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This is a super neat idea, and well executed too!  I have played a lot of game similar to this before, even ones with forced commands along the way, but I have never seen the permutation system in any other game before.  This made the puzzles way more interesting and really forced me to think about every single possibility.   A lot of the solutions were really elegant, although I think I might have cheesed a few levels based on the simplicity of my code.  The visual style and audio work really well together too.  I could honestly see this doing well as a full game if you ever decide to build on it and add more levels.  Really well done, especially in such a short time frame!