Damn, I remember that when I started to learn how to solve a 3x3 I got parity, and then I would always restart the solve thinking that I did something wrong *for hours* . Just to later realise that it was impossible and I just had to do a corner twist. Definetely one of my most frustrating life experiences.
@@lumina_ well 2 and 3 aren't counterexamples for the statement, since 2 isn't odd and 3 is a multiple of 3 as you say. All other prime numbers do serve as counterexamples though, since they are both odd and not a multiple of 3
Lol do you guys realized. He said that corner twist is multiple of 6 . But thats wrong . I know he said better to called multiple of 3. But multiple of 6 is wrong . Cuz ok . Try it now . Set your cube to be 2 corner of twist(clockwise) . And then do the same thing on other corner ,. Then u Will have this .3,4,5. But if you twist 1 more corner its become 6 . And 6 corner twist is twist? Lol thats wrong
once i was doing a solve in public and someone came up and told me to solve their cube. me, being the humble cuber i am, obliged. after i got to pll, though, i realized i had parity. on a 3x3. i guess that solve took a *turn for the worse*
@Glass of Milk just a question from a noob here: If I don't do anything special do my 3x3 cube and I just turn it normally, everything should be fine right?
@@nikotakai8796 yeah, if you learn how to solve it there shouldn't be any problems. Usually you only notice parity at the end and only have to do a corner twist which isn't much of a problem
For megaminx, using the same logic in the video, a turn is 4 edge swaps, so you can swap the two edges, then swap edges twice somewhere else, which doesn't do anything, and there would still be one swap, so it is impossible to have to only have two edges swapped using outer turns on a megaminx.
AT TIMESTAMP 10:40 ) The number of *corner swaps* and *edge swaps* must be _both_ either odd or even on a *Megaminx.* The reason this only applies to odd-layered puzzles (-Minus the *Void Cube)* and not even-layered puzzles is because any puzzle with *centers* has this rule. An *A-perm, G-perm* or *U-perm* is possible because 2 intersecting *swaps* form a *cycle.* A *cycle* is formed when intersecting *swaps* of the same type of *piece (-Edge/Corner)* share a *last piece* (-This is why a *cycle* must have an odd number of *pieces.).*
Wow, this guy knows cubing. Also, the reason why on even layer cubes can have two corners swapped is actually because you also swap the inner pieces, which are edges. So you actually swap corners 1 time and inner edges 1 time.
j perm said he doesnt care about corners for the megaminx question. if we exclude counting corners, then it is definitely possible to have only 2 edges swapped on a 3 by 3 at least(example is T perm, J perm etc.)
Dude i legit have been thinking about this for a while. My best guess was that centers were not fixed. But couldn't figure out for odd layered cubes, and of course the void cube
I think swapping two pieces on the megamix is impossible for the same reason it's impossible on a 3x3. When you turn a face (which is the only legal move), you swap 5 corners and 5 edges. You can probably swap two edges and two corners, or two edges and two sets of two corners, or two edges and any swapping of corners that can be seen as an even number of corner swaps. This is my reasoning: When you turn a face, you do five edge swaps. With some manipulation, you can use this to swap two corners, then swap two other corners four times. This would give you two edges swapped while keeping the rest of the edges undisturbed. However, because this took the equivalent of five edge swaps, you need five corner swaps. It's impossible to have five corner swaps that cycle back to their original state, but you can swap two corners and leave the rest undisturbed. You can do this the same way you do edges, by swapping two with one swap and then using the other four swaps to cancel themselves out. I used the word "swap" 17 times in this comment.
Actually when you turn a face, you do 4 swaps of edges! Try taking the megaminx apart to swap 2, then the next 2, and so on. You'll only have to do this 4 times to move the edges around once
@@JPerm wow, can't believe I missed that. Then is it impossible to swap to edges no matter what? Since any sequence of moves you do will result in an even number of swaps, you can't get an odd number like 1. Thanks for replying btw, made my day :)
Get some drinks and watch this with your friends. Everytime he says swap, everyone has to take a shot. I bet you'll only make it 'till 5 minutes or so.
This was such a helpful video. I’m getting parities on my 4x4 all the time and I don’t know why. Previously, I thought it was meant to be “impossible”, but it turns out it is not.
Whenever I am unable to solve a weird state of my 4x4x4 cube I just scramble it a lot, start over and hope for the best. I’m not a speedcuber or anything but it is in my interest.
Reasons why megaminx cannot have two esges swapped: 1: You cannot perform an 'm' move which means 4 edges move 2:there are 5 edges on one side and that means the edges cannot have a two edge cycle because there is 10 total pieces to solve in the last layer and most permutations have a clockwise rotation or two pairs of two edges swap and if that were to occur on a megaminx that means the one remaining edge needs to swap but it cannot. If you guys agree or disagree let me know and thanks for reading have a good day
For the 3x3 edges... Imagine wanting to flip two edges. In order for the rest of the cube to be solved, you need to flip one edge, replace it, then RE-FLIP it. In an odd number of cases, you cannot reflip the same number of edges which leaves the cube unsolved, hence why you can only have an even number of edges flipped.
