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

Today I’m going to tell you about
something that’s really close to my heart. It’s a super simple trick that allows
you to find your own solutions to pretty much any Rubik’s Cube on that shelf. That sounds too good to be true but it’s
actually true, it’s really quite amazing. So, what I’m going to do is I’m going
to explain the trick using the normal 3x3x3. My audience is going to be
this guy here my 11-year old, Karl. Say hello Karl. (Karl) Hi. (M) He is there in the background and what he can do is he can solve the first layer of the Rubik’s Cube and the
main message of this whole video is going to be: “If you can solve the first layer of
any of those cubes, you can solve them. You don’t have to
look up any sort of recipe.” With the trick that I’m going to tell you about
you will be able to design your own solutions. Anyway, he can do the first layer, a lot of people can do the first layer,
probably millions have gotten to the stage where they’ve solved the first layer. So first layer, again. You look at a Rubik’s Cube you
basically see one of those things, completely solved. Why is it so hard to get beyond that
stage. Well what’s really, really difficult
there is that as soon as you do something now, pretty much anything,
you’re going to cut into what you’ve just solved and you’re gonna destroy it. That gets very frustrating very quickly and there’s pretty much three
different outcomes now for most people who got there. The first one is you give up, that
probably happens in the majority of cases, second one is you go to internet
and look up somebody else’s recipe to go beyond that and the third outcome is you
actually persist and somehow get your own solution. So what I want to do today is to enable
as many as possible among you who are watching this video to
actually get into this third category where you find your own
solutions of the Rubik’s cube. Ok, let’s get going. Anything you do now is going to
destroy things. So what we’re looking for at this stage is some magic moves, really sequence of moves, what the magic moves are going to do is
they are going to leave pretty much all the Cube intact and only touch and
manipulate small parts of it. For example, one thing you might want
to do is you want to look for magic move that just flips that edge here. Just flips that edge here, how hard is
that? Hmm, very hard, just think about
it. There is just no way I’m going to do be able to do this. To find a
sequence of moves that just flips one edge is actually not too hard if you
just have to worry about the first layer so just flip that edge and leave the
rest of the top layer unchanged. In fact, if you are a master of the
first layer you can permute that first layer any way you want. You can actually
do this. You may not be aware of this but you can as long as you don’t worry
about the bottom. So let’s just do that. So, go home do it, right? I’ll show you an example of how to do this. So what we can do is we can maybe do something like this turn things out of the way so the sides
come up again and we turn this guy over, we do that, we do that, sides back and, well, we’ve just found a
move that just flips this edge here and leaves the rest of the top layer
unchanged. Ok everybody here, Karli, still understand it? (Karl) Yes. Very good, alright, ’cause this is for
you, Karli, you’re supposed to understand this, alright? Now let’s unleash the whole thing
on a solved cube and see what happens. Your move, let’s unleash it on a solved cube and see
what happens. Well it’s getting messy but
basically the top layer is fine, right, the top layer is fine except for this one
flipped bit. Of course the bottom is messed up. And now comes the really really, really
important question: “How can we restore the cube really, really easily? Karli? (Karl) You do it in reverse! (M) Exactly and we didn’t even
rehearse this. Ok, so we do it in reverse. Obviously if we do the whole thing in
reverse it’s going to solve the thing, right? So let’s do this in reverse, here we go,
doing it in reverse, and, doesn’t come as a surprise, the whole thing is back to
normal. Let’s just put in the move again. Put in the move again. Now what does
the reverse move actually do? So in the top layer what does it do? Well it leaves everything in peace except
for this one edge which gets flipped. And what does it do to the bottom part Karli? Does it fix it? (Karl) No (Karl’s sister in the background) It fixes it Karl! Ok, so what does it do to the bottom part, Karl? (Karl) It fixes it. (M) Exactly, it fixes the bottom part. Very good, very good, we’re getting there.
It fixes the bottom part. Now we’re not going to run it in reverse straight
away. Here comes to trick and it’s so simple you won’t believe it, really. What we
do is, we just give the top layer a twist and now we’re running it in reverse. And
now we’re going to try and predict what’s going to happen and then we have
it happen. So what is going to happen is, well, if you run your move in
reverse now well it should just flip that edge piece
on the top and it should restore the bottom. Let’s just see what happens. So run
it in reverse, here we go. Alright that already looks very very promising.
We can make it look even more promising if we undo that twist of the top, so
let’s just do that and turn it around. And now in total we’ve come up with one of those magic
moves, a magic move that only affects two edge pieces, flips those two edge pieces. Pretty amazing, right? So, for example, if we’ve got a messed-up cube like this and our aim is to just flip
those two edges, we can just use this combined move now to achieve this. So, we’re doing your move, then we’re doing
the top twist, then we’re doing your move in reverse and then we’re doing
just the top in reverse. And then at the end that whole thing would look exactly
