About Lights Out

Lights Out is an electronic puzzle game originally released by Tiger Electronics in 1995. The objective is to turn off all the lights on a 5×5 grid, but pressing a button toggles not only that light but also the lights directly adjacent to it (up, down, left, right - not diagonal).

Controls

Action	Control
Toggle a cell	Click / tap the cell
New puzzle	New Game button
Keyboard navigation	Arrow keys to move, Enter/Space to toggle

The Chase the Lights strategy

The most reliable solving method works row by row from the top:

Start at row 1. For every lit cell in row 1, press the cell directly below it in row 2. This toggles row 1's lights off using row 2 as the lever.
Repeat for rows 2 -> 3, 3 -> 4, 4 -> 5, always pressing in the row below the target.
After reaching the bottom, check the bottom row. If any lights remain, press the specific top-row cells that fix the bottom row (there are only 32 possible bottom-row states; each maps to a fixed top-row sequence).
Repeat the downward sweep with those top-row presses applied.

The mathematics (GF(2))

Lights Out is a system of linear equations over GF(2) - the finite field with only two values, 0 and 1, where 1 + 1 = 0. Each cell's state is a bit; pressing a button XORs a pattern of bits. A puzzle is solvable if and only if the initial state lies in the column space of the toggle matrix. The 5×5 board has a null space of dimension 2, meaning some boards have up to 4 equivalent shortest solutions.

Solvability

Not every starting configuration of a Lights Out board can be solved. For the standard 5×5 grid, the toggle matrix has a null space of dimension 2, which means the 25 cells span only a 23-dimensional solution space. In practice, roughly 25% of all random configurations are unsolvable - pressing every possible button combination still leaves at least one light on.

The four "null patterns" (also called "quiet patterns") are specific button sets that, when pressed together, leave every light unchanged. Adding any quiet pattern to a solution gives another valid solution, which is why solvable boards can have multiple shortest solutions.

Solving the bottom row

After completing the "Chase the Lights" downward sweep, the bottom row may still have lit cells. There are only 32 possible bottom-row states (2⁵), and each maps to a specific set of top-row button presses. Experienced solvers memorize these 32 mappings (or use a lookup table). After applying the top-row fix, a second downward sweep clears the board - if the initial configuration was solvable.