Understanding the Rubiks Cube
February 8, 2018

Analyses of the cube with results-

Rubik’s Cube computers -http://www.cubersisland.com/wp-admin/edit.php

Analyses of the cube

Researchers make the claim that any scrambled cube can be solved in 20 moves or less. It’s something that has been studied for years. Google’s supercomputers are able to make very fast calculations by testing for solutions by running algorithms.

Analyses of the cube

They are able to achieve results in a few weeks that would take a normal home PC to achieve in about 30 years. You can see the difference.

A group of American and European mathematicians used the Google supercomputers to develop an algorithm to show that any scrambled Rubik’s Cube could be solved in 20 moves or less.

The average Rubik’s Cube tutorial would struggle to teach it with less than 70 moves to solve it.During this experiment they tested a large number of possible cube positions. There are a possible 43,252,003,274,489,856,000 positions of the Cube.

Google computers

The modern Google supercomputers were not able to check all these positions of the Cube individually. Instead these Cube positions were split into 2.2 billion sets of positions , each of which could be solved in about 20 seconds.

Analyses of the cube

All these  sets was then reduced by about a factor of 40 by symmetry arguments and ndash: basically, it doesn’t matter what way round in space the Cube is, and mirror images can be discounted.

The researchers estimate there are about 100 million Cube positions that can be solved in 20 moves although this is only their estimation and so it is not a guaranteed result. Their experiment wasn’t aimed at getting the best results but only for solutions of less than 20.

Analyses of the cube

Since the invention of the Cube in 1974 mathematicians have been working to solve his problem.

It is known for a fact that the maximum amount of moves required to solve any scrambled Cube is larger than 18 and below 52. At one time at least one fifth of the world’s population had played with a Rubik’s Cube. Today many National and International competitions are held worldwide.

Nobody has ever solved a Rubik’s Cube in as low as 20 moves in competition. Some competitors are even able to solve the cube with their feet. Researchers now hope to analyse the minimum amount of moves to solve from any position of a 4 x 4 Rubik’s Cube.

Analyses of the cube

Rubik’s Cube in virtual reality

 

Technology has now advanced so much that today an app on Oculus VR share that gives the Rubik’s Cube a new lease of virtual life.

Rubik VR includes a timer and music player.

No one is aware of how the app was made.

Virtual cubes can be reset, undone, redone or scrambled.

Vive Rubik’s Cube Solve is a Virtual Reality video of the Rubik’s Cube.

Rubik Vr was made at the Virtual Reality for Multimedia degree.

Augmented Reality is a new invented method of solving a cube.

It is self guiding. It solves by affecting the permutation of the cube.

Analyses of the cube

Faces of the cube are revealed in an arbitrary order. It corrects your mistakes and it is able to solve the cube in 20 moves or less. Augmented reality also shows the next correct turn right away.

Analyses of the cube

Virtual reality Rubik’s Cube videos

Vive rubik’s cube solve is a video that shows a Rubik’s cube being solved in virtual reality. To begin with you see a solved cube and then it is scrambled. In this video the Rubik’s cube is solved in about 55 seconds. This video was uploaded about a year ago.

Analyses of the cube

Natural virtual hand interaction with puzzle cube in vr is a video that starts off showing three solved Rubik’s cubes on a table. It then shows a pair of virtual hands scramble one of the cubes and then place it on a device and then places a solved cube on an identical device.

Analyses of the cube

Both the cubes begin rotating on their devices. The scrambled cube is solved very fast whilst rotating on its device, and when a yellow button on the bottom of the device is pressed the cube is quickly messed up.

Another device with the solved cube has that cube removed from it and the scrambled cube on the other device is now placed on this device. It is rotating on this device. The green button on this device is pressed and the cube is quickly solved.

Solved cubes in virtual reality

Another solved Rubik’s cube is then placed on the other device and rotates.

The solved cube on the device where the green button was pressed is removed from that device and placed on the table. That device is then placed on top of that Rubik’s cube. A solved Rubik’s cube on the table is then placed on top of that device and rotates.

Analyses of the cube

The other device is then removed from beneath the solved Rubik’s cube and the Rubik’s cube on top of the device is then placed on the table. This cube is then instantly picked up and then scrambled with the virtual hands. It is then placed on top of the device that’s on top of a solved Rubik’s cube.

The cube then rotates. The other device is then picked up and then quickly placed on the table near to the solved cube that’s by itself.

A virtual hand then picks up this solved cube and places it on this nearby device. The cube then rotates. During all of this video there is a mirror on the table that showed everything that happened.

Analyses of the cube

Virtual reality cube sizes

Cubing in vr is a video that shows three different Rubik’s cubes in virtual reality. These cubes consist of the 2 x 2 , 3 x 3 and 4 x 4 Rubik’s cubes. In this video these cubes are messed up and made into certain patterns. The video shows two long metal looking devices that are used to solve the cubes.

