Fifteen (Number Puzzle)

The Fifteen (15-puzzle), also called Gem Puzzle, Boss Puzzle, Game of Fifteen, Mystic Square and many others - is a sliding puzzle that consists of a frame of numbered square tiles in random order with one tile missing. The puzzle, if 4×4 tiles, the puzzle is called the 15-puzzle or 16-puzzle named, respectively, for the number of tiles and the number of spaces.
The object of the puzzle is to place the tiles in order (from 1 to 15) by making sliding moves that use the empty space. The Fifteen is a classical problem for modelling algorithms involving heuristics. Commonly used heuristics for this problem include counting the number of misplaced tiles and finding the sum of the taxicab distances between each block and its position in the goal configuration. Note that both are admissible, i.e. they never overestimate the number of moves left, which ensures optimality for certain search algorithms.