No it isn't I literally solved a square-1 with no help when I got parity I remembered this video I knew I am at even slices then I counted my slices and solved parity on square-1 (+ I am Asian)
I have watched these videos for about a year, I never had a cube. Not even a 3x3 or 2x2 but I’m finally getting a go cube with some birthday money! I know a lot of techniques, ways to solve, and algorithms. I’m really excited to get my first solve!
learning, watching and reading before you pick up a cube is probably really smart. In the 90s, somehow I started receiving Golf Digest for free weekly. I read it for about 7 years before picking up a club. I decided to go play golf one day and shot in the 80s first time round. That's pretty amazing by the way.
So I "knew" all of this... but hearing your explanation of it made it seem like something completely new and gave me that mind blown feeling. Best cube video of 2020. This will not be topped for the rest of the year.
The permutation group of the megaminx group (ignoring the normal subgroup of orientations) is a product of alternating groups, so clearly there are only even permutations of both edges and corners, even considered separately. So you can't even have a transposition of corners and a transposition of edges on a megaminx (as in something like a T-perm on 3×3).
I actually figured a bit of this out without realizing in middle school when I was learning beginner method. I noticed that the amount of times uou had to repeat R’D’RD in the last step was always a multiple of 6 and I figured out how many repetitions each corner orientation required to correct and that it was always even.
This reminds me: Some kid at my school had just learned the 3x3, and this kid was getting super braggy about it, so I asked them if I couls scramble it for them, they said "sure go ahead", so I walked out of sight with the cube. I then proceeded to yank two edges out and swap them, creating void parity. I then gave it a good scramble to disguise my mischeif (obviously). I gave it back to the kid. Boy did I have a good time watching them struggle. It was hilarious
he is definitely the best cubing youtuber out there... others just post cubing videos, but he also posts these kind of interesting videos talking about the overall nature of twisty puzzles
On the void cube you also functionally have centers, they're just invisible and have multiple solved states Like if you ignore the centers on a normal 3x3. You'll have the same experience
Know what, just ignore that comment. I couldn’t think of how to spell it so I just did that. And half way through of typing all that I thought myself as DUMB!
the absolute SPEED when you do the 2x2 swap thing is terrifying i feel like you could turn a rubiks cube into a weapon and murder me with it and use the cube to absorb all the evidence and then use the cube as a portal to escape into the fourth dimension so they never find you
Not sure if you’ll see this comment, but I’ve been getting into speed cubing lately and watched most of your videos in a very short period of time. I love your content, it’s beyond helpful! I have a QiYi cube that somehow got the last layer corners swapped and seems to be impossible to be solved like you mentioned at 0:35. I’ve never had this cube apart, and I swear by that. I have no idea how it happened, and without taking it apart, there has to be a way to get it back, right? Thanks in advance if you see this. Keep up the great work!
Kinda late lol but this happened to me. It turned out to be center parity, where four centers were basically rotated around a slice layer by popping off the center caps so they looked right but were swapped causing odd center swaps which allows for odd edge swaps, and thus parity. U could always just disassemble the cube too, or swap the centers back
very late, but here's an explanation for why a megaminx must have both even edge and corner parity: turning a layer cycles 5 edges and 5 corners (4 swaps each) so parity for both is always even
I stopped watching Z3cubing over a year ago and I completely forgot that he changed his YT name to Z3cubing, it used to be legoboyz3. If you go to some of his older vids, he says legoboyz3 in his intro
How to resemble a U-move's cycles and prove the existence of 2e2c, 2e2e, 2c2c, 3e, or 3c with PLLs: A 1-quarter-turn U-move is a 4e4c. A U2 move is a 2e2e2c2c. Take the J-perms(2e2c) or R-perms(2e2c) and add a U2 AUF (4e4c). Take the H-perm(2e2e) and add a 1-quater-turn AUF (4e4c). Take the Aa-perm(3c) or Ub-perm(3e) and add a U AUF (4e4c). Take the Ab-perm(3c) or Ua-perm(3e) and add a U' AUF (4e4c). Take the E-perm(2c2c) or Z-perm(2e2e) and add a U2 AUF. Take the N-perms(2e2c) and add a 1-quater-turn AUF (2e2e2c2c).
The answer for the megaminx is that you can't. Because when you do a turn in megaminx, you do 4 swaps of corners and 4 swaps of edges, and that's even. So you can never have two edges swapped and every edges at the right place, regardless of where the corners at. And that's why when you take out all the pieces in megaminx and put it back randomly and try to solve it, you only have 1/24 chance to solve it. (1/2 chance the edges are in the right place, 1/2 chance the corners are in the right place, 1/3 chance the corners are correctly oriented, 1/2 chance the edges are oriented correctly). In a 3x3 rubik's cube the chances are 1/12.
AT .42sec into the video , this is the first time I have every seen anyone demonstrate how I solve Rubik's cubes lol , it has been my go-to solution since I was 7yo lol
I remember having a few beers one night and trying to solve a 3x3 for at least an hour, scrambling it, getting to the end and 1 corner was always out, I put it down to the beers, next morning I tried again and remembered that corners could twist. Possibly the most infuriating time I've had cubing.
I love this cube theory type of video. I kind of want more of it, so if anyone knows something interesting, or even better doesnt know something interesting please suggest it to our mr j perm so he can spread his knowledge even more.
