Monday, May 20, 2013

Cubes, Pyramids, and more!

by abelchen777, This post originally appeared on Function of a Rubber Duck.

With the unveiling of the 6th generation Rubik’s cube, I am going to do a blog post on Rubik’s cubes. I first started to get interested in Rubik’s cubes August 2012, when I went over to my friend’s house. As he showed me all the cool things he could do with the hundreds of Rubik’s cubes he has (an exaggerating, but not by much), I decided that I wanted to learn. So he taught me, and I practised for a few days. As I got better and better, I was also more intrigued by this toy, which was simple but complicated at the same time. I looked up some facts on it. There are over 43 quintillion possible possible permutations of a Rubik’s cube, taking into account the physical limitations of the cube. So, you probably won’t be able to solve a Rubik’s cube if you are trying to do it randomly. On the bright side, the greatest number of moves it takes to solve any of the 43 quintillion possibilities is only 20 moves. There was no elegant mathematical proof to show it, a team of mathematicians just borrowed Google’s computing power to try all the combinations using brute force, while reducing the cases that were necessary to check. Some cases are exactly the same, except for the colors, and some were identical if it weren’t for it’s orientation. Cases like these reduced the cases needed to be checked, and with the ever growing computing power steadily solving away, they finally proved that 20 is the most turns you need to perform to solve any permutation. This is called “God’s number” because you would need to be God to know the optimal solution for each permutation.
I will leave you with some decidedly different “twisty” puzzles. Can you solve any of the following?

These are not too exciting- They are just bigger versions of the familiar 3x3x3 cube.
 Here’s something more exciting. It’s a 3x3x3 cube, with long diagonals added in. This cube is still not too weird yet-it still retains it’s cubic shape however you twist it.
This one is called the mirror cube. All three layers have different heights. The result is a hard to manage mess, shown on the right.
Moving away from cubes, now. How about a pyramid?
This puzzle is called the pentaminx. It’s almost a sphere, and I’m not even sure how many faces it has!
I have one last cube to show you. This one is a 2x2x2 with an extra twist to it. Actually, it has 6 extra twists. Each face of the cube comes with a rotating dial with numbers, which you have to put in order in addition to matching it’s colours. Have a great spring break!

About this contributor: Abelchen777 is a grade 11 student with a special passion for mathematics. He also enjoys playing badminton, soccer, and reading both fiction and non-fiction books. His favourite field of science is quantum physics.

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