Slashdot Mirror
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.
Rubik, the Hungarian mathematician, invented his cubic toy as a playful model of quaternion math in group theory. Has playing with the Cube influenced a generation of people who could actually learn quaternion dynamics from it as children? Can the puzzle be used to demonstrate to the unenlightened the quantum computing techniques those grownups are now inventing?
--
make install -not war
* 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.
-
Among corner pieces, all positions are possible (reachable from a given configuration), but only one out of 3 orientations are possible.
-
Among edge pieces, only half the positions are possible (diagonally opposite edge pieces can't be switched) and only half the orientations are possible.
-
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.
-
Corner positions: 8! (8 factorial)
-
Corner orientations: 3^8
-
Edge positions: 12!
-
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.
Those truly interested in the importance of the Rubik's cube should dig into the archives of Scientific American (if it's not online as a subscriber, try a library). There was a very good, in-depth (cover) story published as the popularity was beginning to wane. For the mathematically inclined, the Cube delves heavily into Group Theory and the article points this out. It also refers to "God's Algorithm", which means if you were to take a cube of any arrangement, hand it to a machine programmed with the algorthim, it would solve the problem with the same twists & turns with no decision making - just the same twists & turns. If you stop to ponder this - a universal algorithm with the same steps applied to any arrangement - this is pretty incredible! IIRC, the number of steps is on the order of 10^60 steps. Back to the mathematics. The arrangement of the tiles is important: at least if any of the pieces are pulled off of the framework and put back on (and this is not the same as peeling the colored paper off). When I was in college, there was a guy named Bert (seriously - his middle name could have been PointDexter) who bragged he could solve a cube in any arrangement in thirty seconds. Someone came to my room and asked if there was any way to shut this guy down. I grabbed a cube, took a corner cube off, gave it a 1/3 twist, and snapped it back into the framework. Scramble the puzzle a bit more, and down we went to visit Bert. Thirty seconds, forty seconds, fifty seconds. At three minutes, Bert exclaimed, "Someone's been tinkering with this cube!" (and he was pretty worked up by now) Obviously, this was pretty funny because his "any cube in thirty seconds" rep was gone and the fact he'd tried harder & harder as time progressed over the goal was gone. By 1982 or 1983, you could go to Target and buy Cubes for $0.50 (closeout). For those with a passing knowledge of the Cube wanting to delve into the history, one of the good places to go is eBay. There was a Saturday morning cartoon (copies sell on eBay), earrings, keychains, 4x4x4 cubes, 5x5x5 cubes, etc. I'm sure there are plenty of web pages and other online resources dedicated to the Cube as well (remember, there was no web when the Cube was hot).