Why Are There 43,252,003,274,489,856,000 Rubik's Cube Combinations?
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- čas přidán 22. 06. 2020
- The math behind the number of Rubik's Cube combinations/permutations/positions or whatever you want to call it.
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in a 2x2 there are only 8 combinations because there are 8 pieces. thanks for choosing my comment as the right answer in advance 😊
SERIOUSLY J PERM WHY DO YOU KEEP DELETING MY REAL SOLUTION HERE LOL
EDIT: WHY AGAIN J PERM. I'VE TRIED IT 3 TIMES ALREADY
EDIT 2: i get that some people want to do it themselves, so just find my other comment (or someone else's), but good luck finding one lol
EDIT 3: J Perm said that he isn't deleting them and CZcams is, so I'll contact CZcams to see the reason.
Matthew Liu maybe there’s a blacklisted word, or maybe CZcams in censoring something, or maybe he actually is deleting your replies lol
@@twistiicuber1055 that is true
How bout a 1x1
@@twistiicuber1055 also he still hasn't deleted my third attempt doing it
Teacher: what's 3x3x3?
Me: 43 quintillion
U-U..............😅did you get it correctteacher:😳okay....
Edit 1: like for a part two of dis
😡WRONG *teacher is so done* .....
Edit1:hope you enjoy dis little skit I made
B̑̈lue rain c͜͡loudsꨄ Thunder clouds lmao
It’s quintillion
3 x 3 = 9
For 2x2: no matter how scrambled it is, you can always rotate the cube to solve the UFR corner(red white green), so instead of having the centers as a reference, we need to have the ufr corner. On a 2x2, you can just swap 2 pieces and you explained why in the impossible case video. There are 8 corners but one is fixed so there are only 7 corners that can be unsolved. 7!. They can al be twisted freely except for one of them, the ufl for example. So 3^7/3x7!=3674160
Having 1 fixed corner and 7 moveable corners is a great way of thinking about it!
Nice!
My solution was just to multiply 3^7 and 8! together and then divide by 24 because there are 6 × 4 = 24 ways to orient the puzzle
Your solution took out that 24 in the first calculation, which is in my opinion, a better way of thinking about it :)
No idea. Oh yeah, it’s Big Brain Time
That’s really smart thinking, but I don’t get why you can swap only two corners on a two by two, isn’t it related to the inter edges in some way
@@603.F0Z lol you can think of it this way
There are 3^7 ways of orienting the corners and 8! ways of permuting them (like J Perm said in the video)
The difference is that there are no centers on a 2×2. A solved state with White Top Green Front is the same as a solved state with Green Top and Red Front etc. There are 24 ways of orienting the cube, so we divide what we have be 24.
3^7 × 8! / 24 = 3674160
Finally a CZcamsr that went to college
Hey, do not measure intelligence by
people who went to college or not
@@johnp.6692 he ment math and stuff. Not inteligence theres a diffrence
@@sparkgaming5100 math? colleg£?
A difference
@@johnp.6692 when did he do that...
@@Its_FamilyGuy what?
This guy teaches me more than my school ever will.
No he is not
Really again? I ALWAYS SEE THIS COMMENT
im sorry im a rage man
Facts
In what school do you go? 🤣
In a public school
There's a new method:
You need to memorize all 43 quintilion combination and just reverse it all
Thats genius lol!
@Seth Tate homie it was a joke, relax
ez
big brain time
Lol
Everybody's gangsta until he smashes the cube
There are 3,674,160 possible solvable combination of pieces in a 2x2 Rubik's cube. The corners can be positioned in any way so there are 8! = 40,320 possible combinations. 7 of the 8 corners can be oriented in any way so there are 3^7 = 2,187 combinations. Multiplying these two results gives us 88,179,840. But there are no fixed centers on the 2x2, and there are 24 ways to orient the centers, so we divide 88,179,840 by 24 which gives us the answer of 3,674,160.
What about a 1x1 and a 0x0
When you're a cuber and a maths teacher
Is he a maths teacher!?
Alexander Watson no he’s just smart
U got 69 likes my dude
@@603.F0Z its actually pretty basic math.
