# The 20MM (20 Move Method)



## Calamity Strike (Dec 7, 2015)

It is widely known in the cubing community that, a cube, no matter what state it is in, can be solved in 20 moves or less. But it is also known, that this can only be achieved by a computer, well, I intend to change that. Now i know that this has been attempted multiple times by multiple people, and hasn't resulted in anything. But i believe we are overthinking this, i have found something very interesting, (look at the title and you'll see it) that i think may be something completely new, and could result in, if not understanding the method, then getting close to. However, since i am fairly new to cubing, i thought i might see if some more advanced cubers might want to help me with this project, anyone who is interested can add me on skype, where we have a group for this, or, just discuss it here.


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## Mollerz (Dec 7, 2015)

If you really want this to be taken seriously you need to post everything you have currently done. If you haven't really come up with anything, then do so before asking for help.


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## Sajwo (Dec 7, 2015)

What did you found?


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## Calamity Strike (Dec 7, 2015)

Sajwo said:


> What did you found?



I found that, rather than an algorithm, it is a variable method, meaning the method may change, but it is still the same concept. CFOP, for example, is an organized method, meaning you do the same thing everytime: cross, f2l OLL then PLL. But with the 20MM, you may do the steps differently, or in a different order.


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## Goosly (Dec 7, 2015)

You should just peel the stickers off.


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## Calamity Strike (Dec 7, 2015)

Goosly said:


> You should just peel the stickers off.



Takes to long


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## Jaysammey777 (Dec 7, 2015)

or take the pieces out and switch them. 20 pieces total = <20 moves everytime.


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## Calamity Strike (Dec 7, 2015)

Jaysammey777 said:


> or take the pieces out and switch them. 20 pieces total = <20 moves everytime.



Do you know how hard it is to take a thunderclap apart? Or, put back together i should say.


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## Sajwo (Dec 7, 2015)

Calamity Strike said:


> I found that, rather than an algorithm, it is a variable method, meaning the method may change, but it is still the same concept. CFOP, for example, is an organized method, meaning you do the same thing everytime: cross, f2l OLL then PLL. But with the 20MM, you may do the steps differently, or in a different order.



You should abandon your researches at the start then. Optimal solution is nothing more than a random sequence of moves, you won't see the solution till the very last few moves. Try with ~10 moves scrambles and you will se


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## DELToS (Dec 7, 2015)

Calamity Strike said:


> It is widely known in the cubing community that, a cube, no matter what state it is in, can be solved in 20 moves or less. But it is also known, that this can only be achieved by a computer, well, I intend to change that. Now i know that this has been attempted multiple times by multiple people, and hasn't resulted in anything. But i believe we are overthinking this, i have found something very interesting, (look at the title and you'll see it) that i think may be something completely new, and could result in, if not understanding the method, then getting close to. However, since i am fairly new to cubing, i thought i might see if some more advanced cubers might want to help me with this project, anyone who is interested can add me on skype, where we have a group for this, or, just discuss it here.



I'm barely sub-20 on 3x3, I think that I would be considered intermediate, not advanced, but I'll still try to help, and I also have a skype


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## guysensei1 (Dec 7, 2015)

Do you have a method currently or do you want people to find a method with you?


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## mark49152 (Dec 7, 2015)

Is this for speedsolving or FMC?


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## Siddharth (Dec 7, 2015)

Maybe both.


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## RicardoRix (Dec 7, 2015)

So with FMC you have the current best cubing minds taking up to an hour to solve the cube, and the current world record average for this is 25 moves. I think you have a lot of people to convince.


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## irontwig (Dec 7, 2015)

What you're looking for does not exist.


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## Calamity Strike (Dec 7, 2015)

This is just to see if it can be done, in the future it may become a speedcubing method, but i honestly believe that cfop/roux will be faster. It would be very helpful for FMC however. And i don't want to be rude, but i made this thread for people interested in helping, not people interested in telling me it can't be done, so if you don't believe it can be done, fine, but please keep it to yourself. Just a heads up for anybody who doesn't know, you can send me a contact request on Skype by clicking on the Skype icon under my name, and choosing send a contact request.


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## Ollie (Dec 7, 2015)

I wrote a proper answer, but it got deleted somehow.

First suggestion - read up on FMC methods. It is basically what you're describing.

