Impossible Cube Positions (The Cubing Mathematician?)

[@TheCubingHistorian]

Re: criticisms - They're valid, and I agree this video could have been made a lot better, with better explanations. However, this was literally the 14th time I had refilmed it, and I really didn't want to delay the video any further. I may remake the video in the future, but for now I want to get back to history.

[@TheCubingHistorian]

+Big Rube That was faked, it was an April Fool's joke I believe.

[@dhruvchawla5476]

Big Rube well you are

[@hamizannaruto]

LOL

[@lindakientz6106]

CORNER FLIP FOR THE WWWWWW

[@deepacs2635]

Cowboy dance boy

[@kaxymonoxy]

I'm gonna put this video on a QR code, print it out on a couple little cards, and give to people that say im cheating when i twist a corner or am fixing my cube after a pop

[@sq5321]

Give me that QR code right now please 😂

[@LeafyGrovyle]

Me too

[@carlos_adventures9018]

kyugames! Can I has one?

[@dickensfamily4481]

Same

[@Az-ve4jm]

Modern problem require modern solution

[@velocics8979]

here is a simpler explanation - 10002010201201021020120120102102012102012010210201201021021020120110002010201201021020120120102102012102012010210201201021021020120110002010201201021020120120102102012102012010210201201021021020120110002010201201021020120120102102012102012010210201201021021020120110002010201201021020120120102102012102012010210201201021021020120110002010201201021020120120102102012102012010210201201021021020120110002010201201021020120120102102012102012010210201201021021020120110002010201201021020120120102102012102012010210201201021021020120110002010201201021020120120102102012102012010210201201021021020120110002010201201021020120120102102012102012010210201201021021020120110002010201201021020120120102102012102012010210201201021

[@Mr-qm8fi]

The bumbling bafoon in the video didnt make any sense, so thank you for explaining it

[@mintyturd9]

Oh my go-

[@monicamastromauro2813]

*Now it's your turn!* Me: Shit.

[@konstantinkodzhabashev1694]

Here's a easier explanation and yes thats not just spam உங்களுக்கு ஒரு மொழிபெயர்ப்பாளர் தேவைப்பட்டால் நீங்கள் ஒரு டம்பஸ் மற்றும் நான் என்ன சொன்னேன் என்பதைக் கண்டுபிடித்த உங்கள் நேரத்தை செலவிட்டதற்கு நன்றி

[@airlegoland]

Could you do one on the history of blindsolving methods?

[@joeycubes68]

Can you do a video on why the rainbow cube and Siamese cube were taken out of the wca.

[@joeycubes68]

BedwarsFoxy thanks so much!

[@joeycubes68]

BedwarsFoxy lol

[@AndrewTyberg]

BedwarsFoxy Yeah, me too.

[@AndrewTyberg]

Also 3x3 no inspection.

[@jackolopecuber7112]

They were never in it.

[@MathijsHerremans]

Great video! Could you explain how parity works on a 4x4? Also could you make an history video of big inventions in (speed)cubing, like the Dayan GuHon, Magnets, etc?

[@EduTradeStudio]

Mathijs I think it is simply explainable. Since even number cube has no true center. If you take out the center on 3x3, it will act the same as 4x4

[@MathijsHerremans]

Kyonika Yes, I understand how it works, at least I think to understand it. Basically you misalign the centers and built your cross (if you do it on a 3x3) for example on orange. Someone I teach how to solve a Rubik’s cube a few weeks ago and he told me in the ISS Station the have a ball wit 3 rings and if the make the right movement all the lines are at the right position, if the don't the lines are not on the right position. I will ask him what is it, but is is basically the 4x4.

[@salute4392]

I Can, since you make the center then edges, the thing is when you make the edges it might be flipped and not Normal, like flipping an edge around on a 3x3. If I could show you in person I would explain it better

[@MathijsHerremans]

But would it be possible to see if you can get parity, and make the edged and centers "right" so you can force yourself to skip both parity's? I don't think so, maybe if you mark something, but that would be illegal in comps.

[@salute4392]

Yeah you could do that. So you could mark L and R for left and right on the edges so when white is on top they should be on the left and right

[@wompastompa3692]

You also can't swap a single pair of opposite centers unless you're on an even cube bigger than 2x2. One thing I like doing to friends getting in to cubing is swapping each center on a 4x4 with the opposite side and letting them have at it for a bit.

[@pickletickle8407]

I've been trying to solve a cube with the centers swapped, but I just found out I can't do that

[@bobmarley6306]

More maths videos like this would be great. I thoroughly enjoyed this one good work!

