I think it would've been good to explain how we know there are 43 quintillion total possible states of the cube, as that was a fact used to prove earlier lower bounds.
@@danielbulletcubing In this video you still haven't given an explanation why (at 2:32) «only one-twelfths of all of the Rubik’s cube scrambles are actually solvable» ("its lowkey just something that everyone knows»). Are you serious?!?
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@@borisvik9989 I know it, but I'm not everyone. And I don't remember the exact prove. So would be useful to explain.
When I did my first research project for my bachelor they hammered in the importance of building on previous results. Its good to try your own approach, but research is a collaborative tasks where you need to communicate and build on each others results. This video illustrates this really well.
This also means that any valid starting position can be changed to any valid destination position in 20 or fewer moves. Good luck figuring out those 20 moves. 😎 Great video.
@@grnarsch5287Since all pieces of the same type(corner, edge, center) are symmetric and identical in all ways(I don’t think I should have to prove that, unless you want me to) there is no difference a “solve” and any other valid position due to substitution property of geometry. It should be about as simple as that.
Well, in fact it's equivalent to solving at any position. Just change the map the colors of the target position to the colors of a solved cube, and the colors of a solved cube using the same mapping. Then solve the cube.
Nicely done! Regarding the last part """scrambling the cube for 10 min better than just 1min is not true because you're just cycling through previous positions""". I disagree! Think of a 1D random walk, sure enough in N steps you can reach a maximum distance of N, but if you pick a left or right step randomly, the distance will only grow as sqrt(N). The analogy here would be a random walk along a circle, and indeed once sqrt(N) becomes of the order of the perimeter P of the circle, then you don't gain additional mean distance w.r.t your starting position, but this only happens for a number of steps proportional to N~P^2. I would expect something similar for the rubik's cube, though the symmetries of the move may alter that quadratic power. It should be easy to run a Monte-Carlo simulation applying random moves to a solved starting setup and plotting the average length of the optimal solution from the resulting cube to see how many random moves are necessary to get close to the average solution length that can be determined from the table you showed (where the distribution is very skewed, so the average should like around 18 I guess). I wouldn't be surprised then to see that it takes quite a bit more than 20 moves to get there, so the 10 min scramble may not be completely overkill afterall :).
Some months ago, I did a presentation on the rubik's cube to my company. Part of it was explaining the process of finding god's number. Really cool to see other people with the same interest! Very nice documentary 😊
I gave a like for popularizing the topic (albeit with the left hand, which in the terminology of the fingers-tricks 3x3 Rubik's cube is denoted as t). I expect the topic to develop over time (t), because the story about the G-d number depends on what is considered the first move of the solution. There are several metrics that determine this. You only told about the G-d's number in one metric of half a turn (HTM). The story about another G-d's number in the metric of quarter a turn (QTM) is no less fascinating, because it was found only 4 years later, in 2014. But there are still unsolved problems. For example, the optimal solution, what is it? It is clearly not in the two above-mentioned metrics of movement. And how to calculate the G-d's number for it? I have never understood why the rules/standards for counting turns follow the "range of motion metric" and not the "efficiency metric". (c) Anthony Snyder.
Not only does something like R L mean there are only 12 possibilities for the next move, its also the same as L R which technically is a completely new combination
yup! has to use moves only in that move set. (thus only double turns) less things to check! "the most optimal" was not really sought after back then - it was really just, given that we won't make our computers spend 50 years on this calculation, what's the best that we can do?
Could another solution be what is the minimum moves required to make a rubix cube seem scrambled to most people? Like they can’t just see which moves you did and reverse them? Edit: because the true solution would be just undoing the moves, so if most people considered a cube to be scrambled after a sequence of say 8 moves, couldn’t the 8 moves to undo that be the answer?
well, here we’re just trying to mathematically and scientifically calculate the minimum number of moves needed for any possible combination of the cube. but yeah, that would be a subjective take on it
@@danielbulletcubing Sure: When I hear "set theory" I'm thinking of the ZFC axioms, transfinite induction, continuum hypothesis, Gödel's Incompleteness Theorem - all kinds of really foundational math. So I didn't know if you were referring to that, or whether "set theory" meant breaking the problem space into various sets that are then handled with different methods.
