A simple trick to design your own solutions for Rubik's cubes

The vast majority of people who tackle the Rubik's cube never succeed in solving it without looking up somebody else's solution. In this video the Mathologer reveals a simple insight that will enable all those of you who can solve the first layer to design your own full solution for the Rubik's cube, as well as for many other highly symmetric twisty puzzles.
For more details about this really very fundamental idea behind many twisty puzzle solutions have a look at this article by the Mathologer from a couple of years ago www.qedcat.com/rubiks_cube/
Googling "commutator, Rubik's cube" will also produce links to a lot of very good articles on this topic.
For a few footnotes you may also want to check out this video on Mathologer 2: • Footnotes to the video...
The Rubik's cube animations in this video were produced using the program CubeTwister by Werner Randelshofer: www.randelshofer.ch/cubetwister/
Thank you also to Danil Dmitriev the official Mathologer translator for Russian for his subtitles.
Enjoy :)

[@primusavenged]

CUBERS HATE HIM mathematician solves ALL twisty puzzles with one weird trick!

[@harribrickboy2175]

Mason J Rice

[@alexwong9058]

Mason J Rice is that the word autofill

[@poophedcalvert1961]

he going to ducking fasr

[@thijsbeentjes4008]

Maria Hartmann which method do you use?

[@Jay-S04]

primusavenged HIS SHIRT IS FUCKING STUPID

[@Mathologer]

17 Nov 2016 This is the first video on Mathologer with 1M views. Party time tonight :)

[@GrzesiuG44]

Congratulations! I was wondering if there is any simple way to apply this trick for 4x4x4 cubes and their edge parity. Do you have any hints?

[@Mathologer]

Let's say you've solved all the corners, and let's also say you've solved all the edges except for some in the top layer and you discover an edge parity there. Then just give the second layer from the top a quarter twist and then resume solving. It's important at this stage to use nothing but the algorithms you designed using the trick from this point onward. Hope this helps :)

[@adolfotapiagallardo]

felicitaciones por el millón de vistas! soy de Perú en Sudamérica y te planteo esta pregunta: ¿como fueron inventados los algoritmos de Jessica Fridrich? ¿cual es la secuencia o cadena de ideas que llevan a estos famosos algoritmos? saludos! y que sigan los éxitos!

[@sivad1025]

Mathologer Congrats!!!! I'm always a fan of your videos!!!

[@523101997]

this guys my math lecturer !

[@farrankhawaja9856]

I'm an experienced speed cuber (but not an expert) and I learned commutators but never really understood why they worked. Now I have the intuition behind them. Thank you Mathologer!

[@Mathologer]

That's great :)

[@Mathologer]

I thought it would probably a good idea to stress again that the main purpose of this video is to enable people to find their own solutions to twisty puzzles based on a very simple (in hindsight) but at the same time extremely powerful trick. If you are not interested in finding your own solutions and just want to be able to mechanically unscramble these puzzles, then you are better off memorizing one of the readymade methods that were designed by expert cubers. To understand how the trick works is quite easy, I think, and very much worth knowing about, regardless of whether or not you ever want to touch a Rubik's cube. However, to be able to implement the trick to really find your own solutions you have to be able to fix the first layer of a 3x3x3 Rubik's cube or the corresponding moving element in other twisty puzzles without anybody else's help/looking up recipes. In any case, have fun :)

[@vectorsorbet9581]

+Mathologer Would this trick work for square-1?

[@Mathologer]

+Victor Armenteros In general this trick works very well for highly symmetric twisty puzzles but is not that much help when it comes to puzzles with few symmetries. Having said that, you can definitely get quite far with commutators in the case of square-1, it's just a little bit harder to find "your moves"; :)

[@vectorsorbet9581]

+Mathologer Thank you. I really enjoy your channel

[@TonyFisherPuzzles]

+Mathologer Brings back memories of June 1980 when I worked out my own solution including this "trick". Such a shame most kids don't even try to solve puzzles themselves nowadays. That feeling of cracking it on my own for the first time is what got me completely hooked. Obviously by teaching people this (I have done that too) they aren't really solving it by themselves either.

[@Mathologer]

+Tony Fisher Glad to see you here. Have been watching your videos for AGES :) In fact I just directed a couple of people to your 13x13x13 disassemble video (people who suggested that it is a good idea to simply take apart and reassemble a twisty puzzle). Personally I think teaching this trick to someone who really gets stuck is the way to go. Even if you know the trick, it's still a nontrivial exercise to actually implement it and extend it to other twisty puzzles. And if they end up making up solutions for something like the Rex cube just having watched this video, then I'd be quite happy to give them my seal of approval "You really did this by yourself!"

[@redkb]

Another great video! You explained this very well.

[@Mullemeckmannen97]

+RedKB lol hey man, ur awesome

[@Mathologer]

+RedKB Glad you like it. You put all this very well too in your cube theory videos, but of course our target audiences are quite different :)

[@ianmoore5502]

+RedKB Oh hi kenneth

[@alvinknumpihc3680]

+Mathologer at 11:43 wouldn't it be A B B^-1 A^-1, not A B A^-1 B^-1

[@alvinknumpihc3680]

+Dexter C Joyner nevermind, i watched the rest of the video :/

[@sharonjuniorchess]

Many years ago when it first came out I went for a job interview and the person interviewing me pulled out a Rubik's cube scrambled it and then said "I'll give you 10 minutes see if you can solve it" and then left the room. 10 minutes later he came back and asked how I had done. I said that I had not succeeded but I knew it was possible because I had seen my brother do it but that when I got one part solved it would mess up somewhere else. I asked him what the purpose of the exercise was and he said he just wanted to see how I approached a seemingly intractable problem whether I just gave up or persevered. Being willing to keep trying to solve the problem even if it did not work was what he was looking for.