You will find that the best solvers use a combination of techniques, depending on what the scramble looks like. If you break down the solution, it will probably have 'steps' but will not always look like a typical speedsolving method. The solution might use the inverse scramble, block-building, orienting edges, commutators etc.

But optimal solutions tend to not look like anything 'human'. You may struggle to see any sense in those solutions without a computer and a good knowledge of FMC methods, which is exactly what some of the most computer-savvy cubers are doing.



Calamity Strike said:


> This is just to see if it can be done, in the future it may become a speedcubing method, but i honestly believe that cfop/roux will be faster. It would be very helpful for FMC however. And i don't want to be rude, but i made this thread for people interested in helping, not people interested in telling me it can't be done, so if you don't believe it can be done, fine, but please keep it to yourself. Just a heads up for anybody who doesn't know, you can send me a contact request on Skype by clicking on the Skype icon under my name, and choosing send a contact request.



You need to explain exactly what you mean. You're basically just calling for a new method, without a proper knowledge of previous methods for speedsolving and FMC, how they differ, what they're good for. You're saying that people can't do it but you have found something interesting and new, but you haven't actually said anything interesting or new. 

You're saying that the steps of speedsolving methods don't change, but that a new method might exist where the steps aren't always the same, which is what the best FMC solvers do now. 

You've just said "x exists, who wants to help me find it?"


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## irontwig (Dec 7, 2015)

Look, people have a hard enough time to solve a 2x2x3 block optimally. It's not like plenty of pretty clever people have not tried to solve in as few moves as possible.


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## shadowslice e (Dec 7, 2015)

Calamity Strike said:


> This is just to see if it can be done, in the future it may become a speedcubing method, but i honestly believe that cfop/roux will be faster. It would be very helpful for FMC however. And i don't want to be rude, but i made this thread for people interested in helping, not people interested in telling me it can't be done, so if you don't believe it can be done, fine, but please keep it to yourself. Just a heads up for anybody who doesn't know, you can send me a contact request on Skype by clicking on the Skype icon under my name, and choosing send a contact request.



I would be interested in helping but I don't have Skype.

Exactly what *is* this "interesting thing" you have found?

Cause until then, *cough* Snyder *cough* vapourware *cough*

And what do you mean that people are overcomplicating things? We have people here whose job it is to simplify very complex things (like mathematics professors and software engineers) and people whose job it is to solve complex problems (again above) and a lot of them have been trying for years.



Sajwo said:


> You should abandon your researches at the start then. Optimal solution is nothing more than a random sequence of moves, you won't see the solution till the very last few moves. Try with ~10 moves scrambles and you will se



This, however, I disagree with. The moves are not random and there are patterns you can find in them. This is the essential nature of groups within a fixed range.


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## Calamity Strike (Dec 7, 2015)

Ollie said:


> I wrote a proper answer, but it got deleted somehow.
> 
> First suggestion - read up on FMC methods. It is basically what you're describing.
> 
> ...



I'm not saying other people haven't found anything, obviously people have been able to solve the cube in 20 moves, and also, i have a good idea how the method works, but im not positive. I have come close to intuitively solving the cube within 30 moves just by observing how computers solve it. What im trying to do, is find a way to solve the cube in 20 moves, in a relatively short time period, just being able to pick up a cube, and being able to solve it in 20 moves, now your welcome to say this isn't possible, and im not sure it is, but based on what Ive observed, i believe it is. If your willing to help, i can walk you through it and show you, if your just going to say "what you've found doesn't mean anything", I'm not going to waste my time.


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## irontwig (Dec 7, 2015)

30 moves is like a million times easier than 20 moves. And 30 moves is not easy without backtracking and plenty of time.


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## shadowslice e (Dec 7, 2015)

irontwig said:


> 30 moves is like a million times easier than 20 moves. And 30 moves is not easy without backtracking and plenty of time.



This. Just this.

If you want to be able to solve within 20 moves consistently, you're going to have to go a lot more abstract than blockbuilding/NISS/insertions.


/side note

Atm, one way that seems promising to be is to identify stationary points and group cubes in that manner (with symmetries in the same group obviously) then have a look at the inverses of the scrambles and generators to see what patterns there are in them. This would be good for permutation but I'm not sure how orientation would work at this point. I'm currently seeing what happens to this on a 2x2 permutation only solves and if I find a way then I will likely try to extend the basic principles to other cubes.