@@modolief I am not familiar with the papers, but a lot of set theory has overlaps with combinatorics and stuff like graph theory (e.g. I first heard of Ramsey Numbers and similar in a set theory course before they came up in the others)
he went through every 18 move solution after g1 and checked if either of U2 R2 F2 B2 took the cube to another 18 move state, it didnt, which means you can invert the last move before reaching G1 to go to a 17 move state
Also, when we'll find a method for the optimal solution of any scrambles, solves would have to be arrenged by the number of moves (fastest time to solve a 19-mover, etc). Otherwise someone could have like a 15-mover and no one could beat that unless they're lucky too
good point! although - considering 2x2, which most optimal solutions can be predicted (at least up to 6-movers), 4-movers and 6-movers are still regarded as "2x2". I guess luck will always be present. Maybe have a rule of any scramble has to be solvable in more than 15 moves, like the 4-move rule for 2x2?
God's number should really be God's numberS, since every size has a different one. 1x1 is trivially 1 2x2 is 14 quarter turns 3x3 is 20 quarter turns God's numbers for 4x4 and above are still unknown. That still excludes 4D cubes, and other polyhedronic puzzles (like the pentaminx).
true true, but the term "God's Number" is usually referring to that on the 3x3, whereas you'd have to specify "2x2 God's Number" for the 2x2. similar to how the standalone term "Rubik's Cube" refers to 3x3 and not the 2x2?
😂 Who would have thought that after so much work… That God’s number is actually just the number of turnable pieces on the cube 😮? Of course, I am assuming that this is absolutely just a coincidence, however, it would be very interesting to see what God’s number is on different cube sizes such as super cubes. I wonder 🤔 if any pattern can be found, considering odd and even numbered cubes, being that all odd numbered cubes have fixed centers in the middle while even ones do not. Such as the 2x2 ice cube, and the Rubik’s Revenge 4x4, and so on. I found that very ironic that the 8 corners and 12 edges add up to exactly 20 turnable pieces 🤔🤷🏻♂️
I am willing to bet all my money on the fact that the 3x3 cube is uniquely special in that it is mostly likely the only cube size that has the same number of turnable pieces equal to it’s God’s number.
well, the way i phrased it, i said “the minimum number of moves needed to solve any scramble”, e.g. 2 moves can’t solve any scramble, 3 moves can’t solve any scramble, it’s only 20 (the lowest) that can solve any scramble. i see where this could be misleading though!
@@danielbulletcubing "2 moves can't solve any scramble" is wrong tho, there's a bunch of scrambles that can be solved in 2 moves. it's minimum 20 moves to solve EVERY scramble but maximum 20 moves to solve ANY scramble.
The reason its called God's number is because that's the number of moves an omniscient diety would make to solve the cube, not because you'd need to be omniscient to find that solution- i think you were making a joke but the real explanation is worth having :)
that's easy, to solve the cube, you need the same amount of moves you spent to scramble the cube. just unscramble it the exact order in reverse and you're done! (I still didn't watch the video)
that’s one of the main ideas of the video LOL: if you use 10483 moves to scramble the cube: it’ll still be solvable in under 20 moves for its most optimal solution
There's an easier way to prove god's number is greater than 2. Give me a scramble, and if you can't solve it in 2 moves, then god's number must be greater than 2.
well yeah, but the method i illustrated can be systematically applied to larger numbers by simple calculations (although be cautious of repeats! combinatorics skills go brrr), but i don’t think you could just take a look at a scramble and be like “yeah no that, that can’t be solved in 14 moves” which makes a systematic method more rigorous!
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you missed the most important part. how the algorithm worked that found the shortest solutions. there is a video about the involved graph theory stuff on youtube. without that part this video is virtually useless
i do not think so. 2 moves can’t solve any scramble. 3 moves can’t solve any scramble. the minimum number of moves needed to solve any scramble is 20. maximum would just be positive infinity
yes! you would be correct! except that’s not the statement i said. you’re saying “the maximum number of moves for the shortest solution for any scramble” is 20 moves, which is right. however, i said “the minimum number of moves needed to solve any scramble” is still a valid statement. changing “min” to “max” in this case would yield a false statement: “a the maximum number of moves needed to solve any scramble.” in this case i could use 3 billion moves to solve a scramble and that’s still not the maximum.