He is really smart though (like solving a square 1 with no help, solve a 4x4 into a 2x2 etc)
@@MatthewLiuCube yeah, it's not that hard to do that math, but explaining it so easy is kinda hard.
2x2 has 3.674.160 possible combinations. Here's why:
Any permutation of the eight corners is possible (8! positions), and seven of them can be independently rotated (3^7 positions). There is nothing identifying the orientation of the cube in space, reducing the positions by a factor of 24. This is because all 24 possible positions and orientations of the first corner are equivalent due to the lack of fixed centers. This factor does not appear when calculating the permutations of N×N×N cubes where N is odd, since those puzzles have fixed centers which identify the cube's spatial orientation.
So, the number of possible positions of the cube is (8!*3^7)/24 = 3.674.160
Good explanation!
@@JPerm that was my solution, I've also seen the fixed corner solution (which you replied to, so I won't explain it here)
How did you solve this problem?
@@MatthewLiuCube Wow, first I thought that both solutions are the same but I was wrong...
The cool thing about orientation of the 2x2 is you can determine it 2 different ways.
Given the fact the 2x2 is engineered like a 3x3 you actually can use the core as a reference point, the corners could be in a solved state in 6x4=24 different orientations as mentioned by SpaceDragon.
But the cube's orientation is also determined by choosing a corner and it's orientation which is actually Not the same maths: it's 8x3=24. So here 8!/8=7! and (3^7)/3=3^6 which gives you the calculation of fixed corner solution.
TLDR:
1. Take a 3x3 and cancel the orientation relative to the core (6x4=24) out
OR
2. Cancel the orientation with fixed corner (8x3=24) and then calculate the canceled version.
@@sevopaper984 technically it is the same, but at the same time it is not
@@MatthewLiuCube Yeah, I think it is cool that with different approaches you get the same answer.
On a 2x2 the number is:smaller
Reason:less pieces
4x4 bigger it has more pieces
no shit sherlock
@@charleswang6152 yeah really
I counted them
@@charleswang6152 It's a joke.
“We have to think about what the rubiks cube actually is” *smashes cube*
i shit my pants
surprise necropost.
This guy sounds like a combination of MrBeast and Daily Dose of Internet.
Underrated
Yea
Lmao
So true lmao
can't unhear it now
I love how you simplified this for the ones who are new to cubing or not into the math as much. You also did a very good job making the process very clear. Very well done!
I love how organized the pieces are.
I learned more in this video than my math teacher ever has taught me
Same
Same
Same
😂😂😂😂same
SAMEE
imagine if someone just said he’s bad and he’s lying about impossible cases
JpErM iS bAd At SoLvInG a RuBiKs CuBe!! ThErE iS nO sUcH tHiNg As A iMpOsSiBlE cAsE. YoU kNoW wHaT? jUsT pEeL oFf ThE sTiCkErS!
Alberto is a duck please be a joke
@@2chill2bbored72 i spent 3 minutes writing that and you think that isnt a joke?
Chillboard’s Alt Wasteyard If someone does the alternating upper case lower case thing, it means they’re joking
Non-cubers'd say that
My dad once tried to make me solve an edge flip
I hope this is right:
For 2x2 because there aren't any edges the corners can be permuted in any way so there's a total of 8! ways, or 40320 possible permutations. As for orientation the first 7 corners can be oriented in any way, whereas the last one must be oriented in a specific way, so the total possible orientations is 3^7, or 2187. Multiplying 2187 by 40320 yields 88179840. However, the lack of fixed centers on a 2x2 is not accounted for. The above calculation assumes fixed centers, and since centers can be oriented in 24 different ways the number must be divided by 24 (because changing center orientation doesn't have an impact on the scramble for 2x2), and 88179840 divided by 24 gets the actual answer of 3674160 possible scrambles on a 2x2.
Correct! For anyone wondering, the reason there are 24 cube orientations is because of 6x4. You can have any of 6 sides on top, and then any of its 4 sides centers on the front.