In megaminx, we cannot obtain parities, since this puzzle is a variation of a 3x3, without adding any more layer, as a result, only outer moves can be made, and no exchange of centers can be made to produce a parity . Megaminx, in a nutshell, is a 3x3, but "extended" then it is impossible to obtain a parity
With a Megaminx, one turn would equal four swaps of edges and corners. "If, for some reason, we can only do an even number of swaps, then we can't reach any odd number of swaps, because we can never add even numbers to produce an odd number."
𝐈. Why permutations are important and why they make up the nature of Rubik's puzzles. 𝐈𝐈. Why parities are discussed, especially in accordance to the behavior of Rubik's 3x3x3 Cubes 𝐈. 1.) All of this can be traced down to how permutations work. In a Rubik's puzzle, *permutations are what exist, not combinations.* Permutations mean switching the POSITION of things with one another, which is normally what we see on Rubik's puzzles. In this sense, we can regard that COMBINATIONS *can not only SWITCH THE POSITIONS of pieces, but their ORIENTATION too.* 2.) *We usually see the 3x3x3 Cube as like the *borderline on how we assess situations in regards to how permutations work or behave on Rubik's puzzles, and not any other iteration of the cube or puzzle* (e.g. 2x2, 4x4, 5x5, etc.). In that matter, we know that *these permutations or "swaps" usually comprise of a lingering aspect in which EVEN numbers are abruptly discussed.* (This is what this JPerm video entails.) We must denote that a 3x3x3 Rubik's Cube has 43 quintillion states in which it can reside in. When you think of it, a puzzle is A RUBIK'S CUBE *if, and only if, that puzzle has the same configuration as what a (normal/usual) Rubik's Cube would have.* 2.1.) Let's use the 3x3x3 as an example. Let's use a common situation such as "twisting one corner or one edge" -- it can be any situation as long as the thing about ODD number swaps/etc. exists, because we've tackled that *on a 3x3x3, it is a usually observed and widely accepted trend that an EVEN number of swaps* (or any other term in regards to the behavior of how a 3x3x3 becomes unsolved THAT ARE NOT PERMUTATIONS) *is a recurring theme.* In that regard, if we do anything of the sort where an ODD number of non-permutations (swaps, etc.) is done to manually modify how a 3x3x3 seems or behaves, *that puzzle is NO LONGER a Rubik's Cube,* so to say, because you'd by then have *arbitrarily opened a new range of states and possibilities for the puzzle you modified, whether it be 43 quintillion as well or similar.* The point is, what we've done does not qualify the puzzle as a Rubik's Cube anymore. Why this generally IS is because what we've done to our puzzle is NO LONGER a PERMUTATION, but rather a COMBINATION (or "orientation"), *where the same pieces can be normally rearranged into a solved state* (in regards to what a solved state in a Rubik's Cube would look like), *but, while the pieces are at their respective positions, you have changed the configuration of that piece, which no longer translates as a permutation, and in the long run no longer denotes THAT puzzle as a Rubik's Cube or Rubik's puzzle any further.* Put bluntly, you shouldn't do these in the first place, which is why they're called "illegal moves" -- wherein if you do, that puzzle is no longer a Rubik's Cube and you have opened up a new scope of possible permutations, with each being different from a normal Rubik's Cube's. 𝐈𝐈. Parity is something that is usually regarded towards 3x3x3's (see 𝐈., #2). 1.) *A parity does not occur within a 3x3x3 Rubik's Cube. A parity is a phenomena that is usually denoted as a SWAP* (non-permutation) *which is normally in regards towards anything outside the normal behavior of a 3x3x3 Rubik's Cube.* We use the 3x3x3 as a reference or borderline for that matter. *Parities in non-3x3x3's* (4x4x4's, 5x5x5's, etc.) *are usually discussed in account to how 3x3x3's normally perform.* 2.) Let's use the 4x4x4 as an example. 4x4x4 Rubik's Cubes are the same as 3x3x3's, except a 4x4x4 only has more permutations. When you think of it, *BECAUSE a 4x4x4 is NOT a 3x3x3, you can get away with having situations that are not particularly in accordance towards how a 3x3x3 normally behaves.* Having 2 "wings" swapped (OLL Parity) is definitely something you CAN, in fact, experience on a 4x4x4. It's just a matter towards what you CAN do in a 4x4x4, or every possible permutation that a 4x4x4 presents, whereas *parity, something that is usually regarded towards something which performs or occurs outside the boundaries of a normal 3x3x3's behavior, is a part of.* 𝐈. The 3x3x3 Rubik's Cube generally sets the *borderline or acts as a reference* towards phenomena that are discussed which are *usually outside the behavior of a non-3x3x3 Rubik's puzzle, such as PARITY.* *Permutations make up the nature of Rubik's puzzles.* If you manually configure a Rubik's puzzle wherein its "solved" state would be different than usual, then that puzzle is *no longer a normal Rubik's puzzle.* *Non-EVEN configurations usually result in this.* (This is explained very thoroughly in this JPerm video.) You're *not supposed to change the configuration* in the first place, which is why they're called "illegal movies", but if you do, you run into risks of changing the configuration wherein that puzzle no longer behaves the same as a normal Rubik's puzzle. ALTHOUGH, you CAN, in deed, manually change a Rubik's puzzle's configuration *ONLY so much so that you RUN into a situation where that situation ACTUALLY resides as one of the possible permutations in a normal Rubik's puzzle,* thereby still being able to solve it normally, and ACTUALLY still being regarded as a nornal Rubik's puzzle in the end. 𝐈𝐈. *Parity is a postulate in non-3x3x3 Rubik's puzzles.* Parities are often regarded as *phenomena in which their nature does not qualify as normal behavior which you can expect from a 3x3x3.* However, in spite of popular disputes, parities are in fact only true to the configuration of these puzzles. Parity is *not a crime, it's a phenomenon.* 𝑹𝒆𝒈𝒂𝒓𝒅𝒔. @JPerm
if you look at beginner method the last step is orienting the last corners and it always adds to a multiple of 3 algorithms to solve, also you cannot switch two edges on a megamink
Damn, I remember that when I started to learn how to solve a 3x3 I got parity, and then I would always restart the solve thinking that I did something wrong *for hours* . Just to later realise that it was impossible and I just had to do a corner twist.
