Nice question. The largest period is 1260. For example, (R U2 D' B D') has a period of 1260 - perform the action 1260 times and you will visit 1260 different combinations before ending up back where you started. But that's nowhere near the 43 quintillion combinations of a Rubik Cube.
Srinjoy Majumdar No. it’s on the completely opposite end of the spectrum. It is literally the furthest thing from being solved and any one move can be used as the first move of the algorithm thus making it one less move away from being solved.
Yes it is my living (if that is what you call it?) A video can take an hour or two from idea to upload... or it can take many weeks.... I'm usually doing quite a few at the same time, so it is really hard to judge how long one video takes. I'd guess about a day on average?
I've been solving rubik's cubes for over 4 years now, and my friends ALWAYS try to get it so that 2 colors are not directly adjacent, not caring about diagonally, and they could never do it. This is just amazing :)
Are you sure that 20 moves is THE MOST? Cause seriously I could solve a rubiks cube for 100000000000000 and more moves. A rubiks cube can be solve AT LEAST 20 moves alright? Were you even watching the video
I am so happy that Numberphile have started the Rubik's series! I've been watching Numberphile for a year or so, and started cubing recently, so my 2 favourite things at the same time!!
If anyone wonders: a state where all corners are turned, let's say, clockwise (it's the same for counterclockwise) would also have this commutative property. But this state does not exist, since there are 8 corners and if you want to turn a certain number of corners in the same dorection, it has to be a multiple of 3.
Thanks, I see what you mean: The superflip commutes with *everything* and not just with *one* other move. That's what makes it special. (By the way, I meant "R and then L" in the comment above.) I am a fan of your singingbanana videos, too. Thanks for taking the time to make them.
This video and others in the series convinced me to buy a Rubik's cube. After having one as a child and being endlessly frustrated I'm happy to finally be unlocking the secrets. I figure I will learn the methods first and let the principles unfold then I'll start puzzling over the math. Thanks for including the Superflip notation & reminding me to follow Dr. Grimes on Twitter. I came back just to make sure I was using the same notation as numberphile. It's much better than the one I made up.
There is a move that looks similar, but doesn't have the same properties. From a solved cube, R2, L2, U2, D2, F2, B2. It swaps the edge colours with the colours of the opposite side.
Another way to superflip your cube is to solve it using the beginner's method, except purposely making all the second layer edge pieces flipped in the right place, continue solving as normal, flip the edges to the right position, and the top layer should now be superflipped. Now flip the cube upside down and flip the edges once more. The cube is now superflipped. How many times did I say flip?
Another interesting thing, if you apply this algorithm after (or before) the superflip, you wind up with absolutely no colors adjacent to each other, horizontally, vertically, or diagonally. U2 (R U R' U')3 (L' U' L U)3 (L U L' U')3 (R' U' R U)3 U2
I've been playing around with Rubix cubes for over five years now. I can solve fairly complicated ones, although I am no speed cuber. But I had no idea about Superflip. Loved the video!
This is true. And there are other positions where it doesn't matter which one you do first. Any one where the location does not change, only the orientation. So if you were to turn the corners for example that would work.
@Ibakon Ferba: it doesn't matter if it is B2 or B2' because either way the back face moves 180 degrees. If you think of the cube as a circle, 180 degrees clockwise is the same as 180 degrees counter-clockwise
i think thats because he missed some notation on the order. when i does the back the second time he turns it twice anti-clockwise. but doesn't note the "back dash" :-/
Superflip has order 2, so it is its own inverse, and superflip is in the center of the group, which means it commutes with everything else in the group. Since the superflip and 'do nothing' are the only moves which commute with everything we can see that the center of the Rubik's cube group is isomorphic to Z/2Z.
The explanation is not simple I'm afraid. From what I can gather, you need some pretty deep group theory, including the structure of the Rubik Group, some group theory tricks, and some computing power.
