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Just gonna drop a bit of magic here. I finally figured it out and I couldn't believe it was so easy.

There are several layer permutations in Square-1 solving that go to a U-perm after the regular J-perm or N-perm CP is applied (with correct alignment, of course). These are T, F, V, Y, G, R, and A. Of these, the first four (T, F, V, and Y) can be aligned two different ways before applying a J-perm to produce either direction of U-perm. A can be aligned two different ways, but it produces the same U either way. A bit more on that later.

These permutations can be divided into two different groups:

Group 1: T, Y, Ga, A (clockwise)

Group 2: F, V, Gb, R, A (counter-clockwise)

If you get two permutations from different groups, perform them with the same alignment. If you get two permutations from the same group, they should not be aligned. G and R have a specific alignment that they must be held at in order to go to U, so you should match the other to that. Because the alignment of A doesn't actually affect the permutation, you must always misalign the other permutation instead.

Even when you can't affect the permutation, this can be useful for lookahead. For example, you can't actually force anything if you end up with G/R, but you can tell whether or not you'll end up with good Us.

Examples:

T/F. T and F are in different groups, and so in this case, you'll just perform J/J without any adjustments, leading to good Us.

V/F. These are in the same group, so apply 1,0 or 0,-1 before performing the N/J corner permutation alg.

R/T. R and T are not in the same group, so they should be aligned the same way. However, you need to adjust the R to make it go to a U-perm (preserving the 1x2 block). Since T has to match, you'll need to do 1,-1 before applying the J/J alg. This same principle also applies to G-perms.

F/Acw. These are in the same group, so they must be misaligned before performing J/J. Since adjusting A doesn't change anything, you must do 1,0 before solving CP. In fact, if you do 1,-1, you'll end up with the same result (just a different AUF), so at this point only the adjustment of the F matters.

This is a very simple rule to remember that can help improve your Square-1 "luck". If you have any questions please don't hesitate to ask.

Oh yeah, also: if you align a J incorrectly (e.g., in a way that solves CP but DOESN'T solve EP), it falls under group 1 as well. This is actually MORE useful than the other permutations, since U/solved is much slower than either good OR bad Us.

There are several layer permutations in Square-1 solving that go to a U-perm after the regular J-perm or N-perm CP is applied (with correct alignment, of course). These are T, F, V, Y, G, R, and A. Of these, the first four (T, F, V, and Y) can be aligned two different ways before applying a J-perm to produce either direction of U-perm. A can be aligned two different ways, but it produces the same U either way. A bit more on that later.

These permutations can be divided into two different groups:

Group 1: T, Y, Ga, A (clockwise)

Group 2: F, V, Gb, R, A (counter-clockwise)

If you get two permutations from different groups, perform them with the same alignment. If you get two permutations from the same group, they should not be aligned. G and R have a specific alignment that they must be held at in order to go to U, so you should match the other to that. Because the alignment of A doesn't actually affect the permutation, you must always misalign the other permutation instead.

Even when you can't affect the permutation, this can be useful for lookahead. For example, you can't actually force anything if you end up with G/R, but you can tell whether or not you'll end up with good Us.

Examples:

T/F. T and F are in different groups, and so in this case, you'll just perform J/J without any adjustments, leading to good Us.

V/F. These are in the same group, so apply 1,0 or 0,-1 before performing the N/J corner permutation alg.

R/T. R and T are not in the same group, so they should be aligned the same way. However, you need to adjust the R to make it go to a U-perm (preserving the 1x2 block). Since T has to match, you'll need to do 1,-1 before applying the J/J alg. This same principle also applies to G-perms.

F/Acw. These are in the same group, so they must be misaligned before performing J/J. Since adjusting A doesn't change anything, you must do 1,0 before solving CP. In fact, if you do 1,-1, you'll end up with the same result (just a different AUF), so at this point only the adjustment of the F matters.

This is a very simple rule to remember that can help improve your Square-1 "luck". If you have any questions please don't hesitate to ask.

Oh yeah, also: if you align a J incorrectly (e.g., in a way that solves CP but DOESN'T solve EP), it falls under group 1 as well. This is actually MORE useful than the other permutations, since U/solved is much slower than either good OR bad Us.

Last edited: Dec 16, 2011

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