Going to submit my probably-not-a-puzzle-game-game: rhythm games. The game tells you exactly what to press and when you're supposed to press it, it's just up to you to actually press the buttons. See: DDR, Rhythm Doctor.
Note that there are rhythm games that have more decision making like crypt of the necrodancer (rhythm roguelike)
To be clear, that's Cataclysm:Dark Days Ahead or CDDA. It's quite removed from the original cataclysm by whalesdev, and is more focused on strict realism. There is also Cataclysm Bright Nights which is closer to the arcadey feel of the original. Both are great and are open source.