I often wondered what the upper bound on the minimum number of moves was. I remember memorizing the solution when I was a kid, but it was probably 100 moves or so. (Get all one layer right, then the 2nd layer, then the top layer.) The sequences for keeping the lower layers intact while working on the 2nd and 3rd layers were complicated — maybe 10 moves or so each.
But I thought the optimal solution was probably a lot lower than that.
Every possible combination can be solved with at most 20 moves.
http://www.bbc.co.uk/news/technology-10929159