Editing 15 puzzle (section)

{{Short description|Sliding puzzle with fifteen pieces and one space}}
{{redirect|Magic 15|the numbered grid where each row and column sums to 15|Magic square}}
{{Use British English|date=July 2022}}
[[File:15-puzzle magical.svg|thumb|To solve the puzzle, the numbers must be rearranged into numerical order from left to right, top to bottom.]]
The '''15 puzzle''' (also called '''Gem Puzzle''', '''Boss Puzzle''', '''Game of Fifteen''', '''Mystic Square''' and more) is a [[sliding puzzle]]. It has 15 square tiles numbered 1 to 15 in a frame that is 4 tile positions high and 4 tile positions wide, with one unoccupied position. Tiles in the same row or column of the open position can be moved by sliding them horizontally or vertically, respectively. The goal of the [[puzzle]] is to place the tiles in numerical order (from left to right, top to bottom).

Named after the number of tiles in the frame, the 15 puzzle may also be called a ''"16 puzzle"'', alluding to its total tile capacity. Similar names are used for different sized variants of the 15 puzzle, such as the '''8 puzzle,''' which has 8 tiles in a 3×3 frame.

The ''n'' puzzle is a classical problem for [[Modeling language|modeling]] [[algorithm]]s involving [[heuristic (computer science)|heuristic]]s. Commonly used heuristics for this problem include counting the number of misplaced tiles and finding the sum of the [[taxicab distance]]s between each block and its position in the goal configuration.<ref name="Korf,2000"/> Note that both are ''[[Admissible heuristic|admissible]]''. That is, they never overestimate the number of moves left, which ensures optimality for certain [[search algorithm]]s such as [[A* search algorithm|A*]].<ref name="Korf,2000"/>