There exists a simple toy that captures the interest of countless people, regardless of age, gender, or education, a toy that requires no batteries or electricity and costs only a few dollars to produce. What type of toy could possibly encompass all of these elements? The answer is deceptively simple: a cube.
History of Rubik’s Cube
The face of each octagon is parallel to the face of the imaginary central cube. The eight sides of each octagon are perpendicular to that imaginary cube. These will be referred to as the sides of the octagon.
There are twelve edge pieces total (Fig. 4), each with two visible faces. There is an extension off the non-visible faces of each edge piece to connect it to the core. This extension’s shape is similar to a smaller cube.
One side piece, four corner pieces, and four edge pieces fit together to form one face of a Rubik’s cube. Each face is labeled with a unique solid color. The side piece is the center of the face, and the edge and corner pieces become the edges and corners of the face. The extension off the side piece fits directly on to the core’s octagonal face. The other extensions fit on to the edges of the octagon.
As a Mathematics Teaching Tool
Rubik’s Cube in Computer Science
Rubik’s cube has also been a useful tool to measure artificial intelligence, otherwise known as AI. AI learns new material by computing different inputs with different weights to gain a result . Weights are numerical values that determine how much emphasis an input has on the output. By comparing the calculated result to the desired result, in this case a solved cube, the AI should modify the weights to get closer to the desired result . The Rubik’s cube has been used as a test for the AI to learn and develop its own algorithm. Programmers will give the AI a scrambled virtual cube and observe its attempts at
solving the cube.
Solving Rubik’s Cube
Solving Rubik’s cube by reading step-by-step instructions is too easy. It takes the challenge out of the cube, and with it, the fun. Instead of listing out steps to solve the puzzle, try these three different moves that help in solving the puzzle by switching or adjusting different pieces. Adjusting a piece means to rotate the direction a color faces on a piece (Fig. 6). Switching pieces refers to swapping the position of two different pieces (Fig. 7). A row is one of the three horizontal divisions of the cube. A column is one of the three vertical divisions of the cube.
Move #1 – a move to adjust two consecutive edge pieces (alters nothing else) (Fig. 8)
1. Hold the cube so that the two edge pieces being adjusted are vertical on the top face
2. Rotate the center column up
3. Rotate the top row left
4. Repeat steps 2 and 3 two more times
5. Rotate the top row left
6. Rotate the center column down.
7. Repeat steps 5 and 6 two more times
8. Rotate the top row left two times.
Move #2 – a move to adjust three corners of a face (alters adjacent edge pieces) (Fig. 9)
1. Hold the cube so that the corners are facing you and the unaltered corner is to the top right
2. Rotate the top row right
3. Rotate the forward face clockwise twice
4. Rotate the top row left
5. Rotate the forward face clockwise
6. Rotate the top row right
7. Rotate the forward face clockwise
8. Rotate the top row left
9. Rotate the forward face clockwise twice
Move #3 — a move to switch the positions of three edges on the same plane (alters nothing else) (Fig. 10)
1. Hold the cube so that the plane to be altered is the center column
2. Position the fourth edge in the plane to the bottom position away from you on the cube
3. Rotate the center column up
4. Rotate the top row left twice
5. Rotate the center column down
6. Rotate the top row left twice
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-  “The Novelty Toy Hall of Fame.” Maxim, Apr. 2001, pp. 146-147.
-  A. Billard. Class lecture. Computer Science 499. University of Southern California. Hedco Neurological Building. March 2002.
-  Rubiks.com. (20, Mar. 2002) “Brief History of the Cube.” Rubik’s Online [Online]. Available: http://rubiks.com/cubehistory.html
-  W.D Joyner. (20, Mar. 2002) “Lecture Notes on the Mathematics of Rubik’s Cube,” [Online]. Available: http://web.usna.navy.mil/~wdj/rubik_nts.htm
-  D. L. W. Miller. “Solving Rubik’s Cube” [Online]. Available: http://www.sunyit.edu/~millerd1/RUBIK.HTM
-  Encyclopedia Britannica Online. (20, Mar. 2002). “Rubik, Erno” Encyclopedia Britannica. Encyclopedia Britannica Online. Search: Rubik, Erno [Online]. Available: http://www.britannica.com