I think another interesting fact about the superflip position is that the cube is technically solved. All of the pieces are permuted in their proper positions, just not oriented properly (facing the right way). Great video :D
I don't know why, but i like this guy, just seeing passion in he's eyes and smile everytime when talking about math make this video more interesting! :D
And the superflip isn't the only alg that has the unique property about stuff then superflip is the same as superflip then stuff, I tried it with one of the first that came into my head, the four spots alg (M2, E M2, E') and it does the same thing (most of the time)
+Eoghan Spillane If you can choose "stuff" in such a way it doesn't work, then it doesn't work for all cases. With the superflip, it works for any "stuff", no matter what you choose. Always. And the superflip is the only move that does that (apart from identity moves, obviously)
Actually if you made an algorithm that rotated all corners clockwise wouldn't that do the exact same thing as the superflip just for corners and therefore be another move that has the stuff then move = move then stuff
Eoghan Spillane That would work, but such an algorithm cannot exist. You can only rotate one corner clockwise and one anti-clockwise. You can use the algorithm again, rotating a different corner clockwise and the one that rotated anti-clockwise again, you essentially rotated three corners clockwise. But the cube has 8 corners. If it had 9, this would work :)
I have, on top of my desk, a 2*2, 3*3. 4*4. 5*5, 6*6, 2*2 mirror, 3*3 mirror, 3*3 star, skewb, pyraminx and a void cube that I 3d printed, Eat that unpopular guy.
So the Superflip commutes with all other algorithms, or it's commutator is 0 with all other operators. And when you look at the physical implication of just flipping edges it makes perfect sense. Very elegant.
M' is the middle slice, between the left and right sides away from you. U' is up anti clockwise. y is a cube rotation, and means rotate the cube so the Front becomes the Left. x' is a cube rotation and means rotate the cube so the Front becomes the Bottom.
Something just clicked for me watching this video. A cube has 6 faces. There are 6 kinds of quarks (up, down, top, bottom, strange, charm). Coincidence?
I think so; this would imply a universal set of axis for which each type of quark would be associated, otherwise the type of quark would depend on which direction you are looking at it from (and what would be the expression of looking at a quark from a non-axis direction)?
I like that a lot. How would you translate them, if the convention was to name the Cube's sides in quarks? Strange = Left, Charm = Right, that's easy thanks to Sinister and Dexter. But is the top of the Cube "Top" or "Up"? :)
I have a completely different way of completing the superflip. It takes 36 moves instead of 20, but is faster to complete. The basic motion is rotate the center column away from you 90°, then rotate the top clockwise 90°. Do this 4 times, then rotate the cube CCW about the axis that runs through the upper left corner closest to you. Do this process 3 times, and the cube should be superflipped.
I always sucked at solving those Rubik's Cubes. I once got to a point, where I got a superflip (by just randomly messing around with the cube, not actually trying to solve it). I thought, that pattern looked rather beautiful and interesting. Now I got this video and know, that it actually is.
Only simpler for experienced cubers. Without explaining what M, x and y are, most people would prefer the one that James does. For those who want to know, M is a turn of the middle vertical slice going from Front to Back, so M' is a turn of this slice that follows the direction of L. x and y are rotations of the ENTIRE cube about those axes, so x is in the same direction as R, and y in the direction of U.
I saw this vidoe and then I wanted to try it myself but then I realized that I didn't had a Rubik's Cube! Now I got one and it's an amazing thing! If you dont have one you should get one because in a Rubik's Cube there are 43,252,003,274,489,856,000 twistable combinations of fun! Clearly worth 10 £!
I suppose it would be accurate to conclude that the superflip order thing works because the outcome of the super flip is in relation to the _whole_ rubik's cube - it's a re-composition of the entirety - whilst a single move is merely a change in one certain area. Say you were to fold out the cube so that all the sides were visible at once. The superflip would then be one set of combinations to preserve a certain relation/symmetry between the units/colours. Perhaps I'm being obvious.
It's flossing for the mind, it increases intelligence and after you memorize the algs you start seeing and understanding the puzzle in your mind. For some people with speech problems or motor controls it rehabilitates the nervous system.
[(U M')x4 x' y]x4 M= Middle: the layer between L and R, turn direction as L (top-down) Same as doing L' R x' (see below for x') x=rotate entire cube on R axis y=rotate entire cube on U axis (U M')x4 = U M' U M' U M' U M' (the x4 after the parenthisis means do () 4 rimes So: [(U M')x4 x' y]x4 means: 1. U M' (4 times), then x' y 2. Repeat #1 4 times (The last "x4 means to do everything in the [bracket] 4 times.) Like a main routine and a sub-routine in a program.
