Rubik's Cubes
I was first introduced to the 3x3 Rubik's Cube when I was in 6th grade, and it interested me greatly. I was puzzled on how complicated the cube seemed, yet the speed at which one could solve it. After Googling, I had found a very good website that taught me the basics of solving the cube, soon, I had memorized all the moves, plus some faster shortcuts to solve it. At the end, I had reduced the time it took to solve the 3x3 from 5 minutes to less than a minute and a half.
I then got a 4x4 Rubik's Cube. When I tried to solve it, it turned out that the guide for it was really simular to the 3x3 Rubik's Cube. Only with minor additions at the beginning and a few parody cases, I really didn't have to learn anything new, and the same techniques from the 3x3 still applied for the 4x4 Rubik's Cube.
What is awesome about the 4x4 Rubik's Cube, is that you can make it into a 2x2 cube, by pretending that some of the small squares merge into a bigger square. I thought solving the 2x2 would be a challenge and would require more memorization, but it turned out I was wrong. It was so simple. The moves I used were just from the 3x3 Rubik's Cube.
In summary, I learned that the 2x2 is the easiest the solve, and the bigger you get, the more you need to learn. So my idea to learn how to solve most of the Rubik's Cubes was to learn from the very biggest (maybe a 10x10), where there are the most moves to learn, so then the smaller cubes' moves would be 'included.' This would require a huge commitment at the beginning, but then, solving the smaller cubes would be easy as pie... Though I haven't tried it. :)