The “God Number” for a Rubik’s Cube is Exactly 20
Tuesday, August 24th, 2010
Researchers have proven, using mathematical techniques and a heavy amount of computing power, that 20 is the maximum number of moves necessary to solve any Rubik’s Cube configuration by the shortest method. This value is known as God’s number. They were able to mathematically reduce the number of unique patterns from 43,252,003,274,489,856,000 to a mere 1,090,175,792,696,524,800 (one quintillion). Then they used something on the order of 35 CPU years of processing to verify that each of the remaining combinations could be solved in 20 moves or less.
Thanks to Josh for this link.
Link: http://www.cube20.org/
Here’s an interesting study by Takahiko Masuda,
I have no idea how this is possible, and the math is beyond me, but an IBM employee named Craig Gentry has found a way to add and multiply encrypted data without first decrypting it. It’s called “fully homomorphic encryption.”
From the article: “A paper in the current issue of Science discusses the ability of a single-celled creature to create a robust network while foraging for food—one that mimicked the Tokyo rail system in complexity.”
Scientists can now make a drop of oil traverse a complex maze by itself. Be sure to watch the video.
Whenever I hear an expert say that life would not be possible if some physical constant or feature of the Earth had been slightly different, I remind myself that it’s really life as we know it that would not be possible.