[@DaNewWrksOfMeh]

That's a good mindset. Sometimes it feels irrelevant to keep going, especially if you've fallen behind. However; if you keep going, you can have as many chances as you want.

[@aurelia65536]

“Does it fix it?” “No-“ *”IT FIXES IT, KARL!”*

[@h3nnn4n]

Woow, nice video. I am glad that you talked about commutators. Peole who can solve the rubiks cube blindfolfed usually have to use commutators while blindfolded.

[@Mathologer]

+Renan Silva Glad you like the video. I've never blindsolved a Rubik's cube but I've had a look at how people do it. Actually seems quite doable. In fact, I would think that anybody with reasonable skills should be able to learn how to do this trick in a day or two. Have you tried ? :)

[@h3nnn4n]

+Mathologer Yes, I tried and I could solve both the 3x3 and 2x2. It is not that hard, it is very rewarding and it is very interesting since it relates to the Futurama Theorem. Definitively worth a try.

[@Mathologer]

+Renan Silva Cool, once I run out of all those other fun things to do ... :)

[@h3nnn4n]

+Mathologer A mathematician never runs out of fun things to do =D

[@Mathologer]

+Renan Silva ... which is both a blessing and a curse ...

[@DGCubes]

This video is so cool! I wish I had taught myself to solve the cube like this from the start. :)

[@GERcub3r]

hi DG :D

[@Mathologer]

+DGCubes Just checked out your channel. Nice! Glad you got something out of this video :)

[@DGCubes]

Aw, thanks! It was an awesome video! :)

[@danielinoyatov5009]

hey dg cubes I subscribed

[@hanniffydinn6019]

+DGCubes You should know these moves already if you speed solve? These moves in this video are the moves used to solve the last layer ! I can currently solve in about 1 min ish using Friedrich 2 Look, but getting any faster than that means learning every case. Which frankly, is no fun. well not yet anyway.

[@IdoN0TneedTherapy]

This is one of the most impressive videos I've ever seen. In

[@ffggddss]

Another fun (& instructive!) vid! Thanks, Mathologer! An additional note about the commutator. The reason that ABA⁻¹B⁻¹ ( sometimes abbreviated as [A,B] ) tells you whether A & B commute, is that the second half of that commutator can be written as A⁻¹B⁻¹ = (BA)⁻¹ and since the inverse of any group element is unique, (BA)⁻¹ = (AB)⁻¹ if and only if AB = BA.

[@myfuzzyslippers08]

Thank you!!! I was 14 when the Rubik's Cube first came out and could easily do one layer but struggled after that. I ended up buying a book and memorized a few sets of moves that would let me solve the rest, but I never felt good about that because I hadn't figured it out on my own. I know the insight you provide doesn't come close to the fastest solution, but it's ONE thing you need to know after you can do the top layer yourself. I will now be able to solve it on my own after 35 years! I'm going to play with this for a while just for fun, then I'll have a look at the intuitive faster methods mentioned in some of the comments.

[@Mathologer]

+myfuzzyslippers08 Great, if you need some more practical tips on how to implement these tricks maybe have a look at footnotes video on Mathologer 2 or the writeup I link to in the description :)

[@NorbertHarrer]

Fantastic!!! I was never able to remember the moves from solution guides. So far I was only able to solve the top two layers by myself. This is the missing key to finally go all the way. Thank you so much. :-D

[@Mathologer]

+Norbert Harrer Find out about this trick really was a life-changing experience for me as far as twisty puzzles are concerned. I did find my own solution when I was still going to high-school but I still remember it being really, really hard work and in retrospect what I did there was not pretty at all. Anyway, wish you luck with tackling the Rubik's cube again. If you need some more pointers check out my write-up in the description and the footnotes video on Mathologer 2. And if you succeed please let me know :)

[@NorbertHarrer]

+Mathologer Thank you for the nice answer! And btw.: You create a really awesome channel. It became one of my most favorite KZbin channel among many otherwise more engineering themed channels.

[@Mathologer]

Glad to be able to sneak in amongst the engineers :)

[@NorbertHarrer]

+Mathologer Yesss!! I sat down for an hour or two and finally solved the cube by myself for the first time without any outside recipe. :-D It is very rewarding to be able to solve it AND to understand how all the moves work. Now I can put down the Rubik's cube and pick it up in a couple month or years, and I would still be able to solve it (given some time) without any outside help. Any memorized instructions would be long forgotten by then. (Hey, you never know when you need to solve a cube to escape a death trap on a deserted island). However. Sometimes I have the problem that two edges and two corners are swapped at the same time in the final layer. And I am only able to either cycle three corners or three edges with the commutator magic. I googled and found out that a Y-Perm move is needed. Is it also possible to solve this with the commutator trick?

[@Mathologer]

If you fix the corners first before doing anything else you don't get this situation you are describing :)

[@wroth]

Wow, for once a click-baity title that actually delivers on its promise! That actually is both simple, and applicable to all rubiks cubes, thankyou!

