Someone might have said it already, but if not I will. Technically, the 0x0x0 has 1 permutation, as nothingness in multiplication is characterised by 1 (compared to 0 in additions). An example is x^0 = (arguably even for 0^0), another is 0! = 1. Nothingness is always in the solved state
Nah only the 4th Dimension and not even fully at that. From what it looks like, it's just several ordinary cubes contorted to create a mega cube when combined
@@maddyvonnestpetersburg No, What you cant see in the pictures is that you can turn the 3x3x3x3 for example in the Fourth dimension too The only reason it looks so weird, is because the only way to display the higher dimension cuben is beacause you have to make one side invisible, because otherwise you wouldnt be able to see the other ones, and the invisible side changes with every turn in the higher dimensions
You can create a Rubik's Cube in any number of dimensions using math. And there are some computer programs that let us render and play with them. So while they don't exist in real life, there's still enough of a thing to be interesting, and get a permutations result from
@@meraldlag4336 No, because thats just turning the entire cube. Like on the 1x1x1, if rotating the cube was a different permutation, then it wouldn’t be just 1 permutation
Some thoughts about the comments: 1. "Actually 0! = 1, so a 0x0x0 has 1 permutation" I get the arguments for why a 0x0x0 would have 1 permutation. Because 0! or 0^0 = 1, because there's only 1 way to arrange 0 things. But if you use the mathematical formula to find the number of permutations for any nxnxn, you get a divide by 0 error. So really It should actually maybe be *Undefined*? 2. "How does the 3x3x3 have more permutations than a 3x3x4?" The 3x3x4 has 4 sides that are restricted to ONLY 180 degree turns. This means that all the edges and corners are ALWAYS oriented, which reduces the amount of permutations by a lot. 3. Also yes, I did mess up the scientific notation for 3x3x3, it was a copy paste error from the previous puzzle, I am sorry 😭
I kinda love how it starts with low numbers and then casually spikes up to 282,870,942,277,741,856 536,180,333,107,150,328,293,127,731,985,672,134,721,536,000,000,000,000,000
0:55 The scientific notation for the 3x3x3 seems to be wrong, it should probably be 4.3x10^16 instead of 4.1x10^16, seems to be copy-paste error from the 3x3x4.
just think about how many permutations that last cube has The universe has 10^80 atoms. If each of these was it's own universe, with it's own 10^80 atoms, it would still only have a googolth of a googolth the atoms. it would have to have about 1100 nested universes to get the amount of permutations that that monstrosity has.
It's really interesting to see that the Skyoob and 222 have a really similar number of permutations, same thing with FTO and 345. I'm curious to know how many states the Dino, Rex and Curvycopter puzzles have. Also, is it easy to calculate the number of states the Clock has?
iirc dino has around 20 million, rex has 400 sextillion, and curvy copter has 1.5 sextillion without jumbling, and 15 dectillion with jumbling. also yeah clocks permutation is literally just 12¹⁴
That's true for 3d cubes too though. In fact, you're better off with the 4d cubes because you can see 7 of the 8 cells at once as opposed to 3 of the 6 faces of a 3d cube
@@LeoCowie I said WAY WAY WAY over. This only accounts for one object and all of the settings except for colors. This is the LOWEST end of the spectrum.
I first made the images for each puzzle section, and then I made pictures of 4 of those at a time. Then just in my editing software, I made them all move to the left.
I really love this overview and links you provided, thank you -- but I think you may have a couple of mistakes here. the few I noticed are that you took a domino cube *with pictures* number from one of the sources, but that's higher than a regular domino, that you illustrated the entry with, as center orientations are relevant -- its like on a supercube. From one of your sources: "There are 8 corners and 8 edges, giving a maximum of 8!·8! positions. This limit is not reached because the orientation of the puzzle does not matter. There are 4 equivalent ways to orient the puzzle with a white centre on top, so this leaves 8!·8!/4 = 406,425,600 distinct positions. If the centre orientation is visible, then there seem to be 4·4 possible orientations of the two centres. There is a parity constraint however, as the parity of the number of quarter turns of the centres must be equal to the parity of the corner permutation. This means that the centre orientations only increase the number of positions by a factor of 8, giving 8!·8!·8/4 = 3,251,404,800 distinct positions." The second one that seems half-wrong is the 3x3x3 . The full number is right, but you must have accidentally copy-pasted the previous entry, 3x3x4 for that number in scientific notation; it says just 4.1 x 10^16 yet the number above is clearly the correct and much greater value of 4.3 x 10^19. Apologies for repeating this, I've seen others have notified you of this one -- after already writing this. Also I also can't find the 8,617,338,912,961,658,880,000 for square 1 in your stated sources. It describes a couple of ways of counting, but as far as I can gather even the largest number it gives is the much smaller 62,768,369,664,000 (and quotes even smaller ones in the table, not that -- so I guess it doesn't think that's the right count either). soo at best just around 1e13 to 1e14, and not on the order of almost 1e22 as stated.
