A Rubik’s cube algorithm is a specific sequence of moves, written in shorthand notation, that you perform to rearrange pieces on the cube in a predictable way. Each algorithm is like a mini recipe: follow the steps in order, and a particular set of pieces will move to exactly where you want them without scrambling the rest of your progress. Solving the cube means learning a handful of these sequences and knowing when to apply each one.
How Move Notation Works
Every algorithm is written using six letters, each representing one face of the cube: U (up), D (down), R (right), L (left), F (front), and B (back). A letter by itself means turn that face 90 degrees clockwise, as if you were looking directly at it. A letter followed by an apostrophe, like R’ (pronounced “R prime”), means turn that face counterclockwise instead. A letter followed by the number 2, like U2, means turn that face 180 degrees.
So when you see an algorithm written as R U R’ U’, you’d turn the right face clockwise, the top face clockwise, the right face counterclockwise, then the top face counterclockwise. That particular four-move sequence is one of the most common building blocks in cube solving and shows up inside dozens of longer algorithms.
Why Algorithms Work
A Rubik’s cube has roughly 43 quintillion possible configurations (about 4.3 × 10¹⁹). That number comes from the mathematical reality that the cube has 8 corner pieces and 12 edge pieces, each of which can be positioned and oriented in different ways. Mathematicians describe the cube using group theory, treating each move as a permutation, a rearrangement of pieces that can be composed and reversed like functions.
This mathematical structure is what makes algorithms reliable. A given sequence of moves always produces the same permutation of pieces, regardless of what colors happen to be where. That’s why you can memorize a sequence once and use it every single time you encounter the same situation on the cube.
Two structural patterns show up repeatedly in algorithm design. A conjugate follows the pattern: setup moves, do something useful, then undo the setup moves. This lets you target a specific piece by temporarily moving it into a convenient position. A commutator chains two move sequences together and then reverses both, cycling a small number of pieces while leaving everything else untouched. Most beginner algorithms are built from these two ideas, even if solvers don’t realize it.
The Beginner Layer-by-Layer Method
The most common way to learn the cube is the layer-by-layer method, which solves the cube from one face down to the opposite face in five stages. Each stage has its own small set of algorithms.
- First layer cross. You place four edge pieces around one center (usually white) to form a plus sign. This step is mostly intuitive, meaning you figure it out by logic rather than memorizing sequences.
- First layer corners. You slot the four corner pieces into place around the cross, completing the entire first layer. This typically requires one short algorithm repeated with different setups.
- Second layer edges. You move four edge pieces from the top layer into their correct positions in the middle layer. Two mirror-image algorithms handle this, one for edges that need to go left and one for edges that need to go right.
- Last layer cross. You flip the edge pieces on the final layer so they all face upward, forming a cross on top. One algorithm, applied up to three times depending on the starting pattern, handles every case.
- Last layer corners. You orient and then position the four remaining corners to finish the cube. This typically involves two more algorithms.
In total, a beginner needs roughly six to eight algorithms to solve the entire cube. The sequences are short, usually between four and eight moves each, and the whole solve takes somewhere around 100 to 150 moves.
Advanced Methods Use More Algorithms for Fewer Moves
Speedcubers trade memorization for efficiency. The most popular advanced method is CFOP (also called the Fridrich method), which has four stages: Cross, First Two Layers (F2L), Orientation of the Last Layer (OLL), and Permutation of the Last Layer (PLL). The full method requires learning 119 algorithms: 41 for F2L, 57 for OLL, and 21 for PLL. Each algorithm handles a specific pattern you’ll recognize on sight, so instead of repeating a short sequence multiple times, you execute one longer sequence that solves the entire stage at once.
The Roux method takes a completely different approach. Instead of solving layer by layer, it builds two 1×2×3 blocks on opposite sides of the cube, then solves the remaining pieces using mostly turns of the right face and the middle vertical slice. Roux requires fewer algorithms overall and produces shorter solutions, but it relies more on intuition and spatial reasoning. The heavy use of middle-slice moves makes it feel quite different from layer-based methods.
God’s Number: The Theoretical Limit
In 2010, a team of researchers proved that every possible scramble of the Rubik’s cube can be solved in 20 moves or fewer. This upper bound is known as God’s Number. The proof required evaluating all 43 quintillion positions (using clever mathematical shortcuts and massive computing power) and confirmed that about 12 million positions actually require the full 20 moves. No position requires 21.
In practice, nobody solves the cube in 20 moves during a timed solve. Finding the optimal solution for a given scramble is a computational problem, not something a human can do on the fly. Speedcubers using CFOP typically average around 55 to 60 moves, prioritizing recognition speed and finger execution over move efficiency.
How Cubers Execute Algorithms Quickly
Knowing the right algorithm is only half the battle. Competitive solvers use finger tricks to execute moves as fast as possible. Instead of gripping the cube and rotating their wrist for each turn, they push and pull individual layers with specific fingers. A clockwise turn of the top face might be a quick flick of the right index finger. A counterclockwise turn is a pull with the same finger in the opposite direction.
The goal is twofold: minimize regrips (moments where you have to reposition your hands on the cube) and overlap moves so that two turns happen nearly simultaneously. Elite solvers can execute a 12-move algorithm in well under a second because their fingers are performing consecutive moves in a fluid, almost continuous motion. When cubers talk about a “good” algorithm versus a “bad” one, they often mean how smoothly it flows with finger tricks, not just how many moves it contains. Two algorithms that accomplish the same thing on the cube might feel completely different in the hands, and solvers frequently choose the one that allows faster physical execution.