Aha! I tossed and turned all night, reeling with the confusion of potential ideas. My wife was playing Bejeweled in bed, and I was thinking about Cluesweeper (flash game, fun, look it up), which crushed me in the monthly Kongregate contest once. Discussing with her the idea of a game that gave you clues via Bejeweled instead of Minesweeper. Thinking that wasn't gonna work. Thinking about a murder simulator (just as Jack Thompson feared!), like it would track where a bunch of people were at a party for a series of hours, where weapons were (like Clue!), and then you could interview the guests, and of course the murderer would lie. I couldn't figure out offhand a way for that to not be trivial and be fun. I slept.
I woke up this morning back on the idea of a game of objects on a board (Bejeweled), and I have the answer! It's a game where the board is filled with runes (or animals, or some other symbols). Lights indicate rows and columns that aren't valid. It's up to you to figure out the (randomly generated) rules that determine validity. Maybe this row isn't valid because every row has to have one of every rune, or maybe it's that you can't have the same rune next to itself. Experiment! As you make changes, the rows get righter and wronger, and you start to discover the pattern. The longer you take to complete it, the more of the rules are shown to you. Solve the board faster for more points. Discover
the rules! Easy to have easy/medium/hard with larger board sizes and more rules. Tricky to actually make sure the board is solvable. Will figure that out.