the 334 has an axis that's restricted to 180 degree turns. So basically the corners and edges are always oriented, unlike a 333 which has edge orientation and corner orientation. Even though it has an extra layer, the piece orientations make it much smaller number of permutations
The 3^9 has 9,1556069*10^118409 permutations. I did the calculations for the 3^8 and 3^10 too, but i cannot find the numbers nor the calculation rn. But if i remember correctly. the 3^8 had something like 10^35000 permutations and the 3^10 something like 10^500000.
I guess I’m not quite understanding the 3x3. I know it’s a 2 dimensional puzzle, but I can’t figure out why it’s 24, I can only see 12 permutations I imagine it’s something incredibly simple, but yeah 😬
For the 2D square puzzles, just imagine mirroring each side. So only the corners can move around. So then it's just 4! factorial, which is 4x3x2x1 = 24
@@RowanFortier hmmm…I’m still not quite getting it, I’m sure if I saw it in action it would be obvious, but I’m just kinda bad at picturing these things. Definitely appreciate the reply though 👍🏻
What about the maple leaf skewb? We have that one and it's easy enough to solve without any knowledge beforehand and doesn't have that many permutations but I'm wondering where it's at on this list.
So true. I was thinking about this, and ultimately decided that because 0x0x0 = 0, there is no puzzle, which means it doesn't exist so of course it has 0 permutations. But I also completely see the logic behind "it has 1 permutation, that of existing"
@@RowanFortier ! (read: factorial) is a common method to calculate the number of positions/permutations something has. n!=1x2x3x..x(n-1)x(n) ex. 3 toilets can be arranged in 3! (1x2x3=6) ways. but 0!=1 acording to mathematicians and calculators, because there is only one state of nothingness, which is: nothingness.
difficulty easy 1-10 0:05 medium 11-50 0:21 hard 51-1M 0:41 insane 1M-1T 0:51 imposple 1T-666SX 0:53 ho no :( 666sx-969No 1:08 no No NO DX 969no-1vt 1:13 !!!! 1vt- inf 1:18
I kept thinking about it, and I think I've come to the conclusion that the 0x0x0 has an indeterminate number of permutations. Counting the "permutations" of twisty puzzles is just a tiny bit misleading, because it technically includes both the permutations and the orientations of the pieces For example, a 2x2x2 has 7! permutations of its pieces (assuming one is stationary), multiplied by 3^6 orientations (still assuming one stationary piece, and dividing out the orientation of the last corner which is forced by the others) equaling 3674160 total permutations. If we apply this logic to the 0x0x0, which has 0 pieces, each with 0 possible positions, and 0 possible orientations, we find that the total permutations would equal the number of permutations of the pieces (0!) multiplied by the number of orientations (0^0) This yields the result of 0!*0^0 = 0^0, which is indeterminate. I guess it kinda makes sense for the number of permutations for a puzzle that doesn't even exist ¯\_(ツ)_/¯
i dont think it makes sense to extend that formula exactly as it is to the 0x0x0. if you look at it from a more practical viewpoint, it seems like it should be 1 for the same reason 0! = 1
I understand everyone's arguments that 0^0 is 1, and 0! is one, and that there's 1 way that nothing can be in. The way that I thought of it originally was if you don't have anything in the first place, than what are you arranging? You can't arrange objects that you don't have any of. It's like the question doesn't even make sense, like how anything/0 is undefined. I actually think a 0x0x0 should have Undefined permutations
@@RowanFortier I think it actually makes some sense for there to be undefined permutations, though 1 permutation still makes more sense to me. Ig it depends on the persons perception on a 0x0x0.