I believe that one way you could represent the operations that you do to a Rubix cube are as a set of Tensor operators with what's called a discrete rotational symmetry. From that you could determine some properties about manipulating Rubix cubes, I imagine. So In that way they seem related.
Make sure when you are making moves Di, Li and Bi that you are rotating the counterclockwise while it is facing you. Example: The moves F and Bi will actualy turn in the same dirrection if the front face is toward you. This was a big problem I had with the algorithms.
I used to just solve it to be like this, I didn't know there was a simple way to do it. I did this on something called a "megaminx" one time, and it was almost seizure-inducing. So many colors!
Well, it took me three tries to get it. At 1:29, when he says "Bottom twice", he really means "Back twice". I kept thinking that he meant the bottom, or "down" side, when he really meant the back. I hope this helps anyone else trying to do it!
If you consider each side as a dimension (an axis), each configuration of the cube as a 6d coordinate and each "step" in the notation as a relative movement in that 6dimensional space, what shape is formed by connecting all the configurations to their neighbors (configurations that can be achieved with one movement from that one) as the vertices of a 6-polytope?
A Hamiltonian cycle exists for the Rubik's cube, which is an algorithm that, starting from the solved state, goes through every permutation exactly once before returning to the solved state.
It has to do with the fact that the amount of moves required to generate the Superflip is 20. That's the maximum number of moves required to solve any Rubik's Cube, a.k.a. God's number. Every other configuration of a Rubik's Cube can be solved in less than twenty moves, so they are "closer" to the solved state than the Superflip.
i tried it myself too, and i saw the loop of srambled to solved on parts with a rotation of certain pieces which makes me think that eventually, after a very long time it would solve itself. I wish i could run a simulation on one of those virtual rubric's cube to see if it actually would or not. I think it would just because i think that is how the cube works, but I can not say for certain. thanks for making me question what I thought I knew for certain, though. ive hadfun trying to figureitout
i used to solve a rubiks cube with interesting patterns all the time and this was one of the ones i did in high school. didn't realize the significance behind it.
He was stating that the superflip is the only move that, when you do it twice, you get the exact formation as the first time before you do the first superflip. In your comment, you were stating moves that are reversed (R and R'). What was said in the video was that you do the exact same superflip move TWICE, and then the cube returns to the original position.
I do not know anything about Rubik's cube, but the two properties didn't surprise me at all. In the first, all the "sides" were turned, and then returned, that's logical. And in the second, the only thing that the super flip does, is to flip the "sides" so it doesn't matter if you do it first or no, the result will be the same, because the pieces are in the same place, but flipped.
What you're saying is that you are aware of a move A and a move B such that if you start at a certain position and do A then B or start at the same position and do B then A, you will arrive at the same result. What you're misunderstanding about the property he's describing about the Super Flip is that it can be done with ANY other move. It might be the case that with a different move C, A then C and C then A do not result in the same position. With a Super Flip in place of A, it always will.
There will be cases where order makes no difference (as you say if you turn U then D it's the same as D then U. But there will be some set of moves you can do as "the stuff" for which changing the order will matter. The claim is that for *all* "the stuff" (i.e. it is true for all sequences of moves) the super flip will give the same result whether done before or after. Compare doing L then D with doing D then L. Clearly order matters for the one move case.
correction, any pattern of moves will eventually bring it back to the solved state, it may have to be repeated more than twice, but that property is not unique to the superflip.
No, speed cubers have quick patterns that can correctly orient 1-3 pieces at a time. and can take up to 50+moves. It is a completely different competion to solve it in as few moves as possible because it takes heavy calculations.
It is because it does not matter if you turn a face anti-clockwise or clockwise when turning it twice(He had a B2 instead of a B). You get the same result either way. Where as it is important to turn the face the correct way when turning it just once.
I have a video of me doing a trick using the superflip, and another with an explanation where I show the easier (non-optimal) way to perform the superflip. The trick makes it look like I solve a scrambled cube behind my back.
