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  1. It's a fun game, it could benefit from a math background to generate levels on the fly; for instance using a random rule and then a level in the shape of the rule (like the L level but for custom shapes). In other words, a simple custom level maker/editor and a way to share new puzzles.
  2. One can luck out on harder levels like king queen and knight (chess), but overall group theory underlies the logic of all the puzzles.