@@JPerm hey Jperm any idea on bigger cubes? eg a 4x4 where you also should take center pieces and another edge piece
Ok ur smart I’m dumb. I’ll just have to deal with it
You can become a really good professor. I really like the way you explain, and I am sure many people also like your way of explanation.
💀
@@anoobguy8350 i forgor💀
Yeah
this is a great visual explanation, awesome video
That's why we all love Jperm: clear explanation as always, best tutorials ever...
Thanks Jperm for making such interesting content!
0:17 *Cube Solve Hero wants to know your location*
Give me bread for my ducks 🦆
Z1hcツ but bread is unhealthy for duck since it causes bloating which eventually causes erosion which is bad
Canadialand
Amazingly explained!
Wonderful derivation, thanks man
Me: Watching food videos.
Notification: Jperm just posted a video.
Me: Food is not good.
Same thought bro
Spongebob: air is not good
Finally, real-life math usage.
A 2x2 has no centers, so there is technically only one way to insert the first corner, meaning 7! corner permutations. For this same reason, the first corner can only be flipped one way, and the last corner cannot be flipped for it to be solvable, which means 3^6 orientations. Thus, the total ends up being 7! * 3^6 = 3,674,160 possible positions. Great video! By far the best explanation on this topic that I've ever seen!
Clever approach!
Cause why not
You are 1st, congrats
Ryan Spicer You do realize nobody cares
Zixuan Lei I misread the title as is there blank blank blank combinations so I said yes
@@cristiansigua6664 my friend, you really are first
Yo man, this story is true...
I was walking down the street when suddenly a V PERM came and stopped me..
He warned me that no matter how good cubing techniques I learn, he will still come again and again to ruin my solves.
He also told me that his partners 'THE G PERMS' will also help him.
😥😥😥😥😥
Why V perm
Sooo True 😂
I needed this for my assignment thanks
I had watched this video a while back not having done any probabilities at the time. This week we started learning about it and I remembered this video, thnx to u I already have a pretty clear understanding
This uploaded 1 min ago, but i can tell this will go viral
Math teacher: this is very easy, learn it N O W
Me: what does this mean
Because it is very easy and you never went to school
I learn probability in this video, thanks man, everytime when i tried to learn I have some confusion, you teach me more than my school, i appreciate it. Thanks.
Incredible video jperm
This is whole new level of PROBABILITY
The dislikes are cubesolvehero fans who are mad he stole his breakdown techniques
Lol
No, they’re people who failed math class. The cubing community is too nice
Indeed
True
and theres like 50 dislikes lmao
Thanks for the best explanation ☺️.....
THAT'S AMAZING BRO!!!
cube solve hero:Satisfying Cube Magic
Jperm: I am about to steal his magic
cube solve hero :Noooooooooooooooooooooooooooooooooooooo
J perm: Just a simple multiplication problem.
Me: Visible confusion.
Thanks for the math class
Easily Explained Very Interesting !!!!!!
Me: ImMa geT hErE eARlY
CZcams: "379 comments"
me: shoot
STONKS intensifies
Ivan Jones *STINKS
@@goldenwarrior1186 no... he meant to say that
Rohit I don’t think STONKS fits OP’s comment though
friend: i am sub 40, now i am a real cuber!!
me: do you know Jperm?
friend: no who is that
me: sorry but you are not a real cuber...
friend: oh now im sad :(
Well technically as soon as you try to solve a cube as fast as possible you're a cuber
@@rnoze6938 nope... u need to know j perm to be a cuber :)
Nice gate keeping there bud.
Friend : I am sub 40, now I am a real cuber!
Me (a cuber) : do you know J Perm?
Friend : no, who is that
Me (a cuber) : a famous Youcuber, watch his channel so you'll become a better cuber
Use the similar logic from the 3x3x3 corner permutations (8!*3^7). Realize that the cube itself doesn't have a fixed position like the 3x3x3 due to a lack of fixed centers. Count the number of possible ways of orienting the 2x2x2 in space (24). Exclude those possiblities by dividing the former by the latter (8!*3^7/24): 3,674,160. Q.E.D.
This was fun! :)
very good video!