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## guysensei1 (Dec 7, 2015)

In light of recent 'hey look I found cool new method' threads, *SHOW US WHAT YOU'VE DONE. PLEASE.* 

If you simply put up some claims without any actual material to show for it, we will be sceptical by default, if you actually made something up, show us. Perform a walkthouh solve with your method maybe.


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## Ollie (Dec 7, 2015)

Calamity Strike said:


> now your welcome to say this isn't possible, and im not sure it is, but based on what Ive observed, i believe it is.


What have you observed? Why does what you've observed suggest that there is a method that averages 20 moves or less?



Calamity Strike said:


> If your willing to help, i can walk you through it and show you, if your just going to say "what you've found doesn't mean anything", I'm not going to waste my time.



I didn't say that, I'm just asking you to clarify what you've found. If it's new, interesting and/or good enough, then myself and others will help you. We don't want to waste our time, either.


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## Goosly (Dec 7, 2015)

Calamity Strike said:


> I have come close to intuitively solving the cube within 30 moves just by observing how computers solve it.



Cool. Make a video and show us please.


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## Attila (Dec 7, 2015)

Here is, how to do that:
http://www.keptelenseg.hu/keptelenseg/szuper-gyors-rubik-kocka-kirakas-78867


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## Calamity Strike (Dec 7, 2015)

Ok, what i have found is that, when a computer is solving the cube, it seems to orient certain pieces, then build a block of some sort, almost like ZZ, then, using the oriented pieces, it solves the rest of the cube in 7-10 moves.


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## Ollie (Dec 7, 2015)

A bit of a vague description. But it sounds somewhat like the two-phase algorithm: http://www.cs.brandeis.edu/~storer/JimPuzzles/RUBIK/Rubik3x3x3/READING/KociembaPage.pdf 

1. Orient to <U,D,R2,L2,F2,B2>.
2. Solve.

For example:

D' R U F' D2 L F' D2 L U' F B2 U' R' F' B D' U2 R' F R2 D' F' can be solved:

U F2 D2 F U2 B' // orient edges, preserve some blocks (6)
D2 L' B2 D' L' F2 D' F2 D' F2 U2 L2 U B2 D2 R2 // finish (14)

My knowledge of how it works ends there, it's witchcraft to me.


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## Lucas Garron (Dec 7, 2015)

Calamity Strike said:


> Ok, what i have found is that, when a computer is solving the cube, it seems to orient certain pieces, then build a block of some sort, almost like ZZ, then, using the oriented pieces, it solves the rest of the cube in 7-10 moves.



Good observation!

I highly recommend that you read up on Thistlethwaite (and Human Thistlethwaite), Kociemba (also see my explanation), and Jaap's computer cubing page to see if you've thought of anything that isn't already well understood.

Chances are, there is no easy way for a human to find a short combination of orientation and permutation phases without spending a lot of time searching like a computer (or using a ton of lookup tables).


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## Berd (Dec 7, 2015)

I hope you can pull off what you've described!


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## Calamity Strike (Dec 7, 2015)

Ollie said:


> A bit of a vague description. But it sounds somewhat like the two-phase algorithm: http://www.cs.brandeis.edu/~storer/JimPuzzles/RUBIK/Rubik3x3x3/READING/KociembaPage.pdf
> 
> 1. Orient to <U,D,R2,L2,F2,B2>.
> 2. Solve.
> ...



Ok, so I'm not completely crazy. This is actually part of the method.



Lucas Garron said:


> Good observation!
> 
> I highly recommend that you read up on Thistlethwaite (and Human Thistlethwaite), Kociemba (also see my explanation), and Jaap's computer cubing page to see if you've thought of anything that isn't already well understood.
> 
> Chances are, there is no easy way for a human to find a short combination of orientation and permutation phases without spending a lot of time searching like a computer (or using a ton of lookup tables).



Was this sarcastic or real?


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## Chree (Dec 7, 2015)

Calamity Strike said:


> Was this sarcastic or real?



Lucas is the realest.


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## Ollie (Dec 7, 2015)

Calamity Strike said:


> Ok, so I'm not completely crazy.



Can't say that for certain! 



Calamity Strike said:


> This is actually part of the method.



But seriously, yeah it is. 

