Wednesday, October 28, 2015

Hypercube

As a writer, I should research a lot of information about Rubik's cube before coming to this article, but I feel lazy today and am content to direct your attention to a long list of sayings about cubers.

My family received several Rubik's cubes from a visitor when I was in 5th grade. It came with a set of pictorial instructions that taught me how to solve the cube layer by layer. I learned the algorithms and began showing off in middle school where kids would pay me a quarter to fix their cubes for them. I once solved it in 46 seconds, but it was a lucky break where the pieces fell just right. I never got too far in speed cubing, but I can regularly finish in under 3 minutes. While watching the Double Fine Adventures documentary about how the Broken Age adventure game got made, I was fascinated by how often Tim Schafer was playing with his set of cubes ranging from 2x2x2 to 5x5x5. I purchased a set for myself and they finally arrived in July. For much of the summer and early fall, I had been lost in cubing, distracting me from chess. I had never signed on to Rubik's Revenge or the Professor's Cube sequels, but now I have. Two of my chess friends have been cube crazy.

My best times for the 2, 3, 4, and 5 cubes are 0:32, 1:20, 4:45, and 8:51, respectively, which aren't anything special. One friend told me he can do all 4 in under 8 minutes cumulatively.

For some reason, I wanted to compare some of the astronomical numbers that come out of chess and cubing. Here is what I collected:

FieldPermutations
2x2x2 - Pocket Cube, Mini Cube, Ice Cube3,674,160
3x3x3 - Rubik's Cube, Magic Cube43252003274489800000
4x4x4 - Rubik's Revenge, Master Cube7.40x10^45
5x5x5 - Professor's Cube2.83x10^74
Atoms in the Universebetween 10^78 and 10^82
Positions in Chessbetween 10^43 and 10^47
Chess Game Tree Complexity10^123

Hypercube refers to an n-dimensional cube of which the standard 6-sided cube is the 3-dimensional version and the tesseract, popularly introduced in Madeleine L'Engle's A Wrinkle In Time, is the 4-dimensional version. Don't watch the movie "Cube 2: Hypercube"; it sucked.

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