[@Mathologer]

+wroth I was actually really agonizing over whether or not I should put the "all" in the title because although the trick gets you all the way with a lot of highly symmetric twisty puzzles you need to know one or two more tricks for others (and for the really screwed up puzzles with few symmetries it is not very useful at all) In the end I decided that getting this really very powerful trick out warrants the title as it is :)

[@markonikolic1386]

As a speedcuber this looks very interesting to me. I almost wish that i don't know how to solve my cubes so i can try this out, but enyway l will probably order some new weird puzzle and try to come out with my own solution. Thanks for the video. You realy explaned it well!

[@Mathologer]

Glad you got something out of this. If you watch the next video (will come out in two weeks' time) you'll find plenty of opportunities to try and make up your own solutions to some really outlandish twisty puzzles :)

[@PreservationEnthusiast]

Most of the so called "speed cubers" of today are just autistic OCD dropouts who slavishly learn other peoples algorithms.... And practice for months on end. It is not intelligent or clever. The idea of these "puzzles" is just that... they are puzzles. You are supposed to think and use your own brain power and develop your own moves to solve them. Not just look up someone else's work. This typifies all that is wrong with the USA today. Everybody wants instant gratification and solutions. Even on video games, people are not prepared to work. They just want the "cheat codes" so they can finish as quick as possible and them onto the next game.

[@markonikolic1386]

heelfan1234 It is true that it is the easy way and that is not clever but it is fun and that is the most important thing. By learning how to solve 1 twisty puzzle you develop a new way of thinking that will help you solve other twisty puzzles. That is why collectors usually know how to solve all of their puzzles, even weird ones that don't have solutions already made, but they still use well know solutions to solve ordinary puzzles like 3*3, 4*4, piraminx, megaminx, etc because is much more fun. And you still have every solve different because the first 2/3 of a 3*3 solve are intuitive.

[@PreservationEnthusiast]

Marko Nikolic I don't think it is more "fun" to learn by rote 57 OLL algs and 20 odd PLL ones, all other people's work. It may be "fun" to a braindead OCD person, but the real fun is to work out enough algs on your own to solve the puzzle. Even if they have been found before, if you find them yourself, they are personal to you. They may not be the best or the most efficient, but they represent your brain power. The problem with speed cubing is that everyone wants the most efficient method which basically means just cheating, looking up everybody else's solutions.

[@markonikolic1386]

heelfan1234 Since i never solved a twisty puzzle using my brain power i can't write about that, but i know from some other types of puzzles ones u find a solution it's not fun eny more. Methods like CFOP, Yau, give you the ability to to practise something and get faster and for me that is more fun then solving a puzzle ones or twice and stoping there,or stearing in the computer screen all day. Speedcubers have a life to, they do sports, ther go out with friends that are not speedcubers.

[@spooncastro]

This is the exact method I have been looking for for years! Thank you so much! I love math so much and I subscribed to your channel earlier today only to finally find exactly what I needed to never have to look up algorithms any more. Thank you!

[@Mathologer]

Great, now have some fun thinking your way through a pile of twisty puzzles :)

[@EddtheRexMan]

Great video, but as a speedcuber, it really bugs me seeing so many unsolved puzzles :P

[@GrashalmTuts]

Same here xD

[@andrewfitzgerald9118]

Same

[@KarstenJohansson]

+Edward Dibley I think his view counts would skyrocket if Karl brought you on the show to speed solve all of them.

[@Booskop.]

+Edward Dibley You don't have kids, do ya?

[@martinpolanco1142]

I am sorry but I don't understand

[@jayreynolds8647]

As with many who have replied here, I am already a cuber myself, with a decent beginning of a collection. In truth, this video did not teach me anything new, but it completely reinforced the way I solve cubes. I am not, nor will I most ever likely be, a "speed" cuber. That said, In most ALL the cubes I have, the simplicity described here of performing a sequence to isolate a single piece, move that piece out of the way (or another piece into that spot) then reversing the sequence, is exactly the principal I have applied to not only the 3x3, but each larger cube in turn. Of course there are some "special" cubes that require learning a new algorithm (like the crazy 3x3 planet series I am currently enjoying!) but the basic principal remains the same for them all. Extremely well done. Thank you for posting this.

[@Mathologer]

Glad you got something out of this video :)

[@GyanPratapSingh]

One of my favourite videos so far! No wonder you were able to solve the hyper cube

[@grantmacdonald3904]

I thought a commutator was someone who was both a communist and a dictator

[@MrDeyzel]

nice

[@Mathologer]

+Leeroy Jenkins Very funny :)

[@grantmacdonald3904]

+Mathologer omg you replied

[@ayadalhilo]

Leeroy Jenkins thanks to you, I will never forget this word ever! very clever, very funny :)

[@trueriver1950]

Surely its the bit in a DC electric motor that the brushes contact with

[@avananana]

As a long time solver, I'm not a speed cuber but I know how to solve the majority of the cubes on the market, this is really interessting, Sometimes during this video, I actually wish I had no clue about how a cube worked. Hmm, I'm going to see what I can do to fix that issue.

[@Haze01Smash]

Thank you for this video! Your explanation of the concept was exactly what I needed! I'd previously doubted my confidence and understanding for doing anything beyond solving the first layer, without looking up someone else's solution. Your explanation highlighted that many of the moves that come naturally in solving the first layer can be applied to unfinished sides of the cube, with the target side oriented to the top, that I need be mindful only of how my moves affect that one layer, and that I can undo the resulting mess on the bottom layer while simultaneously applying the desired change to another part of the top layer. A long winded way of saying that I feel pretty accomplished for designing my own "magic moves" and solving the cube on my own without following someone else's pre-made step-by-step guide.

