![]() ![]() Only 1/2 of the permutations have the same edge-flipping orientation as the original cube, and the edge and corner pieces combined exhibit two cycle parity, and therefore only 1/2 of their arrangements would result in a solvable cube. In the Rubik’s cube, only 1/3 of the permutations have the rotations of the corner cube pieces correct. Now, you may think that this is the final number of possible arrangements, however this is not all there is. The center pieces are fixed and therefore are unimportant in determining the possible number of ways the cube can be mixed up. Each edge piece has 2 possible orientations, so each permutation of edge pieces has 2 12 arrangement. There are 12 edge pieces in total which can be arranged in 12! ways. However, this is not all! 1 corner piece has 3 orientations, giving 3 8 possibilities for each permutation of the 8 corner pieces. So if we take these 8 corner pieces out, the total number of ways we can rearrange these back is 8! Ways There are 8 corner pieces on the Rubik’s cube. If we simply think about it, to find that number may seem daunting. But how do we reach that number mathematically? So many of you may have heard people talk about the immense number of ways the Rubik’s cube can be scrambled up. The Total Number of Possible Arrangements on the Rubik’s Cube In this article, I have tried to simplify and explain some of the mathematical concepts that surround the Rubik’s cube. I found the results extremely interesting and in this article I have attempted to share some of my findings. I am inclined towards the mathematics side of everything and I was eager to dig deep and research about the math residing in this puzzle. But what really is the mathematics behind the famous Rubik’s cube? However, all said and done, speed cubing is simply all about the memorization and mastery of long and complex algorithms. My collection of cubes adorn my desk and I love doing a few solves a day to keep in touch with this mind-stimulating activity. Today, I average 20 seconds on the 3×3 Rubik’s cube. That was the beginning of my cubing journey. Within a month, I learnt all the algorithms and could solve the cube easily in under a minute. I spent that entire day trying to solve one face side and by the end of the day when I finally managed to do so, I ran around the house ecstatically to show every single person my achievement. I was fascinated by the popular puzzle since the day I Iaid my hands on it. ![]() “ We turn the cube, and it twists us” – ERNO RUBIKīy the time I was 10, I could solve the Rubik’s cube in under a minute. ![]()
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