I am including my method for solving the cube. It enables me to solve the
cube in 20 seconds on average (since I am not as fast as I used to be 14
years ago :-( ).

1. Do the four edges (white first) (2 sec.)
2. Put the white corner including the corresponding edge from the second
slice. When you put all four white corners, two slices on the cube will be
done. In this stage, almost no algorithms are necessary. Most positions
can be solved with intuition. (4 x 2 sec = 8 sec.)
3. Turn all 8 small cubes from the last slice so that the last face has
the same color. There are only 40 different positions (not counting
symmetrical positions). On average, 10 moves are necessary to do this
phase.(3 sec.).
4. Move the cubes in the last slice so that the cube is solved. There are
only 13 different positions. On average, 10-15 moves are necessary. (4
sec.)

For the whole system, 40+13=53 algorithms are necessary. One also needs
about 8 short algorithms for the second phase. Altogether, 61 algorithms
will enable you to solve the cube in 17 seconds on average, if you can
turn 4 turns per second, and if you can minimize time gaps between
algorithms.

The handling of the last (3-rd) slice is probably the most efficient
approach ane can come up with. One only needs to carry out two
algorithms to do the 3-rd slice. That is very effective. Breaking the last
slice into four stages (turn edges, turn corners, move edges, move
corners) is less demanding on the algorithmic part, but needs much more
moves and more idle time between algorithms.

Jiri Fridrich