But apart from the a and the s at the end if you used that code as U,U,D,D,L,R,L,R and added F2,B2 you would get a checkerboard pattern. So the konami code translates very closely to U2,D2,L2,R2,F2,B2 which creates a checkerboard pattern. Idk why i mentioned this it's just kind of neat how close they are.
@illegalwaffles SAME HERE. I think I may be doing the super flip in a way, but I've done it so no colors of the same are adjacent. I'll have to dust off my cube and see what I did..
Nice question. The largest period is 1260. For example, (R U2 D' B D') has a period of 1260 - perform the action 1260 times and you will visit 1260 different combinations before ending up back where you started. But that's nowhere near the 43 quintillion combinations of a Rubik Cube.
I love your videos.
12th on a verified goal of 100
It actually goes through 6300 states because after every move, you have a new state, not just after every repetition of that sequence.
you are quite right
I've added an annotation and more details in the description, including the superflip instructions...
The important bit is that the superflip 'commutes' with *everything*.
So the superflip belongs to the centre of the group of all possible combinations of a Rubik's cube? 🤔
Srinjoy Majumdar No. it’s on the completely opposite end of the spectrum. It is literally the furthest thing from being solved and any one move can be used as the first move of the algorithm thus making it one less move away from being solved.
@@zahven I didn't mean it that way. The centre of a group is the set of all such elements of the group which commutes with every element of the group.
Srinjoy Majumdar ok this is clearly some math concept that I’ve never learned so I have no idea what that means
@@zahven it's alright. Just chill.
you are right... see video description for more on this.
We would say the superflip 'commutes' or is in the 'group centre'. Because the superflip has order 2 it is 'self-inverse'.
Nice observation.
Wouldn’t L2 R2 U2 D2 F2 B2 have the same property ?
it's now in the video description too
Interestingly, if you do the superflip algorithm on a 2x2, nothing happens and the cube is exactly where you started.
thats because it has no edges
This is obvious, but it's still fun when you realise it.
Jamm3z133 r/woooosh
@@youtubequeen7751 wat
@@Jamm3z133 it has them but they're hidden
Yes it is my living (if that is what you call it?)
A video can take an hour or two from idea to upload... or it can take many weeks....
I'm usually doing quite a few at the same time, so it is really hard to judge how long one video takes. I'd guess about a day on average?
A 10 year old comment with no replies?? I’m gonna change that
what screwed me up was when he said bottom... instead of back
then follow the algorithm in the description
haha same
If you rotate it it become bottom easy xD
Isn't bottom different than bAck?
He moved the cube
I've been solving rubik's cubes for over 4 years now, and my friends ALWAYS try to get it so that 2 colors are not directly adjacent, not caring about diagonally, and they could never do it. This is just amazing :)
looks much cooler on pillowed big cubes (7x7, 9x9, 11x11, etc)
Exactly oh MMAP’s channel pic
So does this mean every Rubik's cube can be solved in at most 20 moves?
Yes
Marconius at least*
"in as few as" might have been clearer
Zebella Barmosa no at most
Are you sure that 20 moves is THE MOST? Cause seriously I could solve a rubiks cube for 100000000000000 and more moves.
A rubiks cube can be solve AT LEAST 20 moves alright? Were you even watching the video
Basically, superflip is "just" flipping edges, right ?
e-penser Yes mon cher e-penser
Tiens tiens... on s’intéresse aux rubik’s cube ?
e-penser oui
Il fallait y penser
Enfin le superflip et l'identité constituent le centre du groupe du cube, donc ça va plus loin
I am so happy that Numberphile have started the Rubik's series! I've been watching Numberphile for a year or so, and started cubing recently, so my 2 favourite things at the same time!!
I use this one too
omg
underrated redkb
ayyyyyyyyyyyy
If anyone wonders: a state where all corners are turned, let's say, clockwise (it's the same for counterclockwise) would also have this commutative property. But this state does not exist, since there are 8 corners and if you want to turn a certain number of corners in the same dorection, it has to be a multiple of 3.
So it's like multiplying by -1.
The effect of this algorithm on the 2x2x2 is awesome.