Definetely one of my most frustrating life experiences.
There are a lot of people who run into that problem!
F
F
@@JPerm My kids do this to me a lot! Think it is funny...
Me Too;)
"1 is a multiple of 3 if you're clever"
Great vid, loved it
3 * 1/3 = 1
"Every odd number is a multiple of 3" -J Perm
Prime numbers other than 2 and 3: am I a joke to you?
Abysmal Luck lol
@@bambo418 lol
How bout 5 xd
@@lumina_ well 2 and 3 aren't counterexamples for the statement, since 2 isn't odd and 3 is a multiple of 3 as you say. All other prime numbers do serve as counterexamples though, since they are both odd and not a multiple of 3
Legends say that the number of times he says "swap" in this video has to have an even parity.
wait... let me just save some real estate on this great comment.
🏠🏡🏘
Lol do you guys realized. He said that corner twist is multiple of 6 . But thats wrong . I know he said better to called multiple of 3. But multiple of 6 is wrong . Cuz ok . Try it now . Set your cube to be 2 corner of twist(clockwise) . And then do the same thing on other corner ,. Then u Will have this .3,4,5. But if you twist 1 more corner its become 6 . And 6 corner twist is twist? Lol thats wrong
@@dumguyawesome what? That is becuse quantum physics or you just explained it poorly?
It's a twist if you twist it.. not because it's twisted
?
once i was doing a solve in public and someone came up and told me to solve their cube.
me, being the humble cuber i am, obliged.
after i got to pll, though, i realized i had parity. on a 3x3.
i guess that solve took a *turn for the worse*
Some Nerd
Probably 7/10 solves I do on a noncuber's cube has parity on a 3x3 because they corner twist and remove pieces and put them back wrong
@Glass of Milk just a question from a noob here: If I don't do anything special do my 3x3 cube and I just turn it normally, everything should be fine right?
@@nikotakai8796 yeah, if you learn how to solve it there shouldn't be any problems.
Usually you only notice parity at the end and only have to do a corner twist which isn't much of a problem
@@nikotakai8796 yeah, if you don't corner twist it or take out pieces you shouldn't get parity on 3x3
You make the types of videos I can watch over and over again without getting bored.
Me to
Yea lol its like the 4th time I watch this one
Yeah
Me too
Ikr
For megaminx, using the same logic in the video, a turn is 4 edge swaps, so you can swap the two edges, then swap edges twice somewhere else, which doesn't do anything, and there would still be one swap, so it is impossible to have to only have two edges swapped using outer turns on a megaminx.
AT TIMESTAMP 10:40 )
The number of *corner swaps* and *edge swaps* must be _both_ either odd or even on a *Megaminx.* The reason this only applies to odd-layered puzzles (-Minus the *Void Cube)* and not even-layered puzzles is because any puzzle with *centers* has this rule. An *A-perm, G-perm* or *U-perm* is possible because 2 intersecting *swaps* form a *cycle.* A *cycle* is formed when intersecting *swaps* of the same type of *piece (-Edge/Corner)* share a *last piece* (-This is why a *cycle* must have an odd number of *pieces.).*
Why no replys???
Wow, this guy knows cubing.
Also, the reason why on even layer cubes can have two corners swapped is actually because you also swap the inner pieces, which are edges. So you actually swap corners 1 time and inner edges 1 time.
@@bilingualchad :
Thanks, and yes.
j perm said he doesnt care about corners for the megaminx question. if we exclude counting corners, then it is definitely possible to have only 2 edges swapped on a 3 by 3 at least(example is T perm, J perm etc.)
@@asr2009 we cant do that bc a turn does 4 swaps or even number of swaps for edges so we can never reach odd number if swaps only for edged
Dude i legit have been thinking about this for a while. My best guess was that centers were not fixed. But couldn't figure out for odd layered cubes, and of course the void cube
That is exactly what happens
Try it on a 3×3 only solve 2 centers
Centers are fixed
I think swapping two pieces on the megamix is impossible for the same reason it's impossible on a 3x3. When you turn a face (which is the only legal move), you swap 5 corners and 5 edges. You can probably swap two edges and two corners, or two edges and two sets of two corners, or two edges and any swapping of corners that can be seen as an even number of corner swaps.
This is my reasoning:
When you turn a face, you do five edge swaps. With some manipulation, you can use this to swap two corners, then swap two other corners four times. This would give you two edges swapped while keeping the rest of the edges undisturbed. However, because this took the equivalent of five edge swaps, you need five corner swaps. It's impossible to have five corner swaps that cycle back to their original state, but you can swap two corners and leave the rest undisturbed. You can do this the same way you do edges, by swapping two with one swap and then using the other four swaps to cancel themselves out.
