Guimond Method

The Guimond Method is a 2x2 speedsolving method invented by Gaétan Guimond. It first orients both layers, then permutes both layers (PBL). This method is very popular because it is move efficient, and can be reduced to a 2look method for more experienced users. Guimond requires 23 algorithms (or 16 without reflections).
Contents
The Steps
 Solve just 3/4 of a face of opposite colours. 'Opposite' colours are colours which appear at opposite ends of the cube. White/Yellow for example (western scheme). For colour neutral solvers this step is often skipped. If not it rarely requires more than 1 move, which makes for easy planning of the next step.
 Solve 2 opposite faces of opposite colours. This step has 16 cases (15 excluding solved, 8 excluding mirrors). The majority of algorithms are 3 or 4 moves, with the exception of 4 cases.
 Separate opposite colours to create two solved opposite faces. There are 6 cases (4 excluding the solved and trivial case, 3 if using x2 rotation). The optimal algs have a move counts of 1, 3, 3 and 5 moves.
 Permute both layers PBL. This is exactly the same as the final step in Ortega, making these two methods complementary.
Guimond as a Beginner Method
Guimond makes a slightly more efficient and intuitive alternative to Beginner LBL. The beginner method procedure is as follows:
 Use intuition to orient three cubies on both U and D faces. Mixing U/D colours at this stage is fine, as long as each U/D face has three oriented cubies (ie. with U or D colour on top).
 Using a U face turn, place the misoriented Uface cubie in URF. Flip the cube using x2 and do the same for the opposite layer.
 Now check the orientation of the misoriented URF cubie. If the U/D colour is facing you, use x2 to flip the cube. Now the misorineted cubie should have the U/D colour facing to the right.
 Apply the algorithm R' F U' R to complete orientation of the U/D faces.
 Using F2 R2 and U moves, swap U/D cubies until the Uface contains only U colour.
 Now look at the U layer only
 If you see 1 bar, position the cube (using y turns) so that the bar is in the back face. Apply the algorithm R' F R' B2 R F' R' B2 R2 (Aperm).
 If there are no bars apply Aperm to create a bar.
 Do x2 and repeat step 6 for the D layer to complete the cube.
Guimondstyle 3x3x3 Method
It is possible to solve the 3x3x3 cube using the same basic phases of the 2x2x2 Guimond method. The method is broken down into:
 Orientation of all the pieces
 Orientation of edges (see EOLine)
 Orientation of corners (same as Guimond, but preserving EO)
 Separation of the U/D Layer
 Move all midedges into Eslice
 Corner Separation (same as Guimond)
 Edge Separation
 Permutation of all the pieces
 Final solve of ESlice
 U/D layer permutation (Using PLL)
Predicted Separation
This is a more advanced form of regular Guimond, which allows one look to be eliminated. During inspection the solver works out the separation case (step 2), so that the separation alg can be executed immediately after the first step, without pause.
2 Step Guimond
This goes one step further than predicted separation and actually carries out separation and orientation (steps 1 and 2) all at the same time. The solver starts with three corners, then uses a larger set of algs to solve orientation and separation in one step. This is similar to the SS Method, but requires more algorithms.
Ortegastyle OLL
Where a scramble leaves one face with four oriented U/D corners, it is possible to simply use an Ortega OLL alg to bring the cube straight to the separation step. Because mixing of U/D colours doesn't matter in this step, slightly more efficient algorithms may be used. See OLL (2x2x2)
See also
External links
 funpic.org
 Martijn Bakker' doc on RapidShare
 Zarxrax's Complete Guimond Tutorial
 Speedsolving.com 2 Alg Guimond
 Speedsolving.com What is the "fridrich" of 2x2x2 cubing? (info on 2step Guimond)
 Speedsolving.com 3x3x3 Guimondstyle Method