The Search For God's Number | Rubik's Cube
If God had a Rubik's Cube, how many moves would he need to solve it at most? Can we just solve every scramble to figure it out, or is there more to the search?
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if we have god's number why has nobody called him yet
too shy
@@JPerm lol
@@JPerm Stage Fright From God. Lol
Actually I’ll call him *ring ring* *ring ring* God: how do you have my number Me: it’s j perms fault he made this video showing us your number J perm: yeah I guess
bruuuhhh
"What if you tried to write a full list of solutions to every single possible scramble? Well, you would die" - JPerm 2020
WOW!
Like me please!
@@alexanderbabich shut up
@@ninjaseth4357 Look at his last name lol
@@alexanderbabich I like you 😍
I can't believe you bought 43 quintilion cubes just for this video You're a legend
Please 💀
Please 💀
@@gl_eo please 💀
Please 💀
@@spaceyvoid4202 Please 💀
really nice video! I love the way you had a visual number line showing the range between the lower and upper ranges over time.
Hello cary love your videos :D
Lol it's cary
Hi
J Perm uploaded video on 2:00 AM (India), then too we Indian gang will watch it because it is of _J Perm_
wow
0:07 “So I did a little work off camera”
lol
He uploads with a phone actually
@@TPerm700 I thought he uses his phone for recording video and his laptop for editing and uploading
@@TPerm700 Bruuu rip off J Perm
@@TPerm700 r/woooosh
Honestly I didn’t understand this but I still watch it because it’s jperm
Keep watching it until you understand and also don't skip the ads ♥️
@@JPerm KZhead Premium ;)
@@JPerm same :)
Same
I was just about to comment this You read my mind
‘69... of you ask me that’s a pretty great upper bound’ absolute legend
7:12
“The 3x3 has 20 pieces invented 20 years before the end of the 20th century” - Jperm
And any permutation of it can be solved in at most 20 moves
And the amount of minutes in this video is 20
And the God's Number is 20
And 20 is 20
Actually it has 20 pieces and 6 centre pieces, but they are fixed so it makes sense it can be solved in 20 moves
Its honestly incredible that humans were able to compress 17 million years of work in to a couple of weeks... Its so amazing
Procrastination is amazing
@@jeremyfarr304 bruh
I don't understand, am I stupid?
it really is... and it's actually 10^17 years which is much much much much higher than 17 million
@@jeremyfarr304 I'm talking about the comment by @Rat lol
Fun fact: Jperm has more cube pamphlets than the 43 quintillion possible permutations.
This truth is true but sad
Max Park vs Feliks Zemdegs at Redbull Rubik's Cube World Cup kzhead.info/sun/ediyZaqnfnebdo0/bejne.html
Naw, mats :D
@@goombagoomba2329 Hahaha
Hey Dylan, this was an excellent video! It was a nice little change of pace from the tutorial stuff that a lot of us know you for, and I appreciated the amount of research that clearly went into this. Awesome stuff!!
As a cuber and math student (huuuuuge nerd) I really enjoyed this video. I already looked into this in the past because it interested me but to have the entire history of this in one awesome video is amazing and you explained all the stuff very well and understandably.
0:26 then you’d be a noncubers cousin
I wish I was a non-cuber's cousin, then I'd solve the cube in, like 2 seconds, every time!
@@JPerm lmaoo how is this basically a quote from my cubing skit. Great minds👀👀👀
@jperm What is gods number on 4x4?
@J Perm
Underrated
Great video! Small mistake at 16:57: it is true that a cube has 48 symmetries, but only 16 of them (48 / 3) preserve the vertical axis (i.e. the axis perpendicular to the U and D faces). The vertical axis is important because phase 1 is defined in terms of the U and D moves. So in Kociemba's algorithm only those 16 symmetries can be used.
That's a good point, Kocimebas algorithm isnt symmetric in that way. Regardless, I found on cube20.org that they did have a reduction of about 48x, so I assume they found a way to get around this. I didnt learn exactly how, but I assume it has to do with the way they grouped the cases before solving.