[@victordelmastro8264]

I thank you for your enlightening perspective on group theory. I never would have thought to fiddle my own way through w/ 4 magic moves.

[@magmaticly]

Brilliant! Absolutely brilliant! I'm scratching my head now, saying ”That's so obvious, why did I never think of that?"

[@kenney9120]

A very good video for beginning cubers. Rather that simply convey solutions this videos teaches you how to actually THINK through the puzzle.

[@SteveFrenchWoodNStuff]

You've got a great collection of twisty puzzles! Very nice.

[@DivnoorCubes]

It's a photo...

[@SteveFrenchWoodNStuff]

+Universal Force - Yeah, a photo of his puzzle collection.

[@DMNDSbyDaylight]

+Wood 'n' Stuff w/ Steve French lol owned

[@ivovelo]

I just wanted to come by and say hat after having watched this video some 3 days ago, I solved my cube 3 times today! Thanks for giving me the trick that made me keep going!

[@IcyShard1001]

Ahh the famous cupboard with all the cubes.....

[@Mathologer]

+ShadowVyrus Yep, and now we want to solve them all :)

[@IcyShard1001]

Good luck! Although I'm sure you dont need it haha

[@aleksawower]

God damn I love Rubik's cubes.

[@El_Andru]

What does he have fucking cancer?

[@gmoorthy4564]

Get cancer B-)

[@phyranios9091]

+Andy Panda no the dude shaved his head for a hair cake and someone pointed out he looks like a cancer patient (can't remember who) and this channel has jumped on that

[@El_Andru]

Ballistical 935 Lol, I know I have watched too much IdubbbzTV, but in the "Hair cake video" in a part of the secons "cancer skit" he is like standing and coughing and a voice says that "What does he have, fuckin' cancer? It makes me laugh every time and the voice is so perfectly timed. But yeah, I know

[@aleksawower]

Andy Panda Can you give me the cancer, please?

[@themasstermwahahahah]

I feel like that kid is smarter than me, so im not sure i can do this

[@Galacticavatar]

+omegadan Being the child of the Mathologer is a pretty unfair advantage.

[@pastasandwich]

+Brendan O'Neill those god damn "enriched" math classes but seriously smart kid

[@ryan-rs7mj]

+PastaSandwich its easy

[@ramenmurugadoss1026]

You don't need smartness to solve a rubiks cube

[@Mathologer]

+RM CUBER If you do want to find to find your own solutions you've got to be very persistent and a pretty good problem solver :)

[@georgesmith4776]

Absolutely incredible! I've learned to solve over a dozen twisty puzzles, but I've never found the underlying technique - thanks for enlightening me :)

[@Mathologer]

+George Smith Glad you got something out of this video :)

[@richardcoppin5332]

This single video completely demystified for me the problem of solving a Rubik's Cube.

[@groszak1]

What if you can't solve the first layer? What if you can't turn the first layer, like in Skewb? What if odd permutations are possible, like in 4x4 (OLL parity)?

[@sebastianjost]

Another nice trick: If you make any move, you can just repeat the exact same move and you will always get to the starting position. That way you can develop your own algorithms too although they ore often quite long and tedious

[@louiswouters71]

This is true IF you repeat a pattern starting from a solved cube.

[@trueriver1950]

@@louiswouters71 in which case it must be true for all other cubes.

[@louiswouters71]

@@trueriver1950 Yes it is, never said that wasn't the case

[@filipemtx]

Rip square1

[@RevYars]

Great insight. I looked up how to solve the 3x3x3 and 4x4x4, but it was a really wonderful experience to then use those skills to solve the 5x5x5 by myself. Thanks for the video

[@JKKnudsen]

Great video! There is actually a pretty neat demonstration of quark confinement in this demonstration. Note that you can not make a solitary twist, it must come with another piece twisted, if the remainder of the cube is to be solved. Consider the solved cube the vacuum state, a twist is a quark. For the rotation example we got a meson(two quarks), and the translation a baryon(three quarks). Things to look up is the Rubik's group and SU(3), if anyone wish to learn more.

[@NicosMind]

*This is both the best and worst method for solving a cube ^_^*. Let me explain, if you've got brains and memory then its the best method because it teaches you how to think and learn for yourself how to tackle a Rubik's cube. However its the worst because many people will forget moves, forget the method, make simple mistakes when moving the layers and just give up and will still be no closer to solving a cube. These are the type of people who cant follow the algorithms which most people learn from and theyre convinced that theyre broken. However being of the former kind of person and not the latter I think its excellent :)

[@Mathologer]

+NicosMind I agree, it's not a trivial task to actually apply the trick and come up with your own solutions. However, I am mostly talking to people who actually managed to do the first layer by themselves and by doing so have demonstrated that they may well have what it takes to go all the way using this basic insight. Anyway, even if someone doesn't ever attempt to find their own solutions I think this insight is possible the single most important thing that people should know about twisty puzzles :)

[@aleksinuutila2315]

Thats why its better to solve F2L minus one intuitively, then orient and permute all the rest edges, and then solve the 2-5 unsolved corners with commutators. Then the start is straight forward, no memorisation needed, and the rest is easy eight move commutators that are relatively easy to invent on the fly.

[@aleksinuutila2315]

+Aleksi Nuutila First layer is easy and second layer could be solved using key hole, that is very intuitive aswell, and since you wont do the last F2L pair you can have that slot as a buffer that can and should be destroyed in order to solve the rest of the F2L.