I used the word "swap" 17 times in this comment.
Actually when you turn a face, you do 4 swaps of edges! Try taking the megaminx apart to swap 2, then the next 2, and so on. You'll only have to do this 4 times to move the edges around once
@@JPerm wow, can't believe I missed that. Then is it impossible to swap to edges no matter what? Since any sequence of moves you do will result in an even number of swaps, you can't get an odd number like 1. Thanks for replying btw, made my day :)
Well I like nerdy stuff but I didn't knew this, thank you
I genuinely enjoy the "cube theory" format, keep doing them my guy!
i absolutely love this, i live for this kind of nerdy stuff, i hope you do more cube theory videos in the future
me too!
someone need to count how offten he said "swap"
Get some drinks and watch this with your friends. Everytime he says swap, everyone has to take a shot. I bet you'll only make it 'till 5 minutes or so.
Why can't that "someone" be you
@gamer.20years.and thats true i have no freinds ;-;. Do you wanna be my freind ?
@@Sora-iu2kc I'll be your freind
I'm pretty sure the amount of times was even parity
My mom: So what did you learn today?
Me: I learned Dylan's law of slice turns and parity explanation
This is a multipel of 3, iF YoU’Re CLevEr.
-jperm 2020
Not funny,didnt laugh
Doge Yay
Don’t care, still don’t care.
@@bluecreeperboybcb4399 ok and??
In what way is this funny?
@@lumina_ can i drink u
This was such a helpful video. I’m getting parities on my 4x4 all the time and I don’t know why. Previously, I thought it was meant to be “impossible”, but it turns out it is not.
This video is super interesting, I really love cubing + maths vids. Make more of these kind!
Whenever I am unable to solve a weird state of my 4x4x4 cube I just scramble it a lot, start over and hope for the best.
I’m not a speedcuber or anything but it is in my interest.
You're literally doing group theory with your hands, proving theorems by manipulating plastic pieces and counting stickers. It's beautiful.
Sorry Professor Dylan,
I forgot my megaminx homework at home.
A dog ate my megaminx!
0:30 here we have his channel logo
Lol how'd u spot that
@@maaziboy3088 i just noticed it looked like his logo
I think it could be interesting to extend this discussion into supercubes, where the orientation of the centres need to be solved too.
you mean 4x4 and 6x6?
@@CzyanKnox no like the windmill cube where you have to rotate the centers
@@CzyanKnoxa 231
But hey, that's just a theory, a CUBE THEORY!
e
"every odd number is a multiple of 3"
*Every Prime Number (that isn't 2 or 3) wants to know your location*
And what are you trying to say by this
I’m assuming he’s saying That every odd number isn’t a multiple of three, which is true. Proven by any prime number bigger than 3. Like 7, or 13
@@antoniomolina3612 9 is odd and a multiple of 3
@@eduardoxenofonte4004 duh that’s the sarcasm. I said every as I’m not every single one, but obviously there are some
@@antoniomolina3612 how am I supposed to know that that's sarcasm?
Reasons why megaminx cannot have two esges swapped:
1: You cannot perform an 'm' move which means 4 edges move
2:there are 5 edges on one side and that means the edges cannot have a two edge cycle because there is 10 total pieces to solve in the last layer and most permutations have a clockwise rotation or two pairs of two edges swap and if that were to occur on a megaminx that means the one remaining edge needs to swap but it cannot.
If you guys agree or disagree let me know and thanks for reading have a good day
Can you move the corners so that the edge can be 2 swap?
@@dumguyawesome no
Just came back to the hobby after two years and I'm excited
A bit late but uh congratulations
Jperm uploads: *clicks on video with military precision*
For the megaminx question: No. Because when on Last layer, you can only have 1, 2, or 5 edges oriented and permuted correctly
For the 3x3 edges... Imagine wanting to flip two edges. In order for the rest of the cube to be solved, you need to flip one edge, replace it, then RE-FLIP it. In an odd number of cases, you cannot reflip the same number of edges which leaves the cube unsolved, hence why you can only have an even number of edges flipped.
"I can just rotate the cube and that moves the centers"
- J Perm 2020
Who is just confused.
Me 😂
Me too😂
No it isn't I literally solved a square-1 with no help when I got parity
I remembered this video I knew I am at even slices then I counted my slices and solved parity on square-1
(+ I am Asian)
learning issue
Me
This is the single most comprehensive and intuitive explanation for parity on twisty puzzle I have seen to date! Thank you!
I can’t swap 2 edges on a megamix because I don’t have a megamix !!!!!
I have watched these videos for about a year, I never had a cube. Not even a 3x3 or 2x2 but I’m finally getting a go cube with some birthday money! I know a lot of techniques, ways to solve, and algorithms. I’m really excited to get my first solve!
it’s been 7 months since you made this comment, how are things going so far? :D
@@LRexx Lol I’m genuinely curious. What if he got the cube taken away :(
learning, watching and reading before you pick up a cube is probably really smart. In the 90s, somehow I started receiving Golf Digest for free weekly. I read it for about 7 years before picking up a club. I decided to go play golf one day and shot in the 80s first time round. That's pretty amazing by the way.
