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Rubik's Cube Comeback
aheath writes "Today's Boston Globe has an interesting article on the revived popularity of the Rubik's Cube. The article mentions that Winning Moves Games 'hopes to capitalize on the renaissance of the original Rubik's Cube in the next several months by rereleasing a version of the supersize 'Rubik's Revenge,' a 4-by-4 cube with 16 squares per side.' You can compare your best Rubik's Cube solution speed to the world champion's record. If the manual solution method doesn't appeal to you, you can always use the Lego Robotics automated method." I remember having a cube that had letters on each sticker instead of colors, so that the solved product spelled words across each face. That thing got me through a lot of childhood car rides.
I could never figure out how the darned things worked. I took a few apart, but it still seems like magic to me.
I tried and tried to solve that maddening little cube... ended up taking it apart.
OK, I cheated. I'm a bad person. Happy now?
Even if a man chops off your hand with a sword, you still have two nice, sharp bones to stick in his eyes.
I used to do the cube in under a minute regularly. My best averages were around 50 seconds. Nowhere close to the world champion of course, but still more than enough to impress your friends
I used the corners first algorithm. Its not what the fastest cubers use, but its much easier to learn, because its more "natural". It also has a shorter average number of moves (under 60, IIRC). Though I say "easier", it takes several months!
Here are a couple of links if you want to get better at solving it:
Lars Petrus' method for speed
Dan Knight, the world champion
Jessica Fridrich. Her method is used by many.
www.speedcubing.com
www.rubiks.dk
A solution some think is easy.
I bought my first cube 2 months ago and today I completed it in 56.98 seconds! After loads of practice of course.
* The inventor Rubik used to solve it in about 3 minutes
* To measure your average the standard procedure is to do it 12 times, remove the smallest and largest, and take the mean of the remaining 10
* The fastest cubers have averages of about 17 secs
* The best average anyone ever got is (IIRC) 12 secs (Imagine that!!)
* Some people can solve the entire cube blindfolded!! (Study it once, get blindfolded and then solve it). Its based on group theoretic invariants of the cube. You can do certain operations without changing most of the cubies
* Some people can solve a 20x20x20 cube (a software simulation of course)
* There are some incredible videos of people speed solving it available. One by Dan Knights for instance
* The best known computer algorithm can solve random instances in 18 moves (human solutions take about 60 moves). This is optimal on average; There is a lot of work going into finding "God's algorithm", a worst case move-optimal solution
Disclaimer: I used to do it 2 or 3 yrs ago so my info might be somewhat outdated.
In the time it took to read that submission, Rubik's Cube came and went. Again.
You can't push a fad, you know.
Groovy.
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Among corner pieces, all positions are possible (reachable from a given configuration), but only one out of 3 orientations are possible.
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Among edge pieces, only half the positions are possible (diagonally opposite edge pieces can't be switched) and only half the orientations are possible.
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Among center pieces all positions are possible.
So that means only 1/12 of the total configurations are possible!So if you take the cube apart and put it back randomly, chances are you'll end up with an insoluble position :)
This also allows us to count the number of possible configurations.
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Corner positions: 8! (8 factorial)
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Corner orientations: 3^8
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Edge positions: 12!
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Edge orientations: 2^12
Total = 8! 3^8 12! 2^12 / 12 = 43252003274489856000 = 4.3 * 10^19Now a math teaser:
The set of operations (operation = sequence of moves) you can perform on a cube forms a group. Two group elements x, y are said to commute if xy = yx (in this case, 2 operations commute if it doesn't matter in which order you perform them). Question: Find an operation that commutes with every operation.
Rot13d spoiler follows.
Syvccvat nyy gur rqtr cvrprf.
In fact this is the only answer. If you know group theory, this is the only group element other than the identity which lies in the center of the cube group.