@@scrambledmc3772 This notation system is called "Bub's Notation". It goes like this Thousands: K Type-1 ones (before Decillion): M, B, T, Qa, Qi, Sx, Sp, Oc, No Type-1 ones (after Decillon): U, D, T, Qa, Qi, Sx, Sp, O, N Type-1 tens: De, Vg, Tg, Qd, Qt, Se, Sg, Og, Ng Type-1 hundreds: Cn, Du, Tc, Qr, Qn, Sc, St, Oi, Ni Type-2 ones: Mn, Mc, Nn, Pc, Fm, At, Zp, Yt, Xn
how does the 3x3x4 have less than the 3x3x3 (if the vertical rotations dont work it would make more sense but it just would be the dodo cube but with 4 instead of 2 layers)
Someone might have said it already, but if not I will. Technically, the 0x0x0 has 1 permutation, as nothingness in multiplication is characterised by 1 (compared to 0 in additions). An example is x^0 = (arguably even for 0^0), another is 0! = 1. Nothingness is always in the solved state
🤓
@@Icedonot he’s right tho
@@rax1899 but funny nerd emoji
@@Icedonot 🗿
@@Icedonot 😎
I love how the cubes casually ascend into the 7th dimension
Edit: came back and 300 LIKES?! That’s the most that I’ve had
Nah only the 4th Dimension and not even fully at that. From what it looks like, it's just several ordinary cubes contorted to create a mega cube when combined
@@maddyvonnestpetersburg No, What you cant see in the pictures is that you can turn the 3x3x3x3 for example in the Fourth dimension too
The only reason it looks so weird, is because the only way to display the higher dimension cuben is beacause you have to make one side invisible, because otherwise you wouldnt be able to see the other ones, and the invisible side changes with every turn in the higher dimensions
@@endevomgelende8634 I assumed that this cube was based on an irl toy.
You can create a Rubik's Cube in any number of dimensions using math. And there are some computer programs that let us render and play with them. So while they don't exist in real life, there's still enough of a thing to be interesting, and get a permutations result from
@@RowanFortier There are actual 3d puzzles with states analagous to 4d puzzles
I knew gear cube was restricted, but it's honestly insane that it has fewer scrambles than a 2x2...
Good comment, "Ryan", who lives at [[REDACTED]] 😳
@@RowanFortier what
Yo what 💀
@RowanFot
@@RowanFortier bro doxxed the dude 💀
I like how the 0x0 exists. Everyone has it but it’s invisible
🧠🧠
Everyone solved it in -9 months because since you were a little cell you already solved it
You have to solve air💀💀💀
You can only hear it
The video is also wrong about it, the empty puzzle has 1 permutation, not 0. There is exactly one way to arrange nothing.
I love how the high ones on this list have more combinations than the amount of atoms in the observable universe
the estimation of Atoms in the observable universe is 10^82~10^87
The 150x150 almost has the amount of atoms in the universe ^10,000. That's like nesting a universe in every atom of the universe 10,000 times.
@@raspexsaurus7 isn't it 10^78 - 10^82
@@cythism8106 That's not how you use conjunction operator.
No way I can’t believe that the (insert puzzle name here) had (n) different permutations!
no way!!
Realq
Does rotating a cube count as a permutation? Surely all the pieces can be put in a different location that way, or is permutation the wrong word
@@meraldlag4336 No, because thats just turning the entire cube. Like on the 1x1x1, if rotating the cube was a different permutation, then it wouldn’t be just 1 permutation
@@nhaJn so how is permutation defined in the video then
its crazy how some 3d ones have more permutations than higher dimensions
Yeah, it was interesting when I was researching it
Like the 33x33x33 and the 19x19x19
3x3 in 7th dimension: "I WIN!"
150x150 in 3d, "No, son.."
150x150x150 has 7.2 x 10^86707 and the 3x3x3x3x3x3x3 has 3.3 x 10^8935
based pfp
Some thoughts about the comments:
1. "Actually 0! = 1, so a 0x0x0 has 1 permutation"
I get the arguments for why a 0x0x0 would have 1 permutation. Because 0! or 0^0 = 1, because there's only 1 way to arrange 0 things. But if you use the mathematical formula to find the number of permutations for any nxnxn, you get a divide by 0 error. So really It should actually maybe be *Undefined*?
2. "How does the 3x3x3 have more permutations than a 3x3x4?"
The 3x3x4 has 4 sides that are restricted to ONLY 180 degree turns. This means that all the edges and corners are ALWAYS oriented, which reduces the amount of permutations by a lot.
3. Also yes, I did mess up the scientific notation for 3x3x3, it was a copy paste error from the previous puzzle, I am sorry 😭
@@cewla3348 0^n=0
🤓🤓🤓
@@Bumpus. the funny
@@Bumpus. 😐😐😐
@@Bumpus. you are being unkind.
Bro I love this guy he researches so well from what I’ve seen in the comments, and the video was interesting too
Glad you enjoyed!