There are 3,674,160 combinations on the 2x2 rubik's cube. If one corner always stays the same, it eliminates any impossible solutions. So, the other 7 corners (7!) multiplied by their twists, with the last one as you said, being one (3^6) - multiply, and you get 7! * 3^6 = 3,674,160
Right! Good comment, I was a bit to late for the video to write one myself.
The number in the title just made me click the video
0:17 when you have been watching a tutorial for hours and can't figure out the last part.
That smashing noise when he destroyed the cube was so satisfying.
4:18 What in god's holy name was that
0:17 Cubesolvehero: Impossible
I don’t get it I’m sorry 😐 please don’t say r/whoosh
@@eduardorizo8264 r/wooosh
@@eduardorizo8264 jk it's a youtuber check hes channel
@@eduardorizo8264 Cubesolvehero is a CZcams cubing channel that is famous for his cool editing and how he breaks apart his cubes
J Perm,
I'm 55, I first saw a 3 by 3 in 1981 when I was in 8th grade. I didn't own one however I did fiddle-faddle around with one for a while but was soon overwhelmed so figured it was something for The Geek Squad kids to mess with. Fast-forward the tape to 40 odd years later and I've just now solved my first Cube thanks to your video I think I have set some kind of record! That young guy that did it and under or just over three seconds yeah I'm on the other end of the spectrum J it took me like 42 years 9 months 6 days and 3 hours LOL, anyhow I love you videos I love how you break it down and explain things so the common person can understand I am a machinist by trade as you well know by my title I'm no dummy it's just I never figured it out but your algorithms and stuff surely help so far my fastest time is 7 minutes and 16 seconds. Certainly not earth-shattering by any stretch but I'm working on it I just want to thank you again. Mike The Machinist
Awesome video ❤💚💛🤍🧡💙
I swear this guy is secretly like a Einstein reincarnated as your friendly neighborhood cuber
it's not that complicated lmao this is like highschool math
@@Hisname22 im sorry if im insulting Einstein
Poor Dylan had to promote cubesolvehero by smashing his beautiful XS on a hard wooden desk
RIP Eric the Edge piece
Edit: thanks for that crazy amount of likes
rip the xs, thank god he has like 7 of them
he may have taken a stock xs and put on the j perm logo, but i obviously can't confirm that
@@MatthewLiuCube Speedcubeshop made an exclusive gan xs just for him and sent it to him. That's the cube in the video. They also did this for some of other cubers that they sponsor.
@@hex2926 ik. what im saying is if he wanted to spare his special XS he could have taken the center cap off and put it on a stock xs
I'm kinda sad even tho it was cut but I can't even afford a Gan XS
I didnt get any of this but it was so interesting I kept watching
Very good video
Me:This is like a math question
My brain: EMPTY!
0:05 me when I just did 1000 solves
love the mathematics angle
Very nice and fun brain exercise
6:51
"Non-cubers were right
cubing is math-related "
A 2*2 has 3,674,160 combinations because
a 2*2 doesn't have a core so every face of the solved state is different and we have 4 different positiins for each face which is 6*4=24 then for every corner we can put a corner anywhere except the last one (like you said) which becomes 8! then we have 3 positions for each corner except last one so that becomes 3^7*8! divided by 24 which equals 3,674,160
Congratulations,if you read the whole thing
Omg mind blowing 🔥
im learning this probability math in algebra rn :O
0:16 *reminded me from something...*
Do you have bread I need bread
@@cuberdoge22 bro your chicken is hungry or it was dog I suppose 🤣🤣🤣🤣
CSH....
They say that mimicry is the greatest form of jealousy. -Tyler Toney of dude perfect. Lol
I'll sleep early tonight,
Also me at 3 am:
Happy new year
I hope this video finds it way into math classes!
0:08
"Number EXE had stopped working"
check out Grahams Number and TREE(3), if you think thats big then this will make your mind explode.
A tree of threes
I guess nobody took notice that the video is 6 minutes and 54 seconds long.
6 sides and 54 squares...
Round a applause
i really just actually learnt what a factorial is in this video
0:16 Cube solve hero's style of dissasembling cubes* SMASH!