[@kyazarshadala8114]

The way I think of the last one is each turn does a 4 cycle of edges and a 4 cycle of corners. A 4 cycle is equal to 3 swaps, so a single turn has 6 swaps

[@thefallingpi341]

*HE’S ALIVE*

[@bamboocarver]

YES!!

[@bagduster9381]

SynergyRayzer probably came from the cubing revolution back in 2000s

[@exmbird]

@thefallingpi lol

[@lalafirdous5717]

And he's dead again

[@atharvanargund]

this channel deserves more attention

[@origamikatakana]

Your corner twisting explanation isn't actually an explanation. If you explained why you have to always end up at zero, then it would be an explanation, but as it is it is just a demonstration.

[@JasperJanssen]

origami katakana that really depends on your definition of explanation. It may or may not be an explanation by your definition, but it *is* a mathematical proof. In this case, a proof by exhaustion: all options are enumerated. If you want t9 provide a proof by group theory, that’s fine, but it is neither more nor less valid.

[@origamikatakana]

Yes, it is a proof, but it does not really get at any underlying structure (which a group theory explanation would.)

[@seansiquig]

origami katakana did it not make sense to you? because it made sense to me, whether or not it was a some sort of “scientific” explanation. idk why you guys are being so critical when its simply a video about a rubik’s cube, not some NASA equation.

[@EpiCuber7]

@@origamikatakana What's the explanation by group theory?

[@origamikatakana]

@@EpiCuber7 the corner twists are ismorphic to the finite abelian group (Z/3Z)^7. You can see this by finding an invariant of the corner orientations under a 90° face turn.

[@scudlee]

It's worth noting that in terms of permutations, a single face turn on a cube is actually two ODD permutations, one on the edges and one on the corners. ODD + ODD = EVEN This also applies to larger cubes where you always have an even number of odd permutations on each of the different sets of pieces. It's why you can have seemingly impossible "parity" positions on a large cube, because the odd permutation on the edge pieces is really coupled with another hidden odd permutation on identical-looking center pieces. On the other hand, on a megaminx (or larger), a single face turn is an even permutation on the edges and corners (and centers) separately.

[@spacevspitch4028]

That was great! You should do a video explaining how parity works. Also, the center rotations on picture cubes! I read somewhere it was called "virtual parity" because on a regular 3x3 cube with single colored sides, you aren't aware of the centers turning.

[@nabranestwistypuzzler7019]

4:17 You can also reach 0 by twisting another one clockwise, or 2 counter clockwise.

[@nabranestwistypuzzler7019]

For permutation, you actually can’t switch just 2 corners and 2 edges. It’s just that on 3x3, one 90 degree turn (AUF) will cycle 3 edges, and also cycle 4 corners, and also cycle 4 edges. That’s 3 swaps for each type of piece. However, for the Megaminx, it’s 4 swaps for each type of piece (obviously not centers). It’s also physically impossible to rotate a single center 90 degrees & have it solved. However, it is possible to do a single center rotation on a Megaminx (72 degrees) because it’s the equivalent to doing 4 (288 degrees) in the opposite direction.

[@thephysicistcuber175]

plz do more of the cubing mathematician!

[@angusmglfraser]

I think a better explanation of the bit about permutations is to point out that any 90 degree move of a face does a 4-cycles of edges and of corners. This then extends to all possible manipulations of the cube since any sequence of moves, or a wide move or a slice or whatever else can be reduced to a sequence of 90-degree face turns. This also lets you point out that the parity of exchanges of edges and corners has to be equal i.e. if an odd number of edge swaps has been made, an odd number of corner swaps has to have been made as well, and the same for even. This also then lets you understand why certain puzzles have the parity issues they do, for example, the master kilominx can have an edge parity issue because you can do two 3-cycles of wings to essentially swap 2 edges, but a similar situation does not exist for the corner pieces because every move that affects the corner pieces just does a 5-cycle of them.

[@douglasshamlinjr.392]

I think you should do a similar thing for other puzzles too. I know that it is impossible to: flip an odd number of edges on a pyraminx or megaminx, Switching two edges *and* two corners on a megaminx, flipping any number of edges on a dino cube, master skewb, or face turning octahedron, rotate a single center 90 degrees on a picture cube, have oll and pll parity on a gigaminx, switch exactly two centers on a skewb, rotate a single corner on a megaminx or skewb have more than 4 different colors on a single face for a face-turning octahedron

[@felixrowan3740]

Blimey! A very interesting and clear way of explaining it! I'm quite keen to refer some people to this video.

