Create a sliding block puzzle app which only does 1 puzzle, but starts first by presenting initial positions close to the solution, and after each solve, progressing towards more difficult initial positions.
Player gets a feeling of getting better.
Player might learn a mental map of the puzzle, inspired by the map of the "Century" in Winning Ways. However, absolute distance to solution might not be the best way to teach or learn such a map, missing out on the repeated structures of mini-puzzles described in Winning Ways.
Goal position too can also be altered, perhaps after all initial positions are mastered. Having a map helps in navigating between arbitrary points.
Similar to learning chess endgames.
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