> For larger versions of the n-puzzle, finding a solution is easy, but the problem of finding the shortest solution is NP-hard.[1][2] For the 15-puzzle, lengths of optimal solutions range from 0 to 80 single-tile moves[3] or 43 multi-tile moves;[4] the 8-puzzle always can be solved in no more than 31 single-tile moves or 24 multi-tile moves (integer sequence A087725). The multi-tile metric counts subsequent moves of the empty tile in the same direction as one.[4]
The number of possible positions of the 24-puzzle is 25!/2 ≈ 7.76×1024 which is too many to calculate God's number. In 2011, a l…