Schiebepuzzles

Schiebepuzzles, or sliding puzzles, are mechanical puzzles in which tiles are placed inside a frame on a grid and can only slide to adjacent empty spaces. The object is to reach a target arrangement, typically the ordered sequence of numbers or a complete picture.

History: The most famous example is the 15-puzzle, also known as the Gem Puzzle, which appeared in the 1870s and quickly became a global craze. Since then, many variations have been developed, varying in grid size, number of tiles, and shaping.

Mechanics and solvability: A move consists of sliding a tile into the neighboring empty square. On most boards there is exactly one blank. Not every initial arrangement is solvable: for example, on the standard 4x4 puzzle solvability depends on the permutation parity of the tiles and the row of the blank from the bottom.

Variants: The 3x3 version is the 8-puzzle; the 4x4 version is the 15-puzzle. Other sizes such as 5x5 exist, and there are puzzles with non-square frames or with sliding blocks of different shapes. In modern times, sliding puzzles appear in digital games and as brain teasers like Rush Hour (though that is a sliding-block puzzle) and other puzzle collections.

Solving: Humans typically solve by planned sequences, often using row-by-row methods, placing tiles while preserving already solved sections. Computers solve using search algorithms such as A with Manhattan distance heuristics; the problem is a classic benchmark in artificial intelligence.