Bombe

Minesweeper, but you only solve each situation once.
Regions (number bubbles connected by lines) generated from clues on the board
Rules act on regions to mark bombs, clear squares or create new regions
A checker tells you if your rule is formally correct
Rules are auto applied forever after, resolving the situations you have solved before
Only the hard situations remain.
A hint system can mark the determinable squares and remove all unnecessary regions from the board.
Regions can be hidden or discarded using rules
Thousands of levels to play, all solvable without guessing.