When a cuber teaches you more than you're math teacher
yOu SpElLeD yOuR wRoNg
FeLcon oFo
He’s Asian
When someone finally uses “you’re” but it’s a situation where you need “your”
when your english teacher doesn't do their job properly
When the teacher asks you to explain
التوافيق والتباديل علم رياضي جميل 🌹😘
For 2x2: The intuitive answer would be 8! x 3^8 / 3 (88,179,840). But since there are no middle pieces, the first corner you place does not really have 8 choices because there is nothing it is being positioned relative to. But after the first piece is placed, the second piece has 7 positions relative to that and so on. Also, we would have to lock the position of the first piece in terms of orientation, otherwise we'd get duplicates because every actual position could be attained three different ways, one for each of the ways we orient the first piece. Seems if we divide that first number by 24 we'd get the right number. (3,674,160).
I love how he just did not care about smacking the Rubik’s cube on the floor
“I thought cubing wasn’t math related”
There are 3674160 permutations on a 2×2 Cube.
We can calculate this similarly, but not completely the same.
There are 8! × 3^7 ways to arrange the corners and permute them, like how J Perm said in the video, but there are no centers on it, which means that you will get duplicate scrambles. This number is 88179840
Think of it this way. If you had a solved 2×2 when holding white top green front, it is the same as holding it green top white front, both are the same scramble (in this case, the solved state)
You have 6 options for which side it on top and 4 for which is on the front, and then the last four sides will be determined automatically. This means that we have 6 × 4 = 24 times too many permutations.
All we need to do now is to divide 88179840 by 24 to get the magic number 3674160.
Me too
YS Cubing heh thats what i said
@Carbonic Potassium Detection Contraption 20
kinda is kinda not
0:17
Cube: What's happening!
jperm is so good at math bro like BECOME MY TEACHER for both speedcubing and math
Not a single soul:
Me: Tries to figure out how to say that number
Forty three quintillion two hundred fifty two quadrillion three trillion two hundred seventy four billion four hundred eighty nine million eight hundred fifty six thousand
@@jared4575 w o w
@@jared4575 43.252Qi
Lol so with davidbird754’s pinned comment theory the 3x3 would have 43.252.003.274.489.856.000 pieces 🤣
Basic perumatiation amd combination..easy easy.
The reason that on 2x2 you can't just take the corners of 3x3 equations is because on of the corners is attached to the center on a 2x2 so it can not be removed or corner twisted, meaning that instead of using 8 in the eqaution, you would use 7.
This video teaches me more than my whole life in school will ever will.
ikr
Well' I've been thinking about that 43 quintillon permutations and finally, an explanation that I can understand.
J Perm: Casually breaks Rubix cube
Me: *Spits out water*
its taking it apart not breaking
by a 2x2 you can have swapped corners, so it is 8! x 3^7. you can have swapped corners because if there are 2 corners swapped, there are also 2 edge pieces swapped which you can't see. (the internal pieces)
Welcome to everyone that got this reccomended this at 2 AM
Sorry buts its 1 am
Hey Ruskie bro
@@shahanshahpolonium I'm not from Russia, but hii
@@militsa7214 Im Indian but still hi
I got recommended for this at 4 AM!
My sister accused me of lying when I told her this
so I showed her this video
her brain is now mush
anti-sibling tactics
0:16 Gosh that was smooth
This man just gave me a mental breakdown with a god damn *CUBE*
Your jump cut is smoother than cube solve hero’s
WHEN THERE IS PLL PARITY ON 4x4, WHY IS THERES NO ALGS FOR THE PARITY CASE?
Because a 4×4 has hidden edges inside. A 3×3 dont.
There are algs for parity on 4x4. Learn Lucas Parity and Drew Parity.
@@Charovfam5364 I know, im talking about an pll alg for all cases instead of doing parity plus the pll. By the way Lucas and Drew is for oll
David Mousaelian there are set of algs to solve the PLL along with the PLL parity. One of them is the O Perm. Search it on google.
*NICE CALCULATION*
this guy sounds like a math teacher making a youtube video