If you're interested, I left Cube Explorer running and the first optimal it found for that scramble is 18 moves:

U F' B2 L D' L' U2 R' F2 R' U2 L2 // make lots of pairs and blocks , but not quite at the EO stage yet (12)
F // orients edges (1)
D R B2 U' R' // witchcraft (5)

To me, this makes even less sense than the previous 20 move solution. The first solution is somewhat like ZZ, but the second solution orients all the edges towards end. At this point, it can solve the rest of the cube in 5 moves.

If you read either Lucas's or Herbert's explanations, this will make a bit more sense. But from a speedcubing point of view, if there is an 'easy' explanation to why the optimal and the 20 move solution are so different, then that _would_ be crazy.

Edit: It's based off the inverse solution. *Fun!* Now go and read FMC stuff.

Edit2: Might be a NISS thing? The ending of the scramble is very similar to the optimal solution.


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## irontwig (Dec 7, 2015)

Does anybody know how much searching (on average) CE needs to find a 20 move solution? Should be some orders of magnitude too many for humans.


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## mjm (Dec 7, 2015)

What's the Skype group?


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## Calamity Strike (Dec 7, 2015)

mjm said:


> What's the Skype group?



Its just called cubers, you can add me on skype by clicking on the skype icon under my name, and ill put you in the group.


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## DGCubes (Dec 7, 2015)

Very interesting. I always like to keep an open mind, and if something does exist, it could really bring cubing to a new level. The hardest part (for the speedsolving aspect) would be getting inspection sub-15, but I won't say it can't happen.


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## Petro Leum (Dec 7, 2015)

has anyone tried looking at optimal solutions by computer programs and analyzing all the edge and corner cycles and looking if there are patterns of similar cycles/similar moves in the solution that repeat themselves?

i know i know, i'm just throwing some weird thought out of my twisted mind.


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## IRNjuggle28 (Dec 8, 2015)

I often wish I was more like you, Calamity Strike. I'm the type to be logical to a fault, often at the expense of emotions and optimism, and to not chase whims or uncertainties. If I were in your shoes, I'm sure I'd assume that someone would've already found evidence pointing towards the possibility of a 20 move method if one was possible to find, or even accuse myself of being arrogant for thinking that, as a newer cuber, there was a chance of me understanding something about the cube that more experienced cubers hadn't. Assuming that I didn't immediately dismiss the idea, I'd still be tentative to post a thread about it, fearing being wrong in a way that embarrassed me, or being ridiculed. Like many others on here, I'm skeptical that such a method exists, but I am completely sincere in saying that the fact that you're hopeful enough to think there's a solution and brave enough to post a thread about it inspires me.

One question I have about the possibility of this method is why you think it would take 20 moves? It doesn't make sense that a 20 move scramble would be solvable in 20 moves, but a 15 move scramble would also be solvable in 20 moves and not necessarily less. I think that if there's a method that leads to consistent <20 move solutions that's achievable by a human, it's most likely a method that leads to consistent optimal solutions. I would name your concept "optimal solution method" rather than 20MM. Your choice, though. Good luck with your search and with cubing in general.


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## shadowslice e (Dec 8, 2015)

Petro Leum said:


> has anyone tried looking at optimal solutions by computer programs and analyzing all the edge and corner cycles and looking if there are patterns of similar cycles/similar moves in the solution that repeat themselves?
> 
> i know i know, i'm just throwing some weird thought out of my twisted mind.



Well, that's essentially what in trying to do with permutation for corners using stationary points at the moment.

Basically, I'm grouping scrambles according to stationary points and some other factors (like what cycle the other corners are in) and trying to find patterns in the generators and matrices but I can't spend much time doing it atm cause of college.


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## whauk (Dec 8, 2015)

shadowslice e said:


> Well, that's essentially what in trying to do with permutation for corners using stationary points at the moment.
> 
> Basically, I'm grouping scrambles according to stationary points and some other factors (like what cycle the other corners are in) and trying to find patterns in the generators and matrices but I can't spend much time doing it atm cause of college.



The last days I have read "stationary points" very often in this forum. Is it something else than just fixed points of the permutation? Because the notion of stationary points is usually used in the context of differentiable functions, whereas fixed point is a term for arbitrary automorphisms.


