Rubik's Cube: Why are some cases impossible to solve?

A full explanation on parity, and why it happens on the void cube and 4x4 and not 3x3!
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[@kaikyc.5072]

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.

[@JPerm]

There are a lot of people who run into that problem!

[@angryarachnid0]

F

[@ankithmahesh1182]

F

[@paulyp1919]

@@JPerm My kids do this to me a lot! Think it is funny...

[@joachimprz]

Me Too;)

[@Spatzna]

"1 is a multiple of 3 if you're clever" Great vid, loved it

[@puerlatinophilus3037]

Legends say that the number of times he says "swap" in this video has to have an even parity.

[@deekay1306]

wait... let me just save some real estate on this great comment. 🏠🏡🏘

[@dumguyawesome]

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

[@batrongordeg]

@@dumguyawesome what? That is becuse quantum physics or you just explained it poorly?

[@liandremarcoricafort6606]

It's a twist if you twist it.. not because it's twisted

[@leborenday]

?

[@vinuthabhandary6543]

You make the types of videos I can watch over and over again without getting bored.

[@idealsolutions4569]

Me to

[@mikelito0058]

Yea lol its like the 4th time I watch this one

[@xxswaftxx31]

Yeah

[@SagarCubes]

Me too

[@kiwicuber]

Ikr

[@leo17921]

"Every odd number is a multiple of 3" -J Perm

[@bambo418]

Prime numbers other than 2 and 3: am I a joke to you?

[@10kwithnovideochallengemem91]

Abysmal Luck lol

[@cuberrificdan5539]

@@bambo418 lol

[@jisaarmaliai4050]

How bout 5 xd

[@bambo418]

@@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

[@rahulsahay7330]

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

[@naeemfarooq8784]

That is exactly what happens Try it on a 3×3 only solve 2 centers

[@korianjunakuvaaja7801]

Centers are fixed

[@eyeturtle]

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.

[@crimson3362]

i absolutely love this, i live for this kind of nerdy stuff, i hope you do more cube theory videos in the future

[@cheesemunchkins]

me too!

[@danielsaad9196]

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*

[@nhlvideosforkids1761]

Some Nerd

[@lumina_]

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

[@nikotakai8796]

@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?

[@kaikyc.5072]

@@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

[@lumina_]

@@nikotakai8796 yeah, if you don't corner twist it or take out pieces you shouldn't get parity on 3x3

[@maxcrenshaw]

I genuinely enjoy the "cube theory" format, keep doing them my guy!

[@Inspirator_AG112]

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.).*

[@danay996]

Why no replys???

[@bilingualchad]

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.

[@Inspirator_AG112]

@@bilingualchad : Thanks, and yes.

[@asr2009]

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.)

[@oualidbazzaoui1989]

@@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

[@Sora-iu2kc]

someone need to count how offten he said "swap"

[@puerlatinophilus3037]

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.

[@nischalmr5978]

Why can't that "someone" be you

[@Sora-iu2kc]

@gamer.20years.and thats true i have no freinds ;-;. Do you wanna be my freind ?

[@Daaljeli]

@@Sora-iu2kc I'll be your freind

[@wheezybread]

I'm pretty sure the amount of times was even parity

[@VictorArets]

This is a multipel of 3, iF YoU’Re CLevEr. -jperm 2020

[@funcuberdeadchannel5426]

Not funny,didnt laugh

[@bluecreeperboybcb4399]

Doge Yay Don’t care, still don’t care.

[@funcuberdeadchannel5426]

@@bluecreeperboybcb4399 ok and??

[@lumina_]

In what way is this funny?

[@funcuberdeadchannel5426]

@@lumina_ can i drink u

[@pathfindernutsinurface3296]

My mom: So what did you learn today? Me: I learned Dylan's law of slice turns and parity explanation

[@natanfurman2467]

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.

[@JPerm]

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

[@natanfurman2467]

@@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 :)

[@vishalarora8454]

Well I like nerdy stuff but I didn't knew this, thank you

[@sinpi314]

This video is super interesting, I really love cubing + maths vids. Make more of these kind!

[@baileycooper2307]

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.

[@noahve]

I loved this video! Keep making more cube theory videos, it's really interesting to watch!

[@JediJess1]

This is the single most comprehensive and intuitive explanation for parity on twisty puzzle I have seen to date! Thank you!

[@tracingtheta]

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.

[@MinutemenSyndrome]

Sorry Professor Dylan, I forgot my megaminx homework at home.

[@konoacda9935]

A dog ate my megaminx!

[@GuggleBum]

Loved this video, keep making these it's fun understanding the cube

[@F33DtheF34R]

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.

[@patstaysuckafreeboss8006]

Cringe

[@nathanbegel4505]

@@patstaysuckafreeboss8006 ?

