Sliding puzzle

A puzzle in which pieces move by sliding within a constrained space, typically to arrange them into a target configuration.

N-puzzle: A square-grid sliding puzzle with numbered tiles and one empty cell, commonly exemplified by the 15-puzzle. Its numbered tiles and single vacancy make the classic sliding-puzzle mechanism precise.
A* search algorithm: A best-first search algorithm that ranks paths using cost so far plus an estimate of remaining cost. A* uses tile-distance estimates to find short solutions efficiently.
15-puzzle: A 4-by-4 sliding puzzle with fifteen numbered tiles and one empty space. This famous instance popularized the sliding-puzzle form in the late nineteenth century.
Jigsaw puzzle: A picture puzzle assembled by fitting interlocking pieces together. Its pieces are lifted and joined, unlike tiles constrained to slide in a frame.
Permutation: A rearrangement of the elements of a set into a particular order. Every tile arrangement can be represented as an ordering of the tiles and vacancy.
Permutation group: A group whose elements are permutations and whose operation is composition. Tile arrangements are permutations, though legal moves reach only a subset of them.
Iterative deepening A*: A heuristic search algorithm that repeatedly explores depth-first paths under increasing cost bounds. IDA* solves large instances while using far less memory than A*.
Sam Loyd: An American puzzle inventor and recreational mathematician known for popularizing mathematical and mechanical puzzles. Loyd promoted the 15-puzzle with a prize challenge that helped make it famous.
Klotski: A sliding-block puzzle in which rectangular blocks move through a tray to free a designated block. It replaces numbered tiles with differently sized blocks while retaining constrained sliding.
Inversion (mathematics): A pair of elements in a sequence that appears in the opposite order from a specified ordering. Inversion counts help determine whether a numbered-tile arrangement is solvable.

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Rubik's CubeCompared with: It rearranges pieces through sliding rather than rotating puzzle layers.