Isn't 0x0x0 1? Only one case, which is nothing? Many combinatorics problems (especially recurrence relation problems) has the same logic.
it doesnt literally exist, you can make nothing(0) with it.
@@quantdev 0!=1
i was thinking the same, it should be one as many combinatorics problems also have similar answers
@@quantdev That is still something
Well if its 0x0x0 then it doesnt exist, meaning that its 0, not 1, if it was 1 it would exist
edit: nvm
I kinda love how it starts with low numbers and then casually spikes up to 282,870,942,277,741,856 536,180,333,107,150,328,293,127,731,985,672,134,721,536,000,000,000,000,000
0:55 The scientific notation for the 3x3x3 seems to be wrong, it should probably be 4.3x10^16 instead of 4.1x10^16, seems to be copy-paste error from the 3x3x4.
Oh yikes - that is really embarrassing. Thanks for pointing that out!
It's 4.3×10^19, not 4.3×10^16, because 3×3×3 has 3 more digits.
Lol i was going to say this
Where is the minx of madness 😡
How does the 0x0x0 have zero permutations? It actually has one, and that one permutation is where the “cube” isn’t in existence.
Bug brain
someone said the 0x0x0 exists lol
just think about how many permutations that last cube has
The universe has 10^80 atoms.
If each of these was it's own universe, with it's own 10^80 atoms, it would still only have a googolth of a googolth the atoms.
it would have to have about 1100 nested universes to get the amount of permutations that that monstrosity has.
🤯🤯🤯
and also its googol^867 x 72000000
It's really interesting to see that the Skyoob and 222 have a really similar number of permutations, same thing with FTO and 345.
I'm curious to know how many states the Dino, Rex and Curvycopter puzzles have.
Also, is it easy to calculate the number of states the Clock has?
iirc dino has around 20 million, rex has 400 sextillion, and curvy copter has 1.5 sextillion without jumbling, and 15 dectillion with jumbling.
also yeah clocks permutation is literally just 12¹⁴
@@PuyoTetris2Fan I thought clock was 12^15?
@@bigbosspanda1976 No, it's 12^14 because all of the 14 pieces are independent
That last one takes "I'm 4 dimensions ahead of you" to a whole other level
Pyraminx has 933120 but only if you dont count the tips. If you count the tips, multiply it by 81
So 75,582,720
Respect to the guy who tried out all these combinations 🙏
yeah I love the 4th dimensions cubes, they are hard since you don't see some faces you have to guess where they are 😂
@A Random Gamer oh ok, i'm not really good at understanding all this 4th dimension thing so I just told what passed through my mind
Nah... 3x3x3x3x3x3x3 is harder... You need to see the small piece and also need 1m+ turning face to complete it
@@luparty..gwmatycoysampaiba8701 that's a bit too hard fo me to imagine it
You can just rotate the side in higher dimension in 3rd dimension, that's how I solve it.
That's true for 3d cubes too though. In fact, you're better off with the 4d cubes because you can see 7 of the 8 cells at once as opposed to 3 of the 6 faces of a 3d cube
All the puzzle permutations:
0x0x0 - 0
1x1x1 - 1
1x1x2 - 4
1x2x2 - 6
1x1x3 - 16
3x3 - 24
1x2x3 - 48
1x3x3 - 192
1x2x5 - 1,152
Gear Cube - 41,472
2x2x3 - 241,920
Pyraminx - 933,120
Skewb - 3,129,280
2x2x2 - 3,674,160
2x3x4 - 418,037,760
3x3x2 - 3,251,404,800
Clock - 1,283,918,464,548,864 (1.2 x 10^15)
Corner-Turning Octahedron - 2,009,078,326,888,000 (2 x 10^15)
3x3x4 - 41,295,442,083,840,000 (4.1 x 10^16)
3x3x3 - 43,252,003,274,489,856,000 (4.3 x 10^16)
Square-1 - 8,617,338,912,961,658,880,000 (8.6 x 10^21)
Face-Turning Octahedron - 31,408,133,379,194,880,000,000 (3.1 x 10^22)
3x4x5 - 41,102,509,778,424,299,529,000 (4.1 x 10^22)
Square-2 - 1,240,896,803,466,478,878,720,000 (1.2 x 10^24)
2x2x2x2 - 3,357,894,533,384,932,272,635,904,000 (3.3 x 10^27)
4x4x5 8,881,841,338,276,800,000,000 (8.8 x 10^30)
4x4x4 - 7,401,196,842,564,901,869,874,093,974,498,574,336,000,000,000 (7.4 x 10^45)
Pyraminx Crystal - 1,667,826,942,558,772,452,041,933,871,894,091,752,811,468,606,850,329,477,120,000,000,000 (1.6 x 10^66)
