Lights Out — the free browser version of the 5×5 light-switching puzzle

Twenty-five lights, some on and some off. Tap any one of them and it flips — but so do the four lights next to it, up, down, left and right. Your job is to get every light off. It sounds trivial for about ten seconds, right up until the moment you fix one corner and discover you have lit the other three.

Every board here is generated by scrambling a switched-off grid with random taps, so a solution always exists — you are never handed an impossible puzzle. Your score is the number of moves you used, so lower is better, and the same board can usually be solved far more cheaply than your first attempt manages. Free, no download, and a new board every game.

How to play

• Tap a light to flip it and its four orthogonal neighbours. Diagonals are unaffected.
• Get every light off to finish the board.
• Your score is moves — fewer is better, so undoing your own work costs you twice.
• Tapping the same square twice returns the board exactly to where it was. Order never matters.

Chase the lights: the method that always works

Lights Out looks like a puzzle you solve by feel. It isn't — it is a system of linear equations over the integers mod 2, and it has a mechanical solution that fits in one sentence. Work down the grid: for every light that is still on, tap the square directly beneath it. That switches the light above off, and whatever mess it makes lands in rows you have not dealt with yet. Repeat row by row and, by the time you reach the bottom, the first four rows are completely dark.

What remains is the whole puzzle in miniature: some pattern of lights in the bottom row. There are exactly eight patterns that can survive this process on a 5×5 board, and each one is fixed by tapping a specific set of squares in the top row and then chasing down again. The classic example: if the bottom row ends up with lights 1 and 2 lit, tap the top-row square 1, chase down, and the board clears. Learning three or four of those top-row keys turns this from guesswork into a two-minute routine.

Two facts that follow from the maths and are worth knowing. First, order truly does not matter — only which squares you pressed an odd number of times — so there is no such thing as a move you must play "before" another. Second, because pressing a square twice is the same as never pressing it, no minimal solution ever presses the same square twice: if you find yourself undoing a move, you have already left the shortest path, and on this board that costs you two moves against your score. Solve it however you like the first time, then try the same trick on the next board with the chase method and watch the move count fall.

More games

More puzzles that punish a wrong guess: Peg Solitaire, Dots and Boxes, Minesweeper, 15 Puzzle, or Sudoku. Or browse all games.