3x3 blindfolded methods

The methods differ in how many targets one algorithm solves and how many algorithms there are to learn. Old Pochmann solves one target at a time with a setup and a fixed swap; M2 does the same for edges with a single slice turn; Orozco solves two targets with two short algorithms through a fixed helper; 3-style solves two targets with one commutator.

Old Pochmann, by Stefan Pochmann, swaps the buffer with one spot using a permutation algorithm and brings each target there with a setup that keeps the buffer still. The corner buffer is UBL; the swap is a Y permutation without its first and last turn, exchanging UBL and RDF (and the UB and UL edges, which an even number of corner targets swaps back). The edge buffer is UR, swapped with UL by a T permutation, or with other spots by J permutations.

With Old Pochmann, every edge swap also exchanges two corners. After an odd number of edge targets those corners stay exchanged, so solvers do one more permutation algorithm before the corners to swap them back, and memorise the corners with that swap in mind.

M2, also by Stefan Pochmann, uses DF as the buffer and a half turn of the middle slice as the swap: M2 exchanges DF with UB. Each target is brought to UB with turns that keep the middle slice still, then M2, then the setup undone. Because every M2 also moves UF and DB, the targets in the middle slice have their own algorithms, and the ones for UF, FU, DB and BD depend on whether an odd or even number of targets came before.

Orozco, by Gabriel Orozco, uses 3-style's buffers (UFR, UF) and a fixed helper (UBR for corners, UB for edges). A pair of targets XY is solved as XH, which sends the buffer's piece to X, then HY, which is the algorithm for YH done backwards. One algorithm per target, each a short commutator, makes it a stepping stone to 3-style.

3-style solves every pair of targets with one commutator: the piece in the buffer goes to the first target, that piece to the second, and that one to the buffer. Nearly every fast blindfolded solver uses it, with UFR and UF as the usual buffers. The cases are every pair of stickers on two other pieces. Many solvers first learn to build commutators by understanding, as below, then refine them from lists like these.

A commutator [A, B] is A, B, A', B'. Typically A is an insertion, three moves that swap a piece in one layer with a piece out of it, and B is a single turn of that layer that brings the second target where the first was. Everything A disturbs is put back by A', and everything B moves is turned back by B', except the three pieces. When the three targets are not in that shape, a setup move S first ([S: [A, B]], that is S A B A' B' S') brings them there.