When people first start learning about speedcubing or the mathematics behind the Rubik’s Cube, one of the most fascinating questions they ask is how many perms are there in cubing? This question opens the door to a deeper understanding of how the cube works, how algorithms are classified, and why solving the cube efficiently requires much more than random turning. Permutations, often shortened to perms, are a core concept in cubing, and understanding them helps explain both beginner methods and advanced speedcubing techniques.
What Does Perm Mean in Cubing?
In cubing terminology, a perm refers to a permutation, or the rearrangement of pieces on the cube. When solving a Rubik’s Cube, especially using popular methods like CFOP, a solver often reaches a point where all pieces are oriented correctly but not in the correct positions. At this stage, a specific algorithm is used to permute the pieces into their correct spots.
In simple terms, a perm is an algorithm that moves pieces around without changing their orientation. These algorithms are essential in the final stages of solving the cube and are a major focus for speedcubers who want to reduce their solve times.
Understanding the CFOP Method and Perms
The most common context in which people talk about perms is the CFOP method, also known as the Fridrich Method. CFOP stands for Cross, F2L (First Two Layers), OLL (Orientation of the Last Layer), and PLL (Permutation of the Last Layer).
Perms are primarily associated with the PLL stage. At this point, the solver has already oriented all the last-layer pieces correctly, and the goal is simply to move them into their correct positions. This is where the idea of different permutation cases becomes important.
What Is a PLL?
PLL stands for Permutation of the Last Layer. It refers to the final step in solving the cube using CFOP. During this step, all pieces on the last layer are facing the right direction, but they may not be in the correct spots.
Each unique arrangement of pieces that needs to be solved requires a specific algorithm, or perm. Learning these perms allows a cuber to complete the cube efficiently and consistently.
How Many Perms Are There in Cubing?
In standard CFOP solving, there are 21 distinct PLL cases. These 21 cases cover all possible ways the last layer pieces can be permuted once their orientation is already correct. Each case has its own algorithm or set of algorithms used to solve it.
These 21 perms are usually grouped into categories based on how the corners and edges move. This grouping helps cubers learn and recognize patterns more easily.
Common Categories of PLL Cases
- Edge-only permutations, where only the edges move
- Corner-only permutations, where only the corners move
- Mixed permutations, where both edges and corners move
Each of these categories contains several specific cases that look similar but require different algorithms to solve efficiently.
Why There Are Exactly 21 PLL Cases
The number 21 comes from mathematical constraints within the Rubik’s Cube. Because the cube’s pieces must obey certain parity and orientation rules, not all possible arrangements are achievable. The 21 PLL cases represent all the unique, solvable permutations of the last layer that can exist once orientation is complete.
This limited number makes it practical for speedcubers to memorize all PLL algorithms, even though it may seem overwhelming at first. With practice, recognizing and executing these cases becomes second nature.
Comparison With OLL Cases
To put this into perspective, the OLL step has 57 different cases, which is significantly more than PLL. That is one reason many beginners learn a simplified version of OLL first, while aiming to eventually master all 21 PLL cases.
Because there are fewer PLL cases, many cubers choose to learn full PLL earlier in their speedcubing journey.
Perms Beyond the Standard 3×3 Cube
While most discussions about perms focus on the standard 3×3 cube, permutations exist in all twisty puzzles. Larger cubes like the 4×4 or 5×5 introduce additional layers and more complex permutation scenarios.
However, even on larger cubes, many solvers reduce the puzzle to a 3×3 state before applying familiar PLL algorithms. This shows how foundational the concept of perms is across different cube types.
Advanced and Alternative Perm Sets
Some advanced cubers learn alternative or optimized permutations that reduce finger movement or improve execution speed. These are often called advanced PLLs or alternative algs. While they still solve the same cases, they may be faster or more comfortable for certain hand positions.
There are also method-specific permutations used in other solving methods, such as Roux or ZZ, though the underlying idea of permuting pieces remains the same.
Why Learning Perms Matters
Understanding how many perms there are and how they work is a key milestone in becoming a confident cuber. Learning PLL not only improves solve times but also builds a deeper understanding of how the cube behaves.
Recognizing patterns quickly allows solvers to react instinctively, reducing pauses and hesitation. Over time, this leads to smoother, more efficient solves.
So, how many perms are there in cubing? In the most common context of CFOP solving, there are 21 PLL cases that represent all possible permutations of the last layer once orientation is complete. These perms form a critical part of speedcubing knowledge and serve as a foundation for advanced solving techniques.
While the number may seem intimidating at first, learning perms is a rewarding process that deepens your understanding of the cube. With practice, pattern recognition, and repetition, these algorithms become second nature, turning what once seemed complex into an intuitive and satisfying part of the solving experience.