Look at the first image. See the empty square on the bottom left? There's a pretty good chance that you will want to move 1 blue square there - temporarily.
See the second image? Now it matters which square goes where. A lot of the puzzles in the multi color levels actually are in the mono color section.
Ready for this? There are 1680 levels. Insane. But they go pretty quickly. Many levels are solved in seconds.
In order to advance to the next section of levels, you must solve 60% of the previous section. Each section has 120 levels.
According to the Game Center Leaderboard, there are only about 300 people playing MoveZ. I'm #2 with about 460 levels solved. Sounds crazy. But really, I've only spent about 20 minutes/day for about 10 days.
Very similar games:
Frozen Ice Cubes came out last year. What's different: there's a point of 'no return'.
Vubu came out 3 years ago. What's different: the vubu men have different powers. Very sophisticated.
Yet another game, reviewed by Nicola Salmoria. He told me about this game ages ago, but I forgot about it.