Ok
The vertical axis is not really important, since the move set is pretty much equivalent to and by just a rotation. I assume this is how they still got close to a 48 factor reduction. By the way, the reason the reduction is close to 48 but not actually 48 is due to some positions being symmetric themselves, like the superflip. The 48 reduction works because most positions have 47 equivalent positions by applying a symmetry, however if a position itself is symmetric then these 48 positions are no longer all different. A theorem called Burnside's lemma makes this more precise and can be used to calculate the actual reduction factor, which turns out to be closer to 40.
J Perm: “computers are slow” Me: Ahh the exact definition of mine
Great video! I really appreciate this math and programming video (two topics I really like) among every other thing you could have covered...
Loving these new longer style videos. A breath of fresh air compared to typical cubing stuffs.
Hey wassup man 😎😎
@@Yadhukuttan6123 ayeee sup dude😎 you already know I'm just balancing spoons and spinning books
@@mediochrist 😂😂
It would be very interesting to find the God‘s Number on other NxN puzzles like 2x2 or 4x4, or maybe even something like a Megaminx. But honestly, could computers of today’s standards even calculate that?
2x2 is quite easy and it has been found long ago to be 11, but 4x4 is still unsolved!
There is also an AI that learned to solve the 3x3 Rubik's cube without any prior kowledge and solved it in the minimal number of moves about 60-70% of the time. So letting an AI train for long enough, you could get a good estimate. However training such AIs also takes a very long time and that time of course depends on the puzzle.
@@sebastianjost It wouldnt really be a proof though.
Man I started knowing so much about cubing just because of you jperm. Thank you
3:34 'Imagine this. What if you tried to write a full list of solutions to every single possible scramble? Well, you would die.'
There’s something so friendly about his face
One of your best non cubing advice related videos yet :). Learned a lot from this one. I always wondered how upper and lower bounds were discovered
Hey loving your videos man! I'm getting some new cubes for Christmas and from your videos I've nailed it down to getting either a Gan xs or a MoYu Weilong GTS 3m but I'm not sure. But thanks for helping get me down to the two. You're vids have saved me a lot of time.
what an amazing video! thank you for putting in the time and effort to make this
Thanks jperm, for everything, you’re making quarantine better for me :)
"Koceimba is my new main speedsolving method."
"What if you wrote a solution to every single scramble. Well, you would die." Or would you? **Vsauce music starts playing**
😳😳😳😳 😂🤣
i got a little nervous when i saw read more
I think Morwen Thistlethwaite deserves a mention; he first came up with the idea of improvement through reducing the set of allowed moves all the way back in 1980, and found an upper bound of 52 (HTM). Thistlethwaite's algrorithm had four steps (1. all moves, 2. no quarter turns of U/D, 3. no quarter turns of U/D or F/B, 4. no quarter turns at all); with more memory and faster computers Kociemba was able to reduce that to just the two steps you mention 12 years later.
Cube solving itself is good, but I think it's also good to listen to some kind of this without stress. always enjoying.
What a great video. At first I thought the brown table at the beginning was brown paper, which would have been fitting because this is Numberphile-quality content.
Nice video! You seem to know a lot about the maths behind the rubik's cube, so I was wondering if you would ever cover some more advanced abstract algebra on your channel? Personally, I think it would be pretty cool if you did.
Gripping. Fascinating. Brilliant. Thanks for sharing. John
Jperm: If you ask me, thats a pretty great upper bound Me: No, its a nice upper bound 7:24
Do jperm do 69?
This is some top notch audience-aware content that also feels like you’re branching out into new kinds of content without betraying your audience at all. We’ll done! Excellent video!
One of my professors in college was on the team who found this out! He showed me the program he wrote. It was super cool!