[@NicosMind]

Mathologer Oh yeah I get that this video was aimed at people with some level of competency. I just loved how this was simultaneously the best advice for some people, yet terrible advice for others. It tickled me. But great video. I did love it :)

[@Mathologer]

All under control then :)

[@vDREEGONv]

CFOP is still my bae, and that was basically PLL XD but its a nice trick for non cubers ^_^

[@GreenArt4]

+(SH) VGamer431 / DreeGon Not really though. This method is basically how people figure out bigger and more complicated puzzles. CFOP is one of the many methods that you nor many other speedcubers have figured out on your own, you looked it up.

[@vdeave]

+GreenArt4 There are no good speedcubers using their own method. It'd be too slow.

[@ogpk3]

oh hey there :D

[@GreenArt4]

***** That's not what I'm saying. My point is that this "own method" thing requires more skill than speedcubing.

[@vdeave]

Learning to solve it from the internet requires little skill. 'Speedcubing' can require lots of skill depending on how fast you are (I would say sub-12 is very skilled, and requires much more dedication). When you say 'speedcubing' that's something that can't be done with these methods. Besides, if you came to this video and then solved it as a result, it's basically the same as looking for the whole method (obviously it's more difficult and skillfull).

[@MuhtasimAlFarabi]

Your dedication to Rubik's cubes are really appreciating. I'm a speed cuber :)

[@Mathologer]

+Muhtasim Al Farabi Cool :)

[@jasonli1895]

I leanrt to solve a Rubik's cube within 25 seconds years ago but now I finally understand where those magic algorithms come from! Amazing video!

[@kajoel]

Moreover, conjugates are a great way to find "shortcuts" in your solution, conjugates have the form A B A^-1 where A often is called setup moves and B is the main algorithm (which might be a commutator). Conjugates can be used to for example cycle three edges around a corner instead of three in the same layer. This "trick" combined with commutators are very useful when developing your own solution to a twisty puzzle and I used it myself to find a solution to the Gear Mixup cube. See this video for more information and examples: kzbin.info/www/bejne/aYivk2OMmcl5hMk

[@Mathologer]

+Joel Karlsson For me conjugates in Rubik's cube solutions more or less go under "common sense": you do a setup move to bring pieces into exactly the position so that you can apply your magic move and then undo these moves again after you are finished, pretty natural I think. On the other hand conjugates really become magical in some fancier settings. For example, in linear algebra when it comes to figuring out the matrix that describes the rotation around an arbitrary vector: you first figure out the matrix A around a vector in the direction of the z-axis which is trivial, and then you figure out a non-singular transformation matrix B that maps your arbitrary vector to a vector along the z-axis (which is pretty neat in itself). Then the general matrix you are after is a commutator of BAB^(-1) :)

[@kajoel]

Mathologer Yes, I have to agree that conjugates are equivalent to "common sense" in cube solving, just a fancier word ;)

[@groszak1]

Assuming lowercase is a slice turn, in 4x4x4 l' U L' U' l is a conjugate, right?

[@ganaraminukshuk0]

One of the simplest algorithms I know is Ri Di R D (or R' D' R D), and I just realised that that's a commutator.

[@khanhnguyennam6007]

Ganaram Inukshuk it isn’t, commutator have to be a 3 cycle or more, that algorithm you list doesn’t follow that rule

[@andrewtan881]

Nam Khanh Nguyen Actually it is indeed a commutator, it’s just that it affects more pieces than just cycling between 3 corners or 3 edges, which is why you wouldn’t use it like you would other conventional commutators. By definition, a commutator is simply an algorithm that follows the form A B A’ B’, but depending on the overlap between the pieces affected by the respective A and B moves, a different number of pieces might move around at the end, hence some commutators are more commonly used, namely the ones that only cycle 3 pieces since they are easier to keep track of.

[@khanhnguyennam6007]

Andrew Tan uh uh, not so fast, as I said commutators have to be 1. 3 gen 2. More than 4 moves 3. Swap in a particular Simply put, if it doesn’t look like a commutator, it’s not

[@andrewtan881]

Nam Khanh Nguyen Those are the requirements for commutators that are practical in a solve, not the outright definition of a commutator. That said, I wouldn’t think of R’ D’ R D on its own as a commutator in a solve either, since it’s not practical to be used as such.

[@trangium]

Nam Khanh There are useful 4-move commutators p, such as M' U2 M U2

[@accidentalengineering]

I've been solving cubes for years now, but never understood how people came up with algorithms without computers. Thank you for this video!

[@Mathologer]

+Gergely Hornich Glad this worked for you and thank you very much for saying so :)

[@solfeinberg437]

Simple insight. Completely clear logic. Empowers us to do something we could never ever have done. The three categories of people. I could've designed my own solutions, but I don't think I'd ever have come up with the insight - design a sequence that makes a single change to the top. Reversing it restores the bottom and the top. If we turn the top before reversing it - we restore the bottom but apply the reverse change to the top relative to a new edge. Man, I'm gonna go find my cube.

[@TankiCubed]

Wow! This is an awesome video! I learned quite a bit of information from this. My best time is 7.18 seconds, but not with this method. Although this method works, it is far easier to solve it while using the common speedcube method called CFOP. I am trying to figure it out like this way (in the video) but it is challenging at times :) Great video!

[@tobycollins9374]

This is for people who struggle memorising algorithms

[@samiam7290]

+Toby Collins Any fool can memorise somebody else's recipe, but only a select few can come up with their own recipes. Speedcubing is pretty much the same skill level as touchtyping (and at the same time reciting the mantra "look how smart I am" for no particular reason)

[@GrashalmTuts]

+Sam I am the challenge about speedcubing isnt memorising algorithmes, its rather looking ahead multiple moves and knowing exactly what to do, and when. By the way, no speedcuber would ever tell you that they think of themselves as superior in intelligence, because they know that it's pretty much only practice and passion that makes the difference.

