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Long time ago I've seen a book on group theory and there was an appendix about rubik cube. I remember there were only three steps that enabled me to solve my cube (three strings with letters encoding some rotation). I don't remember them now and I can't google something similar either (I find only very long and complicated solutions). Can somebody tell me what those steps may have been?

EDIT: Maybe this helps: I've remembered that first subroutine involved swapping edges to make crosses on each side, and the last (the longest) is rotating three corners on front side. The second was about rotating colors on corners in place or something like that.

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Sounds like what you're looking for is a set of three moves that generate the entire Rubik's Cube group, does that sound right? – Rahul Jan 7 '13 at 2:27
@RahulNarain Probably... If someone will write these moves down it would be great. – swish Jan 7 '13 at 4:17
That set of three moves won't let you solve it. It will be true that you could solve it using only those three moves, but it won't tell you what order to use them in. There was a Dilbert where his company bought software from Dogbert. A CD was delivered with all the 1's and 0's needed-Dilbert's company just had to put them in order. – Ross Millikan Jan 9 '13 at 4:28
@RossMillikan I did solve it with those moves many times, it required some thought to it and I liked it :). – swish Jan 9 '13 at 4:35
You might indicate what you are looking for. The three answers are in very different directions. One must be closer to what you want than the other two, but I can't tell which. – Ross Millikan Jan 11 '13 at 16:30
up vote 1 down vote accepted

This method of solving the cube is NOT recommended, but I believe this is the answer to what you want:

  1. Permute 3 edges: R2 U R U R' U' R' U' R' U R'

  2. Permute 3 corners: R' F R' B2 R F' R' B2 R2

  3. Rotate 2 corners: R U R' U R U2 R' U2 R' U' R U' R' U2 R U2

Using 1. it is possible to get a cross with the edges on all sides. After 2. all the corners should be in the right place (but not necessarily rotated correctly). Step 3. should fix that.

Sorry for no drawings but 1. will permute 3 edges on the top face. Step 2. will permute 3 corners on the top face. And step 3. will rotate the 2 left corners on the top face.

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These primitives are not enough if the initial state has an odd permutation of the edges and an odd permutation of the corners. (And even in the states that can be solved, finding a way to get the edges to be correctly oriented is decidedly nontrivial). – Henning Makholm Jan 18 '13 at 16:12

You need a small number of subroutines. I used to solve one layer by inspection and put it on the bottom. Then you need the ability to swap one pair of corners, leaving all other corners alone. You can switch any pair of corners with one such subroutine. Say you know how to swap FLU and FRU, but want to swap BLU and FRU instead. Find and remember a series of moves to bring the corners you want to swap into FLU/FRU, do your subroutine, then undo the moves that brought the corners to FLU/FRU. This type of commutator will make your subroutines general. Then you need to rotate two corners, swap two pairs of edges, and flip a pair of edges and you are done. That is four, not three subroutines, but it is close. This won't get you an optimal solution in terms of moves or time, but it is probably optimal in terms of effort to learn.

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This might help:

See the discussion and references to notation on the associated Wikipedia page Optimal solutions for Rubik's Cube.

This might be looking for: See the attached pdf: Rubik's Cube Solution. It explains notation used, and then proceeds to describe "3 layers" (subroutines) to follow for solving the Rubik's cube.

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It's not the one I'm looking for. This solution I can easily find everywhere, it's more than just 3 steps. – swish Jan 11 '13 at 18:40
Subroutines are more than one step, so 3 times subroutines > 3 steps. I'm simply trying to help, that's all. – amWhy Jan 11 '13 at 18:42

Take from here:

Every position of Rubik's Cube™ can be solved in twenty moves or less.

With about 35 CPU-years of idle computer time donated by Google, a team of researchers has essentially solved every position of the Rubik's Cube™, and shown that no position requires more than twenty moves. We consider any twist of any face to be one move (this is known as the half-turn metric.)

The resulting algorithm has been called God's Algorithm and is explained here. The first page linked above even has code you can download and run on your own desktop machine.

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