[@patstaysuckafreeboss8006]

@@nathanbegel4505 He was trying to be funny and failed miserably

[@nathanbegel4505]

@@patstaysuckafreeboss8006 or he was just honestly expressing how he felt about the video?

[@patstaysuckafreeboss8006]

@@nathanbegel4505 Let that autism shine boy

[@Vidikron]

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!

[@tommik4872]

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.

[@victorcanesin8978]

Honestly, this is one of your best videos! I think you should explore more this type of content

[@radoaahmed2420]

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.

[@NovaStrike118]

"every odd number is a multiple of 3" *Every Prime Number (that isn't 2 or 3) wants to know your location*

[@Ya_boi_ben]

And what are you trying to say by this

[@antoniomolina3612]

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

[@eduardoxenofonte4004]

@@antoniomolina3612 9 is odd and a multiple of 3

[@antoniomolina3612]

@@eduardoxenofonte4004 duh that’s the sarcasm. I said every as I’m not every single one, but obviously there are some

[@eduardoxenofonte4004]

@@antoniomolina3612 how am I supposed to know that that's sarcasm?

[@heusbd]

Jperm uploads: *clicks on video with military precision*

[@Irokesengranate]

You're literally doing group theory with your hands, proving theorems by manipulating plastic pieces and counting stickers. It's beautiful.

[@bobmarley6306]

This is extremely fascinating ... more like this pls.

[@RandomBurfness]

I think it could be interesting to extend this discussion into supercubes, where the orientation of the centres need to be solved too.

[@czyanknoxchannell]

you mean 4x4 and 6x6?

[@finns_thewinner204]

@@czyanknoxchannell no like the windmill cube where you have to rotate the centers

[@classicmelodyvetrivel710]

​@@czyanknoxchannella 231

[@mitkobomba]

"I can just rotate the cube and that moves the centers" - J Perm 2020

[@rememberingunity]

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.

[@sauce790]

Just came back to the hobby after two years and I'm excited

[@witherwings7772]

A bit late but uh congratulations

[@smirkycubes3369]

This was a really cool video! I learned a lot, thanks!

[@zizohno9336]

He actually did it

[@nebu1a441]

He did it He got his wife pregnant This was a joke if u whooooosh me I will slit your... Ummm... Fortnite account.... Yeeeeah...

[@arifwazir3584]

@@nebu1a441 jokes on you i dont play fortnite

[@thepanther9163]

What happened here

[@DrPallaviKher]

6:53 hey vsauce micheal here

[@CreeperSkullDZ]

Hey Jsauce, dylan here

[@tomskinl]

Good Eye opener for me. Did solve that 4x4 cube last weekend till I had that "1 Swap of Wings". Didn't seem logic to me, and thought maybe some piece was changed. But your video explains pretty good what is going on. Will try figure out to fix next weekend. Thank you for the comprehensive an detailed explanation.🙂

[@combustablelemon3482]

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.

[@god5926]

This mans hands when he swaps: *_I am speed_*

[@itsgoofymf7685]

NEEOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOMMMM!

[@itsgoofymf7685]

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!

[@god5926]

@@itsgoofymf7685 lmao ok

[@michelenardin9189]

So you actually made a video about parity... Thank you!!!

[@gauravpallod4768]

Amazing video! I like this cube theory stuff!

[@cubeophilic.x7301]

This video was awesome! Waiting for more such videos

[@saturniunyttech679]

0:30 here we have his channel logo

[@maaziboy3088]

Lol how'd u spot that

[@saturniunyttech679]

@@maaziboy3088 i just noticed it looked like his logo

[@FrozenBirdXD]

wow This is very informative! :)

[@andrerosaesilva]

Best cubing channel. Thank u so much for your vids. Please, keep up the excellent work!

[@lenn_man]

I really like the cube theory vids. Can't wait for more

[@slic3dic385]

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!

[@agungsugiyanto8314]

my brain is overloaded

[@bhanusairam1534]

i clearly understood every thing you explaind perfect.

[@yuxiaoliu7795]

What a great introduction to permutation groups!

[@MTTR01]

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.

[@nmrs4342]

10:24 impossible because a turn on a megaminx does 4 swaps of corners and 4 swaps of edges

[@VicJang]

Great video. I enjoyed this more than the speedcubing ones.

[@royitaqi]

I loved the cube theory videos, e.g. the commutator one, and this one about parity. I wonder if there are other cube theory videos besides these two.

[@Dahea]

"Why are some cases impossible to solve?" "WhY cAnT yOu JuSt UnDo YoUr TuRnS?"

[@peterzo]

The last time I was this early was when I did f2l before finishing the cross

[@Bladavia]

If you're a Roux user you're just in time

[@anegg9108]

@@Bladavia wrong cuz he missed his DL and DR edges

[@Bladavia]

@@anegg9108 yeah my bad xD

[@k_wl]

@@Bladavia you're blad**

[@nutmeggaming11261]

@@k_wl, lol

[@Oscar-42]

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!