[@Lucy-ng7cw]

+Toby Collins it's more for people who enjoy working out how to solve things and thinking outside the box rather then memorising many things to get to the same spot. Like for mods.

[@jesusthroughmary]

This is a video about problem solving, not speedcubing.

[@smoggert]

This is kinda the same way I started solving my 4x4 (after having looked up most of the stuff for my 3x3). But I did get stuck at the very end once I ran into the 4x4 parities. As those involve badly placed centers and I honestly couldn't get my mind around those ^^. Just rescrambling the cube until you randomly don't run into parities works. But that's a bit time intensive :D

[@Mathologer]

+smoggert Once you run into parity just give one of the middle layers a quarter twist and then keep solving just using commutators. That takes care of parity in 4x4x4s :)

[@DurfDiggler]

I finally solved my first cube! After figuring out a few “magic moves” for the “top” layer, the commutator worked. Thank you! I have to brag that I’ve never looked up any moves or used any apps, etc. The side piece flip example in this video was the only move I’ve been taught. I came up with a doozy to swap & flip two sides; I messed that one up a few times! I’ll try to shorten that with my next cube. *write down your moves as you develop them* Thanks again!

[@sanjayrao3257]

I have always wanted to solve the cube without resorting to mugging a solution from the web. Using the concept explained in your video, I was able to create my own solution... far more satisfying. Thanks a ton

[@Mathologer]

Great, congratulations :)

[@user-gi3ro9rm9k]

i know how to crack all rubiks cubes. 1. take a hammer 2. smash it 3. be happy that you cracked a rubiks cube

[@76Raby]

I never thought about it this way, but you are right.

[@firewolfquasar4230]

A week ago I bought a rubik's cube. I managed to solve one layer but then I got stuck. I searched for a method like this but didn't find any. I then memorised a cheat but then I found this video. So I went back and found my own solutions. It feels so much more rewarding solving it now since I understand why it works.

[@ozzyfromspace]

I've designed a few algorithms for solving 3x3's after my college roommate introduced me to the puzzle, but I never fully understood why I did what I did, except that if often worked. I'll pull up a book on commutators after this. :) Thank you for adding reason to my madness! I want to spread the word and explain how people can solve cubes. Fastest time: approx. 20 sec. Wonderful video, Mathologer!

[@raterix2]

9:03 Oh, that's an U perm... easy

[@supergamer-oj9ls]

Exactly😂

[@noahwilliams8996]

Can this work on the Rubik's hypercube?

[@Mathologer]

Yes, however, there are slicker ways of thinking your way through to a solution that build on what you already know about the 3x3x3. Did you already watch my video on the Rubik's hypercube? kzbin.info/www/bejne/r5mzeWRpa56CjcU

[@noahwilliams8996]

Mathologer Not yet.

[@Xaotique]

This was actually a really cool way of looking at it. I memorized the simple algorithms you showed in the video years ago, but it doesn't actually give you much of an idea what you're doing. I did some of this without thinking about it, but being conscious of doing it will make it a much more useful tool.

[@Mathologer]

+Xaotique Not only more useful but also a lot more fun :)

[@squarehead6c1]

With the help of this trick, I finally managed to solve the last layer of the Minx and MegaMinx. Thanks!

[@CubeFace69]

I know how to solve most cubes but next time i get a new cube i am going to try this.

[@Mathologer]

Cool, it is really a lot of fun to do it this way :)

[@CubeFace69]

Mathologer hmmm, any puzzles you recommend

[@Mathologer]

Well, have you done all the puzzles shown in the poster shot of the puzzle yet? In order of difficulty I'd recommend to proceed like this: Pyraminx, the octahedron shaped one in the back, the Megaminx, Curvy Copter, the Rex cube (here the trick will only get you (a large) part of the way)

[@CubeFace69]

Mathologer Hmm i might try the Curvy Copter. i dont have that one thanks!

[@Mathologer]

Have fun :)

[@s4archie]

Thanks for a(nother) great video. After solving for 20+ years using a learned solution I had a lot fun today designing my own. One question though: you say that the method is sufficient for all the cubes in the cabinet, but there's a 4x4x4 in there that needs parity-changing moves. I don't see how you can get those via this method (e.g. flipping two adjacent edge pieces).

[@trangium]

Using Mathologer's method, you can only swap an even number of pieces. If a puzzle has parities, they will always be one move you can perform that does an odd number of swaps. In the 4x4 case, an r move (inner layer) will do the trick. Do an r move, then re-solve the affected pieces with ONLY commutators (Mathologer's Method)

[@StefanReich]

I've thought about similar stuff (minimal set of fixed move sequences to solve a cube), but never thought it out fully. Nice

[@rohangeorge712]

Wow, what a trick to solve any puzzle like that. He even showed examples of a megaminx. So it is possible to use this method to solve any puzzle. Just brilliant.

[@pokefanmelody]

better plan: pai- DANGIT HIS SHIRT BEAT ME TO IT Um... move the stickers! What do you mean you have a stickerless one?! Um... TAKE IT APART AND PUT IT BACK TOGETHER!!!

[@Pete-Logos]

Lets see you take it apart and put it back together faster than a cuber who solves it the right way.

