UCLA Sports. All Sections. About Us. B2B Publishing. Business Visionaries. Hot Property. Times Events. Times Store. But all of them ended up creating algorithms.
An algorithm doesn't have to be anything complex - M U M' is all it takes to do something useful. And beginners solutions typically make heavy use of repetition, and combinations of two algorithms together, to achieve a goal.
These then themselves become an algorithm. All three of them used a logical corners-first approach. When reaching the 'edges' stage, it's almost inevitable that you're going to use algorithms. You've joined a fairly small club, I think.
Even in the early days, there were 'cheat-sheets' circulating around schools, so it was easy to give in to temptation. Now with the internet it's even easier, so hats off to your perseverance.
Joined Nov 15, Messages I solved it. I really didn't use any algorithms, formulas or YouTube videos Thanks! KeationianCube Member. Joined May 10, Messages 29 Location Trying to teach my dog to solve mirror cube. EngiNerdBrian Premium Member. Great work. I often enjoy trying to figure out new puzzles intuitively now, turning for hours and hours.
Im confident I wouldn't have been able to come up with the 3x3 last layer solution intuitively at the beginning of my cubing endeavors. EvanTheCuber Member. Joined Apr 1, Messages Nuuk cuber Member.
My mans knows the Devils algorithm. EngineeringBrian said:. ThisNameIsAlreadyTaken said:. Yeah, I too wanted to try to really solve something after I knew the solution of 3x3. I'd like to try skewb as it seems interesting That is super impressive Any chance that you could show some reconstruction or video of your solve?
Joined Feb 17, Messages Devising your own solution is uncommon, at least these days. Most people, like me, are just curious to learn about how the cube works, and don't want to spend lots of time deciding their own solution. Congratulations on solving it yourself! I'd love to see your solution. Owen Morrison Member. What does piece-type mean, you say? When we look at a 3x3x3 Cube, there are three different piece-types: Centers, Corners and Edges.
When we look at a Tangram Cube Extreme which I recently figured out how to solve myself , we see six different piece-types. It's a bit too advanced and off-topic to explain what each piece-type is, or how the Tangram Cube Extreme works for now.. The important part is, when I've figured out how to solve the Tangram Cube Extreme, I noticed that it's best to start solving the middle-layer piece-types F and G. Kinda like solving the second layer of a 3x3x3 Cube, without destroying the already solved first layer.
After I had solved the middle layer intuitively, I came up with a three-cycle for the big B and C pieces. And finally I used an algorithm I already knew from another puzzles to purely three-cycle the E-pieces to finish the solve.
But how do you come up with algorithms? Where both A and B are a single move or a short sequence, and A' and B' is undoing those moves or sequences. These kind of algorithms are usually used to move pieces around three-cycles, five-cycles, double-swaps, etc. These kind of algorithms are usually used to orient pieces without moving them.
The only thing they have in common is that you solve them layer-by-layer, but apart from that the algorithms and steps can differ a lot :. So, that's the theory around algorithm types, but how do we come up with these ourselves? As I mentioned before, I'm no expert, but personally I always try to do some short four or six move sequences and see how it affects the piece-types in the puzzle.
If it does something useful, like swapping pieces or creating a five-cycle, I make a commutators A B A' B' where this sequence I came up with is either A or B , and I use some in-between setup moves to create three-cycles or double-swaps which I can use to solve the puzzle. My big pitfall when I solve puzzles however, is that I sometimes use this entire 3-cycle I came up with for one part of the solve, as a sequence part A or B for another 3-cycle of the next part of the solve.
This means I sometimes have algorithms of over 40 moves long to three-cycle or orient some of the final pieces. Pretty inefficient as you can imagine although I'm still proud to say I've been able to solve some puzzles myself using these long-ass algorithms, which I came up with entirely on my own. It also all depends on the difficulty of a puzzle, and prior knowledge. A 2x2x2 is obviously easier than a 3x3x3, and a 3x3x3 is easier than a 4x4x4.
If you know how to solve a 3x3x3, you are automatically able to solve a 2x2x2 because it's a corners-only 3x3x3. When you can solve a 4x4x4 using a reduction method you can automatically solve a 3x3x3 and 2x2x2.
Your question however, was how people solved a 3x3x3 Cube without any prior knowledge. Not much different than I solve new puzzles tbh. Both 'cases' are easily to overcome by inserting a random piece in the middle-layer edge position to bump the other out, which you can then insert correctly oriented; or by just using the three-cycle of corners algorithm once, and then one of the four corners should be correct.
Still, I personally think it's impressive when people figured out how to solve a 3x3x3 Cube entirely on their own, without any prior knowledge. Chapeau to them for doing so. And it's always cool to see which method they've developed, and how they came up with it like the video I linked of Tony Fisher in my comment of the question.
