- Solve a different corner using an odd number of quarter-turns, then solve with one commutator.
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 guide for the semi-intuitive corner method I use for Roux:
EDIT: Graphic updated
Update: as of 2024 I'm using the above 2-look CMLL system that uses 7 algs and averages about 15 moves.
Alternative 2-Look CMLL: Permute-First
This is how I do 2-look CMLL in Roux. I prefer intuitive solving, so I've never done a CFOP solve, and I don't have any preference for orientation before permutation. I think permutation first is easier and more intuitive, and it also has a much lower move count. Advantages: Significantly...
www.speedsolving.com
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.
https://www.speedsolving.com/threads/intuitive-4x4-method-with-parity-avoidance.73049/
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:
Intuitive 3-Style as a Beginner Blind Method
I recently learned 3-style as my first blind method. I did it completely intuitively, without memorizing any algorithms. This is an explanation of what I did, and a collection of the resources that I used. I hope that it will be helpful to others who want to learn 3-style intuitively for fun...
www.speedsolving.com
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!
Last edited:
