43,252,003,274,489,856,000 Rubik's Cube Combinations - Numberphile

[@singingbanana]

I almost touched on it in the video. I said there were three ways to orient a corner cube, two ways to orient an edge cube, and there are two ways to swap two pieces (either you swap two pieces or you don't). Each of these will put you in a different orbit. So there are 3*2*2=12 orbits.

[@hewhomustnotbenamed5912]

Imagine being the main speaker in a video but your comment in that video's comment section goes 7 years with no likes and comments.

[@RickMattison314]

Hey, Dr. Grime! I wanted to say that I was given the chance to write a paper on a 7x7 Rubik's Cube (that I happened to have with me at college) for a math project of mine. I just finished it about a minute ago. I wish a video could be done about bigger Rubik's Cubes on Numberphile's channel!

[@fulltimeslackerii8229]

Why divide by 12 instead of multiplying then???

[@rajkumarmalviya8503]

👍👌

[@brendawilliams8062]

It’s like subtracting the one off of 6561 Using 6560 and 375 and making a run for 5 or 3.

[@numberphile]

thank you... these took a while so glad to hear some positive feedback! ;)

[@TheTejpbit]

Awesome couple of videos! Very enjoyable to watch. What you might not know tho is that 43,252,003,274,489,856,000 - 1 = 43,252,003,274,489,855,999 which is a PRIME number!

[@incription]

I'm calling these the Rubik Primes

[@kymiram7865]

@@incription 4x4 - 1 =

[@ProbusMihraban]

@@kymiram7865 4 * 4 -1 = 16 - 1 = 15 = 3(5) Not a prime lol

[@PadsterX]

personal best: 4 years with breaks

[@CollinInGame]

Padster I once got one side of it right.

[@hanchman2]

Collin Kappa I solve it in under a minute 30

[@CollinInGame]

Hanchman Nice

[@cdjwmusic]

Padster i solved it in 17 secs

[@cdjwmusic]

Padster i solved it in 17 secs

[@TonyFisherPuzzles]

Permutations, not combinations.

[@dooplon5083]

I didn't even notice that.

[@chasebrower7816]

+Tony Fisher combinations, not permutations. permuting simply means to move around.....

[@TonyFisherPuzzles]

+Chase Brower No one mentioned permuting. I wouldn't have made my statement if it wasn't correct, would I? Look it up, read, learn.

[@TBgamer-ob3ep]

+Tony Fisher lol

[@casiquekibra]

+Tony Fisher Isn't combinations a fixed set of elements while not being fixed on permutations?

[@singingbanana]

Good question. Let's say I have two cubes. For the first one I put all the pieces in the correct places. For the second one I put in all the pieces as if I had rotated the cube a half turn. These are not the same because the centre pieces do not move. On the first cube all the orange pieces would match the orange centre piece. On the second cube, the orange pieces are on the opposite side of the orange centre piece. Otherwise you would have been correct.

[@jeaniebird999]

When Rubik's Cube came out, my brother and I each got one. I gave up, almost immediately, but my brother worked on it, for a few days. Then, he showed us that he finally solved this crazy, new puzzle craze. We were all _very_ impressed. But I was the most impressed when he admitted, only to me, how he managed to solve it - he simply removed, then replaced, the stickers! I thought that was an ingenious solution! How clever!

[@Nickel287]

I did the same thing when i got the first rubik's cube of my life Till now i have changed 2 rubik's cube and finally solved it my the cross method by learning it from youtube

[@CopCat]

There exist a 17x17x17 rubiks cube. How many combinations does that have?

[@Harry34186]

+CopCat There are 6.69 x 10^1054 possible combinations on that cube...

[@Cube8]

+Chrnan6710 Wow, that's a "very" round number!

[@spookykitty2327]

there is so many combinations there is not a number for it. just consider it infinite

[@bronylike2905]

A whole lot more than the original

[@mrpengywinz123]

+AnimXpert - Everything Animation That's not right, there _is_ a number for it! Of course, it's a massive number, but it's definitely not infinite. The amount of possible 17-rubix cubes and the number 1 are both exactly equidistant from infinity - because it's infinitely distant. To call a finite quanitity infinite just because it's really huge is a terrible generalization!

[@Z3Cubing]

Ugh, I guess I shouldn't have looked at the comments. Its just like every other comment section on rubiks cube videos from popular youtubers. Someone saying they average 6 seconds, Simone saying to peel the stickers off, people arguing about parity errors (???), and then actual cubers coming in and correcting them.

[@na677]

I completely agree.....

[@ToxicTubeAgario]

Woah you are here

[@largepopping9519]

Ikr

[@cuberstache]

You forgot people saying it takes them x hours or x days or x years etc. to solve it.

[@318escapes]

legoboyz3! non-cubers

[@𠂌]

0:08 First I thought that Feliks was talking after his solve!:D

[@Lucy-ng7cw]

They have very similar voices

[@𠂌]

Lucy Hunt true!

[@hlodog]

Brady, you have done an exceptional job with this video. I love how many different videos are spliced into this one

[@MichaelMoore99]

I remember watching a talk show called "Unscrewed with Martin Sargent" and he had a champion Rubik's Cube solver on the show. They gave the guy like 30 seconds to study the cube before attempting it. Then he went at it and solved it in like 20 seconds. There was huge applause, and Martin was floored. After the applause died down, Martin was like "You know, you weren't supposed to be able to solve that! We peeled all the stickers off and stuck them back on randomly!" :-D

[@alfiedemmon4132]

The chances of that happening are very slim. Amazing if true bro.

[@solaimon3164]

@@alfiedemmon4132 actually, the chance are 1/12 as singingbanana mentinonned. But I don't know where this 12 comes from

[@vinlebo88]

@@solaimon3164 The chances are much lower than that as peeling off the stickers enables you to make the puzzle unsolvable in all 12 "universes" of it's current configuration (e.g. putting 3 of the same color on one corner).

[@venkinta3343]

I doubt he was a champion speedcuber. Maybe he was the best in his town but thats not a champion. in 2015 the wr was around 4 seconds.

[@vinlebo88]

@@venkinta3343 If he won a competition, he is a champion.

[@GammersFaze]

It annoys me when people doesn't do finger tricks

[@tk4073]

+GammersFaze It annoys me when people use wrong grammar.

[@GammersFaze]

Tejas Kalyan What do you mean?

[@GammersFaze]

+Tejas Kalyan He did as well. lol

[@claycorpuz1700]

Same

[@RoflZack]

In case english is your second language: "It annoys me when people *don't* do finger ticks" Because "people" is plural, you should use" don't instead of "doesn't". Or "do" instead of "does"

[@catakuri6678]

KZbin Recommendations: 2012: No. 2013: No. 2014: No. 2015: No. 2016: No. 2017: No. 2018: No. 2019: Yes.

[@david_ga8490]

2012 No. 2013 No. 2014 No. 2015 No. 2016 No. 2017 No. 2018 No. 2019 No. 2020 on the Wii; Yes.

[@sourabhsaha6865]

@@david_ga8490 2021: 😢

[@david_ga8490]

@@sourabhsaha6865 the "2020 on the Wii" is a reference to Nathaniel Bandy's video "Just Dance 2020 on the Wii"

[@sourabhsaha6865]

@@david_ga8490 : O

[@DesolateMood]

5:23 was anyone else screaming OLL JUST DO OLL!

[@shehannanayakkara4162]

OLL is pretty hard, there are more than 50 different algorithms you have to memorise.

[@DesolateMood]

Well he had an easy "fish case" is what I call it where all edges are flipped and 2 corners ar flipped.

[@TeaMMatE11]

BRCuber you can just do R U R' U R' U2 R' until you get the fish case. This is why I learned 2-look OLL. Much more easier than full OLL. Full OLL is a killer, and probably not worth learning, but 2-Look will definately save you your time. Hope that helped.

[@DesolateMood]

That wasn't even part of full OLL that was 2-look I'm pretty sure (Haven't watched this video in a couple of months.)

[@albertmendoza1468]

TeaMMatE11 - Another Music Guy Well full oll is faster I'm already know full oll and I average at around 11 seconds . the thing your saying is just easier but not faster

[@WhiteKestrell]

0:47 I can't help myself from picturing that guy when he was like 6. Dad: "So what do you want to do later in life?" Kid : "Study squares! :-D" Then some years later... Mate honestly you're my new hero. :-)

[@Perririri]

0:47

[@ZectonplaysMC]

He's using the beginners method you could see he's using sune over and over again for oll xD

[@sadworm9538]

he's a noob

[@richardkluin6124]

+SuperZecton hes also using a basic rubiks brand cube. nest thing you know hes gonna be speed solving the Cube4you gigaminx

[@AstonCulf]

+SuperZecton The guy doing it in conversation was using a DaYan cube, not sure which one, probably a GuHong

[@ZectonplaysMC]

Aston Culf looks like a gu hong to me maybe a zhanchi?

[@0Architectdude0]

youre one of those guys

[@DekarNL]

Fun fact: The amount of ways to arrange a Rubik's Cube doesn't even come close to the amount of ways you can arrange a standard deck of cards of 52. That number would be 80,658,175,170,943,878,571,660,636,856,403,766,975,289,505,440,883,277,824,000,000,000,000. That means, that if you do a thorough riffle shuffle (at least 7 times), chances are very very very very very likely that array has never happened before, ever in history. Or by comparison: The universe is only about 432,339,120,000,000,000 seconds old. That means that if there were 10 billion people shuffling decks of cards every second for the entire age of the universe, you still wouldn't even come close to that number. (4,323,391,200,000,000,000,000,000,000).

[@rebia5542]

Elroy Kerstens vsause?

[@theoffspringmega-fan2924]

a riffle shuffle 7 times won't have those millions of octodecillions of possible outcomes because the original couple of top cards will remain on the top half for a long time, because of how the mechanics of the shuffle work, so that number is greatly reduced because it would be very difficult to bring the top card all the way to the far bottom positions in only 7 shuffles

[@theoffspringmega-fan2924]

of course, the reduced number would still unimaginably huge. I just find it hard to believe that a shuffle that keeps the top cards in the top slots, and the bottom cards on the bottom slots, done only 7 times, can have the same number of possible outcomes as that Original number

[@Seyer192]

This is the exact video i watched and the reason why i started to learn on how to solve a rubik's cube. Thank you numberphile. I average at 22 secs with PB of 16.37 secs and that's without memorizing and learning all the advanced techniques. I recently got back into solving and started memorizing all the algorithms. Hopefully by a few months i'll be sub 20.:)

[@ryanbutler917]

"So I know if i do that, that, that, that, that, that, that and then double twist, that will have swapped those two pieces." Flawless explanation, i totally understand. 10/10

[@devilmaylol]

Man am I glad he didn't pull a Parker cube.

[@ShehabEllithy]

I was about to comment "Matt memorizes numbers in his free time."

[@ramiel555]

kind of off topic, but I'd love it if somebody made a ridiculous 'cube' that was something like 1x1x25 or in other words, a big long twisty stick >.

[@tristandueck6077]

ramiel555 someone made a 2x2x14

[@ramiel555]

Tristan Dueck yeah, I've seen that, it's pretty awesome, but......NEED MOAR! :P

[@ZacharyFagantheword]

ramiel555 there is a cube made by Oskar's puzzles, it is a 1 x 1 x 27. Cost is close to 1,300 dollars

[@ramiel555]

Zachary Fagan where?

[@ramiel555]

Zachary Fagan that's a 3x3x27 O.o

[@DS-rb1su]

Now go check out the variations of a deck of cards, or 52 factorial!! Mind blowing

[@mugoxmugox]

it's 51 factorial actually. One card has an option of 51 other cards

[@sarasousa1408]

Math and the Rubik's Cube is a perfect combination!! I love both!

[@MinecraftWarriors358]

he had a dayan... numberphile 2 minute solver AND HE HAS A FRIGGEN DAYAN ZUCINI

[@𠂌]

Zhanchi*

[@ssbmfiji5079]

+JSK01 - Agario it's a joke tho

[@dannygallegos1362]

how many possible combinations are there for a 2x2x2 cube?4x4x4 cube? 5x5x5? 6x6x6? etc

[@cubeagami101]

Don't know, but redkb has a video on how many permutations there are for a 7x7

[@alexbutton7340]

Cubeagami101 And 17x17!

[@dashlambda6707]

***** 2x2: 3,674,160 3x3: 43,252,003,274,489,856,000 4x4: approx. 7.4e45 5x5: approx. 2.83e74 6x6: 1.57e116 7x7: approx. 1.95e160 nxn: Kid, the formula isn't so simple. You use factorials for the permutations of each set of pieces, (That's two on a 3x3, three on a 4x4, five on a 5x5, so-on-), then you duplicate the sets for the possible orientations of each piece, then you separate the group of permutations of the system that you can arrive at with a specific set of allowed translations from the initial permutation (solved state), that being slice moves, by identifying changes to the system that can only be done by making an impossible move and eliminating the set that requires that (That's the part where he divides it by twelve, by the way-). Basically, the formula is different for each cube, since it's a different matrix. It's not pre-algebra/algebra, it's early college level probability and carries over into advanced theoretical fields of mathematics.

[@dashlambda6707]

KingHalbatorix The actual work is simple, it's how you get to the work that's complicated. Figuring out which formula to use and working it out is early high school, but a lot of the theory behind it is from later mathematics.

[@waffledoctor87]

***** so 6^(n^^3)?

[@Xclann]

What I'm interested is how you get the fact that there are 12 orbits.

[@Zalcinboy]

Me too..

[@KimJokinen]

2 (number of orientations for one edge) * 3 (number of orientations for one corner) * 2 (Because an odd number of swaps isn't possible) = 12

[@matinatheo8312]

@Numberphile Can anyone of you help me by writing with simple and understandable words why we divide by 12?plz cuz i need an answer immediately... please...

[@coolguy-hc8kt]

@@matinatheo8312 the whole explanation was based on taking the cube apart and putting it back together in all sorts of ways...but if you were to solve a cube (without taking it apart) you'd realise that there's no single (or a set ) of moves that can change the position or the orientation of one sub cube only...in simple terms it means that when u shuffle a cube, the sub cubes shuffle relative to each other...the number calculated was for a cube taken apart...so it had to be divided by 12 (the no. Of different "universes") to get the actual no. Of permutations on a cube...also the no. Was calculated for a standard 3x3 cube...it's different for cubes with pictures or numbers on them, larger cubes, etc....play around with a rubiks cube for a while...you'll understand how it works way better than any explanation on the internet :)

[@Blaz3aTrail420]

my favorite video thus far numberphile

[@OonHan]

*_I LOVE NUMBERPHILE!!! GREAT JOB!! KEEP IT UP!!!_*

[@Hamppzah]

interesting! I was still wondering how you came to the amount of 12 "universes"?

[@PanjaRoseGold]

I know this is an old comment that's probably been long forgotten, but the reason is this: You can't have just two swapped edge pieces on a cube, that's another universe. So that's two universes, swap or no swap. You also can't have a single flipped edge piece, where the piece is in the correct physical spot but with the colors the wrong way round. Those are two more universes, flip or no flip, and 2*2=4. So there are 4 universes so far. Then the corners, you can't have a single twisted corner, which is the same as a flipped edge but with a corner instead, and that there are 3 orientations for a corner, not 2. So that's 3 more universes of the cube. 4*3 is 12, and as such, there are 12 different universes for the cube to be in. This also means that were you to disassemble a cube and reassemble it completely randomly, then there becomes only a 1 in 12 chance of the cube being solvable, because there are 12 universes for the cube, with exactly one of them being solvable.

[@FunnyAndfancy]

REALLY ??????????????????????? AMAZING !!!

[@ScoochCubing]

"So, I'm jut gonna give the Rubik's Cube to Matt..." Who else was thinking of Mats Valk lol

[@arturslunga4226]

I remember it being marketed as having 43 billion combinations. An understatement

[@1959Edsel]

There was an explanation in Rubik's Cubic Compendium (multiple authors, 1987). Basically, you can swap two corners and two edges and still solve the puzzle because that is an even number. You can swap just two edges or just two corners and not solve it because that is an odd number. You can model a cycle of three pieces as two swaps. To get from ABCDE to ADBCE is a three-cycle or two swaps: ABCDE → ADCBE ADCBE → ADBCE I hope this helped.

[@RECuberOfficial]

PB: 17.79 and I've been cubing since December 2014. I've only gotten 3 sub 20's but I've been very close to beating my PB recently. Like this post if you're a cuber

[@picklepower24]

I average 20 and pb is 7.10

[@samzeng1869]

+Picklepower26 how did u get your pb,

[@picklepower24]

super luck

[@sethamajig228]

+RECuber I average about 21-23 seconds. I have recently been getting into BLD, though.

[@AWSMcube]

Sethamajig -Esperanto -Cuber

[@ukraineme96]

I am a speed cubed as well, 16.82 seconds is my best time

[@lightningcreates1271]

Do you still cube?

[@nanamacapagal8342]

PB 22.49. Best average of 5: I forgot

[@jagamclaren2758]

@@nanamacapagal8342 Pb - 11.28 , Pb ao5 - 14.58 , Pb mo3 - 12.21

[@Sam11111ification]

Feliks Zemdegs went to my primary school in Melbourne Australia

[@BlaZe1337YT]

I LOVE FELIX

[@popularnow8930]

Who

[@genericusername4206]

Popular Now world record speedcuber

[@SuV33358]

Wow, these people are amazing....👏🏼👏🏼👏🏼👏🏼👏🏼👏🏼👏🏼👏🏼👏🏼👏🏼👏🏼👏🏼

[@MinikatzArt]

Well that's definitely my new favorite number :3

[@slendercaterpie]

matt is my numberfu

[@siempie4697]

Wrong the last corner only has one possible orientation.

[@Ruminations09]

The last corner still has 3 orientations, the orientation is simply which way the colours are facing

[@siempie4697]

It is impossible to rotate one corner, you always have to rotate at least 2 corners

[@Ruminations09]

Siem De Wit He's not talking about a legit move, he said when you take all the peices off and put it back together.

[@siempie4697]

Then you are right.

[@SoumilSahu]

The "subcubes" are called cubies. Trust me, I'm a speedcube solver.

[@blockcamp]

ok boomer

[@MeiZhang-q5k]

@Blockcamp ok boomer

[@nanamacapagal8342]

@@MeiZhang-q5k nobody asked

[@doublecircus]

@iBrow nobody asked you either

[@qpid8110]

O_O oh my goodness! That 15 piece puzzle is something I had as a kid XD No idea it was that old!

[@1959Edsel]

I wrote a program to calculate the number of patterns on an n-layer cube given only n as an input. It's interesting how quickly the exponent in the scientific notation goes up as n increases. Going from 2 to 7 the exponents are 6, 19, 45, 74, 116 and 160. If you don't like the sound of the word quintillion, you definitely won't like the (questionably valid) names for the higher-order cube permutations.

[@aaron9828]

4:22 I think that's not quite right. You can't just turn one edge around because then you wouldn't be able to solve it anymore.

[@redfalcon2747]

That's true He's right. Same with a corner

[@redfalcon2747]

but also thats why he divided it bu 12

[@MelindaGreen]

I know this is the accepted number but it doesn't seem like the right one to me. For example, when you place the first corner piece, there is a giant set of cubes that can be constructed from there. But if you place that piece in any other corner, it generates an entire extra set of cubes that is identical to the first set and never divided out. You get the same thing with the edge pieces and even a similar color symmetry that you can argue is ignored.

[@motmaos]

I agree

[@rhamph]

The center pieces are never multiplied in because they're static. That functions as the redundant orientations you would otherwise divide out. kzbin.info/www/bejne/h4ecnGmah7aEm5Y

[@motmaos]

+Adam Olsen I think I understand now, since the center pieces don't move every different corner position is distinguishable from the other ones. Thanks!

[@MelindaGreen]

Adam Olsen I never mentioned the center pieces.

[@motmaos]

+Melinda Green yes, but if you start with the red/green/white corner in a different position you don't get the same cube configurations because it is in a different place respect to the centers

[@Blaidan]

takes me 50 seconds - 1 minute to solve it :)

[@connorgaughan9117]

Blaidan what about now? As Brucey always said... Higher or Lower?

[@rafarooni]

Combinations: Permutations Sub-Cubes: Pieces Quarter Turn: Outer turn Arrangement: Orientation Twist: Move

[@1959Edsel]

Let's look at the 2x2x2. It's possible to swap two corners on it because you could consider a similar odd swap of the center pieces. Since the center pieces are hidden from view, odd swaps of visible pieces become possible. Odd swaps are also possible on the Void Cube (3x3x3 without centers) for the same reason. A way you could explain why even-numbered cubes can have odd swaps is because there are odd swaps of invisible pieces to make the total even.

[@renatomaritato1300]

This video is a goldmine for overused noncuber comments...

[@marcushill6551]

2:51 I believe those are called unit Cubes.

[@GatheringDream]

cubies!

[@cristophereikemo6173]

Marcus Hill actually its called pieces

[@FanPlastic]

Marcus Hill cubies

[@marioisawesome8218]

I thought those were the amount of Genders.

[@ashkara8652]

Think more in the neighborhood of Graham's number

[@Al-pb3fm]

Ashkar Ibne Awal Not funny.

[@ChuckNorrisHernandezFraturnHDL]

It's hilarious XD

[@alvarkarjalainen7378]

*nO tHeRE iS OnLy tWo GenDeRs*

[@Giantcrabz]

those are rookie numbers

[@Yoyo4lyf]

The sound of how smooth those cubes are ughhhh

[@1959Edsel]

The total corner twists can add up to an integer + 1 clockwise, 1 counterclockwise or zero. (3 options) The total edge flips can add up to an integer + 1 or zero. (2 options) The total number of two-piece swaps can be odd or even. (2 options) The 12 universes are merely the product of these three possibilities.

[@draloric]

4D Puzzle game by 2080? eh?

[@tessaryan7805]

Did anyone catch For the second corner ill have se-- six left

[@davidcrawford9407]

+Tessa the gymnast he said seh-- seven not six

[@woshua3143]

pb:14 am I cool yet?

[@doancarlosembara3060]

skater Boi yes, my pb is 16 :(

[@woshua3143]

lraC Ae u got this man,we'll be sub 10 in some time!

[@doancarlosembara3060]

skater Boi​ thanks you, i hope so

[@mikusjanisgailis2201]

my pb is 16

[@avananana]

My PB is only 22 ;(

[@aetheos72]

Numberphile. Keeping the brown paper industry alive.

[@freemanedwards5663]

Great vid

[@PurelyAwesomeCuber]

Did Matt have a Zhanchi?

[@gtcubesfan9183]

Yes it was

[@PurelyAwesomeCuber]

:)

[@pjallard1334]

+PurelyAwesomeCuber He needs some lube its pretty springy lol

[@PurelyAwesomeCuber]

Agreed.

[@𠂌]

+WJ50Skillz no

[@sparkspeedyt]

If you got 43,252,003,274,489,856,000 views on this video.....

[@EpiCuber7]

my best is 10.31, as everyone else seems to be saying their bests.

[@EpiCuber7]

Wow that's awfully slow. But now i feel awfully sad that I can't remember my PBs from 2 years ago at all

[@0ARK-E]

mine is 24.81

[@ufopilotFPV]

I love that it's a physical representation of metatrons cube. Something quite special about the rubiks cube.. aside from how addictive they are !

[@SledgerFromTDS.]

43,252,003,274,489,856,000 or if you prefer scientific notation its roughly ~ 4.3252 × 10^19 so yeah I rounded It off but its accurate enough right

[@unlucky-777]

43,252,003,274,489,856,000 wtf is this ?? Is there such a number?

[@a.k.3811]

Yah 43 quintillion

[@unlucky-777]

what is quintillion ? ı thought There are just millions but wtf

[@unlucky-777]

FullTimeSlacker no man ım just kidding

[@robin-vt1qj]

+videogamefan004 g(g(64))

[@pezpeculiar9557]

fourty-three quintillion, two-hundred fifty-two quadrillion, three trillion, two-hundred seventy-four billion, four-hundred eighty-nine million, eight-hundred fifty-six thousand

[@ClosureHD]

I don't want to be the bearer of bad news, but. The way you're going about this, is in someway wrong, yes. there is 43,252,003,274,489,856,000 possible combinations. But, not all are solvable If you were to take the rubiks cube apart, and put it back together again, but just flip 1 corner, the cube will become unsolvable, as it is impossible to flip just 1 corner. So neciserally, the rubiks cube, does not have 43,252,003,274,489,856,000 combinations, if you where to mix it by hand.

[@anonanon753]

***** that is exactly what i thought, the actual combinations are about 5-6 orders smaller

[@Gratorist3169]

***** If you disassemble the pieces, you can assemble it again in 5,2*10^20 different ways. And there are 11 unsolvable stiation. So you want to find out the only solvable stiation. Then divide it by 12. (5,2*10^20)/12=43252003274489856 The solution is correct. Please watch the video again more carefully. And sorry for bad English.

[@radicalsaled5756]

deniz is correct he did take unsolvable combos into account in the video.the original number was around 12 times as large

[@Z3Cubing]

***** I know I am a bit late to this, but just as the person before me said, he originally got a number 12 times 43 quintillion. He took into account the number of parities ("orbits"), which is 12, and divided his number by 12 to get 43 quintillion.

[@WhiteHenny]

The 12 orbits are obtained by these 3 things: 1) flip any edge (2 orbits) 2) rotate any corner (3 orbits) 3) switch any 2 pieces (2 orbits) Each of these 3 are independent, giving 2*3*2 = 12 orbits. This means, somewhat counter-intuitively that if you take a solvable position, switch any two edge pieces AND switch any two corners, you get another solvable position (modulo flips and rotations, of course).

[@audiblemagician6751]

Wow 856 thousand flat. Thats convenient.

[@audiblemagician6751]

What if there were 31,415,926,535,897,932,384 combos that would be legendary.

[@littyfam5136]

Amazing

[@einstin2]

not really. this happens all the time in combinatorics. anytime a 5 and a 2 are multiplied together, the number will end in a 0. in fact, by counting the number of Zeros at the end if a number, you can know how many pairs of the numbers 2 and 5 appear in their factorization. in this case, the zeros come from the 8! (1 zero) and 12! (2 zeros).

[@audiblemagician6751]

Adam Billman Ohhh....duhh

[@torreyrg42]

+Adam Billman I had a homework assignment to find the number of zeroes that come at the end in 100! That's the method used to find it quick, just count the number of 5's in the prime factorization since there are fewer 5's than 2's. Iirc it's 24: one from each multiple of 5 and another from each multiple of 25

[@jmmahony]

He gave the basic details (@4:08) before stating the number (12), without quite connecting them. First, a corner can be twisted +/- 1/3 turn, to get a different orbit (not stated: and there are ways of converting a twist of one corner to a twist of any other, so it doesn't matter which corner), so that gives 3 distinct orbits. Second, a side piece can be flipped, so there are 2 options. And a pair of side pieces can be swapped. So there are 3X2X2=12 orbits.

[@Perririri]

4:08

[@1959Edsel]

The number of universes depends only on whether the cube has an odd or even number of layers. If you have an even-numbered cube you only need to worry about corner twists. There are three universes for that. If you have an odd-numbered cube there are the same 12 universes as with the 3x3x3. The extra pieces that show up from 4x4x4 and higher fall into only one universe unless the extra center pieces are made distinguishable from each other in some way.

[@bigmouthgaming8893]

Personal best: 90 million years

[@bigmouthgaming8893]

Jk I've never used a rubik's cube

[@Untoldanimations]

Girly Card Then shut up

[@CaroFDoom]

PB: N/A

[@robinmoland6942]

+Tebs Productions actually hes typing. even tho ppl mostly talk when they type, so they type the right way i did it while even typing this

[@juanisamazing95]

thechrimsonfucker no new episode yet i see

[@astroash]

*999999th view!*

[@srithangayam5271]

wooooo

[@Tatiana-jt9hd]

dat calculation t lol your channel name

[@astroash]

Anna Walker, bet you'll love my videos😂

[@samuelmiller5984]

thats one in in a million

[@noverdy]

dat calculation tho

[@lukecovington7050]

My best is 28 seconds

[@legomonjones5077]

My best is 2 minutes.

[@bpdoles6034]

 My best is 52 seconds

[@sabin97]

Legomon Jones my best was like 3 minutes, which is not impressive by any standards. now i cant even solve it :(

[@AwesomenessProdx]

55 seconds.

[@piisirrational1758]

1:56 :/

[@LeighzerCuber]

Cool they did a video on it and it was accurate infromation!

[@1KevinsFamousChili1]

As well as being a good tangible representation of symmetry as Matt said. It is also a good tangible representation of entropy

[@LivelifeandLovedoingit]

My best is 8 hours. I am extremley tired.

[@alexnguyen8913]

It's actually really easy to solve a Rubik's cube. First you have any color facing up, then you switch around the stickers. Works every time

[@mrbutter100]

General JoBob My cube is stickerless. Try and peel that now!

[@alexnguyen8913]

Charlie Lettau smash it

[@Obi-WanKannabis]

Charlie Lettau dissassemble it and assemble it correctly

[@mrbutter100]

MrTURBOJOHN That's cheating though c;

[@tsruhnnep]

LOL i have both of the cubes shown in the vid i have the classical and dayan zanchi!

[@woodstock1072]

:P

[@carlton6953]

Learning and practicing to solve it in under 10 seconds is very impressive. But why not put all that time into learning a musical instrument or something?

[@niemelhansa3854]

Cuz cubing is life!

[@bonbonpony]

What if you had to deactivate a Rubik's cube-shaped bomb with 10 seconds left on the display? :q

[@ninshado]

Cubing is more impressive

[@ellie_shrug]

Ben Adams we like cubes. That is why.

[@schwintwr]

This Is 1,001st Of My Favorite Video.

[@Antsaboy94]

Thanks! I was thinking and wondering the exact same thing. :)

[@ethanhonest9206]

Im a cuber pb 17,535 seconds

[@dirtydan6960]

That is about 4 and a half hours I am not a cuber myself but that doesn't sound very impressive

[@purpleapple4052]

I think the comma means to split decimals, not thousands. Some countries have this

[@cl13amongus]

comma means thousands, million, billion eg 999,876,543 but a period is used for decimals eg 12.34456546475 in germany i know its vice versa tho

[@anuragvaliveti448]

i am a speed cuber

[@alexnguyen8913]

43,252,003,274,489,856,000 different combinations... nope, just gonna take the stickers off

[@alexnguyen8913]

SoulRCraft smash it

[@Untoldanimations]

SoulRCraft Stickerless cubes are weird though. I have a stickerless Zhanchi but also a stickered one and I like my stickered one more.

[@TheSubAtomicHedgehog]

i'd just paint it one colour

[@Gamemaster-tf2yw]

+SoulRCraft you can usualy break them apart from the corners and put them back together

[@jens009]

Hello Numberphile! I've solved a number of Rubik's cube myself. For cubes with labeled centers, like those giveaways by some companies, you will notice that a solved state can have rotated centers. You don't notice this in a standard cube because the center is just a single color with no indication for orientation. But, if you account for this I believe you should get an extra factor of (4^6) combinations as there are 6 centers and 4 rotations possible for each center.

