#### PetrusQuber

##### Member

I think it's been coming for a while. As of right now, there have not really been many guides to Petrus, even fewer written ones, and even fewer modern ones. For reference, I average low 13s with Petrus as my main method, in case anybody would question my speed. Petrus is not a popular method though, bear in mind, I might even be one of the fastest Petrus user who uses it as their main method right now.

Anyway, I hope you find this guide useful.

Spoiler: Introduction

Petrus is a speedsolving method invented by Lars Petrus in the 1980s, with a heavy emphasis on free blockbuilding - intuitively solving blocks on the cube to bring it towards the solved state. It is part of the 'Big 4', 4 of the most popular and extensively researched methods. However, Petrus does not have anywhere near the number of users as the most popular method in the Big 4, CFOP - it may even be a couple of orders of magnitude out. This is due to many people believing Petrus to be inferior to the other 3 most popular speedsolving methods, and the rest simply not even coming across the method, as a result of its lack of popularity. And so, Petrus has never obtained any relatively fast averages, collections of guides, or users. The original steps are as follows:

1. Blockbuild 2x2x2 block anywhere on the cube

2. Expand that 2x2x2 block to a 2x2x3 block by blockbuilding a new 2x2x1 block onto it

3. Solve the EO of the cube so the cube is reduced to 2 gen solving, and skips EOLL

4. Using only R and U moves, solve the rest of F2L (usually done by blockbuilding another 2x2x1, then using algorithms to solve the LS)

5. Solve LL. This can be done in many ways - the original being: Solve CP, solve CO, solve EP (an inefficient strategy). Most Petrus solvers either use OCLL + PLL, COLL + EPLL< or ZBLL.
Spoiler: Petrus' Pros and Cons

A method will always be more suited to certain types of people, will always have a certain style of solving, and will always have pros and cons. Petrus is not an exception, however people may choose to believe.

PROS

- Has lower movecount than most viable speedsolving methods

- Very intuitive, not many algorithms needed to be fast

- Orienting edges during solve means fast RU turning during F2L

- Orienting edges during solve means faster LL, and possible 1LLL (ZBLL)

- Being intuitive, it is a lot more flexible than, say, CFOP. This means it almost always has better solutions - having lots of base algorithms may be easier to execute and memorise short term, but are less efficient long term

CONS

- Optimising blockbuilding and getting faster with it is quite hard, harder than simply memorising algorithms and drilling them (blockbuilding at high levels is basically lots and lots of algorithms/basic cases!)

- Until all basic cases and setups are learnt (which might be never), figuring out unique solutions throughout a solve will impact TPS considerably, and if TPS is raised, solutions may become worse and more rushed

- Fingertricks will not really be optimal, especially during the first block. Expect sometimes awkward starts.

-In general a lot harder to use than most other methods, with undefined worth (if speed is your sole goal, Petrus has not yet been proven to match up to other methods).

-3 different intuitive steps, 2 different algorithmic steps. That's a lot of practising unique steps, unlike CFOP for example, where F2L (the main part of the solve), uses the same algorithms, for 4 more or less identical pairs.

Petrus is not for people who just want to be fast, people who don't like working things out themselves, or for people who get frustrated easily.

Petrus is for people who enjoy learning how the cube works, want to use a unique method, want a challenge, or want to feel more like they are actually solving the cube themselves, without using many pre optimised algorithms
Spoiler: Essential starting advice for Petrus

Be Colour Neutral. Petrus relies on being able to solve efficiently in all situations, there is no hope for it if it loses its main advantage over other methods. You might as well be using beginner's method if you aren't colour neutral with Petrus. It might be hard, but it'll be well worth it. Actually, here, colour neutrality and block neutrality (BN) are two different things (though one leads to the other). I could be CN, but only able to choose two blocks - RWG and OYB (note they include all the colours). I could be BN, but only able to solve starting on white and yellow (covers all 8 possible blocks). But like I said, CN leads to BN. So learn to be able to pick any starting 2x2x2 block, and to be able to solve that block on any colour, for optimised finger tricks and positions.

If you really don't think you can do it, then try dual CN and BN. You can pick any 2x2x2 block but only solve on white or yellow for the solve. Ideally, you'd be able to switch between the two colours, for the top 2x2x3 expansion.

For Petrus, you need to know what you're getting into. Getting fast won't be easy. If you don't really like the idea. don't do it. Check out the paragraph above this for who Petrus is for. It's no good choosing a method then abandoning it halfway through unless you are intentionally doing it for fun/to bring into other methods. You'll have to be dedicated for Petrus, work things out yourself, and accept that there won't be much to help you. You are the person who's meant to be making those guides and resources.

Once you find a nice, comfortable technique for creating blocks, do not get too comfortable with it. Getting comfortable with a couple of basic techniques will make it harder for you to keep learning and inventing new solutions. I sometimes ditch all my pre-tested solutions, as a way to force myself to innovate new ideas. And remember that there's probably always a better way to do your case than what you are doing at the moment when you first start learning Petrus.

And finally, don't be too expectant of yourself. Progress with Petrus could be slow. This is a method which is relatively unexplored and pursued, after all. I suggest that a lot of the time, don't do timed solves, just solve casually, and find new ways of doing something. Solves alone won't cut it. I completely redid my techniques and became a lot slower around the 40 second, 25 second, and 13 (now) second mark. It's worth it. And remember, cubing is for fun. Getting faster times is part of it, not the other way round.

Plus, you improve infinitely faster at something when you're actually motivated.
Spoiler: How to practise

I mentioned a bit of this already in the last part of this guide. And although this isn't really a unique aspect of Petrus, I'm still including it. I'll just go over some points and tips here.

-Solving is not the only way to practise

-TPS, lookahead, and solve fluidity is generally gained with just solving. Do not expect much else out of it. Generally, try not to go for TPS if you don't have the two other aspects. And gaining those other aspects should probably be done without pressure, so try solving more slowly, not timing the solves, or putting the solves in a warm-up session.

