courtesy of rubiksmaster: http://www.speedcubing.com/events/regulations.html http://www.speedcubing.com/chris/ -from forum search
To solve it sub 20, you need to memorize about 40. But I'd say that just solving it in 1 or 2 minutes only needs about 7 algorithms.
I used to solve the cube with an average time of 42 seconds. That was about 3 years ago. I haven't solved it since but only a few times.. and it can take me 2 minutes or so. It's about the method and memorizing patterns. The easiest method is layer-by-layer. However, the last layer can be a pain in the ass. The method I used was the Petrus method. It was quite easy and fairly good for speed solving. Basically you solve a corner (2x2). Then you extend it to a 2x2x3. Then you solve the the remaining peice to have the first two layers done. The last layer is then solved in two stages: the solve the corners then solve the edges. http://lar5.com/cube/ It took me about a month to get very good at the method.
Moves an edge piece from the right hand side of the top layer to the left hand side of the front layer, so that the color that was on top of that piece is now at the front. I had that book too!
I had one as a kid, I never figured it out. My mom picked it up one day and in a few days I found it on my bed done!