# How to solve a Rubik's Cube in five seconds

This week, 14-year-old Lucas Etter set a new world record for solving the classic Rubik’s cube in Clarksville, Maryland, in the US, solving the scrambled cube in an astonishing 4.904 seconds. The maximum number of face turns needed to solve the classic Rubik’s cube, one that is segmented into squares laid out 3x3 on each face …

1. #### Re: Or you could

> I tried. Its pretty hard to find one who can beat the rubiks cube in under a minute....

Something something, girlfriend, something something under 5 seconds.

1. #### Re: Or you could

have you tried R U R' ? That might work if the girlfriend is in the wrong position.

1. #### Re: Or you could

"just go out and get a girlfriend....."

Tried it, got tired after a while - every single one of them seems to be a movie buff, and their common favorite seems to be "gone in 60 seconds" (or much less)...

1. #### I wonder how many people have actually solved the cube?

Doing a cube fast is an impressive feat of dexterity and memory. But it's only dexterity and memory. Is it really that big a deal that a fourteen-year-old can do it in five seconds? I wonder if he actually solved the cube himself, as opposed to finding out how it was done on the internet?

The vast majority of people I know who can do the cube have not actually solved it - they were just taught. In my day, it was via a photocopied crib sheet or a book; nowadays, it's on the internet.

I solved the cube - I actually solved it, from scratch, without recourse to help of any kind - back in 1981. It took me about three months. And yes, I found it useful to dismantle the cube and rebuild it. The algorithms I worked out are not efficient - but because I worked them out myself, they are well and truly stuck in my mind. I can still pick up a cube and do it. Normally takes me about five minutes.

So, I wonder how many people world-wide have actually solved the cube, rather than just learned how to do it from some other source? I wouldn't be surprised if it's a few thousand at most.

1. #### Re: I wonder how many people have actually solved the cube?

Until I read this I assumed everyone who'd solved it did so without help - how naive I was!

An IBM colleague in Nottingham, who'd discovered the Rubik's cube some time before they were on general sale in the UK, was selling them to interested colleagues including me. It also took me about three months to solve it the first time but I didn't dismantle it or move stickers. The second time took a few days, and after that I could do it in around 15 minutes. Then I got bored and haven't touched for the last 35 years or so, although I still have it somewhere.

For a time I was fascinated by the mathematics and realised there was a connection with group theory, although I wasn't clever enough to gain any interesting insights from this. I also wrote some code (on my 1kB Nascom 1 computer) to attempt to find useful sequences of moves - the tools described in the article.

Maybe it's time to get the cube out again and see if I can still do it.

2. #### Re: I wonder how many people have actually solved the cube?

The Git solved it and (almost) immediately lost interest in it. Only repeated it to demonstrate that I had solved it. Always thought there was something strange about the pursuit of speed: lubricating the damned thing with vaseline etc.

Mind you, my then new girlfriend and latterly ex-fianceé thought there was something strange about me waking in the middle of the night to test new strategies with the cube. Took around 2-3 months IIRC.

3. #### Re: I wonder how many people have actually solved the cube?

A friend showed my a way to solve it with two repeated moves.

You have to solved one face first quite easy, then do the opposite four corners with a move that swaps two corners and rotates a third.

Once all the bottom corners are solved, it's easy to solve the faces using another move which cycles three edge pieces only.

I could do it in a couple of minutes usually.

4. #### Re: I wonder how many people have actually solved the cube?

Probably more than a few thousand. But a lot less than the number of people who have learnt a solution from someone else. I solved the cube from scratch in three days, while at school. I forget whether it was a geography or a history lesson during which I for the first time got the cube back to its initial state. My first algorithm for solving the cube took about an hour to perform, and I needed a sheet of densely written notes in front of me. I later learnt to solve the cube in under a minute, but the tricks for doing that I mostly acquired from other people and I was never the class champion in the speed trials that took place in almost every breaktime back then...

5. #### Re: I wonder how many people have actually solved the cube?

@Martin, I had more or less the same experience. First I crafted a wooden model after just having seen an assembled Rubik's Cube. It did the job, but you could not turn it fast enough. So I bought the real thing and found a procedure which worked for 50% of the cases. On failure I just scrambled the cube at random and tried again. Eventually I lend my Rubik's Cube to a friend who was recovering from a brain injury. May be it is still in use in the hospital.