-Movecount, algorithms, and weak steps should be improved/learnt specifically, not from solves. If you need to work on your 2x2x2, why spend time solving in other areas when you can practise just that? For movecount, you will definitely not be getting better at it with solving. Solving reinforces habits - whether they are good or bad habits depends. As said before, don't time solves, do some FMC solves, watch example solves, and go slow, looking for optimal solutions.

-Don't force yourself to practise

-Try not to do the bulk of the actual improvement practising early in the morning, late at night, after just having picked up a cube, after doing extensive practising, or when you don't feel like it.

-Upon learning a new technique, remember two things: a. it's better to learn the technique, wait 5 minutes, then practise that technique to see if you remember it rather than learning the technique and practising it straight away (applies to algorithms too), and b. once you've learnt the technique, start using it in solves right away - you won't get better at the technique if you don't use it, and if you're worried about your times increasing for a bit, then don't. If you're using a timer, make a session for casual solves.

-Don't be lazy with practising, don't put off what can be done now. 1 hour of focused, dedicated and varied practising is a million times better than 5 hours of unfocused random solves. (Just an example)

-Have a set goal in mind when practising - you shouldn't just be doing solves and watching some example solves in the hope you'll start to improve, set a specific, reachable practise goal every session, which you can work towards. Having a specific goal means you will reach that goal faster than if you were just solving on the whole(I want to be sub-x is not a valid goal, a goal such as I want to improve my expansion by trying to lookahead more is)

-Be reflective on your solves and keep identifying weak steps and faults. If you can't see anything wrong with your solves, then look harder. Nothing is ever perfect. Whether it be that your expansion takes up a quarter of your solve, or that you just don't like your LL algorithms, there is always something to do.

-Really understand techniques that you got from the outside world - and be able to apply it for yourself and see how it works. This goes with the intuitive side of Petrus and also helps you to be able to use variants of that case, setups, etc

-Be open to all kinds of practising. There are loads of ways to improve, and loads of different aspects of cubing, such as better fingertricks, better algorithms, lowering movecount, making TPS more consistent, trying to see more in inspection, etc.

-Make practising enjoyable for you - however you see fit

-Remember to take breaks once in a while

-When doing solving practise, treat every solve like it has WR potential, like it really matters. Unfocused solves are no good. And at the same time, don't focus too much either - relax, and solve. Being panicked or pressured in a solve does not help. Solving should eventually become an instinct, an unconscious process - you see everything you need to, you know what to do, and you do it. 'Don't think, just solve' - Max Park
Spoiler: The individual steps
Spoiler: 2x2x2
Spoiler: What to look for in inspection

The 2x2x2 is the first step of the Petrus Method. It is generally expected that you are one looking it once you get faster, and can solve it in a reasonable amount of moves without pause (below 8 mostly). Inspection time gives you 15 seconds to consider your options and plan them out. Good solutions may not be obvious at first, and with 8 different possible 2x2x2s as well as infinite ways to solve them, here's a list of things to look out for in inspection.

-Obviously, a completed 2x2x2 block would be very helpful

-A completed 2x2x1 block which just needs to be connected with an edge sometimes happens

-A pair which can easily be made into a 2x2x1 happens a lot of the time

-A solved edge means after creating the 2x2x1 you don't have to waste moves inserting the edge

-A solved partial cross means you can create a pair and insert it CFOP style

-A partial cross which edges just need to be paired up with a single D move (assuming the cross is on bottom) can be turned into the above, or have a corner inserted to create a 2x2x1

-A lined up but not solved edge could be the foundation of two possible 2x2x1s or use one move to turn into a solved edge

-A one move pair will turn into the above pair case

And of course, there are many many more cases like these which you may discover. Often several of these will appear in one solve, and you will have to decide quickly which one to pick. If there are only a few, I generally just quickly look at the follow-up moves and decide what is fastest - if there are many, I just use logic to decide what's best - obviously, a 2x2x1 is better than a solved edge. And if all else fails, just pick a corner and expand it into a 2x2x2, unless the case is exceptionally bad. Continuations of those cases should be left to be figured out as good practise but I will list a few cases in the next paragraph. And do remember that sometimes, you may wish to preserve some cases for your 2x2x3 step, you may find that a few of these may go together (like a solved edge and 2x2x1), you may wish to save the good case for your expansion which you know you are bad at, or you may even think outside of the box and find an extremely efficient but out of the way solution as opposed to the obvious but worse case.
Spoiler: Improving your 2x2x2

Depending on what level you are at, you should probably be focusing on learning new basic cases and implementing them into your solves. It's a good idea to try create the situations I've listed in the previous paragraph and see what you would do in those situations. The line situation, solved edge, partially solved mini cross and pair come up particularly often, and it's good to know how to solve them. I suggest you look at one scramble with one of these in it and use that particular scramble because having different after cases can be confusing. Learning a variant of a basic case and understanding it also means learning how to apply it even when surroundings may be different (e.g. solved pair - there is a lined up edge so you can create a 2x2x1 in one move now, but other scrambles will not be as easy - you may have to setup that easy onemover). Making small changes to your solution or learning where your pair could be before it was in the current situation helps find setups and variants.

At that point, when you start inspecting, you should have a rough idea of what your case is and what you're going to do before fine-tuning and planning out the solution. When just trying to get fast solves, don't go into blind alleys - stick with what you know - this means you already have a rough guideline and can use more of inspection to actually try one looking the 2x2x2 and making it more efficient. Otherwise, when trying to learn new cases, don't be afraid to plunge into new situations and cases - building up your knowledge of how to create blocks is always good. Yesterday, for example, I took one scramble and decided to solve that scramble dozens of times, going down new paths every time. I discovered some interesting solutions and ideas and noted them down for future use. Actually, today I used one of these solutions (it was quite a non-obvious one at first involving a lined up edge and bad F2L case) and without it, I would have to have spent extra time looking for another solution.

One case, in particular, I wish I'd known a long time ago, which will be described later. It came up so often too since it involved a lined up edge and corner adjacent to it, which isn't really very rare.

