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Each match 3 could be an inversion of a chord. Colors could be represented by instrument, pitch and tone could be up and down, left and right.
I might be wrong about this but it seems to me like each step in a match 3 game is like exchanging two faces of a tetrahedron. Doesnt that make solving a match 3 game like doing fluid dynamics step by step? If not, then maybe that's another idea, to make a tetrahedral space-filling puzzle either in 2d visual, tactile or audio display.
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