I can solve it in 12 moves. Just give me a screwdriver and hold my beer.
non cubers be like
I know you’re joking but most 3 by 3 by 3 cubes don’t require a screwdriver to disassemble.
Symmetry makes anything beautiful, but this kind of perfect symmetry is just stunning. The beauty in this video is amazing, loved it.
I really want to send James a Ghost Cube.
send me one ill buy it :3
quite right, see video description everyone else
how about this for the superflip
M,U,M,U,M,U,M,U
turn the whole cube right, then rotate the whole cube 90 degrees left repeat 3 times
Works not as fast but way easier to remember
+swbracere M is middle layer down M' is middle layer up.
+Brayden Robertson That doesn't work but if you do a U' instead of a U it works --> M U' M U' M U' M U' Y Z' M U' M U' M U' M U' Y Z' M U' M U' M U'
+Brayden Robertson m?
+George Christodoulou M is the middle slice
Thanks, I see what you mean: The superflip commutes with *everything* and not just with *one* other move. That's what makes it special. (By the way, I meant "R and then L" in the comment above.) I am a fan of your singingbanana videos, too. Thanks for taking the time to make them.
That's right. Although I didn't want to get technical. Cool isn't it!
This video and others in the series convinced me to buy a Rubik's cube. After having one as a child and being endlessly frustrated I'm happy to finally be unlocking the secrets.
I figure I will learn the methods first and let the principles unfold then I'll start puzzling over the math.
Thanks for including the Superflip notation & reminding me to follow Dr. Grimes on Twitter. I came back just to make sure I was using the same notation as numberphile. It's much better than the one I made up.
There is a move that looks similar, but doesn't have the same properties. From a solved cube, R2, L2, U2, D2, F2, B2. It swaps the edge colours with the colours of the opposite side.
It's called the checkerboard pattern...
foxys2100 Or simple 6X, or pons asinorum.
Easier wasy is M2 E2 S2
R/woooosh?
I love how you say stuff at 3:13 and 3:16
What if I do R L or L R? Those two sequences do give the exact same cube.
He means any move. You just listed one case, while the superflip works in all cases.
The superflip has order 2...
I love hearing abstract algebra come from your mouth. You are awesome
Another way to superflip your cube is to solve it using the beginner's method, except purposely making all the second layer edge pieces flipped in the right place, continue solving as normal, flip the edges to the right position, and the top layer should now be superflipped. Now flip the cube upside down and flip the edges once more. The cube is now superflipped. How many times did I say flip?
Eight times.
Another interesting thing, if you apply this algorithm after (or before) the superflip, you wind up with absolutely no colors adjacent to each other, horizontally, vertically, or diagonally.
U2 (R U R' U')3 (L' U' L U)3 (L U L' U')3 (R' U' R U)3 U2
1:29 B is for back not bottom
+John Trollinski (SalvadorSTM) Did you not read the annotaton there? It says "It is back twice--he mispeaks there but preforms the correct move."
LetsCloneBieber666 No didn't read the annotation.
Yep. D = Bottom/Down
I've been playing around with Rubix cubes for over five years now. I can solve fairly complicated ones, although I am no speed cuber. But I had no idea about Superflip. Loved the video!
I would think that the "stuff" wouldn't change because the location of the pieces does not change with the superflip, just the orientation.
This is true. And there are other positions where it doesn't matter which one you do first. Any one where the location does not change, only the orientation. So if you were to turn the corners for example that would work.
except turning corners is of order 3 because other then edges they can be oriented in 3 ways
@Ibakon Ferba: it doesn't matter if it is B2 or B2' because either way the back face moves 180 degrees. If you think of the cube as a circle, 180 degrees clockwise is the same as 180 degrees counter-clockwise
So gods number for the rubiks cube is 20, and 1 person managed to solve a rubiks cube in 23 moves.23-20=3. OMG, HALF LIFE 3 CONFIRMED!
Cool! I really like the idea of the superflip. It's almost like magic!
Tried playing along... messed it up!
i think thats because he missed some notation on the order. when i does the back the second time he turns it twice anti-clockwise. but doesn't note the "back dash" :-/
if it got srambled, just solve it ;)
Superflip has order 2, so it is its own inverse, and superflip is in the center of the group, which means it commutes with everything else in the group. Since the superflip and 'do nothing' are the only moves which commute with everything we can see that the center of the Rubik's cube group is isomorphic to Z/2Z.