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## shadowslice e (Dec 8, 2015)

whauk said:


> The last days I have read "stationary points" very often in this forum. Is it something else than just fixed points of the permutation? Because the notion of stationary points is usually used in the context of differentiable functions, whereas fixed point is a term for arbitrary automorphisms.



In the context of matrices and transformations on general, it refers to any set of points which aren't affected by the transformation. For example, the line y=x is a set of stationary points for the transformation x=y


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## mark49152 (Dec 8, 2015)

Let me set aside the temptation to write this off as unrealistic, for a moment, and just throw some thoughts out.

Let's suppose the key to finding human solutions that are close to optimal is in avoiding the need to break the solve into phases, whether those phases are to solve subsets of pieces or to reduce to certain groups.

What would it take to have a single-phase solution? 

I would guess there would have to be a metric of some sort that would measure how far the current state of the cube is from being solved. Obvious candidate metrics would be number of pieces solved, number of blocks formed, number of pieces oriented/permuted, etc.

Next, that metric has to satisfy some criteria to be useful for human solving. (1) It has to be possible to calculate the metric quickly enough for a given state, whether for speedsolving or FMC. (2) It has to be possible and practical to see from the current state which moves are preferred for reaching a next state with improved metric. And (3) there must be a linear progression through improving metric values from scrambled to solved - in other words, if it may be necessary to regress by making a move to a state with a worse metric value in order to make bigger jumps forward with subsequent moves, then the search space becomes impractical.

Obviously, metrics like number of pieces solved, number of blocks formed, number of pieces oriented/permuted might satisfy the first two criteria but cannot satisfy the third. And optimal solution length is a metric that would satisfy the third criteria but not the first two.

I have no idea if a suitable metric exists, although my guess would be that the best we could expect would be something workable for FMC, perhaps with some compromises, but not for speedsolving. To my mind it's the third criteria above that really makes it hard to find a suitable metric.


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## SpeedCubeReview (Dec 8, 2015)

Calamity Strike said:


> This is just to see if it can be done, in the future it may become a speedcubing method, but i honestly believe that cfop/roux will be faster. It would be very helpful for FMC however. *And i don't want to be rude, but i made this thread for people interested in helping, not people interested in telling me it can't be done, so if you don't believe it can be done, fine, but please keep it to yourself.* Just a heads up for anybody who doesn't know, you can send me a contact request on Skype by clicking on the Skype icon under my name, and choosing send a contact request.



Welcome to the Forums. Since this is a thread for anyone to post on people can post what they want (As long as it passes the moderators). 

I think people telling you that there isn't a method like you would find with CFOP is actually people trying to help. It may seem like they are putting you down but really its to help you on your quest in a more direct way.


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## shadowslice e (Dec 8, 2015)

ViolaBouquet said:


> Welcome to the Forums. Since this is a thread for anyone to post on people can post what they want (As long as it passes the moderators).
> 
> I think people telling you that there isn't a method like you would find with CFOP is actually people trying to help. It may seem like they are putting you down but really its to help you on your quest in a more direct way.



I think that's he's more refering to posts which say "it can't be done. Stop trying and wasting your time". And I think if people read the thread they would realise that he already said the method won't be like CFOP.


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## adimare (Dec 8, 2015)

mark49152 said:


> I have no idea if a suitable metric exists, although my guess would be that the best we could expect would be something workable for FMC, perhaps with some compromises, but not for speedsolving. To my mind it's the third criteria above that really makes it hard to find a suitable metric.



This would be tough. Even the obvious metrics that you mentioned don't seem suitable. Compare a cube (cube A) that's one T-Perm away from being solved vs a cube (cube B) that's F U R away from being solved:
1) Cube A has 4 unsolved pieces, cube B has 16.
2) All pieces are oriented on cube A, on cube B there are 4 to 2 miss-oriented pieces depending on orientation.
3) This one I'm not too sure about, depends on how you define a block.

The one thing that I can see looks better on cube B than on cube A would be something like "amount of moves that can be performed without decreasing the amount of formed blocks in the cube".


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## Lucas Garron (Dec 9, 2015)

mark49152 said:


> Next, that metric has to satisfy some criteria to be useful for human solving. (1) It has to be possible to calculate the metric quickly enough for a given state, whether for speedsolving or FMC. (2) It has to be possible and practical to see from the current state which moves are preferred for reaching a next state with improved metric. And (3) there must be a linear progression through improving metric values from scrambled to solved - in other words, if it may be necessary to regress by making a move to a state with a worse metric value in order to make bigger jumps forward with subsequent moves, then the search space becomes impractical.