I think it would've been good to explain how we know there are 43 quintillion
total possible states of the cube, as that was a fact used to prove earlier lower bounds.
good point. I should add in a card - I made another video explaining just that a few years ago, forgot to do that when publishing-
th-cam.com/video/sAGxXEXv4iw/w-d-xo.html here it is by the way!
@@danielbulletcubing In this video you still haven't given an explanation why (at 2:32) «only one-twelfths of all of the Rubik’s cube scrambles are actually solvable»
("its lowkey just something that everyone knows»). Are you serious?!?
@@borisvik9989 I know it, but I'm not everyone. And I don't remember the exact prove. So would be useful to explain.
This is a really good and well-researched video, more people need to see it
When I did my first research project for my bachelor they hammered in the importance of building on previous results. Its good to try your own approach, but research is a collaborative tasks where you need to communicate and build on each others results. This video illustrates this really well.
This also means that any valid starting position can be changed to any valid destination position in 20 or fewer moves. Good luck figuring out those 20 moves. 😎
Great video.
Yeah! Thanks :)
Why does it? I would guessed so. But whats the prove? Im just not able to understand how the symetrie of a cube works
@@grnarsch5287Since all pieces of the same type(corner, edge, center) are symmetric and identical in all ways(I don’t think I should have to prove that, unless you want me to) there is no difference a “solve” and any other valid position due to substitution property of geometry. It should be about as simple as that.
Well, in fact it's equivalent to solving at any position. Just change the map the colors of the target position to the colors of a solved cube, and the colors of a solved cube using the same mapping. Then solve the cube.
@@uthoshantm Exactly. Substitution property for the win.
English is not my third leg but this video was a great
As a total non-cuber that was a REALLY good explanation, made it make sense for me
Yay! Love to hear that!! 😄😄
Nicely done!
Regarding the last part """scrambling the cube for 10 min better than just 1min is not true because you're just cycling through previous positions""".
I disagree! Think of a 1D random walk, sure enough in N steps you can reach a maximum distance of N, but if you pick a left or right step randomly, the distance will only grow as sqrt(N).
The analogy here would be a random walk along a circle, and indeed once sqrt(N) becomes of the order of the perimeter P of the circle, then you don't gain additional mean distance w.r.t your starting position, but this only happens for a number of steps proportional to N~P^2.
I would expect something similar for the rubik's cube, though the symmetries of the move may alter that quadratic power.
It should be easy to run a Monte-Carlo simulation applying random moves to a solved starting setup and plotting the average length of the optimal solution from the resulting cube to see how many random moves are necessary to get close to the average solution length that can be determined from the table you showed (where the distribution is very skewed, so the average should like around 18 I guess).
I wouldn't be surprised then to see that it takes quite a bit more than 20 moves to get there, so the 10 min scramble may not be completely overkill afterall :).
yes!! great explanation. thank you so much for pointing that out!
Some months ago, I did a presentation on the rubik's cube to my company. Part of it was explaining the process of finding god's number. Really cool to see other people with the same interest!
Very nice documentary 😊
A grand viewing, sir! Thank you!
wonderful to hear!
I gave a like for popularizing the topic (albeit with the left hand, which in the terminology of the fingers-tricks 3x3 Rubik's cube is denoted as t).
I expect the topic to develop over time (t), because the story about the G-d number depends on what is considered the first move of the solution.
There are several metrics that determine this. You only told about the G-d's number in one metric of half a turn (HTM). The story about another G-d's number in the metric of quarter a turn (QTM) is no less fascinating, because it was found only 4 years later, in 2014.
But there are still unsolved problems. For example, the optimal solution, what is it? It is clearly not in the two above-mentioned metrics of movement. And how to calculate the G-d's number for it?
I have never understood why the rules/standards for counting turns follow the "range of motion metric" and not the "efficiency metric". (c) Anthony Snyder.
Thank you for this summary very well explained!
Magnificent - Looking forward to future videos!
Enjoyed very much even though this topic is completely new to me.
wonderful! speedcubing is a cool world - but the theory behind it is every cooler :)
Not only does something like R L mean there are only 12 possibilities for the next move, its also the same as L R which technically is a completely new combination
this was addressed in the video, no?
