Ah, nice, multiple boardsAll puzzles do indeed have codes for free play.
I now have 46 stars and ~500 coins (still have the 1000 coin star to buy). I already bought the Box for 2000 coins and unlocked the Courtyard's puzzle.
I found another code, for the Stubby Pentagon U L D R U L D R O X and added it to the code list. Do all of the new puzzles (like 1x2x2, Helicopter Third, Pyramid, etc..) have new codes to unlock them in Free Play?