the same, except that these two guys are flipped. Good! Important thing is that the only thing that really requires your input here is to design this move that just
affects the top layer. You don’t really have to worry about
everything else, okay. Let me give you another example. So, maybe you want to twist some corners
in isolation, right? So maybe you want to twist that corner here. Now if you just
worry about the top layer and not about anything else you know it’s pretty easy maybe
something like this, right? If you look at the top now really
only that corner has been twisted. If we unleash that move on a solved cube what do we get? This thing, obviously the bottom is is messed up. Now how do we turn this whole thing
into a magic move. Well we turn the top a little bit. Now we the run things in reverse and
so what’s happening here? Well let’s have a look. Only those two corners are affected, those two corners get twisted,
nothing else is affected. Again, you can design something like this very easily. Just one more example. So
far we’ve just been kind of stepping on the spot, twisting things,
flipping things but obviously you really want to also find some magic moves that
move stuff around. So let’s just do that, let’s move some things around. Let’s have another close look at the top layer. Well if, for example, we move that edge piece
here somewhere. Well, it has to go somewhere so whatever
is there has to go somewhere else and well the simplest thing we can really do
is to of swap those two pieces. And again if you just worry about
the top layer you can do this, design something that does exactly that. Here we go, just an example, you probably come up
with something totally different, it doesn’t matter. The main thing now
is, you’ve recorded your move, you give the top a twist and you run your move in reverse. Okay. And untwist the top and let’s just have
a look around. Everything’s fine except three pieces have been moved around and I’ll just show you exactly what happened
here. This guy here moved over there,
that guy here moved over there and that guy here moved over there. Like that, ok? So this particular magic
move what it does is it cycles three edge pieces and leaves everything else unchanged.
And you can do the same sort of thing for corners, you can designa magic moved that moves corners. And so in total what we’ve done now is we’ve designed four magic moves, one that flips edges, one that twists corners, one that moves
edges and one that moves corners. And together with a bit of a common sense
this is a complete recipe for solving the Cube. Might not be completely
obvious but obviously, you know, if it’s supposed to be YOUR solution so now it’s really time to sit downand fill in the gaps. I’m going to do a footnotes video where I give some more explanations of all this stuff, but that’s basically it. Alright now this guy’s really happy.
Karli are you happy? (Karl) Yes. (M) Very good he’s happy. Did you understand everything? (Karl) Yeah. He’s probably just pretending but anyway. (Karl) Hey! (M) 🙂 I am going to test you on this later, okay? So I claim that this kind of works for pretty much anything here on the shelf and so
just to give you an example let’s have a close look at this puzzle here, it’s called
a Magaminx. Very nice puzzle. This thing also has a top layer,
here it is and again. Very very easy to restore just this top layer and it’s
also very very easy to design a move that flips one of the edges if
you don’t worry about the bottom. And then you take this move, you give
the top a twist, run your move in reverse and untwist the top and the effect
this has is exactly the same as what we’ve seen before with the Rubik’s Cube.
And just like with the Rubik’s Cube, you can design a total of four magic moves and
with those for magic moves you can solve this thing. Now these magic moves are examples of
what’s usually referred to as commutators. That’s actually a mathematical term. So it’s
expressions of the form A B A inverse or A reverse B reverse In our case the A corresponds to your move, the B corresponds to twisting the top, then your move in reverse and then top in reverse. But that A and B can
actually stand for any sequence of moves. So say A is a sequence of moves and B is
a sequence of moves and if we then do A first and then B and then A reverse and
then B reverse that tells us something about the two moves. What does it tell us? Well, order matters
when it comes to the Rubik’s cubes. So usually it matters whether you first do
A and then B or whether you first do B and then A. Usually you get totally
different outcomes. Unlike when you multiply numbers. So for
example if you’ve got 2×3 well that’s the same as 3×2. With
Rubik’s Cube moves it’s different. For example, if
we take this Megaminx here and we twist the top here and then we
twist that side here the outcome is very different from first
twisting the side and then twisting the top. So what does this compound move tell us
about A and B. What it tells us whether they commute or not. So take a solved cube, ok, so maybe a solved
cube like this guy here and then we have a sequence of moves A and we’ve got a
sequence of moves B. Now we do A, then we do B, then we do A in reverse and then we do B
in reverse, unleash it on this thing here and see what happens. Well, if nothing happens, so if that Cube
basically stays unchanged by this compound move, what that means is
that the two moves A and B commute, that it doesn’t matter whether you first do A
and then B or first B and then A. The commutator is a measure for how
close two moves are to commuting. So the less stuff gets shuffled around
here as a result of ABA inverse B inverse,
the closer the two moves are to commuting. Very very important in
mathematics, for example, in group theory but also in physics and quantum
mechanics but, you know, that really goes beyond this video. So that’s it for today.


