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 linear algebra problem in disguise — and a classic example in math courses.

How to play

• You start with a randomized lit/dark pattern, guaranteed solvable: the game builds it by pressing random tiles on a dark board.
• Click any tile. That tile flips state. Its 4 orthogonal neighbours also flip state.
• Goal: every tile OFF.
• Use Hint to highlight one tile from the shortest solution of the current board. Undo takes back your last press and removes it from your move count.
• Change grid size from 3×3 (trivial) to 7×7 (challenging). 5×5 is the default, and your best move count is saved for each size.
• The Min counter shows the fewest presses that can clear the board, so you can see how close to a perfect solve you got.

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. On 5×5 there are 7 possible leftover bottom-row patterns, and each one has a matching set of top-row presses. Make those presses, then chase the lights down again.
• Memorize these and you can solve any 5×5 puzzle without guesswork.

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 searches that whole solution space (each solution is fixed by its top-row presses) and points at a tile from the one with the fewest presses.

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 7 “exit patterns” for 5×5. Top-row press sequences that clear any bottom-row residual.
• Move count minimization. No solvable 5×5 position needs more than 15 presses. Pressing a tile twice cancels out, so never press the same tile twice.
• 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: Here, yes. Every puzzle is made by pressing random tiles on a dark board, so it can always be undone. On a 5×5 board, though, only one in four random light patterns is solvable.
• Q: Optimal moves for 5×5? A: Varies by starting state. No 5×5 position needs more than 15 presses, and our puzzles are scrambled with 8 to 15 presses.
• 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 and 7×7 are harder simply because there are more tiles to chase.

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