10:24 impossible because a turn on a megaminx does 4 swaps of corners and 4 swaps of edges
6:53 hey vsauce micheal here
Hey Jsauce, dylan here
So I "knew" all of this... but hearing your explanation of it made it seem like something completely new and gave me that mind blown feeling. Best cube video of 2020. This will not be topped for the rest of the year.
Cringe
@@patstaysuckafreeboss8006 ?
@@nathanbegel4505 He was trying to be funny and failed miserably
@@patstaysuckafreeboss8006 or he was just honestly expressing how he felt about the video?
@@nathanbegel4505 Let that autism shine boy
The permutation group of the megaminx group (ignoring the normal subgroup of orientations) is a product of alternating groups, so clearly there are only even permutations of both edges and corners, even considered separately. So you can't even have a transposition of corners and a transposition of edges on a megaminx (as in something like a T-perm on 3×3).
Yes I'm late
He actually did it
He did it
He got his wife pregnant
This was a joke if u whooooosh me
I will slit your...
Ummm...
Fortnite account....
Yeeeeah...
@@nebu1a441 jokes on you i dont play fortnite
What happened here
I actually figured a bit of this out without realizing in middle school when I was learning beginner method. I noticed that the amount of times uou had to repeat R’D’RD in the last step was always a multiple of 6 and I figured out how many repetitions each corner orientation required to correct and that it was always even.
This reminds me: Some kid at my school had just learned the 3x3, and this kid was getting super braggy about it, so I asked them if I couls scramble it for them, they said "sure go ahead", so I walked out of sight with the cube. I then proceeded to yank two edges out and swap them, creating void parity. I then gave it a good scramble to disguise my mischeif (obviously). I gave it back to the kid. Boy did I have a good time watching them struggle. It was hilarious
Lol that's funny. You told him what you did, right?
he is definitely the best cubing youtuber out there... others just post cubing videos, but he also posts these kind of interesting videos talking about the overall nature of twisty puzzles
On the void cube you also functionally have centers, they're just invisible and have multiple solved states
Like if you ignore the centers on a normal 3x3. You'll have the same experience
This mans hands when he swaps:
*_I am speed_*
NEEOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOMMMM!
Know what, just ignore that comment. I couldn’t think of how to spell it so I just did that. And half way through of typing all that I thought myself as DUMB!
@@itsgoofymf7685 lmao ok
when you get parity on a 1x1
frolic plays intensely
happened to me yesterday
Weak
I've done parity countless times
i've gotten parity on a 3x3
just take the caps off and make a poor man's void cube
the absolute SPEED when you do the 2x2 swap thing is terrifying i feel like you could turn a rubiks cube into a weapon and murder me with it and use the cube to absorb all the evidence and then use the cube as a portal to escape into the fourth dimension so they never find you
Not sure if you’ll see this comment, but I’ve been getting into speed cubing lately and watched most of your videos in a very short period of time. I love your content, it’s beyond helpful! I have a QiYi cube that somehow got the last layer corners swapped and seems to be impossible to be solved like you mentioned at 0:35. I’ve never had this cube apart, and I swear by that. I have no idea how it happened, and without taking it apart, there has to be a way to get it back, right? Thanks in advance if you see this. Keep up the great work!
Kinda late lol but this happened to me. It turned out to be center parity, where four centers were basically rotated around a slice layer by popping off the center caps so they looked right but were swapped causing odd center swaps which allows for odd edge swaps, and thus parity. U could always just disassemble the cube too, or swap the centers back
Honestly, this is one of your best videos! I think you should explore more this type of content
A megaminx has 5 sides so each turn swaps 4 edges, therefore you can only have a even number of edge swaps and cannot just swap two edges.
its swaps five pieces not 4
I enjoyed this video. I’m as interested in the theory, math, or mechanics of twisty puzzles as I am in general speed cubing. Good video. Thanks!
So you actually made a video about parity... Thank you!!!
I can't believe what a coincidence this is, I started computer science last week and learnt about even and odd parity in a binary register yesterday
"Why are some cases impossible to solve?"
"WhY cAnT yOu JuSt UnDo YoUr TuRnS?"
I loved this video! Keep making more cube theory videos, it's really interesting to watch!
very late, but here's an explanation for why a megaminx must have both even edge and corner parity: turning a layer cycles 5 edges and 5 corners (4 swaps each) so parity for both is always even
I went to this video with expectations that you are going to explain square 1 parity, can you make part 2
wow This is very informative! :)
This made me study and rediscover the four Isomorphism theorems for groups and permutation groups. This is clean mathematics of group theory.
J perm is like zemdegs and z3cubing, but like in the middle of them both
The average human YT I agree, he has similar qualities to both of them. He is fast at cubing like feliks and explains stuff like z3cubing
@@mouhktar4587 cheers 4 agreeing
I stopped watching Z3cubing over a year ago and I completely forgot that he changed his YT name to Z3cubing, it used to be legoboyz3. If you go to some of his older vids, he says legoboyz3 in his intro
@@lumina_ ikr the nostalgia
@@mouhktar4587 Feliks explains many things in his channel cubeskills.
How to resemble a U-move's cycles and prove the existence of 2e2c, 2e2e, 2c2c, 3e, or 3c with PLLs:
A 1-quarter-turn U-move is a 4e4c.
A U2 move is a 2e2e2c2c.
Take the J-perms(2e2c) or R-perms(2e2c) and add a U2 AUF (4e4c).
