Candy Crush as an integer programming problem

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I'm trying to model the basic version of a match-three game, where the player (has a maximum number of swaps) must swap any two adjacent gems (no diagonals) in an 8x8 grid of gems in order to match three of the same color in a row. The gems can be matched horizontally or vertically. Gameplay continues until the user gets the required score or arrive to the limit of moves.

I have a matrix of 8 by 8, each cell contain a certain color (i have 6 in my model). I don't know where to start, I didn't find relevant research papers about that.

  • How can i model gem swapping ?
  • How can i model the scoring and deletion of the 3-matched gems ?