I was a year-old at school in the UK when the Rubik's Cube first came out, in an old-style A-Level class of 10 students, all of us doing "double maths" Pure and Applied mathematics plus another subject i. At that time, there was certainly no internet, initially no published guides, and very little in the way of external resources for how to solve the cube.
So, although there were few if any guides to help, it certainly wasn't true that we didn't use taught algorithms. The key, though, was that we taught ourselves the algorithms. While there may be a very rare, very exceptional people who can solve the cube "holistically", it was almost immediately obvious that any methodical solving of the cube would need a "layered" approach -- you solve part of the puzzle typically starting with one face and then find combinations of moves that put further pieces in the correct place without long-term disruption of what had already been solved.
The key, then, was to find these " combinations of moves " that could put chosen pieces in chosen places. Initially, this was very much trial-and-error and involved an awful lot of disassembly and manually returning the cube to its starting position -- it was much easier to see what a sequence of moves did when starting from a "clean" cube.
Eventually -- and being of a mathematical bent -- we discovered concepts such as conjugation , commutation and repetition that Jaap Scherphuis talks of in their answer. More complex "sequences" could be created by combining two or more "simple" sets of moves -- sometimes noticing that the end of one simple sequence would "cancel out" the beginning of the next simple sequence e. Of course, there was a trade-off: longer sequences of moves tended to be more "specialised" -- would only apply to particular states of the cube -- and the time taken to "recognise" when one could be used not to mention the effort in remembering them all began to take longer than using multiple "simple", more universal combinations.
By using group theory. Why is group theory useful to solving a rubiks cube? Because it turns out that the Rubik's cube along with rotating it forms a group. Loosely put: Every rotation has an inverse and every permutation of the cube can be realized from every other permutation i. A crucial point of understanding how the Rubik's cube works is understanding that there are subgroups inside the Rubik's cube group and how the rotations and permutations of the different subgroups affect each other.
I firstly place the top corners, then bottom corners so I have all the crosses. Then I solve the top and bottom layers middle pieces simultaneously. Then I am left with the 4 middle layer peices which I solve with my longest algorithm. The theory I went with was that every action was always going to have an equal and opposite reaction so my algorithms generally go in one direction to isolate a piece, then I make one move that changes that piece and usually it will affect others then I reverse the moves to put everything else back.
As myself who is still working on it to find my own ways, would like to put some of the ways that didn't work for me. To be precise it worked ONCE :. It doesn't take too much effort to learn how to solve first two layers, and if you are lucky then the 3rd one will be solved as well. As a young teenager I used this method, and if 3rd layer had errors I would first fix those, and then "repair" the damage I did to the first two layers. With sufficient iterations and some luck you can get it solved.
I was left with having everything in place but just two of the center-edge pieces would have to be flipped in-place, which I didn't know how to do before studying tutorials. I talk about rotate face X, then face Y but not any other face on that four moves. This method makes with lot of time you have a book filled with 'tools', some better than others. Most times you get how to move pieces, so solve the puzzle by kind of pieces, not by layers, etc. On 3x3 Rubik for example, you solve first all edges ignoring all corners , then move to correct position each corner till all are in place, then set the correct orientation.
Yes, it is very long 24 moves, but each is ABAB. It is my own challenge of always solve any puzzle by doing only ABAB kind of moves and find them by myself. For some puzzles I also add ABC moves, not just two faces or two corner or two edges, I go for three in cascade.
As more 'tools' you find, you will get how to solve it, which kind of piece first, which next, etc. For example, for the 3x3 Rubik's, if you have a 'tool' to circle 3 edges, but that moves corners, do not use the 'tool' that moves only corners prior to the 'tool' for edges, etc.
The list of 'tools' will tell you what order of piece type. I talk of 'tool's, a sequence of moves, not an algorithm, because it is fixed sequence , not a "do this if that". Sign up to join this community. The best answers are voted up and rise to the top. Stack Overflow for Teams — Collaborate and share knowledge with a private group. Create a free Team What is Teams? Learn more. Ask Question. Asked 4 years, 3 months ago.
Active 3 months ago. Viewed 61k times. Improve this question. Thomas Thomas 1 1 gold badge 4 4 silver badges 5 5 bronze badges. I'll write up an answer in a sec. It took most of them at least a month, but they did it, and almost all their methods are completely different.
Tony Fisher is one of those people, with a pretty unique method. The 3x3x3 Cube was my first puzzle, and I've used a tutorial, but even with my.. So, I've made an edit in an attempt to salvage the otherwise excellent answers here. Apologies for hijacking your question.
If the responses below aren't what you were after, you could reformulate your original question to be a bit less broad and ask it again Minsky then shut his eyes. Show 6 more comments.
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