I think google's super computers were used for like 2 weeks
this video must've been alot of work!!! congrats on the result, I liked it very much :)
Do you have a (public) discord server? I feel like you could make a good server :)
Fr id love to see that
Yo me too
Sameeeee
He has one But It's only for his patreons
Yeeeeaaaaah
I’d rather watch the gods number of Jperm ads. Also Jperm I used your code on speed cube shop and I got the Unicube rs3m, skewb, and more for 40$. Love you dude, your probably not going to see this or reply to this but you inspired and helped me with cubing, and I try to do the same but I can’t explain it as good as you so I send my friends videos of yours. Before you know it they are cubers! You explain things so good with your voice and tone. If you were your my math teacher I would be a mathematician by now! Love you in advance, Stan (Ethan lol)
thanks so much for this one. i thought i knew enough about god's number, but you shared even more interesting fact about the history!
I understood very well as u so clearly explained it. Thanks a lot.😊 I will never look at a 3 by 3 cube the same way again.
J Perm uploaded video on 2:00 AM (India), then too we Indian gang will watch it because it is of _J Perm_
I come back and rewatch this video after one year to review my cube theory. This is definitely one of the best cubing video ever existed
That video is outstanding! Good job!
A+++ video. Love the documentary approach!
0:02 That went real quick
WHO LOVES J PERM
Not tperm
@T Perm 1857 i would still be happy when u were the pll on my pb
ME
@T Perm 1857 😂😂
Meeeeeeeeeeee
i really love this video, so much so i'm gonna recommend it to my dad who thought about the concept of god's number as soon as we talked a bit about cubing
amazing video, combines the mathematical logic with the cube's algorithmic solves
Now we need the devils algorithm
devil’s algorithm is taking the cube apart and putting it back together
It's similar to the devil's three-way
It exists but it is very long
I was literly thinking about that well watching this
"Step 1: solve the cube in 20 moves or less"
I actually interviewed one of the people that worked on this (Tomas Rockcki) . Which was interesting. I didn't ask him specifically how his way of finding God's Number worked, but I did ask generally the steps he took to find it. I didn't ask him the following question at the time, but I think it is a good question so I will ask it here. Rather than splitting the cube's solving into two steps like Kociemba, and then doing what Michael Reid did by optimizing the first part in order to assist the second portion, wouldn't it be better if you just ran a breadth first search from every one of the unique states on the cube? That way you could do it all at once, and since Breadth First Search guarantees the shortest possible solution, the longest of the ones you get is God's Number. You also wouldn't have to do it 43 quintillion times, since if you did it 43 quintillion times, you would find that many of the states lead to other states. Then it would be redundant to run a separate breadth first search from those states, since you already know their shortest solution (it is the portion of the solution that leads to that state that comes after you reached it). I think this would work, and it also wouldn't require you to run like 43 quintillion searches. Not that the actual solution did, but I am saying this would also work. What do you think?
That's interesting. I think what would happen with the simplest version of this (going up to 20 moves) is you'd eventually have to do on the order of 10^22 things, since there are that many possible move sequences up to length 20. That sounds like too much? Most positions would be found after 18 moves which is on the order of 10^20 combinations, and maybe beyond that it's more feasible to try a different strategy. Of course you can add in optimizations to deal with symmetry and pruning repeated positions. With that I'm not sure how feasible this becomes.
The main problem with your breadth-first search is, you have to find enough RAM to store all the intermediate state. I.e., you have to store information about 18 cubes after just 1 step, and 18×15 cubes after 2 steps. The RAM requirement gets unimaginatively huge, very very quickly. Think of it this way. You point out that you don't need to do 43 quintillion searches, because every state you've already reached, you can skip in future. But _how do you know you already reached a given state?_ You have to store that information! At least 1 bit about each state you've reached (the "have we been here yet?" bit, 1 or 0.) And 43 quintillion bits is over 5 million terabytes. Which is kind of a lot. And that's the bare minimum, if each position requires remembering just a single bit of information. I'm guessing it would require more than that, like a move count. There are a bunch of 'hard' problems in computer science that would become much faster if only we had unlimited storage with zero latency. Unfortunately in the real world you have to design algorithms for _both_ CPU cycles _and_ RAM use.
