Wow I really like your core mechanic, lots of potential to build off of it! I will admit, the puzzles had me confused in general: I liked the main menu as a sort of "puzzle" and think that one worked well, but once in the game itself I think it could use a little more guidance to help the player get on the right track with solving puzzles.
All that being said, I still think you have a great core here and solid foundation to work off of, just needs some small tweaks and you can really go crazy with this!