Originally posted by doodinthemood
I was defining move as one side turning, as soon as you switch and do another side, you're onto the second move.
Also, it's 17 and 34. Not 7 and 14. 7 moves would be incredible.
You are wrong. There is a position that is 20 moves away from the monochromatic position.
See the paragraph just above the "contents" box.
What you probably meant is that 17 is a theoretical
lower bound, since you have 18 possible first moves (any face can be turned 90, 180 or 270 degrees) and after that for each move you have 15 possibilities (you don't want to turn the same face again).
So in 0 moves you can reach at most 1 position; in 1 move, 18 positions; in 2 moves, 18*15 positions; in 3 moves, 18*15*15 positions, and so on - in n moves, 18*15^(n-1) positions. This number is bigger than ~4.3*10^19 (number of possible positions) only if n>=17, which proves there are positions which need 17 moves. But this does not prove that all positions can actually be solved in 17 moves.