How to Solve Rubik’s Cube With Algorithm ?
Rubik’s Cube is a widely popular mechanical puzzle that has attracted attention around the world because of its unique characteristics.
As a classic brain-training toy well known to the public, Rubik’s Cube was used for scientific research and technology development by many scholars. This paper provides a basic understanding of the Rubik’s Cube and shows its mechanical art from the aspects of origin and development, characteristics, research status and especially its mechanical engineering design, as well as making a vision for the application in mechanism. First, the invention and origin of Rubik’s Cube are presented, and then the special characteristics of the cube itself are analyzed. After that, the present researches of Rubik’s Cube are reviewed in various disciplines at home and abroad, including the researches of Rubik’s Cube scientific metaphors, reduction algorithms, characteristic applications, and mechanism issues. Finally, the applications and prospects of Rubik’s Cube in the field of mechanism are discussed.
Introduction
Rubik’s Cube is a 3D combination puzzle invented in 1974 by Hungarian sculptor and professor of architecture Ernő Rubik and was originally called the Magic Cube . This invention caused the widespread interest in the world owing to its unique characteristics, which exerted a profound impact on mankind. Rubik’s Cube is listed as one of the 100 most influential inventions during the 20th century . Additionally, it is widely considered to be the world’s best-selling toy . It won a German Game of the Year special award and won similar awards for best toy in the UK, France, and the US.
Although the Rubik’s Cube reached its height of mainstream popularity in the 1980s, it is still widely known and used. It not only attracts Rubik’s Cube enthusiasts conducting research into Rubik’s Cube reduction algorithms but also draws the attention of scientists and technical workers from various walks of life for its sophisticated design and ideas . On the one hand, the Rubik’s Cube structure has several features such as rotation, permutation and combinations, and cycle and symmetry, which were treated as physical models or tools to study specific scientific issues or were studied by using scientific theory or methods in some areas. All in all, the principles of Rubik’s Cube are contained in numerous scientific systems that involve permutations and combinations, symmetries, and cyclicality. On the other hand, scholars began to explore the inner movement principles of the Rubik’s Cube structure. The application prospects of Rubik’s Cube have been discussed according to its rotation characteristics.
Origin and Development of Rubik’s Cube
The concept of Rubik’s Cube originated from the China Luo Book, which can be simplified into a Jiugong map.
Jiugong map is a zero-dimensional third-order cube. The n-order magic square is a certain configuration formed by a combination of numbers 1, 2, 3, …, n2 in an n-order square, which makes the sum of the numbers in each row, column, and two diagonal lines n(n2+1)/2. This is called a magic square constant. The magic square constant of a third-order cube is 15 .
Rearrange Jiugong is a one-dimensional third-order cube and is a game developed from the Jiugong map approximately during the Chinese Yuan Dynasty. This game places eight movable pieces in the nine places in the board by moving the pieces to create another pattern in order to complete the pattern change of Rearrange Jiugong.
Rearrange Jiugong spread to the west, and Sam Loyd invented the 15 chess on its basis. The principle of 15 chess (to move the pieces to achieve pattern changes) is the same as that of Rearrange Jiugong. However, the order of 15 chess is a four-order cube that is one order higher than Rearrange Jiugong.
After that, the development of the cube shifted from the order to the dimension. In the Qing Dynasty, Chinese scholars put forward the thought of using digital pieces of three-dimensional magic squares. In fact, this was a three-dimensional second-order cube prototype.
A Rubik’s Cube is an interesting puzzle invented by ‘Erno Rubik’ which has 43 quintillion possible configurations. But with the use of certain algorithms, it can be solved easily. There are many variations of the Rubix cube nowadays but the most basic one is the 3x3x3 Rubik’s cube.
A 3x3x3 Rubik’s cube is made by joining 21 pieces: 1 principle piece with three axles, 8 corner pieces (corner solid shapes) with three tones, and 12 edge pieces (edge 3D squares) with two tones.
Centerpieces are always at their original position only.
Basic Rotations Of Rubik’s Cube:
R: Rotate the right layer clockwise.
R’: Rotate the right layer anti-clockwise.
L: Rotate the left layer clockwise.
L’: Rotate the left layer anti-clockwise.
U: Rotate the top layer clockwise.
U’: Rotate the top layer anti-clockwise.
F: Rotate the front layer clockwise.
F’: Rotate the front layer anti-clockwise.
Beginners Method:
The easy solution to solve a Rubik’s cube is to follow the approach to first solve the bottom layer, then the middle layer, and then finally the top layer.
Step 1: First choose a centerpiece of any color (say white) and then make a white cross by bringing all the four edge pieces adjacent to the white center.
Step 2: Match colors of all four centerpieces of the lateral face with the edges of the bottom layer one by one and sending the matched pairs in opposite directions and then bringing them again to make a cross of white.
Step 3: Set corners of the bottom layer by first matching the correct corner matching its desired color. Then apply the algorithm R U R’ U’ and repeat the same algorithm till the bottom corner piece is set at its correct position as shown below
Step 4: Make the second layer by matching all four edges at the lateral faces. First, match the color of the top layer edge with its center layer and observe the other part of the piece i.e top facing color.
Case 1: If the other part color matches with the centerpiece at the right side, then apply the algorithm U R U’ R’ U’ F’ U F.
Case2: If the other part color matches with the centerpiece at the left side, then apply the algorithm U’ L’ U L U F U’ F’.
Step 5: Make the yellow cross on the top layer by applying the simple algorithm F R U R’ U’ F’ 1-3 times as shown below.
Step 6: Now match any one edge of the top layer with the centerpiece in the middle layer, and then apply the algorithm F R U R’ U’ F’ until all the edges are matched.
Step 7: Now to match all the corner pieces on the top layer, first see the corner which is already being matched and keep it as the front face and towards the right. If none of the corner pieces are in the right place, you can hold the cube in any orientation with the unmatched pieces on top and apply the algorithm U R U’ L’ U R’ U’ L.
Step 8: In the final step keep yellow as the front face and start from any corner apply the algorithm U R’ U’ R until the corner arranges correctly, then rotate the top layer to bring another disarranged corner on the top right side and repeat U R’ U’ R algorithm again to arrange it, and so on. After arranging all the corner pieces, just move the yellow facing layer 1-2 times if needed to completely solve your cube.
With this final step, the Rubik’s cube is finally solved.
Conclusion
By following these steps, you should be able to solve the Rubik’s Cube using the Layer-by-Layer method. Practice is key, so don’t get discouraged if you don’t get it right away. Over time, you’ll develop the muscle memory and intuition needed to solve the cube faster.