And when you feel you are satisfied with the number of cases you know, for the time being, you should take the opportunity to practise just solving 2x2x2 a lot, making sure you retain those cases in your memory and use them in solves. This will familiarise those cases even further, before you start the cycle again. (Occasionally this may be bad since it might drill in a non-optimal solution, but habits can be broken).

One looking the 2x2x2 should start to become a priority as you become faster (<25 seconds). Ideally, you know the case you are doing well - meaning you don't have to think too much about how to do it or where the pieces will end up. So knowing lots of basic cases is important. If this isn't possible in a solve, try using as much as you know, and imagine what moves you are going to make in your head. It doesn't have to be the entire 2x2x2 block at first, what you visualise, but something which furthers that goal, such as a 2x2x1. Once you have the moves you are going to do to solve a part of the 2x2x2, reinforce that and make sure you don't forget it. You can use your hands to execute the muscle memory for the solution to build up TPS. Then find the remaining piece/s you have to solve not part of your already planned-out area and see how that piece will be moved/affected by your already planned moves. Either you can choose to do the last part separately (find where your piece goes after you've finished your planned section and plan out how to solve the rest of the cube from there), or include it as part of your entire solution if possible - maybe you find you can stop halfway through your planned solution to insert your final edge, before continuing and not having to waste moves later on.

tl;dr, learn as many cases as possible so you don't need to come up with new solutions and know the solution well already, plan out as much as you think you can, then track the rest of the pieces to see where they will end up, and how to solve them from there (or implement them into the solve).

It may be helpful to not worry about the 15 seconds limit (you can improve that), to close your eyes as you solve the planned out part to make sure you are actually planning it out and to not time at first.

And remember that you can find weaknesses in steps too, not just the solve. If you want to improve the 2x2x2, clearly it's not satisfactory and there is probably a problem with it. Find that specific problem and act on it. If you really can't find a problem, then just focus on learning more cases (though there almost always is a weak spot). For example, you may be rotating too much during the solution. Try to solve while not rotating AT ALL. Yes, it may be faster to rotate and do easier fingertricks short term but that just means your fingertricks for initially uncomfortable movesets are not very good and need to be improved. While RU may be faster than FU, is it faster with the rotations added in? After you've trained yourself to not rotate unnecessarily, don't forget you can still rotate - but do so wisely. Never rotate more than once though. And also consider the option of using wide moves to rotate and do moves at the same time. Wide moves are also decently fast.

And for another occasion, you may not be doing efficient enough solutions (8 moves or less generally) or planning out enough. Refer to the above section.

Plus, just do solves.
Spoiler: Useful and common cases

This is a collection of common cases you may come across when inspecting the 2x2x2. If you wish to take a lesson from this section, you should not just be able to use the case but understand how it works. If you can understand how it works, you may be able to solve variants, make setups, or even find a better solution yourself.

This was created by taking random scrambles, inputting them into alg.cubing.net, and stating the possible cases here, so you won't find any particular order. I advise you to focus on the creation of the 2x2x1 block as the last edge doesn't take much thought. Obviously, you won't be able to just stuff all of these into your memory so understanding the thought process (so you can invent your own solutions on the spot) will be more beneficial.

The best solution will be put in the alg.cubing.net link - anything after the 2x2x2 such as a 2x2x3 pair does not count (since unless at high levels this will not be seen and factored in). Any notation I put in the solutions go from the rotation. And also, the solutions I give will definitely not be optimal. They are a starting point and go from identifiable cases (like a pair), which tend to be efficient. I doubt you'll be seriously looking at all 8 corners in inspection. I see something I can use, I quickly check in cases I missed anything, and go with it. Then you can put more inspection time into memorising the solution, planning out, etc.

Spoiler: Scramble 1

Spoiler: Scramble 2

Spoiler: Scramble 3
Spoiler: Resources

Collection of some helpful sites and videos which may be useful to you in getting faster with the 2x2x2. For now, this is just 2x2x2 specific - general example solves and tutorials will be listed later.

- @Metallic Silver

https://lar5.com/cube/blox.html
Spoiler: 2x2x3
Spoiler: Basics

After the 2x2x2, a 2x2x1 is built which is attached to the 2x2x2, to form the 2x2x3. There normally isn't much time to look for good solutions - the 2x2x2 gets a full 15 seconds - so 2x2x3 solutions tend to be more inefficient, rushed, and basic. Plus the solving of the 2x2x2 tends to break up unpreserved, potentially useful starting points, like a pair (or it is used for the 2x2x2). The key aspects of a fast 2x2x3 are: Not taking too much time thinking over efficient solutions, not rushing, lookaheading from 2x2x2 well and knowing as many basic cases as possible.
Spoiler: Improving the 2x2x3

Generally, solutions should take around 7 moves. And in most solves, the 2x2x2 should end up in the BLD corner with the 2x2x1 expansion in the BRD corner. This allows for an FRU gen solution (mostly RU), clear view of all pieces, and good start to the EO step of the solve.

The 2x2x3 seems to be a popular weak spot for several Petrus users and it's easy to see why. There are 3 pieces to solve, 3 faces to look for them on, no inspection time, and lookahead from the 2x2x2 has to be employed to make the step fast.

So, how to improve?

1. Lookahead from 2x2x2

2. Spend some time checking out and learning basic cases (with less freedom, less chance of good visible starting points, it is significantly different from the 2x2x2 enough that some time should be dedicated to it separately.)

3. Figure out the right balance of speed and efficiency.

For number 1... You'll need to be planning out the 2x2x2 completely and be very comfortable with solving it if you are to start looking at other pieces during the solve. Refer to the 2x2x2 section for advice on how to do this. In inspection, make sure you know the possible 2x2x3 expansion pieces that you will consider, so as soon as you start solving, you can start tracking them. And, you might want to start planning out where 2x2x3 pieces will end up in inspection so you can find the other pieces easier. Honestly, just don't look at the 2x2x2 pieces, and your eyes will find something to do.

For number 2... Solving the 2x2x3 lots of times will accomplish this. You should also check out the resources and cases tab for further insight. Again, make sure you understand them. It's so important you do - you'll feel much more confident using them in solves and applying the knowledge to other similar situations. Do some FMC solves specifically targeting the 2x2x3 step. You might want to do some solves starting with the 2x2x2 solved and using a few seconds of inspection to find some efficient solutions, as well as practising them.

