Some quick information on the puzzles; each lock has two dials that will rotate the lock/puzzle by a certain number of places either clockwise or counter-clockwise. For simplicity I have used left and right for all of the sequences. You don't need to finish every lock in under a minute in a single playthrough, you just need to have finished each one in that time at least once on the same game profile.
Lock 1: Garage - You can spin 3 places (Left Dial) or 2 places (Right Dial). The solution is:
Right x2, Left x2, Right x4
Lock 2: Museum - You can spin 3 places (Left Dial) or 5 places (Right Dial). The solution is:
Right x2, Left x2, Right
Lock 3: Jail - You can spin 2 places (Left Dial) or 3 places (Right Dial). The solution is:
Left x 2, Right, Left, Right x2, Left