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

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

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!

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 :)

Another great video! You explained this very well.

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.

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.

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.

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

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.

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

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

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.

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!

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!

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

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.

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.

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.

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

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!

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

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!

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.

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

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

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

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

*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 :)

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

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.

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!

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

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: ukposts.info/have/v-deo/a4d9lmaNm5p3r5s.html

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

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.

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

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!

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!

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

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.

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

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

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!

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)?

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

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

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!

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

God damn I love Rubik's cubes.

My conlang for cube moves makes rhythmic patterns of move sequences. Each move is a syllable, so easy to remember. FaTa Foto Roto Ra / trade two corners FoTo FaTa RoTa RaTo ToRa TaRo / rotate two corners To RosTiRas To & Ta RosTiRas Ta / orbit three edges (RosTa)^4 (RasTo)^4 / flip two edges These moves solve by doing one face first, then remaining corners, then edge pieces last. Faces are Consonants: T for Top, F for Front, L for Left, R for Right Turns are vowel sounds.. Ō for clockwise, Ā for Anticlockwise, and Ī for a for 180’ flip. To turn the Middle “Inner Slice” layer append an S I learned this when cubes first came out and was a master back then at under at 30 seconds. Amazing to see the fast times now. Anyway, I am sure this little constructed language rewired my kinesthetic hand neurons to my verbal language and rhythm neurons. There is a certain feeling I get in my hands when I’m recalling the words that is hard to describe, and also happens when drumming.

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!

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).

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

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.

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.

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

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

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 :)

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

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!!!

Can this work on the Rubik's hypercube?

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.

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.

I saw that tumbnail text reference Lotr

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

That's quite an interesting trick. Many years ago (before the time of the Internet), after I was able to solve the first two layers (using a similar trick of destroying one corner to fix the second layer, moving the destroyed corner around, then restoring the corner together with the last piece), I could have used that solution very well. What I did instead was trying to find sequences of less than 10 moves (turn corner, down, left, up, left, down, 2left, up, for example) that left the top 2 rows intact, applied them on the cube "upside down" and wrote down (and memorized) what they changed, then tried to combine those moves to solve the cube. Until today, I do not know a solution for every case, but usually by trying any of those moves (e. g. that move only corners) a few times at random, I get to a pattern I can solve. Next time I'm trying to solve a cube and am stuck at a pattern I don't know how to solve, I'll try your method :)

+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!

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

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

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👱

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.

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

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

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

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

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

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'

Thank you for this extremely helpful video! After watching this video I got into solving various twisty puzzles and my journey so far has been a very fruitful one. One request - can you make such a video to explain and solve 4 x 4 parity cases? I get stuck at 4 x 4 cube's last layer due to parity cases and then I have to look up other's people recipe to solve it. I have searched the net and could not find a decent explanation and solution to this problem which does not require memorization.

Since i found Ryan Heise's website i've been interested in commutators and conjugates. Watched some videos that helped me A LOT, but yours is by far the most didactic. Thanks for sharing your knowledge

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

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

Out if all the tutorial videos for solving the rubiks cube, this is the best by far!!! Not only it doesn't give you an algorithm, but also lets you CREATE your own solution!!!! There is just one thing, about the commutators. Since we have to run it in reverse it should be ABB(-1)A(-1)

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

My trick is better, I just use a screwdriver.

You can't flip one edge

I came to this trick 16 years ago, it's so simple! In general you can solve every 3D-Puzzle with it, but you may run in some trouble with cubes bigger than 3x3x3, because this solution requires that a puzzle can always be solved in pairs of moves. This is not the case if a slice is rotated 90 degrees. For a 3x3x3 cube you see this problem instantly, because in the last layer exactly one pair of corners and one pair of edges is swapped. Obviously you can not solve this by the shown algorithm but you fix this simply by turning the third layer one time. For bigger cubes, especially those without centre pieces (4x4x4, 6x6x6 ...) you start to combine edge pieces and centre pieces until you have a "virtual" 3x3x3 and solve this, but at last you may see something that is just impossible with a 3x3x3, like one single flipped edge. For me that means turning a slice of this "impossible" piece and starting over again. The second time it goes faster because most things are still grouped together and you are sure that this time it can be solved. I'm sure there are faster ways, but it's sufficient for me that I can solve each existing 3D puzzle and also each still to come :-)