Megaminx - 100,668,616,553,347,122,516,032,313,645,505,168,688,166,411,019,768,627,200,000,000,000 (1 x 10^68)
5x5x5 - 282,870,942,277,741,856,536,180,333,107,150,328,293,127,731,985,672,134,721,536,000,000,000,000,000 (help me) (2.8 x 10^74)
2x2x2x2x2 - 54,535,655,175,308,197,058,625,263:389,197,058,635,263,389,110,963,764,726,777,446,400,000,000,000,000,000,000,000,000,000,000,000,000 (5.4 x 10^88)
3x3x3x3 - 1,756,772,880,709,135,843,168,526,079,081,025,059,614,484,630,149,556,651,477,156,021,733,236,798,970,168,550,600,274,887,650,082,534,207,129,600,000,000,000,000 (1.7 x 10^120)
4x4x4x4 - 1.3 x 10^344 (yay no more chaos)
3x3x3x3x3 - 7 x 10^560
5x5x5x5 - 1.2 x 10^701
19x19x19 - 6.3 x 10^1,326
Yottaminx - 2.8 x 10^2,950
33x33x33 - 1.8 x 10^4,099
120-cell - 2.3 x 10^8,126
3x3x3x3x3x3x3 (7D) - 3.3 x 10^8,935
150x150x150 - 7.2 x 10^86,707
despite the 1 permutation, 1x1x1 is still the hardest rubik's cube
my fellow cubers know
But 2x2x2 😮 has 3M combinations
I have spent 5 years on that cube that was passed down from my grandpa
@@888_kaiwalyarangle6 you are not worthy
@@888_kaiwalyarangle6 inbicel, if you cant scramble it you cant solve it
back on track be like
What about the atlasminx and minx of madness? Also coren's 13 layer pyraminx would be interesting to see too
1:44 still more possible geometry dash levels
By the way there are WAY WAY WAY over 1.9x10^22253 possible geometry dash levels
@thepianokid9378 UHH HELL NO
@@thepianokid9378gd is infinite so there’s infinite combinations for a gd level
Frfr
@@LeoCowie I said WAY WAY WAY over. This only accounts for one object and all of the settings except for colors. This is the LOWEST end of the spectrum.
1:56 love how it just jumps to 9x more zeros than the last one😂😂😂
Awesome video! How did you animate this?
I first made the images for each puzzle section, and then I made pictures of 4 of those at a time. Then just in my editing software, I made them all move to the left.
@@RowanFortier Nice it all looks super clean
@@RowanFortier but why?
How to be a pro at the rubiks cube
1. Scramble properly
2. Swipe fast
3. Solve it
Great job! Now find every combination.
I really love this overview and links you provided, thank you -- but I think you may have a couple of mistakes here. the few I noticed are that you took a domino cube *with pictures* number from one of the sources, but that's higher than a regular domino, that you illustrated the entry with, as center orientations are relevant -- its like on a supercube. From one of your sources:
"There are 8 corners and 8 edges, giving a maximum of 8!·8! positions. This limit is not reached because the orientation of the puzzle does not matter. There are 4 equivalent ways to orient the puzzle with a white centre on top, so this leaves 8!·8!/4 = 406,425,600 distinct positions.
If the centre orientation is visible, then there seem to be 4·4 possible orientations of the two centres. There is a parity constraint however, as the parity of the number of quarter turns of the centres must be equal to the parity of the corner permutation. This means that the centre orientations only increase the number of positions by a factor of 8, giving 8!·8!·8/4 = 3,251,404,800 distinct positions."
The second one that seems half-wrong is the 3x3x3 . The full number is right, but you must have accidentally copy-pasted the previous entry, 3x3x4 for that number in scientific notation; it says just 4.1 x 10^16 yet the number above is clearly the correct and much greater value of 4.3 x 10^19. Apologies for repeating this, I've seen others have notified you of this one -- after already writing this.
Also I also can't find the 8,617,338,912,961,658,880,000 for square 1 in your stated sources. It describes a couple of ways of counting, but as far as I can gather even the largest number it gives is the much smaller 62,768,369,664,000 (and quotes even smaller ones in the table, not that -- so I guess it doesn't think that's the right count either). soo at best just around 1e13 to 1e14, and not on the order of almost 1e22 as stated.
