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From the outside, Void and Bandaged cubes often look like a regular 3x3, but solving them is a completely different story. A Void cube has no centers. In a bandaged cube, some pieces are fused together or the moves are restricted in another way, so familiar algorithms work only partly or not at all. These puzzles are for people who can already solve a classic cube and want a real challenge rather than another cube for speed solving.
The Void Cube was invented by Katsuhiko Okamoto. It is a 3x3x3 cube without face centers and without an inner core mechanism, so you can see straight through it along every axis. You solve it with the same method as a regular 3x3, but without centers it's up to you to decide where each color goes. Because of this, you may run into parity on the last layer, which doesn't happen on a classic cube. If you're just getting started with unusual puzzles, the Void is a good first choice. In this category you'll find QiYi Void cubes in the basic version, with magnets, with a UV coating and in colorful transparent plastic, as well as the Lanlan Void Cube and Lanlan Edges-only-Void. There are also puzzles built on the Void principle but in shapes other than a 3x3, e.g. ShengShou Void Tower and QiYi Void Sandwich Cube.
Fused pieces block some turns. Before you make a move, you have to check whether it's possible at all. Examples of such cubes include the Z-Cube 3x3x3 Bandaged A, Cubetwist Two Bar and MF8 Sun Cube Bandaged. Moves can also be restricted without fusing pieces. A few examples:
Wheel puzzles form a separate group, such as the Calvins Puzzle Void Multi-Star Wheel Cube, Void Tornado Wheel Cube, Void Lantern Wheel Cube and Fangshi Void Star Wheel Cube. You turn them by the corners, and the faces have wheels that spin independently. These are definitely puzzles for more experienced solvers. The Multi-Star is also available as a DIY kit you assemble yourself.
If this is your first unusual cube, start with the Void Cube, as it lets you use what you already know from the classic 3x3. The next step could be the Constrained Cube, Latch Cube and simple bandaged cubes. Here you have to rethink the order of your moves, but the cube always keeps its cube shape. The hardest are the Blanker Cube, Sloppy Cube and wheel cubes. Choose them if you enjoy long brain teasers and don't mind that some of them take several evenings to figure out.