Plays quite well, and having the total moves displayed as a goal is super helpful to figure out roughly how complex the solution ought to be. Got to level 15 so far and it seems reasonably well balanced. Getting the level difficulty scaling right is often quite tricky, having made a fair few games so far that's always been a pain, so very good job on that. May be worth adding one even simpler first level since some people here are apparently having trouble figuring out the mechanics at the very start.

One other suggestion I'd make is regarding the art style, which seems a bit inconsistent. The space wallpaper doesn't really fit with the rest, I'd imagine a wooden table sort of texture might look better. Having the buttons in the same style as the game board tiles would tie the gui together more, etc.