How to Solve a Gear Cube?

Introduction

The Gear Cube was invented in the summer of 2009. At first glance, people think that this puzzle is difficult to solve, but that is not the case. The solution of the Gear cube is not hard because only 180-degree turns were allowed, so there are not so many possible permutations of the puzzle.

Here is a step-by-step solution to solve the Gear Cube.

Notations

Before we move on to solving the puzzle, we need to understand the notations. The notation is the same as the Rubik’s Cube, we have up, down, left, right, front, and back (clockwise rotations marked with U D L R F B) letters. Hold the cube so the top and bottom layers can be rotated 90 degrees so please note that only R2, F2, U2, L2, B2, and D2 moves are allowed because of the structure of the puzzle.

Step 1 - Solving the Corners

Unlike the normal Rubik’s Cube, in which we make the cross as the first step, in the Gear cube, we solve the corners first. The corners can be solved intuitively using R2, D2, and F2 moves and it will take only 4 moves maximum to solve the corners.

If opposite colors of one side match, doing (R2 D2 F2) will solve the corners

If you have two adjacent corners matching as shown

(D2 R2) can be done to solve the corners.

Step 2 - Solving the Centers

In this step, we will be solving the centers of the puzzle. This is also an intuitive step and can be solved by using only R2, F2, and D2 moves. After completing the first step, at least 2 of the 6 centers will be solved. So you can solve the rest of the 4 centers accordingly by doing D4 or R4 or F4.

In this case, doing (D4) will solve the centers.

Step 3 - Permuting the Edges (Gears)

In this step, we will be permuting the edges of the puzzle. This can be done by using this algorithm from the position shown below.

Rotate the cube and repeat this algorithm until all the edges (gears) get permuted.

Step 4 - Solving the Inner Edges

This step depends on the type of gear cube you have. If you have this gear cube, you can skip this step. If you have this gear cube, continue this step.

To solve the inner edges of the puzzle hold the cube in a position in which two inner edges of the center of the same color are facing the top as shown in the picture below : 

Doing (R2 U2)x3 should solve the inner edges.

Step 5 - Solving the Gears

This is the last step of solving the Gear Cube. In this step, the puzzle can be held in any position and turn the R face until the gear gets solved.

Repeat this from the other sides until the gears are solved. And there you go! You have successfully solved a Gear cube!

Conclusion

Solving the Gear Cube may seem daunting at first, but with a clear understanding of the steps and notations, it becomes an intuitive and enjoyable process. By following the outlined steps—solving the corners, centers, permuting the edges, aligning the inner edges, and finally solving the gears—you can master this unique puzzle with ease.

Keep practicing, and soon you'll find yourself solving the Gear Cube faster and more efficiently each time.

Happy cubing!

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