  • 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 🙂

  • Tushar Sil

    can you give me the algorithms of those move?

  • Joel Håkansson

    Wow! Using this method, I just solved my first cube ever (after 30 years of trying)! It was a 2×2, but I think the 3×3 will be solved soon as well. I have of course solved the cube before using someone else’s algorithm, but I never understood how to get from point A to B beyond the first layer. I used to play with the cube quite a lot as a kid and I always found it so frustrating that I couldn’t come up with a solution on my own. Thanks for making this video.

    By the way, the other video you mentioned at the end, is it available?

  • SuperSonic7418

    i cringe every time he says recipie

  • Amusing AJ

    What’s the cube at the very bottom left called, because I really want it, because I solved it intuitively at a hotel because it was the „hotels only cube“ but I don’t have it

  • Striped Zebra

    +Mathologer How long did it originally take you to see this simple trick?

  • Chandan Singh

    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

  • Myriam Marchand

    interest thinking timing labor organ silk down crack rather statement treaty.

  • Linda Allan

    If I could like this video twice I would

  • Mieeetek 4

    Flipping or swaping edges on a megaminx intuitively is not easy at all because there is no middle layer. Great video anyway.

  • Jason Li

    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!

  • KendrixTermina

    Lets appreciate the bonus gradeshoolers.

  • Nathanael

    Interesting, but this still makes the solving process essentially systematic, only with the added step of deriving algorithms for each maneuver. If this method was discovered by the individual, the solve would be entirely genuine, but given it, the solution becomes guided more by spatial processing than true ingenuity. There's still an element of instruction, of pre-established thought, that detracts from the work that must be completed by the solver. This makes it more feasible, but consequentially less rewarding.

  • Alex Fung

    Here is a full solution on the same spirit. Can be viewed as a example of applying the trick to the classic cube.


  • Ggdivhjkjl

    Why did your son get a role in this clip but not your daughter? It seems pretty clear which one's the more experienced.

  • HEALTHY Recipes

    2500 sub

  • HEALTHY Recipes

    Now 299050 sub lol


    You told 3 solutions, the fourth solution is to destroy that cube if you are an angry man.

