My system for solving Rubik's cube

Winter 1996/97: The system described here enabled me to win the First Czechoslovak Championship in Rubik's Cube, which took place in April 1982. When I was at my best, I routinely solved the cube in an average time of 17 seconds. At that time, I was actively using more than 100 algorithms, but the basic required minimum is 53 algorithms. Before I go on and describe the details of my system, I would like to express my thanks to Mike Pugh who retyped the algorithms from my old notebook to HTML and added nice graphics. His enthusiasm helped me to find the cube no less interesting than some 15+ years ago when I met it for the first time. Special thanks belong to Mirek Goljan, my 1982 finale rival, who kindly provided his enormous collection of algorithms as it appears here today.

There are a number of diferent systems suitable for speed cubing, but all can be roughly divided into two main categories: corners-edges and by-layers. My system belongs to the second category even though the first two layers are really formed at the same time rather than in sequence. The basic set of algorithms consists of 53 algorithms for the last layer and a couple of simple moves for the second layer together with a lot of experience. Most of the algorithms were developed by myself during the time period between the summer 1981 and the spring of 1983. However, other speed cubists, most noticeably Mirek Goljan, have also significantly contributed with important moves. Here is my system in a nut shell:

 Action description Averagenumberof moves Time Result Place the four edges from the first layer 7 2 sec. Place four blocks each consisting of one corner from the first layer and a corresponding edge from the second layer. 4 x 7 4 x 2 sec. Simultaneously orient the corners AND edges so that the last layer has the required color (one algorithm out of 40). 9 3 sec. Simultaneously permute the 8 cubes in the last layer without rotating corners or flipping edges (one algorithm out of 13). 12 4 sec. TOTAL 56 17

Unique features

One of the unique features of this system is that the last layer is always solved using two algorithms of an average length of 9 and 12, which is very efficient. The average lengths are based on frequencies with which various orientations and permutations occur and on the length of algoritms for each position. Another interesting feature is that for the first two layers no lengthy algorithms are needed and you can use your intuition and utilize the specifics of the particular initial state and subsequent states of the cube.

The first two layers

In an attempt to make this description complete, I supplied several algorithms which can help you solve the first two layers. Although most of the algorithms will be obvious to an experienced speed cubist, some of them are less trivial and are in my opinion very valuable. In addition to that, one should always try to use the specifics of any given state of the cube rather than blindly apply the algorithms. For example, when two or three corners are already correctly placed, it may be advantageous to keep the last corner free and insert all middle cubes using the free corner. Actually, some speed cubists use this approach as their default. Alternatively, when accidentaly (or intentionally) two or more middle cubes happen to be positioned correctly, one can place the corners from the first layer via the free middle edge(s). All these moves and a lot of practice should enable you to solve the first two layers in about 10-12 sec. Of course, this requires a lot of practicing, but let us say that 15-20 sec. will be realistic for most folks.

Because I was receiving a lot of requests for "additional hints" and advice for the middle layer, I decided to include another section with practical advice for solving the middle layer. Here are a few examples of how I think out loud when doing the middle layer. I hope this will help you to master the system faster!

The last layer

Some systems for solving Rubik's cube "by-layers" divide the solution of the last layer into four stages: orient edges, place edges, orient corners, place corners. It is possible to group together two and two stages to speed up the process. It seems natural to orient and place edges in one move and then orient and place corners in the second one. However, this approach has one big disadvantage - it is very difficult to recognize various positions quickly. A better approach is to orient edges and corners at the same time and place all of them simultaneously. Convince yourself that there are 41 different orientations of the cubies in the last layer, and 14 different permutations of those 8 cubies. Here, we do not count symmetric positions or inverse (backwards) positions as different because they can be solved using one algorithm. Different orientations are easily recognizable by patterns formed by the color of the last layer and a brief look at the sides of the cube. There are two patterns "C", four "I", two "T", etc. Most of the permutations are also easily recognizable. Given an average twisting speed of three moves per second, one can solve the last layer in 3 + 4 seconds (based on the average number of moves).

In theory, we could come up with a much larger system of algorithms which would enable us to solve the last layer in one algorithm. However, the number of algorithms one would need to learn is 1211.