Take the H-perm(2e2e) and add a 1-quater-turn AUF (4e4c).
Take the Aa-perm(3c) or Ub-perm(3e) and add a U AUF (4e4c).
Take the Ab-perm(3c) or Ua-perm(3e) and add a U' AUF (4e4c).
Take the E-perm(2c2c) or Z-perm(2e2e) and add a U2 AUF.
Take the N-perms(2e2c) and add a 1-quater-turn AUF (2e2e2c2c).
The last time I was this early was when I did f2l before finishing the cross
If you're a Roux user you're just in time
@@Bladavia wrong cuz he missed his DL and DR edges
@@anegg9108 yeah my bad xD
@@Bladavia you're blad**
@@k_wl, lol
The answer for the megaminx is that you can't. Because when you do a turn in megaminx, you do 4 swaps of corners and 4 swaps of edges, and that's even. So you can never have two edges swapped and every edges at the right place, regardless of where the corners at.
And that's why when you take out all the pieces in megaminx and put it back randomly and try to solve it, you only have 1/24 chance to solve it. (1/2 chance the edges are in the right place, 1/2 chance the corners are in the right place, 1/3 chance the corners are correctly oriented, 1/2 chance the edges are oriented correctly). In a 3x3 rubik's cube the chances are 1/12.
my brain is overloaded
this is my 4th year being a cuber and this is the first time i hear of this concepts
10:20 Yes but only when you make the checkerboard pattern.
@@MattTacc How'd it go?
@@qlava8553 it flips the two edges obviously.
AT .42sec into the video , this is the first time I have every seen anyone demonstrate how I solve Rubik's cubes lol , it has been my go-to solution since I was 7yo lol
“This is a multiple of 3,if your cLAvEr
Me: ......did he just call me stupid?
0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
It is because
3⁰ = 1
I remember having a few beers one night and trying to solve a 3x3 for at least an hour, scrambling it, getting to the end and 1 corner was always out, I put it down to the beers, next morning I tried again and remembered that corners could twist.
Possibly the most infuriating time I've had cubing.
This is an awesome type of video, really enjoyed watching, and glad you had fun making it aswell! :) Be sure to do more videos about cube theory.
I love this cube theory type of video. I kind of want more of it, so if anyone knows something interesting, or even better doesnt know something interesting please suggest it to our mr j perm so he can spread his knowledge even more.
That was the most ive heard someone say swap
Best cubing channel.
Thank u so much for your vids.
Please, keep up the excellent work!
Loved this video, keep making these it's fun understanding the cube
In megaminx, we cannot obtain parities, since this puzzle is a variation of a 3x3, without adding any more layer, as a result, only outer moves can be made, and no exchange of centers can be made to produce a parity . Megaminx, in a nutshell, is a 3x3, but "extended" then it is impossible to obtain a parity
Can we just acknowledge the fact that he never puts in any ads?!!?
He does your prob just on an apple product
Say hello to speedcubeshop.com
Awesome video. I liked the dive into theory, and I'd definitely want to see more like this. This is the best explanation on parity I've seen yet.
6:51 oh no i’ve run into another type of parity
Or is it?
*Vsauce music starts playing*
I hope no one else has commented this
The One and Only oh dang
finally someone explained it well👏🏻👏🏻👏🏻ggs bro
Thank you so much for putting out this video!!!! I love learning WHY the algorithms work so I can learn to adapt better on the go.
With a Megaminx, one turn would equal four swaps of edges and corners. "If, for some reason, we can only do an even number of swaps, then we can't reach any odd number of swaps, because we can never add even numbers to produce an odd number."
I was like: 4×4 somehow keeps magically swapping pieces. Ok, this cube is definitely weird.
i love these math videos. they get me to think and come up with more "intuitive tricks" for solving big cubes without "knowing" how to solve them
Bro giving us homework
The code to solve 7:04 is r2 U2 r2 (Uu)2 r2 (Uu)2
10:34
No because megaminx is 3x3
Heckmate
What a great introduction to permutation groups!
1:53
Legends are saying that mathematicians are still offended.😂
he said 'for our purposes'
So if ur doing old pochman 2x2, take the number of moves and multiply it by 3 to get the number of swaps to solve it with old pochman
The word "swap" doesn't sound like a word anymore and has lost all meaning.
𝐈. Why permutations are important and why they make up the nature of Rubik's puzzles.
𝐈𝐈. Why parities are discussed, especially in accordance to the behavior of Rubik's 3x3x3 Cubes
𝐈.