8:29 wait so were computers told to never break that moveset bc the optimal solution after htr (G3) often breaks the moveset, such as in R L U2 R’ L’
yup! has to use moves only in that move set. (thus only double turns) less things to check! "the most optimal" was not really sought after back then - it was really just, given that we won't make our computers spend 50 years on this calculation, what's the best that we can do?
I never imagined it took until 2010 to get to this result.
MVP: Most Victorious Player
very good video, keep it up
thanks man!!
I was actually discussing this with a friend the other day!
We had a question
Is R2: 1 move or 2 moves?
Is E1: 1 move or 2 moves?
yay!! it’s interesting, isn’t it?
For HTM: R2 is 1 move, E1 is 2 moves. God's numbers for HTM is 20
For STM: R2 is 1 move, E1 is 1 move. God's numbers from STM. Is 18 to 20
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letssss goo :) giveaway soon!! (when I make the video LOL)
underrated
thanks dude :)
Could another solution be what is the minimum moves required to make a rubix cube seem scrambled to most people? Like they can’t just see which moves you did and reverse them?
Edit: because the true solution would be just undoing the moves, so if most people considered a cube to be scrambled after a sequence of say 8 moves, couldn’t the 8 moves to undo that be the answer?
well, here we’re just trying to mathematically and scientifically calculate the minimum number of moves needed for any possible combination of the cube. but yeah, that would be a subjective take on it
Great video man
this is an amazing video, good work!
The video is rly cool, but i probably have to rewatch it to understand it
Great job!!! Very interesting i always wondered how it was figured oit.
How was set theory used in the solution?
uh, is there a particular point of confusion that you have? set theory is kinda just scattered throughout the entire process
@@danielbulletcubing Sure: When I hear "set theory" I'm thinking of the ZFC axioms, transfinite induction, continuum hypothesis, Gödel's Incompleteness Theorem - all kinds of really foundational math. So I didn't know if you were referring to that, or whether "set theory" meant breaking the problem space into various sets that are then handled with different methods.
@@modolief I am not familiar with the papers, but a lot of set theory has overlaps with combinatorics and stuff like graph theory (e.g. I first heard of Ramsey Numbers and similar in a set theory course before they came up in the others)
I only need 2 steps: First take the cube apart and second rebuild it.
REAL
How did Reid come up with the conclusion in 13:36 I'm a bit confused
he went through every 18 move solution after g1 and checked if either of U2 R2 F2 B2 took the cube to another 18 move state, it didnt, which means you can invert the last move before reaching G1 to go to a 17 move state
@parabolaaaaa4919's explanation is exactly it!
@@parabolaaaaa4919 thanks for the explanation
Good video man
thanks :))
Also, when we'll find a method for the optimal solution of any scrambles, solves would have to be arrenged by the number of moves (fastest time to solve a 19-mover, etc). Otherwise someone could have like a 15-mover and no one could beat that unless they're lucky too
good point! although - considering 2x2, which most optimal solutions can be predicted (at least up to 6-movers), 4-movers and 6-movers are still regarded as "2x2". I guess luck will always be present. Maybe have a rule of any scramble has to be solvable in more than 15 moves, like the 4-move rule for 2x2?
We already found it and it's not. Human learnable. It's called Kociemba
WOOOO❤
why "god's number" is the # of moves needed for a 3×3 cube, and not, for instance, for a 2×2 ?
God's number should really be God's numberS, since every size has a different one.
1x1 is trivially 1
2x2 is 14 quarter turns
3x3 is 20 quarter turns
God's numbers for 4x4 and above are still unknown.
That still excludes 4D cubes, and other polyhedronic puzzles (like the pentaminx).
true true, but the term "God's Number" is usually referring to that on the 3x3, whereas you'd have to specify "2x2 God's Number" for the 2x2. similar to how the standalone term "Rubik's Cube" refers to 3x3 and not the 2x2?
😂 Who would have thought that after so much work…
That God’s number is actually just the number of turnable pieces on the cube 😮? Of course, I am assuming that this is absolutely just a coincidence, however, it would be very interesting to see what God’s number is on different cube sizes such as super cubes. I wonder 🤔 if any pattern can be found, considering odd and even numbered cubes, being that all odd numbered cubes have fixed centers in the middle while even ones do not. Such as the 2x2 ice cube, and the Rubik’s Revenge 4x4, and so on.
