## Huge Rubik’s Cubes

April 6, 2017

Rubiks cube sizes and studies

Scientific studies of the cube have been carried out to create the largest ever Rubik’s Cube . As well as this 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. 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.

Rubiks cube sizes

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.

## Scientific studies of larger cubes

So Erik Demaine, a computer scientist at theMassachusetts 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.

Rubiks cube sizes

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.

## Rubiks cube sizes and studies

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.

Rubiks cube sizes

Doing this would obviously cut down the number of moves because you could now solve several cubies at once.

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).

Rubiks cube sizes

Conclusion

Rubik’s Cube of all different sizes now exist. Science has made it possible to calculate the algorithms needed to solve a Cube of any size by the use of computers. Studies have also been made to discover the minimum amount of moves needed to solve these Cubes.

Rubiks cube sizes