The Rubix cube is the second easiest puzzle in the world. The first easiest is the Rubix Pocket Cube, which is just the corner solution algorithm. Actually, Pyraminx and a couple of others that were popular around the time of Rubix Cube are much, much easier than even the Pocket Cube. But once you have mastered the Cube, a lot of others become much easier for you.
Coming up with your own algorithms for moving things around when the cube is half-solved (so that nothing that has already been accomplished is destroyed) is mind numbingly complicated. Making these algorithms very short is even more difficult. Personally, I figured out my own algorithms for the top and bottom layers, but for the bottom layer I had to resort to algorithms I had memorized from a solution book.
I finally had a breakthrough on Rubix Revenge (4x4x4), which I never actually figured out how to solve on my own, although admittedly I needed a few hints from a Web site before I saw how it could be done. My basic strategy is to match up all the centers and edge pieces, and then solve it as if it were a regular 3x3x3 rubix cube. What's really aggravating about the Revenge, however, is that using this strategy it is possible to get down to the very end and discover a situation that is simply impossible on a 3x3x3 cube (e.g. one edge piece that needs to be flipped, or two edge pieces that need to be exchanged - or, worse, both). The former requires going back almost to the beginning of edge-piece matching and the latter requires going back to about the middle of the 3x3x3 solution, and you can't tell which you need to do (or both!) until you are almost done with the last layer.
There are probably more efficient ways to solve the 4x4x4 rubix cube in fact, I have a solution book for it that is much shorter - but frankly I prefer a solution I can understand to one I must memorize.
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