Damn! As you were talking in the first minute I was thinking about algorithms for calculating shortest paths, like in graph theory, and then you go and talk about upper bounds and lower bounds. Seems kind of related in an odd way. Didn't expect that.
Great video! Keep up the amazing work! Love from Kansas
Hello Jperm I’m Roshan! I’ve failed cubing three times First time I left it Second time also I left but 7 months ago, I finally solved it, but I still was 5 min solver and that’s when I saw your video on f2l, thanks u so much, I’m now a sub 20 solve. 3 yrs ago I left it, which was my try. 2nd time was 2 yrs ago . I also left cubing 7 months ago. So now after 7 months I’m watching this video. You’ve inspired me to be cuber. And now I have a cubing channel called RSJ Cubing. Thanks for inspiring me!
no one asked.
Cube after stage 1 of Kociembas Algorithm reminds me of square 1, also its similar because on square 1 if you do small move on U or D it stays in cube shape.
The main difference is on sq1 you can't do F2 or B2, but it's still super similar since instead of F2 you can just do something like U' D R2
Super interesting! But I wonder something, for a given scramble, do we have a method to find it's shortest solution apart from brute forcing ? And also, with the clever reduction to about 2 billions scrambles possible, it should be possible to write the optimal solution for each one of them in a database < 500GB, so we could get it instantly.
I REALLY liked this sort of video, please do more!
no one: God will just switch the stickers around
He would be able to Make it So the Colours are correct. He won't Need to do any thing. He just needs to say it and it will be right
@@brayden2983 are you aware of the God's paradox? It states: If God is omnipotent, then Can he create a rock so heavy, that even he himself can't lift it?
@@brayden2983 yup
@@diskritis2076 confusion
now what we need to find is "how many scrambles cant be solved in 19 moves"
"How many scrambles require 20 moves"
Great explanation, I now understand God's Number far better! :)
Wow I always loved cubing and mathematics permutations and stuff This mixed both wonderful video thanks a lot🙋
You can make all possible algorithm with in 20 move starting from 1 move by using 20 nested for loops Just think about number system You have 18 possible moves to creat a algorithm and there are 10 possible digits to make a number in decimal system Also there are hexa decimal system where we have 16 possible digits..... 5:13
The superflip is probably the simplest 20 moves combination out there.
I’m pretty sure I heard a Zelda theme in there and man, is it perfect for this kind of video 👌🏽 pretty cool stuff as usual dude 👏🏽👏🏽
Keep posting and keep surprising everyone j perm ... You are my favourite KZheadr
3:58 wheres the M moves at
As a mathematics university student, I feel like this could be solved as an abstract algebra problem. We have 6*9=54 faces, so what we have to consider is a subgroup of S_54 (the group of permutations of 54 objects, in this case the cubes colors) that is finitely generated by the different rotations. And I'm sure you could even use the symmetries to reduce it even further. At that point, this could be even used as a mathematical research paper for a bachelor or something like that
Who would win? 1 mathematics bachelor's student, or 3 decades of work by career mathematicians?
@@aime_33 I'm not saying it is easy, I'm just saying that 1. probably not that many mathematicians are interested in this particular problem, and 2. this could be a potential way to transfer this problem to an area that has been studied much more thoroughly. Algebra, especially finite groups and rings, have been studied to the point that we have classified all finite groups. However, if you are not specialised in the field of algebra, you only know the basics, I for example would need at least a year of research to understand enough about groups and the specific problem to at least try to transfer it in a way that is helpful. And sometimes the easiest solutions are the hardest to find, a fresh pair of eyes can be the thing to get you on the right path
woah that was awesome! I've always wondered how they found it.
I love these kind of cube theory videos.
I just learned OLL and PLL. Now I’m working on F2l and I am sooo confused I gave up in five minutes.
It gets easier Dont give up if you’re enjoying it!
@@jj7546 ok I’ll keep trying! 😀
I took me days to finally get it, but it’s worth it!
Yeah I don’t understand F2L at all lol
You learned full OLL before F2L?