For number 3... You should use your own judgement. I pers
Feedback is appreciated

Anyway, I hope you find this guide useful.

__Introduction__Petrus is a speedsolving method invented by Lars Petrus in the 1980s, with a heavy emphasis on free blockbuilding - intuitively solving blocks on the cube to bring it towards the solved state. It is part of the 'Big 4', 4 of the most popular and extensively researched methods. However, Petrus does not have anywhere near the number of users as the most popular method in the Big 4, CFOP - it may even be a couple of orders of magnitude out. This is due to many people believing Petrus to be inferior to the other 3 most popular speedsolving methods, and the rest simply not even coming across the method, as a result of its lack of popularity. And so, Petrus has never obtained any relatively fast averages, collections of guides, or users. The original steps are as follows:

1. Blockbuild 2x2x2 block anywhere on the cube

2. Expand that 2x2x2 block to a 2x2x3 block by blockbuilding a new 2x2x1 block onto it

3. Solve the EO of the cube so the cube is reduced to 2 gen solving, and skips EOLL

4. Using only R and U moves, solve the rest of F2L (usually done by blockbuilding another 2x2x1, then using algorithms to solve the LS)

5. Solve LL. This can be done in many ways - the original being: Solve CP, solve CO, solve EP (an inefficient strategy). Most Petrus solvers either use OCLL + PLL, COLL + EPLL< or ZBLL.

__Petrus' Pros and Cons__A method will always be more suited to certain types of people, will always have a certain style of solving, and will always have pros and cons. Petrus is not an exception, however people may choose to believe.

PROS

- Has lower movecount than most viable speedsolving methods

- Very intuitive, not many algorithms needed to be fast

- Orienting edges during solve means fast RU turning during F2L

- Orienting edges during solve means faster LL, and possible 1LLL (ZBLL)

- Being intuitive, it is a lot more flexible than, say, CFOP. This means it almost always has better solutions - having lots of base algorithms may be easier to execute and memorise short term, but are less efficient long term

CONS

- Optimising blockbuilding and getting faster with it is quite hard, harder than simply memorising algorithms and drilling them (blockbuilding at high levels is basically lots and lots of algorithms/basic cases!)

- Until all basic cases and setups are learnt (which might be never), figuring out unique solutions throughout a solve will impact TPS considerably, and if TPS is raised, solutions may become worse and more rushed

- Fingertricks will not really be optimal, especially during the first block. Expect sometimes awkward starts.

-In general a lot harder to use than most other methods, with undefined worth (if speed is your sole goal, Petrus has not yet been proven to match up to other methods).

-3 different intuitive steps, 2 different algorithmic steps. That's a lot of practising unique steps, unlike CFOP for example, where F2L (the main part of the solve), uses the same algorithms, for 4 more or less identical pairs.

Petrus is not for people who just want to be fast, people who don't like working things out themselves, or for people who get frustrated easily.

Petrus is for people who enjoy learning how the cube works, want to use a unique method, want a challenge, or want to feel more like they are actually solving the cube themselves, without using many pre optimised algorithms

__Essential starting advice for Petrus__Be Colour Neutral. Petrus relies on being able to solve efficiently in all situations, there is no hope for it if it loses its main advantage over other methods. You might as well be using beginner's method if you aren't colour neutral with Petrus. It might be hard, but it'll be well worth it. Actually, here, colour neutrality and block neutrality (BN) are two different things (though one leads to the other). I could be CN, but only able to choose two blocks - RWG and OYB (note they include all the colours). I could be BN, but only able to solve starting on white and yellow (covers all 8 possible blocks). But like I said, CN leads to BN. So learn to be able to pick any starting 2x2x2 block, and to be able to solve that block on any colour, for optimised finger tricks and positions.

If you really don't think you can do it, then try dual CN and BN. You can pick any 2x2x2 block but only solve on white or yellow for the solve. Ideally, you'd be able to switch between the two colours, for the top 2x2x3 expansion.

For Petrus, you need to know what you're getting into. Getting fast won't be easy. If you don't really like the idea. don't do it. Check out the paragraph above this for who Petrus is for. It's no good choosing a method then abandoning it halfway through unless you are intentionally doing it for fun/to bring into other methods. You'll have to be dedicated for Petrus, work things out yourself, and accept that there won't be much to help you. You are the person who's meant to be making those guides and resources.

Once you find a nice, comfortable technique for creating blocks, do not get too comfortable with it. Getting comfortable with a couple of basic techniques will make it harder for you to keep learning and inventing new solutions. I sometimes ditch all my pre-tested solutions, as a way to force myself to innovate new ideas. And remember that there's probably always a better way to do your case than what you are doing at the moment when you first start learning Petrus.

And finally, don't be too expectant of yourself. Progress with Petrus could be slow. This is a method which is relatively unexplored and pursued, after all. I suggest that a lot of the time, don't do timed solves, just solve casually, and find new ways of doing something. Solves alone won't cut it. I completely redid my techniques and became a lot slower around the 40 second, 25 second, and 13 (now) second mark. It's worth it. And remember, cubing is for fun. Getting faster times is part of it, not the other way round.

Plus, you improve infinitely faster at something when you're actually motivated.

__How to practise__I mentioned a bit of this already in the last part of this guide. And although this isn't really a unique aspect of Petrus, I'm still including it. I'll just go over some points and tips here.

-Solving is not the only way to practise

-TPS, lookahead, and solve fluidity is generally gained with just solving. Do not expect much else out of it. Generally, try not to go for TPS if you don't have the two other aspects. And gaining those other aspects should probably be done without pressure, so try solving more slowly, not timing the solves, or putting the solves in a warm-up session.

-Movecount, algorithms, and weak steps should be improved/learnt specifically, not from solves. If you need to work on your 2x2x2, why spend time solving in other areas when you can practise just that? For movecount, you will definitely not be getting better at it with solving. Solving reinforces habits - whether they are good or bad habits depends. As said before, don't time solves, do some FMC solves, watch example solves, and go slow, looking for optimal solutions.

