## FANDOM

155 Pages

A while ago I attempted to write down all the unique five move algorithms for the Rubik's cube, but was eventually overcome with the sheer number of them. This time however, I plan to go much farther; how much farther remains to the level of my patience in finding these by hand.

Middle slice turns and cube rotations have been excluded, note to that double-turns count as only one move, and the algorithms recorded are in the following form: <algorithm><cycle length>. Not all combinations of moves are recorded, because certain sequences of moves like $RU$ and $D'B'$ are isomorphic to one another and therefore have the same cycle length and properties. My list also excludes mirror images of algorithms. In general I have favored right-handed algorithms.

## Zero Move Algorithms

There is exactly 1 0-move algorithm; it is shown below.

$<><0>$

## One Move Algorithms

There are exactly 18 1-move algorithms; the two unique ones are shown below.

$<R><4>$

$<R2><2>$

## Two Move Algorithms

There are exactly 324 2-move algorithms; the 8 unique ones are shown below.

$<RU><105>$

$<RU'><63>$

$<RU2><30>$

$<RL><4>$

$<RL'><4>$

$<RL2><4>$

$<R2U><30>$

$<R2U2><6>$

## Three Move Algorithms

There are 5,832 3-move algorithms; [to be filled in later] of which are shown below.

$<RUD><90>$

$<RUD'><180>$

$<RUD2><168>$

$<RUF><80>$

$<RUF'><60>$

$<RUF2><36>$

$<RUB><84>$

$<RUB'><360>$

$<RUB2><9>$

$<RUL><90>$

$<RUL'><360>$

$<RUL2><168>$

$<RUR><30>$

$<RUR'><4>$

$<RUR2><63>$

$<RU'D><180>$

$<RU'D'><90>$

$<RU'F><60>$

$<RU'F2><63>$

[To be finished.]