How to solve Lights Out: the chase-the-lights method

You don’t need to be lucky or good at maths. One simple routine and a seven-line table solve every 5×5 board.

Two facts that make it easy

• Order doesn’t matter. Pressing A then B leaves the board exactly as pressing B then A.
• Pressing twice does nothing. A second press undoes the first, so a solution never needs the same light more than once.

Together these mean a solution is just a set of lights to press. Your job is to find that set.

Step 1: chase the lights down

Start with the top row. For every light that is on in it, press the light directly below. That switches the top-row light off (and changes some lights further down, which is fine). Then do the same for the second row, the third and the fourth. Now every light is off except, possibly, some in the bottom row.

Step 2: read the bottom row

Look up the pattern left in the bottom row (● = on, read left to right) and press the lights shown in the top row:

Bottom row   Press in top row
●○○○●        ○○○●●
○●○●○        ○●○○●
●●●○○        ○●○○○
○○●●●        ○○○●○
●○●●○        ○○○○●
○●●○●        ●○○○○
●●○●●        ○○●○○

Step 3: chase again

Repeat step 1 from the top. This time the bottom row finishes dark too. Done!

Worked example

Suppose after chasing, the bottom row reads ●○○○●. The table says press the 4th and 5th lights of the top row. Then chase from the top again, row by row, and the board clears.

Interesting facts

• Only 7 bottom-row patterns appear in the table because only 8 of the 32 possible patterns (including all-off) can be left after a chase on a solvable board.
• Only one in four of all possible 5×5 boards can be solved at all. Every board in our game is built from real presses, so it is always solvable.
• Every solvable 5×5 board has exactly four different solutions, and the shortest one never needs more than 15 presses. We checked both facts by computer.

Put it into practice in Lights Off. The chase method won’t always match the level’s target, but it always clears the board.