[@Thelacho7]

I saw that tumbnail text reference Lotr

[@CoolJoe330]

One weird trick

[@ARandomN3rd]

Good job explaining. Although, I do find the method I learned is easier, I still think this is a good idea for non Cubers who don't know the methods I know

[@B42UC4]

I had never thought that way about creating "magic moves". So simple and yet so powerful.

[@lumschente]

I can solve the first layer Wait, I can solve all layers xD

[@augustmoviereviewer]

I laughed my butt of when I saw an unsolved pyraminx duo. It literally only takes 4 moves to solve!

[@Mathologer]

What is your point?

[@augustmoviereviewer]

My point is your talking about being able to solve "any cube on that self" yet so many aren't solved

[@Mathologer]

I actually find that always having a couple of unsolved puzzles lying around is a great way of getting people who visit me in my office interested in actually trying to solve them. In fact I know of at least 20 of my students who got started as speed cubers in this way :)

[@augustmoviereviewer]

Huh

[@serbudder6510]

+Mathologer good idea

[@arabiccompprograming5161]

Mathologer: Professor Thank you for the valuable advice. I really appreciate it Thanks again.

[@keithmanning6564]

Thank you mathologer, you taught me the Rubik's cube, now I've learnt a new method and can solve it in under 20 seconds. It is now one of my favourite hobbies.

[@Mathologer]

That's great :)

[@auaiomrn]

4th outcome: move all the stickers around and "solve" it

[@Rikri]

So commutators? It takes more than just commutators to "solve them all".

[@Mathologer]

That and a bit of brain :)

[@Rikri]

Mathologer For example, if a non-cuber watched this video and understood everything in it, they probably STILL wouldn't be able to solve a 3x3.

[@Mathologer]

Maybe check out some of the comments left by people who've done exactly that, designed their own algorithms based on what I talk about in this video and then solved the 3x3x3 using these algorithms (and a bit of common sense). Obviously, intellectwise you have to register a certain pulse to be able to design your own commutator based algorithms even knowing this trick. However, once you passed that hurdle I'd say you can be pretty sure that you are also sorted enough in the common sense department to use these algorithms to solve a 3x3x3 :)

[@Rikri]

Mathologer That's not what I mean. Most non-cubers don't even know how to BEGIN solving a Rubik's Cube. Making pairs here and there and hoping to get to a point where it's comprehensible. You explained how to make algorithms, not much of the rest.

[@Mathologer]

Well, there are millions of people/non-cubers who've figured out by themselves how to complete the first layer starting from zero. That's a pretty good start. Now my point is that if you got that far, you've got all you need to make up a basic set of algorithms. And, if you actually took the time to go through with this, using those algorithms to solve the Cube should be trivial. And, just in case you need a bit of help along the way (how to record moves and how to apply algorithms), I've provided instructions in the second supporting part of this video on Mathologer 2 :)

[@lisaskanal8706]

Great video! With this trick I came up with my own algoritm (for twisting two edge pieces around in the pyraminx) I am very excited because this is the first algorithm I've ever came up with by my self, so thanx for sharing this trick!

[@Mathologer]

Glad this is working out for you. A whole universe of twisty puzzles is waiting for you to be solved :)

[@EmosGambler]

actually this is a simplest way to solve rubiks cube blindfolded. I do it with different algorithms to impress people by solving it without looking at it :). great video!

[@xseveredsaintx]

a trick to crack all cubes? throw the thing at the floor at the fastest speed possible

[@Mathologer]

That would definitely work too. There must be a channel somewhere that specialises in smashing twisty puzzles :)

[@Pete-Logos]

Ok, on the count of 3, you take your cube and smash it & I'll solve mine the right way, and lets see if you can sweep up the mess you made before I'm done solving the cube. 1, 2, 3,...

[@therecogniser2122]

That's amazing. How easy mathematicians solve rubik cube!

[@ojasrox]

Awesome man! Wish I saw this when checked for online solution for the first time

[@Mathologer]

+Ojas Raundale Well, there are zillions of Rubik's cube variations. So, just try to solve one of the ones you don't know the solution of yet using this approach. Have fun :)

[@anonymousperson4466]

I can proudly say I'm a self cube learner. And when I say self taught that means I had no one whisper anything in my head about cube solving until I was able to solve it. Here is how I learned the 3x3x3 and pretty much everything else... So, I had a 3x3x3 rubik at home and I was kinda nerdy with it. I would just flip it continuously until it could possibly solve itself. With this I was able to understand the logic till the second layer and a base filled with colours(actually it's not that hard just while putting corner pieces just notice the corresponding edge piece as well, but it took me months to learn this). After that what I realised was that you could actually break a cube and put all pieces like you have solved a cube and this is exactly what I used to do. I would just fix cube again and again and then I try something like doing some moves, doing one random move in between and reversing it. This gave me intuition that things repeat in cube....i.e. if you do the same series of moves on a cube continuously, the cube will be solved again after all permutations. After that I started learning how to delocalise the least number of pieces I possibly can(it means getting the least number of pieces around). This was just enough for me to find out that we can displace edge pieces 2 times and corner pieces 3 times to get the whole cube in the same position except for those involved pieces. It was more than enough to solve the cube. Then I found all the 50-51 combinations of the top layer and the most optimal solution to them. After that I analysed a bunch of other cube or other shapes of rubiks as well and pretty much solved every single one of them. After coming back to cube with all algorithm and stuff I now know that a 3x3x3 rubik can be theoretically solved in 9-11 moves!!!! but it's too hard for humans to come up. For a rubiks enthusiast, my message is till you give up don't look up on the internet, explore the cube as much as you can.