  • Niral Shakya

    how to move corner??

  • lazyeffectz

    9:19 freaking U perm

  • bluerizlagirl

    Actually, it is possible to solve a 3*3 Rubik's cube puzzle using only THREE algorithms!

    This algorithm rotates three edges around the upper front left corner (UFL), and flips the one that moves down the left-hand face (FL→FU→LU→FL) :
    u D r U d F u f D u R d U U
    where UPPER CASE letters (Front, Back, Left, Right, Up, Down) indicate clockwise twists, and lower case letters indicate anti-clockwise twists.

    You can use this algorithm to permutate around and orientate the edges on the middle and top layers at once. Remember, the piece that comes down the left-hand side flips over as it drops into the middle layer. But the piece going up from the middle layer and the piece moving around the top layer retain their orientations. So by rotating the entire cube around the upper front left corner, we can choose which piece is going to be flipped.

    First solve the bottom layer (actually, it is easiest to solve the front or top layer and then turn the whole cube around …..) You can make this up as you go along, there are 8 pieces you care about and 12 that you don't, so the odds are in your favour 🙂

    Second, solve just the corners on the top layer (they are all there already, since the other 4 corners are all in the already-solved layer; they just need to be correctly "P&O"ed — positioned and orientated), so as to form an X on the top and a sort of underlined Y on the front, back and sides. Maybe there will be some other bits filled in by pieces that are already solved by chance.

    Third, use the above algorithm to solve all but one of the edge pieces on the middle layer. Find a piece you need to bring down to the middle layer, on the top layer, and hold the cube so it is going to come down from the upper left to front left. If it needs to be flipped, then just perform the algorithm. If it is already the right way around, revolve the whole cube around so it is going to go either up the front or across the top before you do the algorithm. The difference it makes is whether or not the piece which is going up to the old top layer should be flipped or not.

    Lastly, use the "gap" in the middle layer (i.e., the place where you did not solve that piece) to move pieces through in order to position them correctly around the top layer. Move a piece into the middle layer, remembering that if it is going down the left hand face it will get flipped; then twist the top layer so it is going to go to the right place on the next move. Once you have positioned two adjacent pieces correctly in the top layer, then you will fill in the gap in the middle layer automatically on the next move.

    Phew! It is not as hard as it looks, from reading that. When you have an actual cube in your hands, you will see exactly which piece needs to move to where and whether or not it needs flipping.

    I don't know if or not it is possible to solve a cube from any starting position using only TWO algorithms. I guess there probably is some sequence of moves that moves corners around in a "loop with a twist", which then could do double duty for the permutation and orientation stages. But I guess I will have to go and see if I can develop one, or prove it is impossible.

  • Saransh agarwal


  • auaiomrn

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

  • irfan k

    Please give the examples of solving of eight axis six said rubik's cube

  • Christian Mares

    I have a simpler solution, it requires you to think outside the box. All you have to do is remove the stickers and place them on matching sides.

  • B42UC4

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

  • potato psoas

    well I guess if someone out there can solve them then I can too

  • Donald Sayers

    This is exactly how I first solved the cube.

  • Kahlan Bennett

    I do not get it

  • ImpulseRaphii

    Why found new PLL but longer algorithm? xD

  • Ash the Snowman

    I don't understand this

  • Sovereign Shahid

    at least it teaches me commutators

  • FBI

    I dont understand ?

  • __CactusKing__

    why is everyone's square 1 always scrambled?

  • Vidar Kristiansen

    Hello Mathologer

    First of all, thank you for providing some great YouTube content 🙂

    I have a question regarding Rubic's cubes of dimension 4x4x4 and higher that I have been asking myself for a while, without finding an answer to it online.

    Do the Rubic's cubes with dimensions larger than 3x3x3 actually have more than one end permutation that would qualify as a solution?

    I mean, take the 4x4x4. The edge pieces are there in pairs with similar colors, and the center pieces are there in quadruples with similar colors. Will a solved cube always end up with the different physical elements in the same positions in relations to one another or are there multiple apparent solutions, due to the fact that you have pieces that look exactly the same color wise, but are not physically the same?.

