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Cube Puzzles

Cube puzzles develop spatial awareness and logical thinking. They also help improve hand-eye coordination and problem solving.

If you’ve mastered the 3×3, try the 4×4. Then graduate to higher-order NxN puzzles such as 5×5 and 6×6. These are more challenging to solve and have parity cases, but offer a great opportunity to further your cubing skill.

The origin

In the early 1970s Erno Rubik wanted to build a structure that seemed to defy gravity. He experimented with small wooden cubes, magnets and scrap materials. His ultimate goal was to have movable independent parts that could be changed positions without the entire mechanism falling apart.

He patented his invention as a spatial logic toy in Hungary on January 30, 1975. It wasn’t until two years later that it was introduced to the world by the Ideal Toy Company.

Cube puzzles help develop mental dexterity and spatial awareness. They also encourage logical thinking and problem solving skills. They can also be used to practice hand-eye coordination. There is an alternative method for notating moves on a cube called Wolstenholme notation, which makes memorising sequences of turns easier.

The design

The original Rubik’s Cube was designed as a model to help students understand three dimensional objects. He wanted a structure that had movable independent parts and could be scrambled to demonstrate how the pieces moved around each other without falling apart.

Almost any shape of cube can be made using these principles, although it takes considerable work to produce something new and interesting. Often the new cube will need some algorithm that allows the solver to determine the position of some of the centre pieces, as the orientation of these is what counts in a solution.

If you have mastered the 3×3 cube, consider trying a 4×4. You will need to learn some new techniques for this one but it is still fairly straightforward once you know what to do.

The mechanics

There are 519 quintillion[53] possible arrangements of the cube’s pieces. However, only one in twelve of them are solvable. Solving a cube requires transforming a pair of corners or edge pieces into their proper positions. There are many algorithms that can achieve this without interfering with other parts of the cube. Such algorithms are employed early on in the solution and often serve as a building block for more specific algorithms that can change more parts of the cube, such as permuting edges.

The letters R, U, F and indicate rotations of the face of the cube that the letter applies to; i indicates an inverse turn. There are two variations of this notation, the more common being Wolstenholme notation, which is designed to make it easier for beginners to memorize sequences of turns.

The rules

There are many different algorithms that can be executed to solve a cube. Some of them are more complicated than others, but all are designed to return the cube to a solved state. Each step in the sequence requires that the corner pieces on the front, down, and back faces be positioned correctly, and that the centre squares are oriented with respect to one another.

For the beginner, it is recommended that you focus on creating a cross in the white block on the top face. Once that is complete, you can then focus on executing the edge and centre piece alignment steps. There are also higher order cubes that require more sophisticated techniques, such as the 4×4 and 5×5. These use the same principles as the 3×3, but require some new algorithms for orienting the centres.

The solution

There are many other cubes that offer a challenge beyond the standard 3×3 cube. The Megaminx is a baseball-sized dodecahedron that uses similar mechanics as the Rubik’s Cube and offers new algorithms to learn.

Other WCA sanctioned puzzles include the Pyraminx (which has the same mechanical function but has centres that must be oriented) and the Skewb, which is like a pyraminx in shape but solves by corner twisting alone. There are also several different shaped versions of the Pyraminx, including one called the Mirror Cube that scrambles into an impressive looking cube and is an excellent way to improve your intuitive solving abilities.

The 4×4 is a good step up in difficulty from the 3×3 and a great opportunity to apply your skills to a new shape. The last layer of yellow corners on the 3×3 is tricky but once you understand how to permute them the rest is just a matter of practice.

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