Lights Out

Lights Out is the 1995 electronic puzzle by Tiger Electronics. Grid of tiles, each lit or dark. Click any tile and it toggles itself plus its four orthogonal neighbours. Goal: turn every tile OFF. Simple, but a deep linear algebra problem in disguise — and standard study material in undergraduate math courses.

How to play

• You start with a randomized lit/dark pattern, guaranteed solvable.
• Click any tile. That tile flips state. Its 4 orthogonal neighbours also flip state.
• Goal: every tile OFF.
• Use Hint to see the next press of an optimal solution.
• Change grid size from 3×3 (trivial) to 6×6 (challenging).

The “chase the lights” technique

Standard manual solving technique:

• Look at the TOP row. For every lit tile, press the tile DIRECTLY BELOW it.
• Move to row 2. Same process.
• Continue down to the bottom row.
• When you reach the bottom, you may have lights left. 4 specific “starter press” patterns on the top row clear any remaining bottom-row state.
• Memorize these and solve any 5×5 puzzle in 30 seconds.

Why Lights Out is a famous math problem

Each tile press is a linear operation over GF(2) (binary field). The full puzzle reduces to solving a linear system: find a 0/1 vector indicating which tiles to press. On 5×5, the press matrix has rank 23 (not 25) — meaning some starting states aren’t solvable, and solvable states have multiple solutions. This is why the puzzle is studied in undergraduate linear algebra courses. The Hint button literally runs Gaussian elimination on a 25×26 matrix.

Beginner strategy

• Don’t try random presses. Random play rarely solves.
• Use chase-the-lights. Methodical approach works on any solvable position.
• Plan ahead. One press affects 5 tiles. Visualize the result.
• Practice on 3×3. Master small grids first.
• Use Hint. Learn from the optimal solver.

Advanced strategy

• Memorize the 4 “exit patterns” for 5×5. Top-row press sequences that clear any bottom-row residual.
• Move count minimization. Top players solve 5×5 in 8-15 moves.
• Solver-grade play. Compute optimal sequences via Gaussian elimination on the press matrix.

Lights Out history

• 1995 — Tiger Electronics releases Lights Out. Becomes a popular handheld puzzle.
• Late 1990s — academic interest. Studied in math/CS courses.
• 2000s — variants and software adaptations. Many free implementations.
• 2010s — mobile clones. Lights Out style puzzles in many puzzle game collections.

Common mistakes

• Random clicking. Doesn’t converge.
• Forgetting cascade. One press flips 5 tiles. Account for all.
• Not using chase-the-lights. The standard technique works.
• Trying to solve in head. Visualize each press’s effect.

FAQ

• Q: Are all starting states solvable? A: Standard Lights Out implementations generate only solvable states.
• Q: Optimal moves for 5×5? A: Varies by starting state. Most solvable in 6-16 moves.
• Q: Why is it a linear algebra problem? A: Each press = vector addition mod 2. Solving = solving Mv = b.
• Q: Does grid size matter? A: 3×3 is trivial; 5×5 is iconic; 6×6 is harder due to dependency structure.

For other logic puzzles, try Sudoku, Minesweeper, 15 Puzzle, or Tower of Hanoi.