    May I suggest that you make a YouTube video addressing this question?

  • Daryl McCullough

    What are the chords at the beginning of the video from? They sound like the beginning of Kate Bush's "Babooshka"?

  • HellaSinful

    Color scheme on your shirt is wrong

  • Twiggy Pan Cake

    That's right one step


  • Ganaram Inukshuk

    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.

  • Philip Strimpel

    This works easily on shallow cut puzzles to the Nth dimension but not so easily on deep cut puzzles with certain geometrical symmetries.

  • DWORLD 2018

    ???????. You almost had me but then I couldn’t break through the atmosphere later…which has been my problem with mathematics although I love it so. ????

  • Jonathan Walther

    Sweet! Nice vid, thanks a lot and keep on the great work.

  • Blacklight

    simple trick

    14 minute video

  • Rayan Sharara

    One thing, this does not work on a gear ball which was on the shelf at 10:28

  • Kai Le

    That would the hole month! You know what faster

    Look on the internet! No joke

  • Tripti Biswas

    It is bad

  • Changyau Chen

    Great! I had solved Rubik's cube,using other people's recipe. But I didn't feel that I really solve the cube. Math is useful.

  • Константин Меляйкин

    Торжество логики. Я по-другому решал сборку кубика 3х3. 2 слоя быстро получились, а на третьем пробовал простые, однотипные движения и смотрел к какому результату это приводило. Месяц потратил на первую сборку.

  • J Knudsen

    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.

  • Seyoung Jeong

    뭐라는건지 알아야……

  • William Graham

    This takes me back to 1981, before any of the "How to solve Rubik's Cube" books came out.

  • Karver Gluck

    I really hate that I learned how to solve the cube online

  • Hunar Omar

    Can carl solve it now? 2018

  • Sergey Menshov

    Thank you for a good video! It was very interesting to me.

    I also have a similar way for twisting and changing corners and edges – https://youtu.be/OM-5ZYnuzMs

    It's a completed method for corners and edges without any other algorithms – totally 4 algorithms how to do it as you said.

    changing 3 corners – (R'DR)U(R'D'R)U(R'DR)U2(R'D'R) or (R'D2R)U(R'D2R)U(R'D2R)U2(R'D2R)
    changing 3 edges – (FEF')U(FE'F')U(FEF')U2(FE'F')
    flipping 2 corners – (R'DR)(FDF') U2|U|U' (FD'F')(R'D'R) or (R'D2R)(FD2F') U2|U|U' (FD2F')(R'D2R)
    flipping 2 edges – (FEF')(F'E2F) U2|U|U' (F'E2F)(FE'F')
    and also we can changing 3 corners and edges – (R' D'E' R) U (R' DE R) U (R' D'E' R) U2 (R' DE R)
    I've got it on my own in 10 years. Yes, it's a very long way, but it was very interesting. ))

  • Luiz Augusto Prado

    the best explained I find.

  • Frankenstein Insane

    I solved a Megaminx by doing somewhat what you explained here… (But I didn't like this video that much as I am speedcuber all ur other videos are amazing!)

  • Jerry Rupprecht

    My solution is to peel off the stickers and stick them where they belong.

  • John Harold Narvaez

    I will be happier if I can meet Lara lol

  • John Harold Narvaez

    Hi 2018(soon 2019) watchers

  • Ethan Bartiromo

    Amazing video, very insightful

  • Thijs Beentjes

    Doesn't work for square-1 though, does it?

  • 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!

  • Rishabh Gupta

    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.

  • NJ Lewy Productions

    Magic Moves = Algorithms

  • Ali3nat0r

    Am I the only one who hates that sequences of moves are called "algorithms" in cubing? That's not what that word means, at all. The whole process of solving a cube is an algorithm, doing a preset sequence of moves is not.