[@er4795]

One time I accidentally solved 3 sides at once with the rest of it mixed

[@willobrien6788]

Coz that's possible

[@pizzawithmyimaginaryfriend1173]

+Sebastien Cuadrado No

[@funicubing7340]

+Will.I.Minecraft 1 side 2 sides and 3 sides solved are all possible you're wrong

[@cosinev1265]

The edge flipping algorithm is L' R F2 L R' D L' R F' L R' Reverse is L' R F L R' D' L' R F2 L R'

[@groszak1]

The edge flipping algorithm is M D2 M' D M D' M' Reverse is M D M' D' M D2 M'

[@sheilastewart1914]

Josh Costantini is that how u solve it?

[@tariq3d]

Love you Mathologer, great video. I am always try to understand the idea behind those algorithms but could not succeed till you showed me the path to find the hidden truth. Thank you Sir.

[@Mikewee777]

Best video on this topic. I was tired of wasting computer power to solve this.

[@Rikard_Nilsson]

My trick is better, I just use a screwdriver.

[@salonishedbale7679]

😂😂😂😂😂

[@davidlu4742]

it still takes way longer than if u solve it manually

[@Rikard_Nilsson]

I don't have that amount of patience to invest in a game.

[@crazymarkmc]

Life is a game, whats your point?

[@matlacking]

+CrazyMarkSRB not rly if i think about it

[@MASTERMIND2368]

You can't flip one edge

[@fawzibriedj4441]

You can if you only care about the first layer, that's what he did in the begining. But if you care about the other layers, you can only flip an even number of edges.

[@error.418]

And he showed that...

[@trinhhieu6270]

.... unless you're solving 4x4 or higher!!!!

[@ziadapp]

I wish I would seen this video before looking up algorithms online! Great video, sir!

[@Mathologer]

+Ziad Modak Well, there are about a zillion other twisty puzzles waiting to be solved by you !

[@dhruvtiwari6828]

I did it finally,I have my own solution,Thank you so much mathologer

[@technowey]

Thank you for this excellent clear explanation. Great graphics too!

[@Mathologer]

Glad you like the explanation and thank you very much for saying so:)

[@KevinsMath]

What an excellent explanation with great visuals! I've recently come across this channel and really really like it.

[@RedsBoneStuff]

I've come pretty far by inventing all my algorithms myself and without looking up any recipies. I can solve my 2x2, 3x3, 5x5, 7x7, 10x10, 3x3x4, 2x2x4, megaminx, and a few other weird thingies. However, I have been doing it the hard way. When I only had a 3x3 and got the 5x5, it took me over two years to figure it out. What you showed in this video is genius and it will be really helpful to me. I will be able to replace some of my long algorithms with shorter commutator-based ones, and it will be easier to figure out my future puzzles. Thanks!

[@Mathologer]

+RedsBoneStuff That's great. Hope you'll have as much fun using this trick in the future as I've had over the years :O)

[@lucjongman1535]

Solved it on my own after 40 years of frustration. Thanks!

[@Mathologer]

Fantastic :)

[@shenqilu4470]

thank you for your knowledge. I mean I used to learn some of them in class, but never think to apply like that.thank you for your treasure. And it's generous of you to share the trick.

[@Mathologer]

+Shenqi Lu Great, glad you got something out of this video :)

[@dylancalvin2180]

This video is exactly what I've been looking for. Thank you

[@Mathologer]

Great, let me know which puzzles you succeed solving using this trick :)

[@bellab4797]

Fantastic video! It's great to be able to understand the logic behind it all - thank you for sharing your time and knowledge, I appreciate it👱

[@jackackattackack]

Thanks sooooo much, using this I managed to solve my Rubik's cube using my own method! I now looked up a more advanced method but also figured it out myself.

[@Mathologer]

+The grappig group Great, mission accomplished :)

[@Hythloday71]

nice, it's kind of like the advice to start a proof you forget by starting at the conclusion and running backward ... usually meeting up with where you could remember ... or provoking the forward memory.

[@benc8386]

Brilliant! Like many people I could solve the top layer when I was 11... then when I was about 40 I read some pdfs about commutators and things and worked out a solution. But I've never seen commutation explained so intuitively. I could have understood this when I was 11 and also applied it (but would never have thought of it). Now I'm gonna try the 4x4x4 and 5x5x5 and maybe one day the 3x3x3x3 :)

[@kamilerastene5275]

Thanks for the tip, this is exactly what I was looking for!

[@plovet]

+Mathloger. Thanks for the video and for encouraging people to solve it by themselves. I managed to solve the rubik's cube (by myself!) a few years ago and was very-very-very happy and proud to have finally done so. My approach was different but that made it more interesting to hear what you said. Good luck to any who is trying it for themselves! Enjoy it!

[@manishkhatri2080]

It's amazing Now I got it.... I saw this video when I was 16 in 2017 and didn't get anything and bored so I didn't saw whole video.... I was searching for this video from months and I recently saw ur mathmatics video and today I realised u speak the same way the guys I remembered from this video...and u were 😀

[@127gerardo1990]

You made great video on solving the rubik's cube with no spoilers. thank you

[@SpicyTurkey83]

I just wanted to let you know how much of an inspiration you are to me. I am an aspiring engineer, who just doesn't have the natural talent of these genius mathematicians, and have been discouraged. You have really given me a spur of hope with your very easy to understand and insightful videos.

[@Mathologer]

That's great :)