If you aren't familiar with (1) pruning tables or (2) IDA*, I *highly* recommend you take a look at them before going further.

Searching with heuristics is a fairly well-understood subject.
Presumably, if it was easy to find good heuristic that satisfies (3), we would have used it to write puzzle solving programs that generate solutions with almost no work. But so far, no one has found systematic heuristics for a cube that give near-optimal solutions without a lot of backtracking.

For puzzles like the 3x3x3 cube, the best we know how to do is use a few tricks to bring brute force down to the point where computers happen to be able search quickly enough. (But even that breaks down quickly for 4x4x4.)

That doesn't mean that there isn't progress to be made, or that you can't learn from trying. But if you want to make progress in this field, you should at least know the state of the art among algorithms that take your approach.


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## adimare (Dec 9, 2015)

Lucas Garron said:


> If you aren't familiar with (1) pruning tables or (2) IDA*, I *highly* recommend you take a look at them before going further.



Knowing about IDA would definitely help someone come up with an algorithm to solve the cube close to optimally. However, I'm having trouble imagining how knowledge of pruning tables helps when trying to come up with an algorithm that's intended for a human to perform in a limited period of time.

FMC is still in its infancy, you can learn most of what's been discovered from a single PDF and achieve world class status much faster than in any other event I can think of. In other words, there's A LOT of progress to be made. However, it's over ambitious to try to discover a method that consistently produces 20 move (or less) solves (especially if your only insight so far is that "it is a variable method, meaning the method may change"), I'd be happy with one that could get you sub-30 move solves on most scrambles.


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## mark49152 (Dec 9, 2015)

Lucas Garron said:


> Presumably, if it was easy to find good heuristic that satisfies (3), we would have used it to write puzzle solving programs that generate solutions with almost no work. But so far, no one has found systematic heuristics for a cube that give near-optimal solutions without a lot of backtracking.


Yes of course. The point of my post was to speculate that finding a metric (heuristic) that satisfies (3) is the key to near-optimal human solving. I certainly didn't claim it was easy; quite the opposite. Furthermore, it would also have to satisfy (1) and (2), which wouldn't be necessary for a computer solution.

By the way, I'm not working on this, and don't intend to. I was just throwing out some thoughts.


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## cuBerBruce (Dec 12, 2015)

I am going to try to put what the OP is claiming to try to do into a mathematical framework.

Let S be the set of positions that can be solved in 10 or fewer moves. (The value of 10 here is rather arbitrary, but I'll just use this value for this discussion.)

Let G be some subset of the elements of S. (I chose G for "goal". The goal of the first phase is to reach an element of G.) These elements may be chosen based upon some properties of the positions, such as some relationship having to do with the permutation and orientation of the pieces.

Let G[sub]N[/sub] be the set of elements in G that are optimally solved in N moves. (That is, we partition the set G based upon the number of moves required to solve each position.)

We want to find a "method" such that we can show that for every position of the cube, we can reach some position in G[sub]N[/sub], for some N, using no more than 20-N moves.

(And not only this, but we also want this method to be human learnable.)

There are two big obstacles with this.

1. Choosing a set G small enough to be human learnable (the human must know how to optimally solve every element of G). But G must also be large enough to make it possible to accomplish the first phase in few enough moves.

2. Figuring out how to reach an element of G from an arbitrary position in few enough moves. If we ignore the "human learnable" requirement, we "simply" need to show that this is possible.

I think trying to make (2) a manageable size problem is generally going to force increasing the number of elements in G, making the first obstacle worse. Likewise, trying to make the first obstacle manageable is going to tend to make the 2nd obstacle all the more difficult, if not impossible.

In the end, I assume some concessions will need to be made. These could include:

1. Reduce the number of positions that must be solved in 20 moves. If, say, we only require that only 99% of the positions need to be solved in 20 moves, we remove the requirement that all of the millions of 20f* positions need to be solved optimally.

2. Require the average move count to be 20, rather than 20 as the worst case.

3. Relax the move count that is required to be achieved to some larger number (21 or 22 or 23, etc.).


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