I’ve always been interested in sticker patters in which the correct solved position of specific cubies is not obvious when the cube is scrambled. The popular maze 3x3x3 sticker mod is a great example of this. A puzzle like this is considerably harder to solve than a standard cube since you often have to experiment with the placement of cubies while solving and may have to backtrack over and over until you get it right. Even the best cubing experts can find this kind of puzzle frustrating. My first experiment in creating a cube like this was my 16 color 4x4x4 Suduko Cube
. I now present my second experiment in creating these kinds of puzzles.TetraVex
is a puzzle which uses square tiles divided into four quadrants split corner to corner. Each quadrant is a different color and the object of the puzzle is to arrange the tiles so that matching edges touch each other on all four sides of all the tiles. Eternity II
is a board game version of this kind of puzzle which uses 256 pieces and offers a $2 million prize for the first to solve it (still unclaimed). These puzzles are known to be easy to start because at first it is really easy to fit together a bunch of tiles. But they get difficult to complete because you will find that eventually you can’t fit any more tiles and you have to backtrack. I have now applied this to a series of Rubik’s Cubes from 2x2x2 through 5x5x5.
For the sake of simplicity with my description when I refer to “tiles” I will be referring to one stickered surface of a cubie consisting of four stickers (three for corners), not to be confused with cubies although for centers they are one in the same.
I designed these patterns using the following rules:
- There is a neutral color for the borders (white in this case). Some versions of TetraVex such as Eternity II define edge and corner tiles by using neutral colors for the outer edges. Since the tiles as applied to edge and corner cubies are fixed with the other tiles on the same cubie, it really didn’t matter if I assigned those edges unique colors or not. I decided to go with the neutral color because I think it gives a unique look to the cubes.
- The number of colors is kept low enough so that there are multiple possible positions for each tile, but not so low that there are an over abundance of solutions and duplicated tiles. The 2x2x2 uses three colors, the 3x3x3 uses 4, and the 4x4x4 as well as the 5x5x5 use five colors (not counting the neutral edge color).
- Colors won’t be duplicated on the same tile. Each corner tile contains two unique colors, each edge tile has three, and all center tiles have four unique colors. This is not always the case with TetraVex where you may sometimes see the same color showing up two, three, or even four times on a tile.
- If a tile exists on a cube, it also exists on all the cubes bigger then it. All twenty-four tiles from the 2x2x2 are present on the 3x3x3. All fifty-four tiles from the 3x3x3 are present on the 4x4x4 and so on. I felt that this made for a good connection between the cubes in this series. I wanted it to seem like each puzzle builds upon the lower order puzzles, which I guess makes since because that is how I developed them (taking all of the tiles from a cube, rearranging them, and then adding additional tiles to fill the spaces).
-No two cubies can be exchanged without it breaking the solution. This means that all corner, edge, and center cubies are unique even if some of the tiles aren’t. On the 5x5x5 this also applies to centers, center edges, and center corners each as separate groups (you may see the same tile on a center edge and a center corner but since they can’t be exchanged it doesn’t break this rule).
- Orientation matters for all cubies. Corner cubies won’t contain three of the same tiles and edge cubies won’t contain two of the same tiles. Since all center tiles have four unique colors this isn’t an issue for them.
- Each cubie can be placed next to at least two other cubies. I didn’t want any obvious paring of cubies so when you solve this you will have to do some experimental placing of them and may have to backtrack (a common occurrence when playing TetraVex).
- Multiple solutions may be possible (also common with TetraVex). I didn’t design any into the puzzles but I didn’t take steps to prevent them from occurring.