Distinct Sticker Puzzles

In March 2025 I was thinking about the use of Straughan recognition on the Mirror Cube and noticed that even fewer stickers are required to recognize steps. This is because the shapes of each piece are different. I considered how to make Rubik's Cube work in the same way and had the idea to make the individual stickers of each face distinct. After experimenting with this, I had two major realizations:

• Rubik's Cube itself from the very beginning unintentionally partially removed the complete individuality of pieces by making each face a single color.

  • The 3 color cube is a reduction of Rubik's Cube, a 6 color cube. Pieces have reduced individuality compared to Rubik's Cube.

  • Rubik's Cube, a 6 color cube, is a reduction of the Gradient Cube, a 24  color cube. No two pieces are identical, but still have reduced individuality compared to the Gradient Cube.

  • Gradient Cube, a 24 color cube, is the full representation of the 3x3x3 puzzle. Every piece and every sticker have complete individuality. Other ways of making each sticker unique have the same effect.

• Numerous possibilities are opened up by making each piece truly distinct.

  • Pieces can now be recognized using fewer stickers.

  • Fewer faces need to be involved in the recognition. CLL, for example, requires checking just U face stickers.

  • Tracking is easier. This means that look ahead can be improved in solve and potentially deeper inspection.

Below is a Gradient Cube, an example of how stickers can be arranged on a cube to make each piece distinct. The minimum number of colors required is 24. Four colors per face, with the four colors reusable on the corners, edges, and centers of each face because each piece type is distinct. Many other arrangements are possible. Even a 54 color cube of nine unique stickers per face would accomplish the goal. A super cube, the previously mentioned cube, and the use of numbers, symbols, or letters (such as the Speffz letter scheme) also create a cube with completely distinct pieces.

This concept extends to all other puzzles as well. Ryan Hudgens (OreKehStrah) has provided possible gradient layouts for additional WCA puzzles.

Numerous possibilities are now opened up when individuality is restored to the pieces of puzzles. Below are some examples.

The minimum sticker concept behind Straughan recognition is a perfect match for distinct sticker puzzles. All of the major steps can now be recognized using fewer stickers. It is also much easier to find the stickers because, for example, steps involving the last layer can be recognized entirely using the stickers that belong on the U face. This means that side stickers aren't necessary for recognition. The image above shows an example U face gradient.

Blindfold Solving: It is now possible to memorize pieces by looking at a single sticker per piece. This means that it is possible to memorize the corners by just looking at the U, F, and R faces.

Edge Orientation: In techniques such as edge control and edge orientation in methods like Petrus, the orientation can always be determined by looking at a single sticker. There is no longer a need to track certain edges or use look ahead or deduction. On Rubik's Cube there are often situations where edge orientation can't be determined by looking at the U, F, and R faces. The setup R U’ R’ U’ F’ U F is an example where two matching edge stickers are at UL and UB and the orientation of the two can't be determined on Rubik's Cube without look ahead or deduction. But on a cube with distinct stickers it is easily known which of the two are oriented.

DR: In methods such as Polaris, SSC, Square-101, and the separation step of Mehta, the ending DR steps are often easily recognized by checking just the U face stickers. Especially if the corners are already in the <U, R> solvable permutation state.

Roux 4c: One of the minor annoyances of the Roux method on Rubik's Cube is the final M slice permutation step. 3-cycle cases such M U2 M U2 M2 and M2 U2 M' U2 M' look alike and have led to the development of look ahead recognition methods such as the one named DFDB. Using a distinct sticker cube, this isn't a problem because the edge stickers at UB and FD will tell the specific edges at those locations.

Three sticker recognition for CMLL has been developed. The orientation and intuitive permutation are recognized using three U face stickers.

Click to View Gradient Cube CMLL Document

Click to View Mirror Cube CMLL Document

Below are links to five sticker PLL for Gradient Cube and Mirror Cube.

Click to View Gradient Cube PLL Document

Click to View Mirror Cube PLL Document