LightOut

LightOut, commonly known as Lights Out, is a puzzle video game and brain teaser focused on a grid of lights. The standard version uses a 5-by-5 grid, though variants with different sizes exist.

In the game, pressing a light toggles that light and its orthogonal neighbors (up, down, left, right). The goal is to turn all lights off. A move affects lights in the cross-shaped pattern, and presses can be repeated; there is no limit on moves. Some variants allow wrapping around edges or include additional lighting modes.

The original and best-known version was released as a handheld electronic game by Tiger Electronics in 1995. It became widely popular in arcades, homes, and later digital platforms, and has since inspired many clones, adaptations for mobile devices, and online puzzles.

From a mathematical standpoint, Lights Out is a linear puzzle over the field with two elements. Each state can be represented as a vector, and each press corresponds to adding a fixed toggle vector. Solving a given starting pattern reduces to solving a system of linear equations. While many configurations are solvable, not all are; the solvability depends on the underlying grid size and boundary rules.

Legacy and influence: Lights Out has educational value in teaching problem-solving and linear algebra concepts, and it remains a recognizable example of combinatorial puzzles, with numerous fan-made variants and modern reimaginings.