[@radian1243]

Dude seriousley please do more of these maths videos. Really enjoyed it :)

[@NDPuzzles]

That was a great video! I like how much effort you put into it and the explanations were completely logical and understandable. I really would love to see more mathematician videos!

[@peterosudar6653]

Please do this for a 2x2. It will take less time and make extending to 3x3 a little more natural. #Whydoeseveryonestartwith3x3then2x2?

[@aimarlangley4156]

I was about to start with 3x3 but I want to start something easier

[@looperover]

Peter Osudar #becauseyoullgetdemotivatedtolearn3x3onceyourlearn2x2

[@cngefrzn8758]

Finally!!! By the way good to see you back

[@bricc4415]

i love your content!

[@Xeqcme]

I bought a cube from a thrift store...apparently it's the Rubik's speed cube(??) and the video that shows how to take apart cubes told me I should not. I followed a few videos step by step and could not solve it because it left one corner wrong. Thank you. I was going crazy.

[@tomdriessens]

Nice video, very interesting explanation!

[@sunilmishraifs]

Yes another vid.please upload more

[@michael1234252]

You should do a mini series about the mech evolution of each current WCA type of puzzle.

[@tuptim123]

I have always wondered if people take these things into account when doing the calculation that everyone has heard a million times.. "there are 3.2 trillion combinations in a standard rubiks cube" (or whatever number they had somehow figured out) I would love to know what the true number is.

[@TheCubingHistorian]

Actually, the 43 quintillion figure does take these restrictions into account. If you disregard any restrictions and just think about disassembly and reassembly in any order, you get 12 times as many positions.

[@QwertyQwertz]

Ayy, thanks for letting me read the script, great video! :)

[@QwertyQwertz]

?

[@MilanRubiksCube97]

Do more of these! Next time cover something else like even layered cubes or the void cube!

[@h1nkle]

1:33 this is also known as the transitive property of equality.. for example 1+2=2+1

[@origamikatakana]

commutative* property of addition*

[@koopa643]

You uploaded! This made my day

[@Dvd-Znf]

i think you like FMC

[@Dravignor]

I encountered something different tho in the Permutations... F, V & Z Perm on mine seems to cross an odd number of times.

[@peterosudar6653]

Finite fields are the only fields we need.... modular arithmetic makes it seems like "this is different" but its really much more natural than we give it credit. #cubingIsNatural

[@origamikatakana]

There are finite fields of prime power order, too.

[@AndrewTyberg]

I like this video. I would like if you were to move this. I think you explained it very well.

[@jaydenleong6127]

are you back now?

[@arecus54]

I'm not too sure if the permutation explanation is convincing enough, unlike the former two

[@creeksidecubing1009]

Another video on this awesome channel!

[@paper2222]

Can you talk about why square 1 and clock is the most hated wca puzzle?

[@kayak8700]

make a video about the limits of speedcubing

[@depressionhits5383]

I saw another video like this and someone typed “just twist a corner dude” DO NOT TWIST UR RUBIKS CUBE if u do then it will be in an unsolvable state

[@herrreinsch]

this video was awesome my friend, thanks for making.👍

[@s02mb]

"You are not a real youtuber if you don't refilm videos a 1000 times" Great vid!

[@lrrobock]

I got how it is possible to reassemble in a wrong way, but not quite got the Why is it that you end up with a 11 out of 12 chance.

[@thomasarchived246]

what should I do? I got a Rubik's cube its new and I never dissasembelled it, got it today aswell. yet after 2 hours of trying, I went onto rubiks cube solver and it says unsolvable? why is that?

[@jagadishpanambur6515]

Try to solve it methodically. Then u will face some problem in last layer, at which point you remove that particular piece and re insert it so that it's right. If that's too complex, them do two layers from a tutorial and then disassemble last layer and put it in the right spots

[@victorlimpearce1887]

Welcome back.

[@valorantenjoyer1253]

WHAT WAS HIS LAST VIDEO ABOUT

[@Dvd-Znf]

but what if it was oskars iligal cube ??????????????????????

[@VauZed]

Now thats, what I call zeroing!

[@tgbplays658]

Incredible.

[@JAM-rp6fi]

*randomly points at whiteboard and lists off random numbers from 0 to 2*

[@00F]

He’s back!!

[@cpt_nordbart]

Well explained!