[@oscarwhitehead7134]

no

[@noname21x]

whoa awesome vid man! tnx alot!

[@totallymcmylastname9077]

I dont see what's so impressive about speed cubers; they're just following pre-written algorithms. Plain and simple. The ones deserving of praise are the dudes who originally came up with the solution.

[@yk_6169]

You do it then

[@Jimpozcan]

MiningChr1s Perhaps he has. I've always considered the whole point of the puzzle (like any puzzle) to be to figure it out yourself. No, no credit to memorisers of other people's algorithms.

[@cubetuber4024]

Totally McMylastname recognizing, and executing algorithms fast is one part. But for a cfop method, algorithms are less than half of your solve. Intuitice cross, and f2l

[@Jimpozcan]

Cube Tuber It seems to me that Totally McMylastname's point still applies. You write of a "cfop method", "Intuitice cross" and "f2l". Whatever these are, the praise would go to those who came up with them rather than those who just learn them. I don't mean to call speed-cubing worthless. I'm sure it's a fulfilling hobby. However, I agree that it's a little unimpressive. Personally, I don't see the point in learning somebody else's solution to a puzzle; that just ruins the puzzle. You could even call it cheating.

[@cubetuber4024]

Sorry intuitive cross and f2l means that there are no algorithms, the cuber figures it out themselves and every situation is different. So we're not just following pre written algorithms. But i guess it is true that it could be called cheating. However, i don't think it is unimpressive especially if you are extremely fast, which is very difficult. That is why very few people are able to average under 10 seconds.

[@RandomDays906]

An 11x11 Rubik's Cube would have 1.052943 x 10^213 different combinations. Absolutely Mind blowing.

[@CurtisUpshall]

The video mentions that there are twelve orbits, incidentally the same amount of edges on the cube. Taking off a corner piece, rotating it and placing it on the cube again does not form a new orbit. Only edge pieces will form a new orbit when you flip them since the corner pieces get flipped anyway.

[@SalladTM]

I believe every set of 2 cubes excluding centers. So the two edges swapped on the top layer counts as a universe of non possibilities that you must eliminate. As well as the other two edges, then each set of corners in the same way. This is four sets multiplied by three layers. Hope that helps with the understanding

[@mugoxmugox]

Can you calculate total possible solutions of a 3x3 super cube? Centers can be rotated in 4 different ways, and when rotating a centre by 90 degrees, another centre must also turn 90 degrees

[@LordChucky5246]

Another way i like to put the number 43,252,003,274,489,856,000 in to perspective is this. If you were to go through each combination one at a time, one per second, and with the final turn being the solution. I would take about 100 life times (the birth of the universe till now) of the universe to finish. That is (((43,252,003,274,489,856,000/3600)/24)/365.25)/13,700,000,000. Assuming the universe is roughly 13.7 billion years old as of now.

[@anonymousbanana3144]

When calculating this, did they take into account that some combinations were unable to be achieved, for example a combination where only one piece is not permuted?

[@miquelllorca8308]

yes, they take it into account

[@manuelcedillo1477]

awesome video.

[@Chasn555]

I am mind blown as to pose how easy this actually is to calculate... Wow

[@audiblemagician6751]

Personal Best 314,159,265,358,979,323,846,264,338,327,950,288,419,716,939,937,510,582,097,494,459,230,781,640,628,620,899,862,803,482,534,211,706,798,214,808,651,328,230,664 Years NO breaks

[@blackholeentry3489]

Yeah, I joined the craze when they first came out and still have a couple that have been kicking around for 20 years or more untouched.

[@L_T34]

nice video! keep it up!

[@MVBit]

If you could have as many of any color as you want (i.e. 42 green, 12 red), you would have an astounding 1,047,532,535,594,334,222,593,508,922,191,671,036,215,296 combinations. Crazy, huh?

[@mikekaleiwahea7337]

A = 8 corner positions = 8! B = 3 orientations per corner = 3^8 C =12 edge positions = 12! D = 2 orientations per edge = 2^12 E = can't have single corner twisted = 1/3 F = can't have single edge flipped = 1/2 G = can't have two edges swapped = 1/2 A*B*C*D*E*F*G = 43252003274489856000

[@jcortese3300]

You see, this is how you can tell a physicist from a mathematician. I'd just take the thing apart and put it back together solved, upon which point it's effectively solvable in all possible starting configurations. (They just tell you to solve it -- they don't tell you how!) It's a lovely little mechanical device, with many small parts all separate from one another and yet making a single physical whole. It's quite interesting when you disassemble it.