1.) All of this can be traced down to how permutations work. In a Rubik's puzzle, *permutations are what exist, not combinations.* Permutations mean switching the POSITION of things with one another, which is normally what we see on Rubik's puzzles. In this sense, we can regard that COMBINATIONS *can not only SWITCH THE POSITIONS of pieces, but their ORIENTATION too.*
2.) *We usually see the 3x3x3 Cube as like the *borderline on how we assess situations in regards to how permutations work or behave on Rubik's puzzles, and not any other iteration of the cube or puzzle* (e.g. 2x2, 4x4, 5x5, etc.). In that matter, we know that *these permutations or "swaps" usually comprise of a lingering aspect in which EVEN numbers are abruptly discussed.* (This is what this JPerm video entails.) We must denote that a 3x3x3 Rubik's Cube has 43 quintillion states in which it can reside in. When you think of it, a puzzle is A RUBIK'S CUBE *if, and only if, that puzzle has the same configuration as what a (normal/usual) Rubik's Cube would have.*
2.1.) Let's use the 3x3x3 as an example. Let's use a common situation such as "twisting one corner or one edge" -- it can be any situation as long as the thing about ODD number swaps/etc. exists, because we've tackled that *on a 3x3x3, it is a usually observed and widely accepted trend that an EVEN number of swaps* (or any other term in regards to the behavior of how a 3x3x3 becomes unsolved THAT ARE NOT PERMUTATIONS) *is a recurring theme.* In that regard, if we do anything of the sort where an ODD number of non-permutations (swaps, etc.) is done to manually modify how a 3x3x3 seems or behaves, *that puzzle is NO LONGER a Rubik's Cube,* so to say, because you'd by then have *arbitrarily opened a new range of states and possibilities for the puzzle you modified, whether it be 43 quintillion as well or similar.* The point is, what we've done does not qualify the puzzle as a Rubik's Cube anymore. Why this generally IS is because what we've done to our puzzle is NO LONGER a PERMUTATION, but rather a COMBINATION (or "orientation"), *where the same pieces can be normally rearranged into a solved state* (in regards to what a solved state in a Rubik's Cube would look like), *but, while the pieces are at their respective positions, you have changed the configuration of that piece, which no longer translates as a permutation, and in the long run no longer denotes THAT puzzle as a Rubik's Cube or Rubik's puzzle any further.* Put bluntly, you shouldn't do these in the first place, which is why they're called "illegal moves" -- wherein if you do, that puzzle is no longer a Rubik's Cube and you have opened up a new scope of possible permutations, with each being different from a normal Rubik's Cube's.
𝐈𝐈.
Parity is something that is usually regarded towards 3x3x3's (see 𝐈., #2).
1.) *A parity does not occur within a 3x3x3 Rubik's Cube. A parity is a phenomena that is usually denoted as a SWAP* (non-permutation) *which is normally in regards towards anything outside the normal behavior of a 3x3x3 Rubik's Cube.* We use the 3x3x3 as a reference or borderline for that matter. *Parities in non-3x3x3's* (4x4x4's, 5x5x5's, etc.) *are usually discussed in account to how 3x3x3's normally perform.*
2.) Let's use the 4x4x4 as an example. 4x4x4 Rubik's Cubes are the same as 3x3x3's, except a 4x4x4 only has more permutations. When you think of it, *BECAUSE a 4x4x4 is NOT a 3x3x3, you can get away with having situations that are not particularly in accordance towards how a 3x3x3 normally behaves.* Having 2 "wings" swapped (OLL Parity) is definitely something you CAN, in fact, experience on a 4x4x4. It's just a matter towards what you CAN do in a 4x4x4, or every possible permutation that a 4x4x4 presents, whereas *parity, something that is usually regarded towards something which performs or occurs outside the boundaries of a normal 3x3x3's behavior, is a part of.*
𝐈. The 3x3x3 Rubik's Cube generally sets the *borderline or acts as a reference* towards phenomena that are discussed which are *usually outside the behavior of a non-3x3x3 Rubik's puzzle, such as PARITY.* *Permutations make up the nature of Rubik's puzzles.* If you manually configure a Rubik's puzzle wherein its "solved" state would be different than usual, then that puzzle is *no longer a normal Rubik's puzzle.* *Non-EVEN configurations usually result in this.* (This is explained very thoroughly in this JPerm video.) You're *not supposed to change the configuration* in the first place, which is why they're called "illegal movies", but if you do, you run into risks of changing the configuration wherein that puzzle no longer behaves the same as a normal Rubik's puzzle. ALTHOUGH, you CAN, in deed, manually change a Rubik's puzzle's configuration *ONLY so much so that you RUN into a situation where that situation ACTUALLY resides as one of the possible permutations in a normal Rubik's puzzle,* thereby still being able to solve it normally, and ACTUALLY still being regarded as a nornal Rubik's puzzle in the end.
𝐈𝐈. *Parity is a postulate in non-3x3x3 Rubik's puzzles.* Parities are often regarded as *phenomena in which their nature does not qualify as normal behavior which you can expect from a 3x3x3.* However, in spite of popular disputes, parities are in fact only true to the configuration of these puzzles. Parity is *not a crime, it's a phenomenon.*
𝑹𝒆𝒈𝒂𝒓𝒅𝒔.
@JPerm
Im early let me tell a joke
My WCA results
Same lol
if you look at beginner method the last step is orienting the last corners and it always adds to a multiple of 3 algorithms to solve, also you cannot switch two edges on a megamink
This man: exists
Me: who just learned a cube today
This is extremely fascinating ... more like this pls.
The reason why two megaminx edges can't be switched:he megaminx has even parity, and two edges switched is an odd parity configuration.
9:33 "So in this case I can keep twisting any corner 3 more times and that... is funny."
That was hilarious!
Me: I don’t know what this means RUclips gave me this HELP ME
Thank you so much for the taiwan chinese subtitles!
Im literally so confused
Yeah, I understood almost nothing in this video lol
TheCakeMuffinCrew He did a horrible job of explaining
Fake Seattle Sounders FC no. you did a terrible job at listening :)
You need basic cubing knowledge to understand this
learning how a cube works is way better than learning just algorithms