[@macyproductions9523]

Never knew I could twist corners

[@tuwtel]

Awesome video I had just accepted that it doesn't work and moved before this but now I understand lol

[@EnderProGaming]

drink a shot everytime he sais zero

[@TheCubingHistorian]

zero zero zero zero zero zero zero

[@runby6053]

yay you're back :DDD you weren't joking on my comment :D

[@bookiejohnson9660]

There is an algorithm that when you get to the end of the algorithm it has one corner turned

[@TheCubingHistorian]

That was an April Fool's Day joke by MMAP.

[@bookiejohnson9660]

@@TheCubingHistorian not that, when I try to solve a Rubik's cube and I get to the end, there is always 1 corner that is turned

[@TheCubingHistorian]

That'll be because someone took it apart and twisted a corner like a FOOL

[@telvumchonghaokip2109]

Why impposible move happened??

[@papadank1972]

I think my brain just exploded

[@resoshen]

I have three yellow corners on my cube and can't figure it out

[@neilianalmazan6685]

u sound like mumbo jumbo

[@NKCubed]

NEXT VIDEO??? We are blessed

[@黒木真人-m5w]

I was expecting algorithms

[@ChargedCube]

2:06 my test marks

[@husaanshabendri4331]

finnaly A NEW VIDEO BY HIM

[@Zigzagmig]

relatively easy explanation now i feel like a bloody idiot

[@chasemarangu]

group theory, symmetry, and modulus math or something. because your restricted by legal moves

[@yat_ii]

when some said 43 quinntilion combanations how did they manage to not include those?

[@marcozagaria6696]

Nicky Sim yes those are non in tge 43 quintillion

[@hamizannaruto]

You can watch some video explaining.I found Z3cubing video very easy to understand. Simple answer, by excluding the last pieces. The placement and orientation does not matter until the very last piece, which determine if the cube is solvable or not. so they just exclude those one..

[@undonememory7836]

you can switch two corners, it goes like this, put the corners you need to solve at the right of the cube and then do the sequence of R U R' U' R U R' U' R U R' U' then spin the cube to the right and do L' U' L U L' U' LU L' U' L... i'm a gnome and you've been gnome

[@slaier8727]

yay a new upload 🙌🙌

[@HarrisonVig]

Holy cow I think my mind imploded

[@philbarry7979]

but i love math

[@lok7396]

Phil Barry yea

[@aarifahamed6790]

We can finish the corner orientation by doing R'D'RD

[@hamizannaruto]

Me, myself and pi flashback.. Is he dead?

[@विचित्रलड़का]

I didn't disassemble. I was just shuffling a lot. Then when I tried solving it ,I cant

[@want-diversecontent3887]

Ajib sa ladka Must've accidentally twisted the corner then.

[@boscorner]

Showing this vid to the non cubers so they stop acting like twisting corners after they get turned accidentally is cheating!

[@ProVaik]

Da cornah is da twisty

[@alanwakermj4life566]

Bruh to retwist cube apply the algorithm that twists two corners then solve the cube

[@disaus]

3=0 -The Cubing Historian, 2018

[@Gomka99]

More!

[@NJBSports_KH]

One word to describe as of this smart

[@rikishikato5001]

we learn something new everyday

[@cragonoskritirea2982]

What I learned from this video *3 = 0*

[@ClonkyClonky]

*quick mafs*

[@thedylster8165]

still a cool video! :)

[@derpinggaming5962]

It is not exactly that in 12 chance there's only 1 chance that the cube could be solved. Everytime I disassemble my cube there is 95 percent that it could be solved but theoretically it should be much lower than 95 percent

[@BoBoN4Uto]

4:22 korega... requiem da. (yes it is jojoke)

[@kusmandoschanel]

Well, it looks like not the best explanation for permutations as you had to tell us about other sides too For example M2 U2 M2 U2 makes even number of crosses on white face. But it also makes odd number of crosses on yellow face Well, (U2 R2)x4 makes even number on white and zero on yellow It makes something really strange on green and blue faces and permutes only 2 pieces on orange

[@madlad977]

You are great

[@jonbryant610]

You can twist a corner there is an algorithm for it

[@sinhaprabhat9938]

Yes, there is one but it is impossible to twist just one corner.The Algorithm will twist one in front and in back First do this algorithm R U' R' U' R U R' F' R U R' U' R' F R Then do this R (Y perm) R'

[@Oliver-uz9ck]

0:24

[@mspika]

OMG HES ALIVE!

[@SHELLWER]

I new that

[@akramturdiev1075]

I have no idea what yoy just said. My brain

[@trailerparkraccoons5779]

Not true just did a solve and only one edge was not solved

[@werewolfleader1695]

The thumbnail isn't impossible

[@asdfghjkl-be7su]

It is

[@ervinvu6591]

1:20 thrwee