6. #### Re: I wonder how many people have actually solved the cube?

Back in 1981 I was actually in competition with my father to solve the cube, and he beat me by 2 weeks, and even then once he figured it out he refused to show me, I love my father, but sometimes he is a real pain! (yes he is still alive at 91)

So I figured I would get even with him, when they came out with a 4x4 cube I got a couple of them and we re-started the competition, and he beat me again! Ugggg! But I did solve the 4x4 eventually, it took my father about 4 months to figure it out, and it took me 6 months.

Two years ago my adult daughter got me a 7x7 cube for Christmas and I have yet to figure it out. It is devilishly hard, or maybe my brain is getting worn out, but I refuse to give up. Getting old sucks, but I guess it beats the alternative!

2. You could always tell someone that cheated by swapping the stickers as they quickly became loose and fell off. Also if you know how to solve it then it's easy to work out near the end if pieces have been swapped around incorrectly.

I learned to complete it from an A4 set of instructions someone sold me back in the day and I still have them somewhere and practice a few times every year or two to keep the muscle memory working.

I can remember a conversation back when they first came out with a neighbour who in a bit of one-up-manship was convinced she'd completed 5 sides...

1. "I learned to complete it from an A4 set of instructions someone sold me back in the day"

You might want to talk to Graham Marsden, who posted above. But possibly you two already met in the past?

2. #### @hardboiledphil

> I learned to complete it from an A4 set of instructions someone sold me back in the day

Did you ever live in Bristol? Might have been me :-)

3. #### Algorithm./ Technique

Although, as mentioned, it is proved that you can solve a cube in a maximum of 20 moves, it takes a modern desktop computer more than 4.904 seconds to do the calculation (though in cube solving the timing only starts when you make your first move - you're allowed to look and ponder it first).

As I understand it, speed-solvers use a subset of more memorable moves which more typically take about 40 moves in practice - and these methods are far easier and more effective than the books/methods published in the early 1980's e.g. by Patrick Bossert or the math prof's booket from that era.

1. #### Re: Algorithm./ Technique

There is no known algorithm for solving Rubik's cube in the shortest possible number of moves, or even close to it. The proof was existence only, not constructive. One reason is that, for space requirements, they had to throw away any actual representations of the moves that they did find, and another is that the type of coset enumeration that I think they used isn't really well suited to storing this stuff.

1. #### Re: Algorithm./ Technique

I don't know how it counts officially, but a few years ago I did download a very nice Java applet which, given a few 10's of seconds, would calculate a sequence of 20 moves or less to solve any cube position. Probably this site: http://kociemba.org/cube.htm

1. #### Re: Algorithm./ Technique

"I've seen some fast Lego Mindstorms constructions "solving" the cube. Are they cheating by having a desktop plugged in rather than using the programming blocks?"

"I don't know how it counts officially, but a few years ago I did download a very nice Java applet which, given a few 10's of seconds, would calculate a sequence of 20 moves or less to solve any cube position. Probably this site: http://kociemba.org/cube.htm"

Ah, those aren't algorithms. Those are algorithms to find an algorithm, one level higher. An algorithm to solve in 20 seconds would be a series of instructions that took a cube and gave you the moves immediately. What these sorts of programs are doing is computing an optimal set of moves given a fixed state. You give it a different state, it has to do it all over again.

1. #### Re: Algorithm./ Technique

"Ah, those aren't algorithms. Those are algorithms to find an algorithm, one level higher. An algorithm to solve in 20 seconds would be a series of instructions that took a cube and gave you the moves immediately. What these sorts of programs are doing is computing an optimal set of moves given a fixed state. You give it a different state, it has to do it all over again."

Isn't this a case of "6 of one, half a dozen of the other"? The point is, you input the cube's current state and it outputs the way to solve it in in 20 moves or less (which if you want to get technical can then be applied to a mechanical cube turner to perform the feat). Shouldn't matter HOW it gets there, as long as it gets there (sorta like you get the same result whether you use a selection sort, a binary tree sort, or a quick sort).

PS. I once had a Rubik solver (albeit crude) for my Commodore 128 computer.

1. #### Re: Algorithm./ Technique

"Isn't this a case of "6 of one, half a dozen of the other"?"

Well, not really. Firstly, the algorithm does not guarantee to produce the right answer. Secondly there is a very easy algorithm to solve the cube in the shortest possible time: perform all sequences of one move, then reverse them, then all sequences of two moves, then reverse them, and so on. Eventually you will hit the fastest path to do it, although it might take millions of years to do so.

