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# Final layer position index

This is a complete index of all possible corner positions in step 5, and some good ways to solve them. It does not deal with edge issues at all, so after this you are left with step 7. Since Step 5 is about positioning the corners, this index only deals with positions where the corners need to be swapped. If the corners are correctly placed, see the Step 6 position index
 Josef Jelinek has developed a different method for solving step 5+6+7. He thinks it's really good. He's probably right. Check it out here!

#### The Math

I've based this on the 7 possible ways the corners can "look". The top color facelets of the corners can for 7 different patterns, which I've named A-G. It's easy to see fast, and is what I look for when I get here. The next thing is to look for is positions of the corners.

There are 27 different ways that the corners can be arranged. Corners 1, 2 & 3 can show the top color three different ways, while the 4th is determined by the other three. 3x3x3 = 27. For each of those, there are 6 different ways the corners can be placed to show that pattern. So in total we have 27x6 = 162 different corner configurations. In theory.

Of those 6 corner placements, 1 is that they are correctly placed, 1 is that two corners are swapped diagonally, and 4 are that adjacent corners are swapped. I've taken to name them like this:

• Correct already: A, B, ...
• Adjacent swap: Ax, Bx, By, Bz, ...
• Diagonal swap: AA, BB, ...

Due to symmetries etc, the 162 positions are really just 32 distinct ones
Correct: 7 of 27 (A 1, B 8, C 4, D 4, E 4, F 2, G 4)
Adjacent: 18 of 108 (Ax 4, Bx 8, By 8, Bz 8, Bq 8, Cx 8, Cy 4, Cz 4, Dx 8, Dy 4, Dz 4, Ex 8, Ey 8, Fx 4, Fy 4, Gx 8, Gy 4, Gz 4)
Diagonal: 7 of 27 (AA 1, BB 8, CC 4, DD 4, EE 4, FF 2, GG 4) For example, 8 of 162 is 4.94% of the cases.

#### Which should I learn?

Apart from the old standards of Niklas, Sune etc, I've taken in 8 sequences in the "recommended" section. You can always use a Niklas instead, and using the Step 6 "target" rules, you can land in a Step 6 B position most of the time. You don't need to learn all 8 at once, but I really recommend learning them if you're trying to get fast. If you have the energy, learning some or all of the perfect ones will certainly help even more. I invented some new cute and informative names for them.

A lot of the sequences are taken from Bernard Helmstetters computer runs. This just scratches the surface of what is on his site.

 A - Ax, AA B - Bx, By, Bz, Bq, BB C - Cx, Cy, Cz, CC D - Dx, Dy, Dz, DD E - Ex, Ey, EE F - Fx, Fy, FF G - Gx, Gy, Gz, GG