[@LRexx]

it’s been 7 months since you made this comment, how are things going so far? :D

[@user-qx4vs7ne8w]

@@LRexx Lol I’m genuinely curious. What if he got the cube taken away :(

[@jymcotton9904]

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.

[@Kleinian363]

This video was extremely cool, loved it

[@qlava8553]

10:20 Yes but only when you make the checkerboard pattern.

[@qlava8553]

@@MattTacc How'd it go?

[@MattTacc]

@@qlava8553 it flips the two edges obviously.

[@cinnamonkittamon]

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

[@NB69420]

Your videos are awesome!

[@Cruxify_]

You're so close to 1m congratulations on getting so far!

[@Kai_M]

J perm is like zemdegs and z3cubing, but like in the middle of them both

[@mouhktar4587]

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

[@Kai_M]

@@mouhktar4587 cheers 4 agreeing

[@lumina_]

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

[@Kai_M]

@@lumina_ ikr the nostalgia

[@Mateus.007]

@@mouhktar4587 Feliks explains many things in his channel cubeskills.

[@wwa_vy]

Who is just confused.

[@The_Jordanator]

Me 😂

[@ShreyasSiddharth]

Me too😂

[@futureshit-glungis7202]

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.

[@mr.goldenpigman4549]

Hey I liked this style of video. I think you should make more like this explaining how the cube works

[@calumross2482]

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.

[@someguyyt8595]

its swaps five pieces not 4

[@tyl1to104]

That was the most ive heard someone say swap

[@sakuracat3412]

finally someone explained it well👏🏻👏🏻👏🏻ggs bro

[@kryt7955]

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

[@xdlilmanhaider8407]

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

[@dumguyawesome]

Can you move the corners so that the edge can be 2 swap?

[@epiccarpetdog]

@@dumguyawesome no

[@muhammaddaji690]

For the megaminx question: No. Because when on Last layer, you can only have 1, 2, or 5 edges oriented and permuted correctly

[@krzysztof_jablonski]

9:33 "So in this case I can keep twisting any corner 3 more times and that... is funny." That was hilarious!

[@thomasforbes784]

Love these cube theory vids

[@mays_things7945]

“This is a multiple of 3,if your cLAvEr Me: ......did he just call me stupid?

[@Lavanya2B]

0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000

[@EHMM]

It is because 3⁰ = 1

[@cr1spyp1eskingsou17]

when you get parity on a 1x1 frolic plays intensely

[@cheatrzs]

happened to me yesterday

[@Random22]

Weak I've done parity countless times

[@cr1spyp1eskingsou17]

i've gotten parity on a 3x3 just take the caps off and make a poor man's void cube

[@terrencecanny9015]

can you pls make a video on how to get better look ahead and better times? also love your vids and keep up the good work

[@ToninInTheSubway]

very interesting, thanks !

[@fakefirstnamefakelastname8305]

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

[@lumina_]

Lol that's funny. You told him what you did, right?

[@kartikeyagarwal5156]

1:53 Legends are saying that mathematicians are still offended.😂

[@c4d3nx]

he said 'for our purposes'

[@nm5641]

Loved it!

[@kummer45]

This made me study and rediscover the four Isomorphism theorems for groups and permutation groups. This is clean mathematics of group theory.

[@Serkoid]

But hey, that's just a theory, a CUBE THEORY!

[@c4d3nx]

e

[@freshstat1csnow]

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

[@origamikatakana]

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).

[@origamikatakana]

Yes I'm late

[@jirka12sirka37]

Great video!

[@baseballnerd6465]

Can we just acknowledge the fact that he never puts in any ads?!!?

[@jaffil4026]

He does your prob just on an apple product

[@zezus001]

Say hello to speedcubeshop.com

[@max_ishere]

I was like: 4×4 somehow keeps magically swapping pieces. Ok, this cube is definitely weird.

[@violetagarcia829]

Thank you for the video!! It was really helpful, I just found it one day after giving up and starting all over again with my 4x4 and the wings problem 🤣

[@taavimetso9178]

Nice vid more of this kind

[@thaiisfood]

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

[@thaiisfood]

The One and Only oh dang

[@slkgamer-255]

This man: exists Me: who just learned a cube today

[@ItsVasl]

Thank you so much for the taiwan chinese subtitles!

[@kavinbala8885]

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

[@tiny9720]

The word "swap" doesn't sound like a word anymore and has lost all meaning.

[@oceanbeans8546]

Me: I don’t know what this means KZbin gave me this HELP ME

[@Jona69]

When you turn a side on a megaminx you do 4 edge swaps. So it has to be a multiple of 4, though you can add or subtract 2 because you can swap one pair twice. But it's still an even number of swaps so you can't swap just two edges which is one swap. I really enjoyed the video, super interesting and very well explained.

[@ciCCapROSTi]

This was approachable for a noob, so good video!