-Don't force yourself to practise

-Try not to do the bulk of the actual improvement practising early in the morning, late at night, after just having picked up a cube, after doing extensive practising, or when you don't feel like it.

-Upon learning a new technique, remember two things: a. it's better to learn the technique, wait 5 minutes, then practise that technique to see if you remember it rather than learning the technique and practising it straight away (applies to algorithms too), and b. once you've learnt the technique, start using it in solves right away - you won't get better at the technique if you don't use it, and if you're worried about your times increasing for a bit, then don't. If you're using a timer, make a session for casual solves.

-Don't be lazy with practising, don't put off what can be done now. 1 hour of focused, dedicated and varied practising is a million times better than 5 hours of unfocused random solves. (Just an example)

-Have a set goal in mind when practising - you shouldn't just be doing solves and watching some example solves in the hope you'll start to improve, set a specific, reachable practise goal every session, which you can work towards. Having a specific goal means you will reach that goal faster than if you were just solving on the whole(I want to be sub-x is not a valid goal, a goal such as I want to improve my expansion by trying to lookahead more is)

-Be reflective on your solves and keep identifying weak steps and faults. If you can't see anything wrong with your solves, then look harder. Nothing is ever perfect. Whether it be that your expansion takes up a quarter of your solve, or that you just don't like your LL algorithms, there is always something to do.

-Really understand techniques that you got from the outside world - and be able to apply it for yourself and see how it works. This goes with the intuitive side of Petrus and also helps you to be able to use variants of that case, setups, etc

-Be open to all kinds of practising. There are loads of ways to improve, and loads of different aspects of cubing, such as better fingertricks, better algorithms, lowering movecount, making TPS more consistent, trying to see more in inspection, etc.

-Make practising enjoyable for you - however you see fit

-Remember to take breaks once in a while

-When doing solving practise, treat every solve like it has WR potential, like it really matters. Unfocused solves are no good. And at the same time, don't focus too much either - relax, and solve. Being panicked or pressured in a solve does not help. Solving should eventually become an instinct, an unconscious process - you see everything you need to, you know what to do, and you do it. 'Don't think, just solve' - Max Park

__What to look for in inspection__The 2x2x2 is the first step of the Petrus Method. It is generally expected that you are one looking it once you get faster, and can solve it in a reasonable amount of moves without pause (below 8 mostly). Inspection time gives you 15 seconds to consider your options and plan them out. Good solutions may not be obvious at first, and with 8 different possible 2x2x2s as well as infinite ways to solve them, here's a list of things to look out for in inspection.

-Obviously, a completed 2x2x2 block would be very helpful

-A completed 2x2x1 block which just needs to be connected with an edge sometimes happens

-A pair which can easily be made into a 2x2x1 happens a lot of the time

-A solved edge means after creating the 2x2x1 you don't have to waste moves inserting the edge

-A solved partial cross means you can create a pair and insert it CFOP style

-A partial cross which edges just need to be paired up with a single D move (assuming the cross is on bottom) can be turned into the above, or have a corner inserted to create a 2x2x1

-A lined up but not solved edge could be the foundation of two possible 2x2x1s or use one move to turn into a solved edge

-A one move pair will turn into the above pair case

And of course, there are many many more cases like these which you may discover. Often several of these will appear in one solve, and you will have to decide quickly which one to pick. If there are only a few, I generally just quickly look at the follow-up moves and decide what is fastest - if there are many, I just use logic to decide what's best - obviously, a 2x2x1 is better than a solved edge. And if all else fails, just pick a corner and expand it into a 2x2x2, unless the case is exceptionally bad. Continuations of those cases should be left to be figured out as good practise but I will list a few cases in the next paragraph. And do remember that sometimes, you may wish to preserve some cases for your 2x2x3 step, you may find that a few of these may go together (like a solved edge and 2x2x1), you may wish to save the good case for your expansion which you know you are bad at, or you may even think outside of the box and find an extremely efficient but out of the way solution as opposed to the obvious but worse case.

__Improving your 2x2x2__Depending on what level you are at, you should probably be focusing on learning new basic cases and implementing them into your solves. It's a good idea to try create the situations I've listed in the previous paragraph and see what you would do in those situations. The line situation, solved edge, partially solved mini cross and pair come up particularly often, and it's good to know how to solve them. I suggest you look at one scramble with one of these in it and use that particular scramble because having different after cases can be confusing. Learning a variant of a basic case and understanding it also means learning how to apply it even when surroundings may be different (e.g. solved pair - there is a lined up edge so you can create a 2x2x1 in one move now, but other scrambles will not be as easy - you may have to setup that easy onemover). Making small changes to your solution or learning where your pair could be before it was in the current situation helps find setups and variants.

At that point, when you start inspecting, you should have a rough idea of what your case is and what you're going to do before fine-tuning and planning out the solution. When just trying to get fast solves, don't go into blind alleys - stick with what you know - this means you already have a rough guideline and can use more of inspection to actually try one looking the 2x2x2 and making it more efficient. Otherwise, when trying to learn new cases, don't be afraid to plunge into new situations and cases - building up your knowledge of how to create blocks is always good. Yesterday, for example, I took one scramble and decided to solve that scramble dozens of times, going down new paths every time. I discovered some interesting solutions and ideas and noted them down for future use. Actually, today I used one of these solutions (it was quite a non-obvious one at first involving a lined up edge and bad F2L case) and without it, I would have to have spent extra time looking for another solution.

One case, in particular, I wish I'd known a long time ago, which will be described later. It came up so often too since it involved a lined up edge and corner adjacent to it, which isn't really very rare.

And when you feel you are satisfied with the number of cases you know, for the time being, you should take the opportunity to practise just solving 2x2x2 a lot, making sure you retain those cases in your memory and use them in solves. This will familiarise those cases even further, before you start the cycle again. (Occasionally this may be bad since it might drill in a non-optimal solution, but habits can be broken).

