How to solve a Rubik's Cube blindfolded

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The Rules of the Game

In blindfold cubing, the solver first inspects the puzzle to memorize it, without making any moves, before solving it without any aid of vision. The solver can do this by wearing an actual blindfold, as done in official competitions, by blocking the vision with a desk, by solving behind the back, or simply by closing eir eyes. In normal blindfold solving, both memorization and resolution are timed. The entire sequence is as follows:

(1) Timer starts; at the same time, solver starts inspecting the puzzle. (Memorization phase)
(3) Solver blocks his vision.
(4) Solver solves. (Resolution phase)
(5) Solver signals that he has finished solving by stopping the timer.
(6) Solver unblocks his vision; if the puzzle is indeed solved, the attempt is a success.

There is a second type of blindfold cubing, called "speed blindfold cubing," that only times the resolution. 3OP is designed for the first type of blindfold cubing.

Classification of Methods

The most basic classification of the various blindfold solving methods is by the way in which permutation is solved: piece-by-piece, or by decomposition into cycles. Richard Carr's piece-by-piece method belongs in first category, while all modern methods, including 3OP, use cycles (explained later in this guide). Of the various cycle methods, the group that includes 3OP solves the orientation (the flip/rotation) before the permutation (the location), while the other group, which consists of Pochmann, M2/R2, and the various freestyle and restricted freestyle methods, combine orientation and permutation.

Whatever the method, blindfolded solving is very different from normal cubing. While sighted methods aim for fewer moves and affect many pieces at each step, blindfolded methods use a limited number of basic algorithms that move very few pieces. This makes it possible to keep track of the state of the puzzle while blindfolded. In cycle methods, the solver memorizes the necessary operations left rather than the puzzle's state. As a result, the amount needed to be memorized decreases until there is nothing to remember at all, at which point the puzzle is solved.

1.2 Overview
Rubik's Cube has four nearly independent parts: corner orientation (CO), edge orientation (EO), corner permutation (CP), and edge permutation (EP). Each cubie (a corner or an edge) has an orientation (its flip/rotation) and a permutation (where it needs to go). Since a Rubik's Cube has 20 cubies, all the necessary information can be memorized as 40 numbers. The actual memory burden can be signifacantly eased by memorizing visually and is comparable to two 10-digit phone numbers.

3OP solves the cube one part at a time, starting with the two orientation steps. Each piece is first oriented (flipped or rotated) in place, meaning without changing the permutation. Then, each piece is permuted (moved) to its correct spot, now without disturbing the already-corrected orientation. Each of the four parts is solved independently, except possibly to correct the permutation parity involving two corners and two edges. Each step is in turn divided into smaller tasks--in CP and EP, into cycles--each of which is handled by judiciously applying an algorithm. Because everything can be broken into a small number of tasks, 3OP requires only a handful of algorithms.

This guide goes through the four steps and permutation parity in the order they are solved. But first, we need some preparation.