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

I created an algorithm similar to the one at 4:02. I started with an E turn (equivalent to D' U), then I used "R F' U R' F" to reorient the FR edge without affecting any other pieces on the E layer. Then, I undid E, and undid "R F' U R' F". This algorithm flips the FL, FR edges. Here's that algorithm in conjugate form [E, R F' U R' F]. The algorithm modified to flip the same edges as you did is [x' z2 U' R': [E, R F' U R' F]] ). x and z are cube rotations.

Thank you sir for this beautiful video,I am a Mathematics students and can really feel the Mathematics you explained. I really appreciate and love the videos. I am going to give a try to develop an algorithm. Thanks you

That's a bit more clever than what I figured out. I figure(d) out a move that does something that I want, then I perform it twice-once to undo something I've solved, then again (forwards, not backwards) to fix it. Then, (once), I analyzed what the side effects were and pre-positioned as-yet-unsolved pieces to end up correctly-placed when I use the double-move as a move. I can do the cube in 2½ minutes, and I've gotten to the last layer of the Megaminx. The last layer is just a matter of charting it out, but I just haven't bothered. But now you've provided a much better way of working it out. I think most of my moves still work fine, but the last layer has always required some time-consuming move-repetition to work my way through a short cycle of long-ish moves (say 3-4 repetitions of 12-turn moves, then a choice-making step to decide where to do that again, and if it needs to be mirror-image-a couple times).

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

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!

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.

Thanks for this, years ago I could solve the 1st 2 layers easily but then had trouble with the last layer. I then memorized moves from a book (this was before the internet) to swap edges, swap corners, flip edges and twist corners, and could then solve the cube while it was popular. But fast forward 30 years and I had forgotten the memorized moves and was again stuck on the last layer. But thanks to this advice, I can now solve the cube again! Now I know what I'm doing, no memorization! I think I'll put it away again and solve it 30 years from now.

I learned how to solve the Rubik's cube when I was 10. I memorized some patterns that my father had given me (I think they had to mail order the solution) and it's been locked in my head ever since. The trick was to solve one side, then solve the opposite side, and solve the middle layer. Over 30 years later, and that solution is still stuck inside my brain, and I have no idea *why* it works. My parents were very happy that I took and interest in the puzzles, so they got me a Pyraminx (tetrahedron puzzle), a Rubik's Revenge (4x4), and the duodecahedron puzzle (but I don't remember what it's called). I was able to solve the Pyraminx on my own (and don't have any patterns for it) but have never been able to solve the other two. I tried memorizing a new Rubik's Cube solution this past year, where you solve one side, and then start solving layer by layer. I don't have it memorized yet. I was less interested in being fast, but more that I wanted to figure out how to extrapolate the solution from a Rubik's Cube to the Rubik's Revenge. When I saw your video in my feed, I didn't really think it would help. Watching the video, though, was an "Aha!" moment for me. I'll probably need to have a pad of paper with me so that I can write down my moves and replay them, but at least now I have an idea for what direction I need to go in. I'm still not sure if I'm going to solve the cubes layer by layer, or rotate a face in a new direction to solve it, or what, but now I'm excited that I have a new method to try to "figure out" the other puzzles. Thanks a million! I'm also going to share your video with a couple of friends at work. One of them managed to figure out how to solve a Rubik's Cube on his own, and that always impressed me.

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 😀

Interesting! I recently mastered the method to solve the cube in layers, but I think it would be more fun to solve by faces maybe by developing our own moves. I suspect that the layered approach is geared towards speed cubing.

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