Discussion
Why is the number of misplaced tiles an admissible heuristic for the eight puzzle?
Answer: D
Each tile out of place requires at least one move, so the count is a lower bound on the solution length, and it corresponds exactly to relaxing the rules so that a tile may move anywhere. Being smaller than another heuristic does not establish admissibility, the count is of tiles rather than moves, and no measurement is involved. Tracing a heuristic back to the relaxation that produces it both proves admissibility and suggests how to improve it.
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