The explanation is not simple I'm afraid. From what I can gather, you need some pretty deep group theory, including the structure of the Rubik Group, some group theory tricks, and some computing power.
I think another interesting fact about the superflip position is that the cube is technically solved. All of the pieces are permuted in their proper positions, just not oriented properly (facing the right way). Great video :D
who here can solve the rubiks cube?
freddiewm xiopop anybody could
a bit faster by 1 min
like speedcubing but not as common in europe just hongkong
freddiewm xiopop me
Me
all the peeps
I don't know why, but i like this guy, just seeing passion in he's eyes and smile everytime when talking about math make this video more interesting! :D
And the superflip isn't the only alg that has the unique property about stuff then superflip is the same as superflip then stuff, I tried it with one of the first that came into my head, the four spots alg (M2, E M2, E') and it does the same thing (most of the time)
I know he doesn't know what he is talking about
+Eoghan Spillane If you can choose "stuff" in such a way it doesn't work, then it doesn't work for all cases. With the superflip, it works for any "stuff", no matter what you choose. Always.
And the superflip is the only move that does that (apart from identity moves, obviously)
Actually if you made an algorithm that rotated all corners clockwise wouldn't that do the exact same thing as the superflip just for corners and therefore be another move that has the stuff then move = move then stuff
Eoghan Spillane
That would work, but such an algorithm cannot exist. You can only rotate one corner clockwise and one anti-clockwise. You can use the algorithm again, rotating a different corner clockwise and the one that rotated anti-clockwise again, you essentially rotated three corners clockwise.
But the cube has 8 corners. If it had 9, this would work :)
+Yndostrui well I meant that like just rotate all corners
sorry, we added an annotation and note in the video description... he writes and does it correctly, but mis-speaks...
i had a rubiks cube right beside my desk to do this because Im a nerd. Eat that popular girls.
I have, on top of my desk, a 2*2, 3*3. 4*4. 5*5, 6*6, 2*2 mirror, 3*3 mirror, 3*3 star, skewb, pyraminx and a void cube that I 3d printed, Eat that unpopular guy.
So the Superflip commutes with all other algorithms, or it's commutator is 0 with all other operators.
And when you look at the physical implication of just flipping edges it makes perfect sense. Very elegant.
Am I the only one who facepalm end when he said u dash (u') instead of u prime?
Yes
No.
He also said bottom instead of back
Yeah
There is nothing wrong with saying u dash. I say the same too.I am a cuber by the way
Yes! Been waiting for a Rubik's Cube video! Finally! Thank you! Totally subscribing!
JUST AS MY SD CARD RUNS OUT
Only cubers understand
@@jorian_meeuse yup
ah the old days
M' is the middle slice, between the left and right sides away from you.
U' is up anti clockwise.
y is a cube rotation, and means rotate the cube so the Front becomes the Left.
x' is a cube rotation and means rotate the cube so the Front becomes the Bottom.
So the superflip is like the identity matrix?
Not really. The solved state is the identity.
The superflip is kinda like that matrix with 1s on the other diagonal and 0s everywhere else.
Being a Rubik's cube fan, ive actually done this without that algorithm, but saying that it is the furthest from being solved is pretty cool.
Something just clicked for me watching this video. A cube has 6 faces. There are 6 kinds of quarks (up, down, top, bottom, strange, charm). Coincidence?
I think so; this would imply a universal set of axis for which each type of quark would be associated, otherwise the type of quark would depend on which direction you are looking at it from (and what would be the expression of looking at a quark from a non-axis direction)?
I like that a lot. How would you translate them, if the convention was to name the Cube's sides in quarks? Strange = Left, Charm = Right, that's easy thanks to Sinister and Dexter. But is the top of the Cube "Top" or "Up"? :)
6 faces in a Tri-dimensional space equals 666
+rchandraonline Yes, it's a coincidence. 6 is a small and common number; you should expect to find things like that.