One looking the 2x2x2 should start to become a priority as you become faster (<25 seconds). Ideally, you know the case you are doing well - meaning you don't have to think too much about how to do it or where the pieces will end up. So knowing lots of basic cases is important. If this isn't possible in a solve, try using as much as you know, and imagine what moves you are going to make in your head. It doesn't have to be the entire 2x2x2 block at first, what you visualise, but something which furthers that goal, such as a 2x2x1. Once you have the moves you are going to do to solve a part of the 2x2x2, reinforce that and make sure you don't forget it. You can use your hands to execute the muscle memory for the solution to build up TPS. Then find the remaining piece/s you have to solve not part of your already planned-out area and see how that piece will be moved/affected by your already planned moves. Either you can choose to do the last part separately (find where your piece goes after you've finished your planned section and plan out how to solve the rest of the cube from there), or include it as part of your entire solution if possible - maybe you find you can stop halfway through your planned solution to insert your final edge, before continuing and not having to waste moves later on.

tl;dr, learn as many cases as possible so you don't need to come up with new solutions and know the solution well already, plan out as much as you think you can, then track the rest of the pieces to see where they will end up, and how to solve them from there (or implement them into the solve).

It may be helpful to not worry about the 15 seconds limit (you can improve that), to close your eyes as you solve the planned out part to make sure you are actually planning it out and to not time at first.

And remember that you can find weaknesses in steps too, not just the solve. If you want to improve the 2x2x2, clearly it's not satisfactory and there is probably a problem with it. Find that specific problem and act on it. If you really can't find a problem, then just focus on learning more cases (though there almost always is a weak spot). For example, you may be rotating too much during the solution. Try to solve while not rotating AT ALL. Yes, it may be faster to rotate and do easier fingertricks short term but that just means your fingertricks for initially uncomfortable movesets are not very good and need to be improved. While RU may be faster than FU, is it faster with the rotations added in? After you've trained yourself to not rotate unnecessarily, don't forget you can still rotate - but do so wisely. Never rotate more than once though. And also consider the option of using wide moves to rotate and do moves at the same time. Wide moves are also decently fast.

And for another occasion, you may not be doing efficient enough solutions (8 moves or less generally) or planning out enough. Refer to the above section.

Plus, just do solves.

__Useful and common cases__This is a collection of common cases you may come across when inspecting the 2x2x2. If you wish to take a lesson from this section, you should not just be able to use the case but understand how it works. If you can understand how it works, you may be able to solve variants, make setups, or even find a better solution yourself.

This was created by taking random scrambles, inputting them into alg.cubing.net, and stating the possible cases here, so you won't find any particular order. I advise you to focus on the creation of the 2x2x1 block as the last edge doesn't take much thought. Obviously, you won't be able to just stuff all of these into your memory so understanding the thought process (so you can invent your own solutions on the spot) will be more beneficial.

The best solution will be put in the alg.cubing.net link - anything after the 2x2x2 such as a 2x2x3 pair does not count (since unless at high levels this will not be seen and factored in). Any notation I put in the solutions go from the rotation. And also, the solutions I give will definitely not be optimal. They are a starting point and go from identifiable cases (like a pair), which tend to be efficient. I doubt you'll be seriously looking at all 8 corners in inspection. I see something I can use, I quickly check in cases I missed anything, and go with it. Then you can put more inspection time into memorising the solution, planning out, etc.

Scramble

1. x' y' F U' R' F2 R. Continuation D' R D2. Here we can see a line, and nothing else. It is noted that there is an easy one move pair - x' y' F. This connects the corner with the line. And the final 2x2x1 edge is in the top layer, oriented correctly. Easy insertion (U' sets up, R' F2 R). Generally, this approach isn't the most efficient, as the insertion takes several moves itself, and even a one move pair doesn't compensate. But sometimes there is no other obvious option, and it's pretty fingertrickable. 8 moves - meh.

2. x' y' L U D' L. Continuation L U L' B' D2 (2 Ls can be L2) (Blended: x' y' L U D2 B D L D2). Again we see the line, and instead of going for the pair and insertion, this solution goes for the pair which can connect to the line, since it is only two moves (L U). The pair is then connected to the line (D' L), and then the last edge is solved. Unfortunately, the last edge gets stuck in a bad area, so it takes more than half the moves to solve the 2x2x2 from there. It would have been a decent solve apart from that. BUT. It's noted that at the start, the last edge is at DF. It can't be moved easily then, without disrupting the rest of the pieces. But it can be moved out of the way after the pair up, turning the D' into a D2 and being solved, before continuing. Solution: x' y' L U D2 B D L D2, which gives 7 moves - slightly better, and acceptable.

3. z2 y D' R2 F'. Continuation D L D. So, the line is noticed, but this time, I see the other one move pair towards the last edge. It just so happens that if I pair them up, the other 2x2x1 edge just needs an R2 to be made into a line, and connect with the pair. z2 y, D' pairs, R2 makes a line and sets up, F' completes the 2x2x1. The last edge, in this case, is in an OK spot, and the 2x2x2 can be solved in 6 moves - a good solution. Fingertricks are not too awkward.

4. x' R F R F'. Continuation L' B2 D. Yet again, the line is noticed, but on this occasion, the YGR corner is noticed. This ALSO is a one move pair to the line, and has the other edge in position straight away, for an insert. x' R pairs, F R F' inserts, then the last edge is in an OK position and can be solved easily. 7 moves - decent.

Other notable solutions: Red top Green front, instead of pairing up and inserting you can pair up the corner with the insertion edge, and put that in. (U' R U R' F2). Here it's not practical as the U' has to be done to move out of the line edge's way (F U F' pairs up but breaks the line), but if the corner was further up, some people may prefer it over 4.

You can pair up the YGR corner with the RY edge and continue with a yellow 2x2x1 but it's 8 moves.

YBO can be paired with YB but took me way too long to find that.

BWO can be paired with BO but also took me way too long to find that.

