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I love the checkerboard pattern.
The puzzles are also very good.
I really enjoyed this.

(+1)

The only tip I could think of is that puzzle games like this have the tendency to get people stuck in very unpredictable places.
Games like "baba is you" have a solution for that by making it possible to skip a level.
I shouldn't bother for a game-jam game. But if you want to make it a full-on game then it's something to think about.