Neat game, but IX is unsolvable. I tried every possible combination, and several looked like they should have fulfilled the shape requirements, but nothing happened.
Also, it's not clear right away that the game has started after it is finished loading. There should be, at the very least, some kind of "start game" button so people don't end up sitting there thinking it is still loading.
Every level is solvable :P the single lines have a rule that you might be missing (compare V and IX)
Good point about the loading
A fun puzzle to pass the time!