I have a completely different way of completing the superflip. It takes 36 moves instead of 20, but is faster to complete. The basic motion is rotate the center column away from you 90°, then rotate the top clockwise 90°. Do this 4 times, then rotate the cube CCW about the axis that runs through the upper left corner closest to you. Do this process 3 times, and the cube should be superflipped.
Who else here is a speed cube with a sub 20 avg
Adam yea i am the cube
Adam I'm a magnetic Valk 3
And I'm a QiYi Warrior W
Adam 13.1 ao5 at my last comp
me
I always sucked at solving those Rubik's Cubes. I once got to a point, where I got a superflip (by just randomly messing around with the cube, not actually trying to solve it). I thought, that pattern looked rather beautiful and interesting. Now I got this video and know, that it actually is.
Am I the only one that watches all TH-cam videos in 2x speed?
nope
i watch them all in 1.5. theyre too slow
how do you do that?
GoAhead Namal I'm just used to it... If you do it enough it's not that hard to understand.
I get that, but I mean how do you even speed up/slow down a TH-cam video in the first place? :)
Only simpler for experienced cubers. Without explaining what M, x and y are, most people would prefer the one that James does.
For those who want to know, M is a turn of the middle vertical slice going from Front to Back, so M' is a turn of this slice that follows the direction of L. x and y are rotations of the ENTIRE cube about those axes, so x is in the same direction as R, and y in the direction of U.
The guy kinda looks like a Titan from attack on Titan
Thank you numberphile; I now know something I didn't before: that the centre of the Rubik's cube group only has two elements in it :) I love maths :)
I saw this vidoe and then I wanted to try it myself but then I realized that I didn't had a Rubik's Cube! Now I got one and it's an amazing thing! If you dont have one you should get one because in a Rubik's Cube there are 43,252,003,274,489,856,000 twistable combinations of fun! Clearly worth 10 £!
i'm looking for an algorithm to get from randomly shuffled cube to super flip.. is this possible?
This guy cheers me up.
Best guy on Numberphile :D
I suppose it would be accurate to conclude that the superflip order thing works because the outcome of the super flip is in relation to the _whole_ rubik's cube - it's a re-composition of the entirety - whilst a single move is merely a change in one certain area. Say you were to fold out the cube so that all the sides were visible at once. The superflip would then be one set of combinations to preserve a certain relation/symmetry between the units/colours. Perhaps I'm being obvious.
It's flossing for the mind, it increases intelligence and after you memorize the algs you start seeing and understanding the puzzle in your mind. For some people with speech problems or motor controls it rehabilitates the nervous system.
I've done this probably 4 times now and it n e v e r works.
loving these rubiks cube videos !!
Dr. James Grime = young Chris Martin
[(U M')x4 x' y]x4
M= Middle: the layer between L and R, turn direction as L (top-down) Same as doing L' R x' (see below for x')
x=rotate entire cube on R axis
y=rotate entire cube on U axis
(U M')x4 = U M' U M' U M' U M' (the x4 after the parenthisis means do () 4 rimes
So: [(U M')x4 x' y]x4 means:
1. U M' (4 times), then x' y
2. Repeat #1 4 times
(The last "x4 means to do everything in the [bracket] 4 times.)
Like a main routine and a sub-routine in a program.
This is easily explained. He was obviously using... MAGIC!!!!
I believe that one way you could represent the operations that you do to a Rubix cube are as a set of Tensor operators with what's called a discrete rotational symmetry. From that you could determine some properties about manipulating Rubix cubes, I imagine. So In that way they seem related.
Make sure when you are making moves Di, Li and Bi that you are rotating the counterclockwise while it is facing you. Example: The moves F and Bi will actualy turn in the same dirrection if the front face is toward you. This was a big problem I had with the algorithms.
I love it when he starts writing something.
I used to just solve it to be like this, I didn't know there was a simple way to do it. I did this on something called a "megaminx" one time, and it was almost seizure-inducing. So many colors!
Well, it took me three tries to get it. At 1:29, when he says "Bottom twice", he really means "Back twice". I kept thinking that he meant the bottom, or "down" side, when he really meant the back. I hope this helps anyone else trying to do it!
