Sliding puzzle

A sliding puzzle, also known as a sliding block puzzle or sliding tile puzzle, is a combination puzzle in which a player slides flat pieces along routes on a board to achieve a specific end-configuration. The pieces may be simple shapes or imprinted with colors, patterns, sections of a larger picture, numbers, or letters. These puzzles are essentially two-dimensional, though mechanical interlinking or three-dimensional tokens may be used. Unlike tour puzzles, sliding block puzzles prohibit lifting any pieces off the board, distinguishing them from rearrangement puzzles.

This restriction means that finding moves and the paths they open within the board’s two-dimensional confines is central to solving them. The oldest known type of sliding puzzle is the fifteen puzzle, invented in 1880 by Noyes Chapman. This invention sparked a widespread puzzle craze in the early 1880s. Sam Loyd is often incorrectly credited with popularizing sliding puzzles based on his false claim of having invented the fifteen puzzle.

From the 1950s through the 1980s, sliding puzzles that used letters to form words were very popular, with examples including Ro-Let, Scribe-o, and Lingo. These word-based puzzles often had multiple possible solutions. In manufactured wooden and plastic versions, pieces are often linked and encaged using mortise-and-tenon key channels along the edges. In at least one vintage version of the Chinese cognate game Huarong Road, a wire screen prevents lifting while the pieces remain loose.

While some sliding puzzles incorporate mechanical fixtures, these are usually not essential; the pieces could simply be tokens moved on a flat board according to rules. The fifteen puzzle has been computerized as puzzle video games, where the goal is to form a picture on-screen, with the last square displayed automatically once the others are aligned. More recent evolutions, made possible by increased computing power, involve arranging moving animations or video clips instead of static images. Mathematically, the fifteen puzzle can be represented by the alternating group, as its combinations are generated by 3-cycles, and any sliding puzzle with square tiles of equal size can be represented in this way.