1. x' y' F U' R' F2 R. Continuation D' R D2. Here we can see a line, and nothing else. It is noted that there is an easy one move pair - x' y' F. This connects the corner with the line. And the final 2x2x1 edge is in the top layer, oriented correctly. Easy insertion (U' sets up, R' F2 R). Generally, this approach isn't the most efficient, as the insertion takes several moves itself, and even a one move pair doesn't compensate. But sometimes there is no other obvious option, and it's pretty fingertrickable. 8 moves - meh.

2. x' y' L U D' L. Continuation L U L' B' D2 (2 Ls can be L2) (Blended: x' y' L U D2 B D L D2). Again we see the line, and instead of going for the pair and insertion, this solution goes for the pair which can connect to the line, since it is only two moves (L U). The pair is then connected to the line (D' L), and then the last edge is solved. Unfortunately, the last edge gets stuck in a bad area, so it takes more than half the moves to solve the 2x2x2 from there. It would have been a decent solve apart from that. BUT. It's noted that at the start, the last edge is at DF. It can't be moved easily then, without disrupting the rest of the pieces. But it can be moved out of the way after the pair up, turning the D' into a D2 and being solved, before continuing. Solution: x' y' L U D2 B D L D2, which gives 7 moves - slightly better, and acceptable.

3. z2 y D' R2 F'. Continuation D L D. So, the line is noticed, but this time, I see the other one move pair towards the last edge. It just so happens that if I pair them up, the other 2x2x1 edge just needs an R2 to be made into a line, and connect with the pair. z2 y, D' pairs, R2 makes a line and sets up, F' completes the 2x2x1. The last edge, in this case, is in an OK spot, and the 2x2x2 can be solved in 6 moves - a good solution. Fingertricks are not too awkward.

4. x' R F R F'. Continuation L' B2 D. Yet again, the line is noticed, but on this occasion, the YGR corner is noticed. This ALSO is a one move pair to the line, and has the other edge in position straight away, for an insert. x' R pairs, F R F' inserts, then the last edge is in an OK position and can be solved easily. 7 moves - decent.

Other notable solutions: Red top Green front, instead of pairing up and inserting you can pair up the corner with the insertion edge, and put that in. (U' R U R' F2). Here it's not practical as the U' has to be done to move out of the line edge's way (F U F' pairs up but breaks the line), but if the corner was further up, some people may prefer it over 4.

You can pair up the YGR corner with the RY edge and continue with a yellow 2x2x1 but it's 8 moves.

YBO can be paired with YB but took me way too long to find that.

BWO can be paired with BO but also took me way too long to find that.

Scramble

1. x' z B2 D2 L. Continuation R B2 D'. Alright - the pair is blindingly obvious. We can connect it with the GR edge to make a red base 2x2x1 or connect it with the GY to make a yellow base 2x2x1. Let's just go with the GR edge. It needs to be in the bottom layer to connect, so B2. That setups to two two move inserts (too many tos). Either the edge can be swung over with a D2, followed by the pair up (L), or the pair can be swung over with an F2, followed by the pair up (R'). I go with the former, since I prefer D moves to F moves, and my L and R speeds are similar. The pair and edge are paired up, creating the 2x2x1. The last GY edge is at UR, good, and just needs the R B2. 6 moves - good. (I won't make a separate case for if I did the F2 R' 2x2x1, the movecount is the same but different fingertricks which I don't prefer).

2. y2 F B' R. Continuation D' R2 B2 D' (Blended: D2 F B' R L D2). I see the pair again, but this time look at the yellow base 2x2x1 with the GY edge. The pair is misoriented relative to the yellow face, so the quickest ways to bring it down are two movers (B' R and B L'). B L' is on the opposite side of the GY edge and completely solves the pair, putting it in the 2x2x2 spot (this is bad because unless you simultaneously solve the cube with that, you'll have to insert the last edge, moving the 2x2x1 out of the way then solving it), so B' R it is. So, if we choose the aforementioned pair route, the edge will have to be at DF to receive the pair and become a 2x2x1. Luckily, it's one move away - an F puts it in position and B' R can follow, solving the 2x2x1. Unfortunately, the last GR edge gets stuck with the 2x2x1, so it takes 4 moves to get out and solve the 2x2x2 (D' R2 B2 D'). A seven move solution, decent fingertricks. But we might be able to do something about the last edge. Before making any moves, it's on its own in the D layer, so we can move it out of the way using that layer. We'll do a D2 so it's just a move away from being solved. I don't solve it right away because it would be affected by the movement of the pair otherwise. A new solution: D2 F B' R L D2, 6 moves - good.

3.. y U F2 R F. Continuation: D2. So, I saw the solved GO edge. GWO immediately doesn’t look brilliant, so I check GYO. No bad or good situation immediately apparent. I’ll use the Go edge as the last edge instead of a 2x2x1 base I think (more opportunity and 2x2x1 would be in the way fo the last edge then). Lots of 2 and 3 move pairs, I’ll choose the one with the best follow-up. I saw a U F2 pair with the OY edge, and also noticed that the GY edge adjacent to the pair edge, flipped, which is an easy 2x2x1 start: U F2 R F. Doing R F orients the edges and makes a mini cross, so if the OY edge is paired with a corner - it’s a mini cross with a solved corner, in other words, a 2x2x1. And the last edge is solved - the reason we looked at this solution, so the final move is D2, which solves the 2x2x2. A surprisingly good solution considering the starting point - a reminder of why to always check for other better solutions. In a rushed inspection, one could easily just see the obvious pair and go with it, missing the 5 move solution. 5 moves - really good.

4.. x’ z2 D’ R’ F’. Continuation: L’ U B D2 (Blended: U D’ R’ F’ L’ D2). This is one of the more obscure solutions. With some looking, I found a one move pair - BYR to BY (D’). The pair just needs an F’ to connect to the blue base. The BR edge is at FR and I can just do an R’, to receive the pair. The rest is self-explanatory - F’ to complete 2x2x1, then just the last edge. One move can be saved by moving the RY last edge out of the way with a U. U D’ R’ F’ L’ D2. 6 moves - good.

Other notable solutions: BRW is a one move pair to BR. BOY is a one move pair to BY.

