Lights Out parity explained

Written and play-tested by the Budi Games team · Updated August 2026

Lights Out looks like a puzzle you beat by feel. Press a few cells, watch the pattern churn, undo the damage, press somewhere else. Played that way it is exhausting and slightly maddening, because every press disturbs four neighbors and the board never seems to settle.

It is not that kind of puzzle. Lights Out is arithmetic — a very small, very forgiving kind of arithmetic — and once you see the structure, a board that looked chaotic becomes a procedure you can run almost mechanically. This guide explains the structure, then gives you the procedure, then shows you exactly where the procedure needs one piece of extra knowledge to finish. It uses the classic five-by-five board throughout. If you want a live grid to work on while you read, the Lights Out page has one.

The mechanic, stated precisely

The board is a square grid of lights, each either on or off. Pressing a cell flips that cell and the cells immediately above, below, left and right of it. Diagonals are never touched, and a press at the edge simply flips fewer cells because some of its neighbors do not exist — a corner press flips three lights in total, an edge press four, an interior press five. The aim is to reach a board with every light off.

That is the entire rule set, and everything below is a consequence of it.

A light only counts, and it only counts to two

Start with a single light and ignore the rest of the board. That light is flipped whenever you press it, and whenever you press one of its four neighbors — five cells in total can affect it. Whether it ends up on or off depends on nothing except how many times those five cells were pressed in total, and even then only on whether that total is even or odd.

This is what parity means here, and it has two immediate consequences that most players discover the slow way.

Pressing a cell twice does nothing. Not "almost nothing" — nothing whatsoever. The second press flips exactly the same five lights the first one did, returning each to where it started. If you press a cell three times you have effectively pressed it once, and four times is the same as leaving it alone. So no sensible solution ever presses a cell more than once, which shrinks the search space dramatically: instead of arbitrarily long sequences of presses, you only need to decide, for each of the twenty-five cells, whether it is in your solution or not.

Order never matters. Suppose you press cell A and then cell B. Every light on the board has now been flipped once for each of A and B that touches it — and pressing B first and A second gives every light exactly the same flip count. The final board is identical. Nothing in the rule depends on what the board looked like when a press was made, so presses cannot interact, only accumulate.

Put those together and a Lights Out solution is a set of cells, not a sequence. There are 2²⁵ = 33,554,432 possible sets on a five-by-five board, which sounds discouraging until you realize that almost all of the decision is forced.

Chase the lights

Here is the procedure. It exploits one asymmetry: a cell in row 2 is the only cell in rows 2 through 5 that can still affect the light directly above it in row 1. Once you have finished with row 1, no later press can disturb it — provided you never press in row 1 again.

So: go down the board, and for every light that is on, press the cell directly beneath it. Work row by row. After you have handled every lit cell in row 1 by pressing in row 2, row 1 is dark and will stay dark. Then handle every lit cell in row 2 by pressing in row 3, and so on. When you have pressed in row 5 to clear row 4, the first four rows are guaranteed to be off, and whatever is left is confined to the bottom row.

Here is a real board of ours, chased from start to finish. O is a light that is on, . is a light that is off.

   start              after the chase
   . O . . O          . . . . .
   O . O . O          . . . . .
   . O O O .    →     . . . . .
   . O O O O          . . . . .
   O . O O .          O O O . .

Eleven presses, none of them requiring a decision, and the puzzle has gone from twenty-two unknown cells to a single five-symbol pattern along the bottom: O O O . .. That is the whole value of the chase. It does not solve the board, it compresses it.

The last row, and the first row that fixes it

Now the interesting part. You cannot clear that bottom row by pressing in the bottom row — every press there disturbs its neighbors and you would be back where you started. The only place left to press is row 1, which the chase has not touched.

Why does that work? Because pressing cells in row 1 and then chasing again produces a different bottom row, in a completely predictable way. Each row-1 press ripples down through the chase and lands as a fixed signature at the bottom, and since presses only accumulate, those signatures add up cleanly. In other words, the bottom row you were left with tells you precisely which row-1 cells you should have pressed at the very start.

There are only seven patterns that can survive a chase on a solvable board, and each one has a known answer. We computed this table directly from the rules rather than copying it, and verified every line by running the presses back through a board.

The full method is then: chase the board once, read the bottom row, look up the row-1 presses, go back to the top and make them, and chase the whole board again. The second chase clears everything. Our example above finished with O O O . ., so the answer was a single press in row 1, column 2 — and with that press made first, the same chase leaves the grid completely dark.

If you would rather not carry a table, the same idea works as a small experiment: on a cleared board, press one row-1 cell and chase it down, and note the bottom row it produces. Do that for all five cells and you have derived the table yourself in about two minutes. The five signatures combine by parity, so a leftover row that equals two signatures added together needs both of those presses.

Why some boards cannot be cleared at all

Seven patterns are listed above, and there are thirty-one possible non-empty bottom rows. What about the other twenty-four? They cannot appear on a board that is solvable at all. If you chase carefully and end up with a leftover row that is not in the table, one of two things is true: you made a mistake during the chase, or the board you were given has no solution.

Unsolvable boards are not a flaw, they are a property of the grid. On a five-by-five board there exist exactly two independent press patterns — plus the combination of the two — that flip every light an even number of times and therefore change nothing at all:

   . X X X .        X . X . X
   X . X . X        X . X . X
   X X . X X        . . . . .
   X . X . X        X . X . X
   . X X X .        X . X . X

Press every cell marked X in either diagram, in any order, and the board you end up with is the board you started with. These are usually called quiet patterns, and they have two effects. First, any board that can be solved can be solved in exactly four different ways — your solution, plus your solution combined with each quiet pattern, plus your solution combined with both. Second, they cut the number of reachable light patterns to a quarter of the total: of the 33,554,432 arrangements a five-by-five board can show, exactly 8,388,608 can be turned off.

There is a simple way to never meet an unsolvable board: any pattern produced by pressing cells on an all-off grid is solvable by definition, because pressing that same set of cells again undoes it. Boards generated that way are always fair, and it is the standard way to deal a Lights Out puzzle.

Three habits that make it feel easy

Never press twice. If you find yourself pressing a cell you already pressed, stop and re-read the board — you are undoing your own work rather than progressing.

Do not evaluate mid-chase. The board looks worse partway through a chase, because you are pushing all the disorder downward before you clear it. That is the method working, not failing.

Count presses, not moves. The number worth tracking is how many distinct cells are in your solution set. Two people who solve the same board with the same set of cells solved it identically, no matter how differently they clicked.

Once the chase is automatic, Lights Out stops being a test of patience and turns into something closer to reading. If that appeals, the same flavor of exact reasoning shows up in nonograms and in the Tower of Hanoi, where the whole solution is likewise decided before you touch the board.

Questions players ask