Lights Out

How to play

The 5 by 5 grid starts with a scatter of lit tiles, and your job is to switch every one of them off. Tapping a tile toggles it along with its four direct neighbors, which is what makes this tricky: fixing one corner can relight another. Clear the board to advance, and each level starts from a more scrambled pattern.

Tips

• Order never matters, and tapping the same tile twice cancels itself out. All that counts is which set of tiles you tap.
• Try light chasing: sweep top to bottom, tapping the tile directly below each lit one to push all the light into the bottom row.
• Tapping tiles that are already dark is often part of the solution, so do not treat lit tiles as the only legal moves.
• Every board is scrambled from a solved grid with at most 15 taps, so a solution always exists and it is never a long one.

The maths hiding in a 5 by 5 grid

Lights Out was released as a handheld electronic game by Tiger Electronics in 1995, and it has a property that makes it unusually satisfying: it is completely solvable by reasoning. Because pressing a tile twice cancels out, and because the order of presses never changes the result, every puzzle is really a question about which set of tiles to press once. That is a problem in linear algebra over two values, on and off, and it has a clean answer.

The practical upshot is a method called light chasing. Work down from the top row, clearing each row by pressing the tiles directly beneath any lit tile. When you reach the bottom row, the pattern left there tells you exactly which top row tiles to press, and one more chase finishes the board.

Light chasing, step by step

• Ignore the top row. For every lit tile in row one, press the tile directly below it in row two. Row one is now dark.
• Repeat for each row in turn, always pressing the tile below a lit one. Rows two, three and four go dark.
• Look at the bottom row. Only a few patterns can remain, and each one corresponds to a specific set of top row presses.
• Press those top row tiles, then chase down again from the top. The board clears.
• On this 5 by 5 board not every pattern is reachable, so the game only deals you solvable ones. If a level feels impossible, it is not; you have pressed something twice.

Common questions

Does the order I press tiles matter?

No. The final state depends only on which tiles you pressed an odd number of times. Pressing a tile twice is the same as not pressing it at all.

Is every level solvable?

Yes. Not every arrangement of lights on a 5 by 5 grid can be switched off, so the game only starts you from patterns that can.

What is light chasing?

A method that clears the board row by row from the top by pressing the tile below each lit one, then uses the leftover bottom row to work out the finishing top row presses.