How to Play Lights Out: The Chase Solving Method

Lights Out was released by Tiger Electronics in 1995. The format: a grid of cells (5×5 standard); each cell is either ON or OFF. Press a cell to toggle it and its 4 neighbors (up, down, left, right). Goal: turn all cells OFF. It’s pure linear algebra disguised as a puzzle. Here are the techniques.

The math: GF(2) linear algebra

Each cell pressed is a Boolean — pressed or not. Each cell’s final state is XOR of how many times it and its neighbours were pressed. The whole puzzle is a linear system over GF(2) (the field with 2 elements: 0 and 1).

This means: there’s an algorithmic solution. Gauss-Jordan elimination over GF(2) finds the minimum set of cells to press. Our hint button uses exactly this algorithm.

Technique 1: Chase the lights

Press cells in the top row to turn off any ‘on’ cell in the SECOND row below it. After processing all 5 cells in the top row, the second row should be all off.

Press cells in the second row to clear the third row. Continue down. After processing row 4, you may have lights stuck on row 5.

If the bottom row has ‘on’ cells after the chase, refer to step 2.

Technique 2: The top-row dispatch

After chasing, the bottom row is one of 32 patterns (2^5). Only a specific set of bottom-row patterns are solvable; the rest are dead ends.

Look up the bottom row pattern. The solution corresponds to a specific TOP row pattern to press. Press it; chase down again; the entire grid should be off.

This ‘dispatch’ table is what world-class Lights Out solvers memorize.

Technique 3: The ‘parity’ check

Some Lights Out puzzles are unsolvable. The condition: certain configurations create a parity violation across the whole grid.

In a 5×5 Lights Out, every position is solvable. In larger grids, some are not. Check carefully or use our ‘hint’ button (it can identify unsolvable positions).

Technique 4: Solve smaller before larger

Beginners should start at 3×3 Lights Out. 9 cells; 2^9 = 512 possible solutions. Many are solvable. Get the hang of the chase technique.

Move to 4×4, then 5×5 (the classic). Each increases the parity-failure rate slightly.

Technique 5: The ‘inversion’ check

Once you have a solution, you can verify it by simulating. Press each cell in your solution; do they ALL go off? If yes, you’ve found a valid solution.

Multiple solutions can exist for the same starting position. The ‘minimum’ solution (fewest presses) is the canonical answer.

Practice

Play our Lights Out. 3×3 through 7×7. Hint button uses GF(2) linear algebra solver.

How to Play Lights Out — GF(2) Algorithm + Chase Technique