💡Play Lights Out

Lights Out was an electronic handheld released in 1995, and it is one of the few puzzle games whose full solution is a piece of linear algebra rather than a heuristic. Every board is a system of equations over the integers modulo two, and the entire game can be solved by Gaussian elimination.

Two consequences of that are worth knowing as a player. First, order never matters — pressing A then B is identical to pressing B then A — so you are choosing a set of cells, not a sequence. Second, pressing a cell twice is the same as never pressing it, which means an optimal solution presses each cell at most once and there are only ever a finite number of distinct solutions.

Not every arrangement of lights on a 5x5 grid is solvable; roughly a quarter of them are not. Our boards are built by starting from all-off and applying random presses, which guarantees a solution exists by construction — the scramble is itself a valid solution run backwards.

The practical technique is called chasing the lights: sweep down the grid turning off each row by pressing the row beneath it, then use the leftover top-row pattern to work out the correct opening presses. It is mechanical once you know it, which is the pleasure of the thing.