I found that very ironic that the 8 corners and 12 edges add up to exactly 20 turnable pieces 🤔🤷🏻♂️
I am willing to bet all my money on the fact that the 3x3 cube is uniquely special in that it is mostly likely the only cube size that has the same number of turnable pieces equal to it’s God’s number.
I gave a Like in the beginning of the video! And it a good one!
0:02 don't you mean maximum? it's at most 20 moves, not at least.
well, the way i phrased it, i said “the minimum number of moves needed to solve any scramble”, e.g. 2 moves can’t solve any scramble, 3 moves can’t solve any scramble, it’s only 20 (the lowest) that can solve any scramble. i see where this could be misleading though!
@@danielbulletcubing "2 moves can't solve any scramble" is wrong tho, there's a bunch of scrambles that can be solved in 2 moves.
it's minimum 20 moves to solve EVERY scramble but maximum 20 moves to solve ANY scramble.
great video, subbed!
thanks 🤙
WOOOOO
The reason its called God's number is because that's the number of moves an omniscient diety would make to solve the cube, not because you'd need to be omniscient to find that solution- i think you were making a joke but the real explanation is worth having :)
I can solve the 3x3x3 easy. The 5x5x5 still sits on my shelf only almost solved.
YOU JUST ADMITTED ORZ
BANNN
You keep mispronouncing the name "Reid." It should sound like "reed" as in "READing a book."
Thanks for correcting. Sorry for that
that's easy, to solve the cube, you need the same amount of moves you spent to scramble the cube. just unscramble it the exact order in reverse and you're done! (I still didn't watch the video)
that’s one of the main ideas of the video LOL: if you use 10483 moves to scramble the cube: it’ll still be solvable in under 20 moves for its most optimal solution
WOOOO
17:55 wen
14:14 i dont think a 12 bad eo case is good for zz
There's an easier way to prove god's number is greater than 2. Give me a scramble, and if you can't solve it in 2 moves, then god's number must be greater than 2.
well yeah, but the method i illustrated can be systematically applied to larger numbers by simple calculations (although be cautious of repeats! combinatorics skills go brrr), but i don’t think you could just take a look at a scramble and be like “yeah no that, that can’t be solved in 14 moves” which makes a systematic method more rigorous!
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Behold, I stand at the door, and knock: if any man hear my voice, and open the door, I will come in to him, and will sup with him, and he with me.
HEY THERE 🤗 JESUS IS CALLING YOU TODAY. Turn away from your sins, confess, forsake them and live the victorious life. God bless.
Revelation 22:12-14
And, behold, I come quickly; and my reward is with me, to give every man according as his work shall be.
I am Alpha and Omega, the beginning and the end, the first and the last.
Blessed are they that do his commandments, that they may have right to the tree of life, and may enter in through the gates into the city.
you missed the most important part. how the algorithm worked that found the shortest solutions. there is a video about the involved graph theory stuff on youtube. without that part this video is virtually useless
cool! if you could can you drop the link here? i wasn’t able to find anything on youtube.
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Why don’t they call it Rubik’s number? After all God didn’t invented the Cube.
well- don't really know! just a cool name they came up with I guess?
already the intro is wrong,
it is not the minimum but maximum number to solve
i do not think so. 2 moves can’t solve any scramble. 3 moves can’t solve any scramble. the minimum number of moves needed to solve any scramble is 20. maximum would just be positive infinity
@@danielbulletcubing give me any cube, I'll solve it in max 20 moves; minimum will be 0
yes! you would be correct! except that’s not the statement i said. you’re saying “the maximum number of moves for the shortest solution for any scramble” is 20 moves, which is right. however, i said “the minimum number of moves needed to solve any scramble” is still a valid statement. changing “min” to “max” in this case would yield a false statement: “a the maximum number of moves needed to solve any scramble.” in this case i could use 3 billion moves to solve a scramble and that’s still not the maximum.
2:36 a problem is that you're counting R L and L R as two different algs
oops i just watched ahead haha
LOL