The 120 cell is a 4d shape that is made of 120 duodecahedra which consists of 12 pentagons. The 120 cell is the 4d equvelent of a platonic solid.
Nice, why does the 3 3 4 have less permutations than 3 3 3 tho i dont understand
the 334 has an axis that's restricted to 180 degree turns. So basically the corners and edges are always oriented, unlike a 333 which has edge orientation and corner orientation. Even though it has an extra layer, the piece orientations make it much smaller number of permutations
1:55 what about 200×200×201 200×200×200 4×4×4×4×4×4×4 and 500×500×500
1:57
This can branch up to infinite x infinite x infinite even in the 11th dimension which is the last one according to string theory
the last one that exists irl according to string theory. You can have any amount of dimensions if you're thinking purely abstractly
Props to the person who counted how many permutations each of these puzzles have
Do you are have jokes
How tf do you even get a 4d cube? 💀 1:07
A physical 2*2*2*2 exists lol
And even a 3*3*3*3
Respect that guy who actually counted all this
The 3^9 has 9,1556069*10^118409 permutations. I did the calculations for the 3^8 and 3^10 too, but i cannot find the numbers nor the calculation rn. But if i remember correctly. the 3^8 had something like 10^35000 permutations and the 3^10 something like 10^500000.
🤯🤯🤯
im no expert, but like, *thats a big number*
Could you make a video specifically for cuboids like 1x2x3 or 2x3x4?
omg!1!1(1(1!1(1 this really proves that the 1x1x1 is the hardest puzzle made by man!1!1!1!1!1
0:36 already at 3 million
I guess I’m not quite understanding the 3x3. I know it’s a 2 dimensional puzzle, but I can’t figure out why it’s 24, I can only see 12 permutations
I imagine it’s something incredibly simple, but yeah 😬
For the 2D square puzzles, just imagine mirroring each side. So only the corners can move around. So then it's just 4! factorial, which is 4x3x2x1 = 24
@@RowanFortier hmmm…I’m still not quite getting it, I’m sure if I saw it in action it would be obvious, but I’m just kinda bad at picturing these things. Definitely appreciate the reply though 👍🏻
Thanks to the man who tried all of these combinations!
o7
the largest rubix's cube: ΩxΩxΩ
Explains why I could never beat a 2x2 rubix cube
0:05 nothing
0:08 class
0:13 homework
0:17 test
0:20 quiz
0:22 exam
0:25 pop quiz
0:28 beep h note
0:30 d beep
0:33 fetus
0:35 wasn't born yet
0:40 maybe don't exist
0:43 don't exist
0:45 no
0:47 n
0:55
0:58 ybbo obby
1:03 .
1:05 ,
1:07 :
1:44 ;
What people think pop quiz is 1:58
Well,technically 0x0x0 should have one permutation cuz “nothing”is a state of the puzzle 😂
what the hell can u arrange if u have nothing in the first place
what formulas are used to calculate these amounts of permutations?
Some crazy smart math guy found a formula for any nxnxn puzzle
I can solve a 150x150x150, but I can't solve a 3x3x4. Square-1 surprised me with the number of its permutations.
Lies. No one can solve a 150x150x150
@@NikodAnimations its an oversized cube,its same as 5x5 or 4x4
NI LI SITELEN TAWA PONA A!
GREAT VIDEO!
mi kama sona mute tan sitelen tawa ni!
It was very educational!
Toki Riley!
@@RowanFortier toki a, jan Rowan o!
and square-1💀 0:55
You're how I got into hypercubing :) Love your videos
0x0x0 actually has undefined permutations
It's either 0, 1, or undefined 🤷♂️
@@RowanFortier It's basically 0/0 so 2, 3, π, -1, e^i, 69, in fact every number would also technically be correct, but also not really
@@Ascyt That can be true, but if you only try to do the proof using algebraic methods or limits you can only get 1, 0 or undefined
@@gdmathguy "undefined" includes 1 and 0
@@Ascyt That is called "Indeterminate" since we can't determine which answer is correct
What about the maple leaf skewb? We have that one and it's easy enough to solve without any knowledge beforehand and doesn't have that many permutations but I'm wondering where it's at on this list.
I have the gearcube and I can solve it in less then 10 seconds. But I never knew it had 41,472 possible combinations!
mans going to the 18th dimension for this
Prove to me that 0x0x0 has 0 permutations instead of 1
So true. I was thinking about this, and ultimately decided that because 0x0x0 = 0, there is no puzzle, which means it doesn't exist so of course it has 0 permutations.
