slidingblock

Slidingblock refers to a class of puzzles in which a set of rectangular blocks occupies a grid and can slide within the constraints of the grid and block orientations. The pieces typically cannot rotate, and moves consist of sliding a block along its long or short axis until it is blocked by another piece or the edge of the board. The goal is usually to reach a specific final arrangement or to free a particular block to exit the grid.

In most slidingblock puzzles, the board is a fixed rectangular grid and blocks have fixed orientations (either horizontal or vertical). A move is selecting a block and sliding it any number of empty squares along its allowed direction, stopping only when it would collide with another block or the boundary. Common variants include puzzles with a single empty space, as in the classic 15-puzzle, and puzzles with multiple empty spaces or more complex block shapes. Many puzzles require guiding a designated block to an exit or achieving a target layout.

Notable examples include the 15-puzzle, a 4x4 grid with 15 tiles and one empty space; Rush Hour, where cars must be moved to free a red car’s path to an exit; and Klotski, a classic puzzle featuring a larger central block that must be moved to an opening. These puzzles have been popular as brainteasers and as tools for teaching problem solving and algorithmic thinking.

Historically, slidingblock puzzles have appeared in various cultures and eras and gained widespread popularity in the late 19th and early 20th centuries. They are used in education and research as testbeds for search algorithms, planning, and human-computer interaction. For generalized forms, determining solvability or finding a solution can be computationally challenging, illustrating rich combinatorial structure despite simple rules.