Would you call that an algorithm? It takes more than 20 moves because there's a lot of computation to work it out before you do it. It's obviously much slower than a reasonable human algorithm.

2. #### Re: Algorithm./ Technique

"Isn't this a case of "6 of one, half a dozen of the other"? The point is, you input the cube's current state and it outputs the way to solve it in in 20 moves or less (which if you want to get technical can then be applied to a mechanical cube turner to perform the feat). Shouldn't matter HOW it gets there, as long as it gets there (sorta like you get the same result whether you use a selection sort, a binary tree sort, or a quick sort)."

I know I've already replied to this, but I thought of a better example, one appropriate for IT. You phone up a helpdesk with a problem with your computer. Two things could happen:

1) They tell you what to do to solve it.

2) They tell you to just put your symptoms into Google, and after a few hours of frustrated searching you find a solution to the problem.

In both cases the helpdesk solved the problem, but the second isn't quite what we have in mind when we say 'helpdesk'. Or maybe it is...

1. #### Re: Algorithm./ Technique

Point is, either way, you end up with a solved cube, a fixed computer, or in an earlier example, a sorted list. May not be the optimal solution, but unless utmost efficiency is critical, many times you can get away with "good enough". Selection sort may not be the fastest sort around, but it has its uses when space is tight because it can sort in situ.

2. #### Re: Algorithm./ Technique

This is a good point, and finding the algorithm could be rather difficult.

2. #### Re: Algorithm./ Technique

I've seen some fast Lego Mindstorms constructions "solving" the cube. Are they cheating by having a desktop plugged in rather than using the programming blocks?

3. #### Re: Algorithm./ Technique

There are a lot of problems in which is it intractable to have an optimal solution, but sub-optimal solutions are very tractable. A good example of this is the Travelling Salesman Problem - which is known to be NP-Complete. However, if one accepts that we can accept a solution which is less than or equal to twice the optimal solution, this problem becomes tractable.

Although there may be an algorithm that will solve the cube in 20 moves, the one which solves it in 40 may be quicker from a computational point of view.

4. when people take part in competitive tests, does everyone start from the same starting point?

Or are they given random starting configurations of variable complexity?

It seems to me to be difficult to have a real competition without either having either (1) a known starting point for all or - which may favour some who "know" that configuration, or (2) have unequal starting points

1. "It seems to me to be difficult to have a real competition without either having either (1) a known starting point for all or - which may favour some who "know" that configuration"

As the article said, there are 43,252,003,274,489,856,000 configurations. Some are more amenable to certain algorithms than others, but they won't have much experience with the starting position, with better odds than me claiming you won't win the jackpot on the lottery twice in a row.

2. #### Cube Scrambling

Yes. In each round there is a computer generated random scramble which is solved by everyone in that round.

https://www.worldcubeassociation.org/regulations/scrambles/

5. #### That's the way I figured it out

I think I was 12 or 13 when I first solved the rubiks cube. My fastest time was only 5 or 6 minutes, but I basically used the tool you described. I figured out how to move a single corner piece from point A to point B without impacting any other piece.

6. #### Cube envy

I remember at school in 1980 aged 13, there were two kids in my year who in a couple of days had independently worked out their own algorithms for solving the cube. I was in utter awe at their ingenuity and skill, particularly when they repeatedly clocked up solution times of under a minute using an official Rubik's cube that had been disassembled and all hinges greased for optimal speed. It's very liberating to realise your own averageness at an early age: I've been happily underachieving ever since :-)

1. #### Re: Cube envy

I was leafing through a Rubiks Cube solution book at a bookstore a year or so ago and realized (or reaffirmed), in spite of my degree in "Computer Science", I'm not a mathematician. My brain is really, really not wired that way. I never did figure out the cube in the 1980's, and probably won't even if I live until the 2080's. Too boring to me. But building or optimizing a cube's guts so it turns faster? That would be way more interesting than solving the cube itself. To me, anyhows.

7. My best was 43 seconds, fastest in my school. There were only a couple of other guys who could solve it, and it took them well over 10 minutes.

I used to have everyone coming to me at break times to solve their cubes for them. I was doing dozens of cubes a day. At one point I developed RSI and a swollen index finger. My doctor and my mum banned me from the cube for a while.

