Puzzle 32: Lits 3 (Redo)

Well it turns out my first version of Puzzle 32 had more than 1000 different solutions (thanks Prasanna for noticing). I have fixed it, and have verified that this one has only one solution, but I have made the puzzle substantially harder (or harder than I thought it was...). By the way, sorry that I have not been publishing much recently - I have been preparing for the Google Code Jam Qualification Round.