How to solve Lights Out: chasing lights and using parity

Where the game came from

Lights Out became widely known as a Tiger Electronics handheld puzzle in 1995, a milestone described in the research paper Lights Out on finite graphs. Tiger’s original manual, preserved by Hasbro, shows a 5×5 keypad and neighbouring lights that toggle together. Rich Games applies that classic rule to several board sizes.

One switch changes several lights

Pressing a cell toggles that light and its immediate neighbours above, below, left and right. Diagonals are unaffected, and the effect does not wrap around the edges. Your goal is to switch every light off. Both lit and unlit cells can be pressed. A corner press affects three cells, an ordinary edge press four, and an interior press five.

Puzzles offers 3×3, 4×4 and 5×5 boards. There is no separate mistake count: every move changes a fully visible puzzle. A move counter tracks your presses, and restart returns the original pattern.

Two facts that simplify the puzzle

Pressing the same cell twice restores every affected light. Only whether a cell is pressed an odd or even number of times matters to the final result. Any solution can therefore be expressed as a set of cells pressed once each.

Move order does not affect the outcome. This lets you work down the board: for every lit cell in the first row, press the cell immediately below it. The first row becomes dark. Clear the second row using the third, and continue downward.

This method is called chasing lights. It organises the search but does not guarantee that the bottom row will be dark immediately. A remaining pattern at the bottom means a different initial set of first-row presses is needed before repeating the chase.

Worked example: a cross on a 3×3 board

Imagine a 3×3 board with the centre and its four side neighbours lit, while all four corners are dark. Pressing the centre toggles exactly those five cells and solves the puzzle. You do not need to press each lit cell separately.

Now imagine making that same move twice. The first press clears the cross; the second restores it. This demonstrates parity. Overlapping crosses on a larger board combine in the same way: a light affected twice keeps its original state.

What gets in the way of a short solution

The number of lit cells need not decrease after every useful move. Sometimes several lights must be switched on temporarily so a later move can clear the combined region. Choosing only moves that immediately reduce the lit count is unreliable.

Avoid repeating the same sequence without tracking it. When analysing on paper, mark the cells you pressed and cancel pairs of repeated presses. This reveals the actual combination you are testing.

A practice plan

Start on 3×3 and name all the cells a move will affect before pressing it. Then try light chasing on 4×4: work downward while keeping the already cleared upper rows dark.

For a board n cells wide, there are 2ⁿ possible sets of first-row presses. This explains a systematic search; it is not a requirement to enumerate every set mentally. Your first goal is to understand the changes and recognise pairs of moves that cancel.