If you consider each side as a dimension (an axis), each configuration of the cube as a 6d coordinate and each "step" in the notation as a relative movement in that 6dimensional space, what shape is formed by connecting all the configurations to their neighbors (configurations that can be achieved with one movement from that one) as the vertices of a 6-polytope?
A Hamiltonian cycle exists for the Rubik's cube, which is an algorithm that, starting from the solved state, goes through every permutation exactly once before returning to the solved state.
It has to do with the fact that the amount of moves required to generate the Superflip is 20. That's the maximum number of moves required to solve any Rubik's Cube, a.k.a. God's number. Every other configuration of a Rubik's Cube can be solved in less than twenty moves, so they are "closer" to the solved state than the Superflip.
I like the combination that turns cube into a map where no same colors touch each other.
i tried it myself too, and i saw the loop of srambled to solved on parts with a rotation of certain pieces which makes me think that eventually, after a very long time it would solve itself. I wish i could run a simulation on one of those virtual rubric's cube to see if it actually would or not. I think it would just because i think that is how the cube works, but I can not say for certain. thanks for making me question what I thought I knew for certain, though. ive hadfun trying to figureitout
i used to solve a rubiks cube with interesting patterns all the time and this was one of the ones i did in high school. didn't realize the significance behind it.
He was stating that the superflip is the only move that, when you do it twice, you get the exact formation as the first time before you do the first superflip. In your comment, you were stating moves that are reversed (R and R'). What was said in the video was that you do the exact same superflip move TWICE, and then the cube returns to the original position.
I do not know anything about Rubik's cube, but the two properties didn't surprise me at all. In the first, all the "sides" were turned, and then returned, that's logical. And in the second, the only thing that the super flip does, is to flip the "sides" so it doesn't matter if you do it first or no, the result will be the same, because the pieces are in the same place, but flipped.
What you're saying is that you are aware of a move A and a move B such that if you start at a certain position and do A then B or start at the same position and do B then A, you will arrive at the same result. What you're misunderstanding about the property he's describing about the Super Flip is that it can be done with ANY other move. It might be the case that with a different move C, A then C and C then A do not result in the same position. With a Super Flip in place of A, it always will.
There will be cases where order makes no difference (as you say if you turn U then D it's the same as D then U. But there will be some set of moves you can do as "the stuff" for which changing the order will matter. The claim is that for *all* "the stuff" (i.e. it is true for all sequences of moves) the super flip will give the same result whether done before or after.
Compare doing L then D with doing D then L. Clearly order matters for the one move case.
correction, any pattern of moves will eventually bring it back to the solved state, it may have to be repeated more than twice, but that property is not unique to the superflip.
1:14 - Or you can say "U3" since 3 turns equals 1 in the opposite direction.
No, speed cubers have quick patterns that can correctly orient 1-3 pieces at a time. and can take up to 50+moves. It is a completely different competion to solve it in as few moves as possible because it takes heavy calculations.
haha you made me learn a new word on wikipedia. By the way the superflip may be an endomorphims or even an automorphism if I get it right...
:) I've never been so happy to not learn from a TH-cam video
It is because it does not matter if you turn a face anti-clockwise or clockwise when turning it twice(He had a B2 instead of a B). You get the same result either way. Where as it is important to turn the face the correct way when turning it just once.
I have a video of me doing a trick using the superflip, and another with an explanation where I show the easier (non-optimal) way to perform the superflip.
The trick makes it look like I solve a scrambled cube behind my back.
on 0:58 he sais and writes B2 but actually moves B'2...it's the same thing but..o well...nevermind...awesome video!
But apart from the a and the s at the end if you used that code as
U,U,D,D,L,R,L,R and added F2,B2 you would get a checkerboard pattern. So the konami code translates very closely to
U2,D2,L2,R2,F2,B2 which creates a checkerboard pattern. Idk why i mentioned this it's just kind of neat how close they are.
All these videos about Rubik's Cubes make me wish I owned a Rubik's Cube.
@illegalwaffles
SAME HERE. I think I may be doing the super flip in a way, but I've done it so no colors of the same are adjacent. I'll have to dust off my cube and see what I did..
3:23 not true, the supertwists (twisting all corners in the same direction) also has.
The two states where all corners are twisted in the same direction are not legal states.
Sa967St
Oops. You're right.