  • macaco maco

    this bald guy has good ideas but hes so confusing… i cant believe hes a professor of mathematics.

  • Aleksander Rubik


  • Radurty

    4th outcome: cube comes with instructions

  • Gustavo Lopes Perosini

    I would love to see a similar video about the pegs solitaire game!

  • Thaddeus Melchior

    Can you please come to Penrith NSW Australia and meet me in person?

  • Nils Matt

    I can solve the first layer

    Wait, I can solve all layers xD

  • Majid 131

    എങ്ങനെയാണ് സ്പീഡിൽ ചെയ്യുക

  • Pi

    Clock be like

  • Brycen Campbell

    I don’t get the video

  • Taxtro

    Is there any maths that's not applied in quantum mechanics?! Perhaps logic or category theory, I guess…

  • TimePiece Wonderland

    0:00 ok I think this is fake

    0:05 damm that backround yep this is real

  • Dolo03

    Phrase on preview sounds like inscription on One Ring from LoTR

  • TC TrainConstruct

    to swap two edges I use only 9 moves!

  • Michael O'Marah

    Hi Carl

  • PLL Skip

    then why are most of them scrambled

  • Pulse Fel

    gah that animation moves too fast too follow!

  • Dhruv Datta


  • Eric Berger

    I have solved the first, second, third & the fourth layer of it

  • Dhruv Tiwari

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

  • 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.

  • Adam Nahajowski

    For 3×3 the much easier methood to explain is the LBL methood because it has
    only up to 6 short algoritms.

  • Canes Venatici

    One trick to rule them all, One trick to find them, One trick to bring them all and in the darkness bind them.

  • geerky42

    Not sure why but it doesn't seem to work on LanLan Rex Cube

  • The Formal Top-hat

    I finally solved my curvy copter ??

  • Jeremy Redd

    Is this related to Thistlethwaite's algorithm?

  • Biednymaniek

    Why so fast it is ?

  • Saul Savelis

    when I was 14 it took me 3 weeks too to master all layers, but I had 6 different (even more) combinations (2 for centrals and 4 for corners) and didn't believe that others used them…I always thought that better combinations (formulas) exist and the easier ones.

  • Dino Man AJ


  • godwin972

    I can’t help but feel like there’s a group downvote-bombing Rubik’s-Cube-related videos.

  • Paul Justine Matias

    While watching i was playing with my rown rubix cube

  • Sol Feinberg

    I've often wondered how in the hell people thought about these / came up with solutions. And figured it would probably involves some more advanced mathematics than I possess or maybe involve starting from a certain layer, messing it up, getting back to the layer and somehow tracing the steps in between and the impact on the unsolved portion? Anyway, if this video can help me, I'll be impressed. This guy seems to kick ass, though.

  • Sol Feinberg

    Oh, my God! He's turned solving the top into moving the bottom! This is incredible! An algorithm does one thing to the top, in reverse puts the top back and restores the bottom. But doing the sequence, turning the top, and then reversing it, restores the rest of the cube and only affects the top by moving the one edge that was flipped, say, and then after turning the top and reversing the algorithm – does only affects the top by "reversing" the new position (flipping the new edge) but restores the bottom, so we can flip two edges without affecting anything else – we can move bottom edges without affecting the top 2 layers. And we've figured this out, but just moving the top! We've turned solving the bottom into solving the top! Where do we donate money? I don't have much, but I'd like to give something.

  • Sol Feinberg

    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.

  • Sol Feinberg

    Success – Extremely powerful trick indeed – Enabled me to do something I could never have done. But agree completely – super simple in hindsight. I might teach my kids how to do this. I made a lot of mistakes, and some interesting discoveries about parity. So it took me "forever" – in this case a few hours – to do something that I would've been proud to do in a lifetime. I would've been proud if I'd made that insight, though – that would've been an accomplishment. Anyway, thank you very much.

  • Rashmi Peters

    Very helpful thank you keep up the good work
    U just earned a subscriber


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