I can still solve it, but takes me probably about 2-3 minutes now.

Kudos to these speed freaks.

1. Yeah right. Teenage boy gets RSI from a Rubik's Cube... At least that's what you told your mum you were doing, right?

8. #### Bah!

You don't need a screwdriver. Just place the pad of your thumb over the middle piece and pull up. Then you can simply snap it back into place. By doing this carefully, no-one will see you do it. Practice this move until you can do it quickly and out-of-sight.

Now wait for the time some nitwit hands you their cube and challenges you to scramble it and time the solution. Do so, but as your last move pry out one cube and invert it. Turn back to the owner as you give the cube a couple more twists (for obfuscation and misdirection).

Hey presto! Unsolvable cube puzzle.

9. Solving the cube is easy. You just start from a simple case and then work your way up to more complicated cubes by induction.

10. #### No screwdriver required

I made a tenner when I was 7 or 8 at Christmas. Bet all the adults I could show them a completed cube in 30 seconds if they handed me a messed up one. I had two that year ;)

11. #### Why?

Seriously.... why????

12. #### The Job Interview

Interviewer:

What can you do

Interviewee:

Solve a Rubik Cube in <5s

Interviewer:

What else can you do ?

Interviewee

Erm.......

13. #### Here's the problem with this "record"

With a random scrambling of the cube, some solves are easier than others, so it is chance if you get an easier solve that takes less time.

Back when the cube was new I got one and got a booklet that showed various "tools" (using the article's terms) you could use toward solving it - yeah I should have figured them out on my own, but I was an impatient teenager! When I got good at it I could sometimes solve in under 20 seconds, but usually 30 was my average. The fast solves were just lucky in that I needed fewer tools to unscramble it.

Obviously to beat 5 seconds you not only need many more tools than I was using, but to execute them faster as well. But it will still remain up to luck how many tools you need (or tools with fewer individual moves required than other tools) If he got a different cube it might have taken him a couple seconds longer, if someone else who is as skilled as he is (if there is anyone, maybe he's really the best but the record isn't 100% proof of that) got that same pattern they would have got a similar time and owned the record instead of him.

The 15 seconds of inspection probably helps determine where to initially attack, but I found that I rarely had to stop and look at the cube during the solve. It is like anything where as you become good at it your vision becomes "faster" so you can instantly recognize the next pattern you want to attack and go from one tool sequence to the next. Perhaps with the more complex tools he would be using the inspection is more beneficial. What I was using were very simple sequences of 3-5 moves to do one thing, like flip an edge or rotate three edges, twist or rotate three corners, and so forth. He may be fixing all 8 corners in a single tool to start - inspection would really help there.

1. #### Re: Here's the problem with this "record"

Sounds like cube envy to me.

This is an impressive record, so let the kid have it.

1. #### Re: Here's the problem with this "record"

Cube envy? I already said my fastest times (when I got lucky with the initial setup) were almost 4x slower than him so I'm not claiming I was ever remotely in the same class (and I couldn't solve it at all now without re-learning everything, since I haven't touched one since)

All I'm saying is that there are probably others today who are as good or even better than him, who simply didn't get as lucky with the initial conditions in a timed run as he did. That matters. A lot.

14. #### My Rubik's cube story

I never had the patience to solve a Rubik's cube, but there was a boy in my wee sister's class at school who was world champion. He even took a gap year and went around the world, paying for it by entering speed-cubing competitions. The thing that I never thought to ask was how he knew he'd finished, as he was almost completely colour-blind.

15. #### The most impressive solve I've seen...

... is the end of Derren Brown's Infmaous show - NSFW if you've got the sound turned on (which you need).

Once again, the bugger suckered us...

Vic.

16. #### I can remember

In the final days of my high school career seeing a kid that had read a book about Rubiks Cube solving one behind his back. It took him about a minute I guess, and when he was done even he was impressed. Me, the only way I've ever "solved" a Rubik's Cube was to peel the stickers off it, and stick them back on. The cheap knock offs had stickers on them. Damned maddening puzzle from my perspective.

17. If you want to learn the basic beginner method for solving the 3x3x3, I have several tutorial sites, all free.. my latest one is www.fixmycube.com and you can also see my 160+ rubik vidoes at www.youtube.com/user/mountainscooter .. I make all the vidoes and animations myself and I do it for free, cause I want to see more people in the world solve the cube!

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