The puzzle mechanic is a very interesting concept, although a little difficult to understand at first. I agree with littlepuly that the visuals could be better (although I don't exactly have enough experience to offer suggestions here).
It is also a little difficult to tell what path the knight is going to take to get to the selected carrot, meaning it becomes a game a bit more about trial and error than puzzle solving. I also got to a level where even in full-screen I couldn't see the finish. I can't remember which one though, sorry.
Obviously we all have to make sacrifices when making games in such a short period of time, so the issues are understandable. If you had all the time in the world, I would focus on making the tutorial more clear and making what the knight will do when you hit play more clear in some way. Perhaps explain a bit more what is going on under the hood (in the code).
This is definitely the type of puzzle game I would play, though. Definitely a good idea, especially given the time constraint.