But I also completely see the logic behind "it has 1 permutation, that of existing"
@@RowanFortier 0! Is equal to 1 so I think the argument is that even if it exists or doesn't exist it still has one state or permutation
@@RowanFortier ! (read: factorial) is a common method to calculate the number of positions/permutations something has.
n!=1x2x3x..x(n-1)x(n)
ex. 3 toilets can be arranged in 3! (1x2x3=6) ways.
but 0!=1 acording to mathematicians and calculators, because there is only one state of nothingness, which is: nothingness.
You know its gonna be intense asf when you see the numbers rapidly rising
First
difficulty
easy 1-10 0:05
medium 11-50 0:21
hard 51-1M 0:41
insane 1M-1T 0:51
imposple 1T-666SX 0:53
ho no :( 666sx-969No 1:08
no No NO DX 969no-1vt 1:13
!!!! 1vt- inf 1:18
100x100x100 Rubiks cube:2 x 10^38415 permutations!!!
After the Yottaminx, here comes the Xennaminx!
Ah yes, I love my 0*0*0 cube, I highly recommend it
well i already have it
I kept thinking about it, and I think I've come to the conclusion that the 0x0x0 has an indeterminate number of permutations. Counting the "permutations" of twisty puzzles is just a tiny bit misleading, because it technically includes both the permutations and the orientations of the pieces
For example, a 2x2x2 has 7! permutations of its pieces (assuming one is stationary), multiplied by 3^6 orientations (still assuming one stationary piece, and dividing out the orientation of the last corner which is forced by the others) equaling 3674160 total permutations.
If we apply this logic to the 0x0x0, which has 0 pieces, each with 0 possible positions, and 0 possible orientations, we find that the total permutations would equal the number of permutations of the pieces (0!) multiplied by the number of orientations (0^0) This yields the result of 0!*0^0 = 0^0, which is indeterminate.
I guess it kinda makes sense for the number of permutations for a puzzle that doesn't even exist ¯\_(ツ)_/¯
0 factorial is 1, and 0^0 is also defined as 1 (I think), which would actually make it have 1 permutation somehow
The one permutation would be nothing?
@@RowanFortier 0^0 is indeterminate because 0^n=0 and n^0 = 1. 0^0 falls into both of these, so it’s not possible to determine an answer
i dont think it makes sense to extend that formula exactly as it is to the 0x0x0. if you look at it from a more practical viewpoint, it seems like it should be 1 for the same reason 0! = 1
@@brcktn But 0^0 is often defined as =1 especially in these cases where it comes to counting permutations
The 1x3x3 has 192 combinations without shape shifting, but with shape shifting it probably has 10,000-1 million combinations.
The real world can fit numbers bigger than the amount of atoms in the observable universe. Insane.
0:07:easy cubes
0:43 :medium cubes
1:24 :challenging cubes
1:34 :extremely challenging cubes
How on earth did you calculate this?
these are unimaginable numbers
i went to another tab for a few seconds and the numbers went from millions to trillions!
I was expecting to see something like the 65536x65536x65536 lol
Combination Comparison: Rubix Cube
0x0x0 - 0
1x1x1 - 1
1x1x2 - 4
1x2x2 - 6
1x1x3 - 16
3x3- 24
1x2x3 - 48
1x3x3 - 192
1x2x5 - 1.15K
Gear Cube - 41.47K
2x2x3 - 241.92K
Pyraminx - 933.12K
Skewb - 3.12M
2x2x2 - 3.67M
2x3x4 - 418.03M
3x3x2 - 3.25B
Clock - 1.28Qa
Corner-Turning Octahedron - 2Qa
3x3x4 - 41.29Qa
3x3x3 - 43.25Qa
Square-1 - 8.61Sx
Face-Turning Octahedron - 31.4Sx
3x4x5 - 41.1Sx
Square-2 - 1.24Sp
2x2x2x2 - 3.35 Octillion
4x4x5 - 8.88 Nonillion
4x4x4 - 7.4 Quattuordecillion
Pyraminx Crystal - 1.67 Unvigintillion
Megaminx - 100.66 Unvigintillion
5x5x5 - 282.87 Trevigintillion
2x2x2x2x2 - 54.53 Octovigintillion
3x3x3x3 - 1.75 Novemtrigintillion
4x4x4x4 - Tredecicentillion
3x3x3x3x3 - Sexoctogintacentillion
5x5x5x5 - Duotrigintaducentillion
19x19x19 - Unquadragintaquadringentillion
Yottaminx - Septensexagintanongentillion
33x33x33 - Quinsexagintatrucentimillinillion
120-cell - Septenseptingentibillinillion
3x3x3x3x3x3x3 - Septenseptuagintanongentibillinillion
150x150x150 - Unnongentiseptenvigintillinillion
Number List
Centillion - 303 zeros
Ducentillion - 603 zeros
Trucentillion - 903 zeros
Quadringentillion - 1,203 zeros
Quingentillion - 1,503 zeros
Sescentillion - 1,803 zeros
Septingentillion - 2,103 zeros
Octingentillion - 2,403 zeros
Nongentillion - 2,703 zeros
Millinillion - 3,003 zeros
Billinillion - 6,003 zeros
Trillinillion - 9,003 zeros
...
