on Dec 28th, 2011
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Have you ever wondered the sheer number of permutations you can produce with a regular 3x3 Rubik's cube? I know I certainly have. A Rubik's cube is actually a combination of 3 types of smaller cubes, or cubelets. The first cubelet is the center piece of each face. The way the Rubik's cube is constructed, the center cubelet can only turn and not move; the center cubelet doesn't create any extra permutations. Next, there are 12 "edge" cubelets which each have two stickers; they are located in the center of every edge of the cube. Since there are 12 cubelets, there are 12 slots for the cubelets to go. Imagine that you are randomly putting the cubelets into the slots. For the first slot, you can put any of the 12 cubelets, while for the second you can now only put 11. If you continue doing this, there are 12! permutations (12x11x10x9x8x7x6x5x4x3x2x1) due to these pieces alone. In addition, we must multiply by 2^12 (2 orientations for each of the 12 pieces). Finally there are the 8 corner cubelets, which each have 3 stickers. Each of these cubelet could be in any of those 8 places, so multiply by 8!. Moreover, each of those corner cubelets can be in three orientations, so multiply again by 3^8. In practice, only 1 in 12 of these theoretical permutations can be reached without taking the cube apart. So the total number of permutations is (12! x 2^12)x(8! x 3^8)/12, or about 4.3 quintillion.
But whenever I solve a cube, none of these 4.3 quintillion permutations are going through my head. In fact, almost nothing is. I learned 3 years ago how to solve the Rubik's cube with a beginner's method. This method uses several "algorithms" (or a special sequence of moves), to simplify the job. To solve the cube, you do not solve each side individually, you solve the three layers of the cube separately using many algorithms. But not even these numerous and complex algorithms go through my head. In fact, I could not even tell you the algorithms I once spent months arduously memorizing. When I see a Rubik's cube, I don't think, I do.
I see this as the epitome of being nerdy with something. It is taking something incredibly dense, and devoting yourself to it so much that it becomes simple. This is certainly the process I have seen with Rubik's cubes. As a freshman when I first looked at a Rubik's cube, it was hopelessly complex to me; I often looked on in awe as some of my friends would solve them faster than I could blink. Then I dedicated myself to learning the algorithms. I devoted myself to the cube for a month before I learned enough to solve it without any notes; since then it has become second nature. It the nerdiest thing I know how to do not because it is typically seen as nerdy, but because of how all my effort has made the Rubik's cube so simple.