One rule, and why order doesn't matter
Lights Out has a single rule: pressing a light switches it, and the lights directly above, below, left and right of it, between on and off. The goal is a dark board. That sounds like a puzzle about sequences, but it isn't. Two facts take the sequence out of it entirely.
First, pressing the same light twice puts everything back as it was, so a light never needs more than one press. Second, the order of presses makes no difference: pressing A then B leaves the same board as B then A. Put together, a solution is not a list of moves but a set of lights, each pressed once. Every board dealt here has a par, the size of the smallest such set, and a solution that hits par presses each of those lights exactly once.
Chasing the lights
The method that always works is called chasing the lights. Start at the top row. For every light that is on there, press the light directly below it. The press switches the top light off and disturbs only the second and third rows, so the top row is now finished for good. Then do the same for the second row, pressing beneath each lit light, and keep going down. When you reach the bottom, every row but the last is dark.
Whatever is left on the bottom row tells you which lights in the top row to press before chasing again. On the 5×5 board there are only seven patterns that can be left, numbering the lights 1 to 5 from the left:
- 3, 4, 5 on: press 4 in the top row.
- 2, 4 on: press 2 and 5.
- 2, 3, 5 on: press 1.
- 1, 5 on: press 4 and 5.
- 1, 3, 4 on: press 5.
- 1, 2, 4, 5 on: press 3.
- 1, 2, 3 on: press 2.
Make those top-row presses, chase from the top again, and the board goes dark. It is reliable rather than quick, though, so a chase almost always finishes well over par.
Getting closer to par
To beat the chase, look for shapes before you press anything:
- The plus. Five lights in a plus shape go out with one press in the middle. Spot these first; each is a free win.
- Edges and corners. An edge press flips a T of four lights and a corner press flips an L of three. A lit L tucked into a corner is a one-press clear.
- Pairs that cancel. Two presses side by side flip each other back, so the two pressed lights end as they started, and only the six lights around the pair change. A ring of six lit lights around two dark ones is cleared by pressing that dark pair.
Once the obvious shapes are gone, a short chase on what's left usually lands within a press or two of par. Undo a press you regret instead of pressing the same light again: pressing it again also cancels it, but counts two presses where Undo counts none.
Why some boards can't be solved
Not every pattern of lights can be switched off. On the 5×5 board only one pattern in four can be; a single corner light on its own, for example, can never be cleared. The reason is that some sets of presses change nothing at all when pressed together, and on 5×5 there are three such sets. Every solvable 5×5 board therefore has exactly four different solutions, and par is the size of the smallest.
The 4×4 board has even more of these silent sets, fifteen of them, so only one pattern in sixteen can be cleared, and every solvable 4×4 board has sixteen solutions. The 3×3, 6×6 and 7×7 boards have none: every pattern on them can be cleared, in exactly one way.
None of this matters during play, because every board here is dealt by starting from a dark grid and pressing a random set of lights. There is always a way back.
Moving through the sizes
Start on 3×3 to get a feel for the move; most boards there need three to six presses. 4×4 is quick too, and its many equivalent solutions make par forgiving. 5×5 is the classic board, and where the chase table above earns its keep. 6×6 and 7×7 boards need a dozen or more presses, and there is only one shortest solution on each, so hitting par on them takes real planning.
Your record for each size counts the boards you have solved and the ones you cleared perfectly, in par with no hint. A good goal is a perfect 5×5 board without using the chase at all.
