FANDOM


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 AlgorithmsEdit

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

$ <><0> $

One Move AlgorithmsEdit

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

$ <R><4> $

$ <R2><2> $

Two Move AlgorithmsEdit

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 AlgorithmsEdit

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.]