Light Switch Guide: Chase the Lights to Zero

Two facts that simplify the whole puzzle

Order does not matter. Each press flips a fixed set of squares, and flipping is its own reverse, so the final board depends only on which squares were pressed, not the sequence. You can plan the whole solution as a set of squares.

Pressing a square twice is the same as not pressing it. Two flips of the same square cancel. So in a best solution no square is pressed more than once, and the question is simply: which squares get pressed?

Together these mean you should never press a square to "see what happens" and then press it again. Think of the solution as a pattern of presses laid over the board.

The chase-the-lights method

This method clears any board that can be cleared, and it gives you a solution to improve on:

1. Look at the top row. For every light that is on in the top row, press the square directly below it (in row 2). That turns off the top-row light (and flips some row 2 and row 3 squares, which is fine).
2. Now row 1 is dark. Look at row 2: for every light on in row 2, press the square below it in row 3.
3. Continue down the board. After pressing in the last row, every row but the last is dark.
4. Look at the pattern of lights left in the bottom row. It tells you which squares to press in the top row (see the table below). Press those, then chase the lights down again from row 1. The board clears.

The bottom-row table (5 × 5)

For the classic 5 × 5 board, the lights left in the bottom row after the first chase decide the top-row presses for the second chase:

Any other bottom-row pattern cannot occur on a solvable 5 × 5 board, and every daily board is solvable. Other board sizes have their own tables, but the method of chasing, reading the bottom row and chasing again is the same; on small boards you can find the top-row fix by trying each top square in turn, since trying is cheap once you remember that order and repeats do not matter.

Getting closer to par

Chasing gives a correct solution but often not the shortest. Three improvements:

• Remove cancelled presses. If your plan presses a square twice, drop both.
• Try the complementary pattern. On 5 × 5 there are several press patterns that leave the board unchanged (the "quiet patterns"). Adding one to your solution changes which squares are pressed without changing the result, and one of the versions is shortest. The best way to find a shorter solution in play is to chase from a different edge (from the bottom up or from the left) and compare the counts.
• Look for isolated lights. A single lit square with dark neighbours is almost never cleared by pressing it directly (that would light four neighbours); it is cleared as a side effect of presses nearby, which the chase finds for you.

Par is shown from the start. Matching it is the mark of a good solve; one or two over is still a fine result and counts the same for your streak.

Common mistakes

1. Pressing a lit square to turn it off. That lights its neighbours. Press under it (or beside it) as part of a plan.
2. Pressing the same square twice. Two presses cancel and cost two moves for nothing.
3. Starting in the middle. Chase from an edge; the middle is where chasing ends up.
4. Reading the bottom row before the top rows are fully dark. Finish the chase first.
5. Giving up when the bottom row stays lit. That is the normal state after one chase; the table fixes it.

Glossary

• Press: switching a square and its four orthogonal neighbours.
• Chase: turning off each row's lights by pressing the squares beneath them.
• Par: the fewest presses that clear the day's board.
• Quiet pattern: a set of presses that leaves a board unchanged, which lets a solution be rewritten with fewer presses.