Analyses of the cube

EFC # 87 Rubik’s Cube in VR (Virtual Reality) El Friki de los Cubos is a video of a 3 x 3 x 3 Rubik’s cube in virtual reality being solved and it also shows two other cubes of which one is unsolved. After it shows the cube being quickly solved it then shows an unsolved cube.

The front face of the unsolved cube is rotated to the left bringing the left face into view and then is brought back to its face again.

Analyses of the cube

There are algorithms seen which are the moves to solve this cube. The video slowly plays through these sequence of moves to complete the cube.

Analyses of the cube with results

Rubik’s Cube in Science

A group of students at the University of Michigan overcame all the difficulties and finally built the world’s largest Rubik’s Cube. Designing this cube in a way that allowed it to spin was a challenge for the students.

The larger the cube the greater the friction will be. With the cube being so large they had to figure out how the moves of the cube could be carried out. All the students knew that they had to overcome the problems of friction and grip.

Analyses of the cube

They used two teams of mechanical engineering students and an advisor to work out how to deal with the friction and grip of the large cube. This team finally worked it out.

Analyses of the cube

Solving big Cubes

 

A Rubik’s Cube of any size can now be solved. Generally only the dedicated cubers go on to attempt to solve cubes larger than the 3 x 3 x 3. After analyses there is now an algorithm that has been developed that can solve a Rubik’s Cube of any size.

Analyses of the cube

A team of scientists showed that a scrambled cube could be solved in 20 moves or less. This team of scientists was led by Tomas Rokicki of Palo Alto, California.

Scientific conclusions

This has been called Gods number. This implies that even God couldn’t solve it in less moves. But they found this was not the case with the very large cubes.

So Erik Demaine, a computer scientist at the Massachusetts Institute of Technology , looked for an algorithm for solving a cube. This specific algorithm he sought was for solving a cube with any side – length – of n squares.

Rokicki and Demaine had a different approach . One method used computers to check 43 quintillion possible solutions.

Demaine believed that doing the same for larger cubes would be impossible. He believed one couldn’t solve all values of n with computational search.

Demain’s team method was to try and locate a single square into a specific position while leaving the rest of the cube as unchanged as possible.

This will obviously take a lot of moves as it is not possible to make a move of the cube without messing up other cubes. Therefore this requires a number of moves that is proportional to n squared.

Analyses of the cube

Demain and his team found a short cut. They discovered that they should move a group of cubies at once which needed to be moved in the same direction ending in their correct positions. Doing this would obviously cut down the number of moves because you could now solve several cubies at once.

Analyses of the cube

Grouping cubies of similar directions reduces the number of moves required by a factor of around log n. This means that the maximum number of moves that will ever be required for a cube of side n is proportional to n squared /log n (arxiv.org/abs/1106.5736).

Analyses of the cube

Rubik’s Cube and IQ

The Rubik’s Cube is a fascinating puzzle which has awed millions of people worldwide. I estimate that as low as one percent of people in the UK can solve the cube.

Analyses of the cube

Very few people can solve the Rubik’s Cube for the first time without any guidance.

Analyses of the cube

Despite the numerous Rubik’s Cube tutorials that have emerged in the last decade, studying them has led to no success for many. Because of the complexity of solving the cube many people would assume that only intelligent individuals are capable of solving it.

Analyses of the cube

Speed cubing skills

Fast solvers of the cube are often good at Mathematics. Most speed cubers are actually fairly intelligent people.

Analyses of the cube

Certain skills are required to solve the Rubik’s Cube which include pattern recognition,3D movement visualization and a good memory. I would consider these skills more as natural skills than acquired skills.

Analyses of the cube

A speedcuber has a set of skills that include finger dexterity, multitasking, and muscle memory.
I believe these skills are innate skills that can be improved with lots of practice.

Speed cubers are often mathematicians or people that study sciences or Math’s. Speed cubers are definitely academics.

Analyses of the cube

Rubik’s Cube algorithms are based on mathematics. There have been many studies to determine the relationship between the Rubik’s Cube solving and IQ.

Analyses of the cube

Speed cubers need a good memory to produce the fast solves of the cube. A high level of concentration is also a quality speed cubers have.

Analyses of the cube

I can solve the Rubik’s Cube in 14 seconds using the Fridrich method. I found that this methods algorithms are comfortable to use.

Analyses of the cube

Spacial intelligence

Solving the Rubik’s Cube develops special intelligence. Spacial intelligence is about special judgement and the ability to visualize with the minds eye.

Analyses of the cube

It’s like a human computational capacity that provides the ability or mental skill to solve spatial problems of navigation,visualization of objects from different angles and space, faces or scenes recognition or to notice fine details.

Analyses of the cube

Spacial intelligence is a brain skill that is also found in people with visual impairment. A blind person can recognize shapes in a non – visual way.

The spatial reasoning of the blind person allows them to translate tactile sensations into mental calculation of length and visual form.

Analyses of the cube

Conclusion
Today there exists many studies of the Rubik’s Cube with some very interesting results. Researchers are forever exploring the Cube and discovering new algorithms of solving certain Cubes