Rubicks Cube
How to Logically Solve a Rubik’s Cube Kenneth Cason First, as with any problem, it is important to understand what your objective is. In the case of the Rubik’s Cube, the main goal is to arrange the pieces in such a way that each side is the same color. Next lets luck at the structure of a standard 3x3 Rubik’s Cube. It is a cube composed of 6 sides, each side composed of 9 stickers (3x3). There are 8 corner pieces, 12 edge pieces and 6 center pieces (one on each side). It is also important to note that on all “odd” Rubik’s Cube’s the center pieces can rotate clockwise or counter clockwise, but the positions are fixed. “odd” meaning that the cube is a 3x3, 5x5, NxN, where N is an odd number. Also, because the center pieces are fixed it becomes immediately obvious which side is which color. Now that we know the basic structure of a Rubik’s Cube next lets think about strategies to solve it. First, lets examine what is probably the most common way to solve a Rubik’s Cube, the “Layer by Layer” method. For those not familiar with the Layer by Layer method, it involves solving the top, middle, and bottom layer in that order. However, despite this seeming to be the most logical way to approach the Rubik’s Cube, it is actually farm more difficult to solve in this manner. The problem is very simple. If you solve the first layer completely, in order to solve the second layer without messing up the solved first layer the moves grow in length and complexity. Then to solve the bottom layer without messing up the top and middle ayers, the moves again grow even more complex. To add a quantitative example, lets look at the case of trying to place a piece in the second row without messing up the first row it takes 7 permutations, and to switch the bottom layer edge pieces positions without messing up the top and middle layers, permutations can be as much as 15, in which you are more likely to give up before you ever derive on your own techniques. Not to say that it is