1. x' z B2 D2 L. Continuation R B2 D'. Alright - the pair is blindingly obvious. We can connect it with the GR edge to make a red base 2x2x1 or connect it with the GY to make a yellow base 2x2x1. Let's just go with the GR edge. It needs to be in the bottom layer to connect, so B2. That setups to two two move inserts (too many tos). Either the edge can be swung over with a D2, followed by the pair up (L), or the pair can be swung over with an F2, followed by the pair up (R'). I go with the former, since I prefer D moves to F moves, and my L and R speeds are similar. The pair and edge are paired up, creating the 2x2x1. The last GY edge is at UR, good, and just needs the R B2. 6 moves - good. (I won't make a separate case for if I did the F2 R' 2x2x1, the movecount is the same but different fingertricks which I don't prefer).

2. y2 F B' R. Continuation D' R2 B2 D' (Blended: D2 F B' R L D2). I see the pair again, but this time look at the yellow base 2x2x1 with the GY edge. The pair is misoriented relative to the yellow face, so the quickest ways to bring it down are two movers (B' R and B L'). B L' is on the opposite side of the GY edge and completely solves the pair, putting it in the 2x2x2 spot (this is bad because unless you simultaneously solve the cube with that, you'll have to insert the last edge, moving the 2x2x1 out of the way then solving it), so B' R it is. So, if we choose the aforementioned pair route, the edge will have to be at DF to receive the pair and become a 2x2x1. Luckily, it's one move away - an F puts it in position and B' R can follow, solving the 2x2x1. Unfortunately, the last GR edge gets stuck with the 2x2x1, so it takes 4 moves to get out and solve the 2x2x2 (D' R2 B2 D'). A seven move solution, decent fingertricks. But we might be able to do something about the last edge. Before making any moves, it's on its own in the D layer, so we can move it out of the way using that layer. We'll do a D2 so it's just a move away from being solved. I don't solve it right away because it would be affected by the movement of the pair otherwise. A new solution: D2 F B' R L D2, 6 moves - good.

3.. y U F2 R F. Continuation: D2. So, I saw the solved GO edge. GWO immediately doesn’t look brilliant, so I check GYO. No bad or good situation immediately apparent. I’ll use the Go edge as the last edge instead of a 2x2x1 base I think (more opportunity and 2x2x1 would be in the way fo the last edge then). Lots of 2 and 3 move pairs, I’ll choose the one with the best follow-up. I saw a U F2 pair with the OY edge, and also noticed that the GY edge adjacent to the pair edge, flipped, which is an easy 2x2x1 start: U F2 R F. Doing R F orients the edges and makes a mini cross, so if the OY edge is paired with a corner - it’s a mini cross with a solved corner, in other words, a 2x2x1. And the last edge is solved - the reason we looked at this solution, so the final move is D2, which solves the 2x2x2. A surprisingly good solution considering the starting point - a reminder of why to always check for other better solutions. In a rushed inspection, one could easily just see the obvious pair and go with it, missing the 5 move solution. 5 moves - really good.

4.. x’ z2 D’ R’ F’. Continuation: L’ U B D2 (Blended: U D’ R’ F’ L’ D2). This is one of the more obscure solutions. With some looking, I found a one move pair - BYR to BY (D’). The pair just needs an F’ to connect to the blue base. The BR edge is at FR and I can just do an R’, to receive the pair. The rest is self-explanatory - F’ to complete 2x2x1, then just the last edge. One move can be saved by moving the RY last edge out of the way with a U. U D’ R’ F’ L’ D2. 6 moves - good.

Other notable solutions: BRW is a one move pair to BR. BOY is a one move pair to BY.

__Resources__Collection of some helpful sites and videos which may be useful to you in getting faster with the 2x2x2. For now, this is just 2x2x2 specific - general example solves and tutorials will be listed later.

https://lar5.com/cube/blox.html

__Basics__After the 2x2x2, a 2x2x1 is built which is attached to the 2x2x2, to form the 2x2x3. There normally isn't much time to look for good solutions - the 2x2x2 gets a full 15 seconds - so 2x2x3 solutions tend to be more inefficient, rushed, and basic. Plus the solving of the 2x2x2 tends to break up unpreserved, potentially useful starting points, like a pair (or it is used for the 2x2x2). The key aspects of a fast 2x2x3 are: Not taking too much time thinking over efficient solutions, not rushing, lookaheading from 2x2x2 well and knowing as many basic cases as possible.

__Improving the 2x2x3__Generally, solutions should take around 7 moves. And in most solves, the 2x2x2 should end up in the BLD corner with the 2x2x1 expansion in the BRD corner. This allows for an FRU gen solution (mostly RU), clear view of all pieces, and good start to the EO step of the solve.

The 2x2x3 seems to be a popular weak spot for several Petrus users and it's easy to see why. There are 3 pieces to solve, 3 faces to look for them on, no inspection time, and lookahead from the 2x2x2 has to be employed to make the step fast.

So, how to improve?

1. Lookahead from 2x2x2

2. Spend some time checking out and learning basic cases (with less freedom, less chance of good visible starting points, it is significantly different from the 2x2x2 enough that some time should be dedicated to it separately.)

3. Figure out the right balance of speed and efficiency.

For number 1... You'll need to be planning out the 2x2x2 completely and be very comfortable with solving it if you are to start looking at other pieces during the solve. Refer to the 2x2x2 section for advice on how to do this. In inspection, make sure you know the possible 2x2x3 expansion pieces that you will consider, so as soon as you start solving, you can start tracking them. And, you might want to start planning out where 2x2x3 pieces will end up in inspection so you can find the other pieces easier. Honestly, just don't look at the 2x2x2 pieces, and your eyes will find something to do.

For number 2... Solving the 2x2x3 lots of times will accomplish this. You should also check out the resources and cases tab for further insight. Again, make sure you understand them. It's so important you do - you'll feel much more confident using them in solves and applying the knowledge to other similar situations. Do some FMC solves specifically targeting the 2x2x3 step. You might want to do some solves starting with the 2x2x2 solved and using a few seconds of inspection to find some efficient solutions, as well as practising them.

For number 3... You should use your own judgement. I pers

Last edited: Aug 8, 2020