its crazy how some of them have more permutations than there are atoms in the observable universe
0:55 wouldn't 3x3x3 be (4.3 x 10^19)?
Where can I buy a 4D rubiks cube?
Is the 120 cell just a 4d dodecahedron
Yes
4d megaminx
actually, if you think about it, the number of combinations on a 0x0x0 is 1, because there is only 1 way to arrange none.
I understand everyone's arguments that 0^0 is 1, and 0! is one, and that there's 1 way that nothing can be in. The way that I thought of it originally was if you don't have anything in the first place, than what are you arranging? You can't arrange objects that you don't have any of. It's like the question doesn't even make sense, like how anything/0 is undefined. I actually think a 0x0x0 should have Undefined permutations
@@RowanFortier I think it actually makes some sense for there to be undefined permutations, though 1 permutation still makes more sense to me. Ig it depends on the persons perception on a 0x0x0.
1:36 I bet you feel dumb now Tingman
A 1x1 isn’t a real puzzle I can get a world record of 0 second solve
yeah it's crazy how many permutations a 150x150x150 has, but we can go deeper
0:56 A mistake, Not 4.1 x 10^16, it's 4.3 x 10^16
Great video
Thanks!
Aight we saw how big the 150x150x150 is, now someone’s gotta go straight for actually building the 150x150x150x150
You know sh!ts bout to get real when you need to use powers 50 seconds into the video
150x150x150 may sound impossible, but a general person who can solve a 4x4x4 can theoretically solve it
in 4 days
40 tray ones, Hillian combination 0:13
The 150x150x150 Cube Puzzle has 72OVgMnUNi (72 Octovigintimilli-unnongentillion) different Permutations.
Please tell me how this notation works, I’d really like to know how to count past centillion.
@@scrambledmc3772
This notation system is called "Bub's Notation". It goes like this
Thousands: K
Type-1 ones (before Decillion): M, B, T, Qa, Qi, Sx, Sp, Oc, No
Type-1 ones (after Decillon): U, D, T, Qa, Qi, Sx, Sp, O, N
Type-1 tens: De, Vg, Tg, Qd, Qt, Se, Sg, Og, Ng
Type-1 hundreds: Cn, Du, Tc, Qr, Qn, Sc, St, Oi, Ni
Type-2 ones: Mn, Mc, Nn, Pc, Fm, At, Zp, Yt, Xn
@@Baburun-Sama Sorry I didn’t mean the abbreviations, I meant the actual naming system for the numbers.
There's a wikipedia page for big number names I think
@@Baburun-Sama i knew this notation a year ago amd i never knew the name lol
1:11 how does a 4x4x5 have less combinations than 4x4x4 if it has an extra layer?
I'm Japanese, but I'm glad I was able to understand this video.
If you're interested in the detailed maths behind n*n*n puzzle permutations, I did a video on that (in french)
Everyone gangsta until the rubik's cubes becaome 4th dimensional
1000x1000x1000 Rubik's Cube has ABSOLUTE INFINITY possible combinations
Respect for the people who made those Rubik's took like 3 years or higher
can i buy one of the 0x0x0 one? I think its pretty rare that i never saw one before
Its crazy that the 3⁷ has more permutations than a 19x19
how does the 3x3x4 have less than the 3x3x3 (if the vertical rotations dont work it would make more sense but it just would be the dodo cube but with 4 instead of 2 layers)
Wouldn't the 0^n have 1 permutation? Similar to 0! = 1?
Are permutations how much possible pattern you can do?
Man after a year, I finally found it
im wondering does a 4d square1 exist perhaps a cube 1?
0:30
not every 0mm smidge you can turn it and it would have different shape?
It should end with TREE(3)
all these combined are still smaller than that one guy's ego