Imagine 1 year without J perm's video
i guess i would die
The crazy search for god's number aside this is a really well made video! Thanks for this :D
that sign off was beautiful. You may have a knack at making explanation videos tom scott-ish style
The new Cubing Historian
Best video on God's number ever! Seriously, you covered it in a much more engaging way than anyone I've come across so far.
I love these types of videos!!!
The thing about solved cubes: there's 4^5 (1024) distinct solved states, since five of the center pieces can be in any of four orientations (the sixth faces' orientation is fixed once the other five are determined, similar to how the eighth corner orientation is fixed once the other seven have been determined)
This is not pucture cube and center orientation dosen't matter.
Wdym theres literally just 1
12:26 Me: Hey that’s familiar...
J Perm: “That would be 69.” Me: “WOW NOW THATS HOW YOU SOLVE IT!” THANKS SO MUCH FOR 100 LIKES!
"That's a pretty great upper bound"
@@anonymousman4419 One might even say it's... *nice*
He lied, the worst case AUF is 2 lol he cheated to make it 69 lol
@@dpage446 g perm?
@@cavsprod1456 I'm talking about AUF
Nice video, can't wait for a God's number in a 4x4 next!
This is accually a great video You are really good explaining, that's why wheen I want to learn something I come here
7:05 nice
Imagine having 43 quintillion 3x3s to actually show 43 quintillion scrambles in one image.
I came up with this question, its like the oppostie of the gods number. I was thinking if someone needs to solve a cube but for some reason he doesnt want to and tries to take as many moves as possible, there is one rule: If you come to a permutation you halve already seen, you can not do a move that brings you to another seen permutation, if not possible you have to avoid this permutation. What would be the maximum amount of moves you could do (the starting state may be schosen to get a longer answer) after which it has to be solved? I was thinking about it but i got stuck very fast.
Hmm thinking about it for a while, a possible approach could be to group the 43 quintillion possible states of the cube into superflip groups. The upper bound for this move number would be all the permutations of the cube, if it was possible to chain up all the permutations by moving one move to reach the next permutation, eventually ending at the solved state, without repeating any permutation. Since any state can reach any other state in 20 moves or less, with the superflipped position being the state "furthest" from the current position, a systematic way of working thru the states of a rubrics cube could be to start from a "scramble" which is one move from solved, superflip the scramble, add another move, superflip it and so on, taking care that there is no repeated states in the groups. A likely thing that might happen that we find there are pass thru states which you have to reach to reach the more obscure states that show up in many groups that would limit your number.
This reminds me of computer chess endgame tablebases, and how they are made a manageable size by using symmetry and reflection optimizations.
7:41 of course jperm does a j perm
If the WCA made a competition for KZhead channel you can be sure this man will win.
amazing video man, also thanks for mentioning super mario galaxy 2, the best game ever
This prob took forever!!!! You are so hardworking bro!!! U desrve the 1 mil subs!!!
17:54 That was perfect 👌👌😱
7:18 jperm 😐 😂
I'm a newbie at the rubiks cube and i am so happy to get a average of 45!! and still improving. I was thinking about buying those budget 4x4, is it better to get the mfsj meilong with magnets? or is it still okay without the magnets.
Amazing story and video!
My parents hate me cubing, because apparently it is addictive and keeps me from doing my math homework. Now I will show them this.
Lmfao
Your parents Are mad at you for spending all of your time doing sports instead of doing Your Physics Homeword, Just Play Billiards
@@brayden2983 Wonderful idea
*What confuses me most about this video is the people who dislike 🤔*
This is somehow very inspiring!
Can you make a video on a holiday Cubes list for the best gifts of this season?
*The dislikes are from the people who dont believe in god*
If J Perm didn’t exist we wouldn’t know there was such thing has God’s Number
Thanks for that explanation
Hey J Perm great video, im just wondering what you mean by each move you make increases the amount of positions exponentially. When you do a move isn't that 1 new position. Than if you do another one it is 1 more new position. Making it 1+1=2 new positions by doing 2 moves. Isn't this a linear growth?
The possibilities grow exponentially!