Light Switch: twelve different presses can leave the board unchanged.

Verify a nonempty switch pattern with no net effect, then replay three clearing routes on the same board without confusing state with move count.

H5 Free Fun · Published October 25, 2026 · 7 min read

Pressing the same Light Switch square twice restores the lights it changed. A more surprising cancellation is possible: twelve different switches can also restore the entire board. No switch needs to appear twice in that twelve-press list.

The reason is local. Several different switches can reach the same light. If their combined effect toggles every light an even number of times, the final state is unchanged. We will verify one such pattern, try it on a loadable board, and use it to explain why two genuinely different solution sets can clear the same puzzle.

Read this as a switch map, not a light picture

Use this site's fixed five-by-five rule: a press toggles its own light and its immediate horizontal and vertical neighbors. There is no diagonal effect or wrapping at the edges. Rows R1–R5 run top to bottom; columns C1–C5 run left to right.

In the map below, X means press this switch once. A dot means do not press that switch. Neither symbol tells you whether its light starts on. Call this switch set Q:

X · X · X
X · X · X
· · · · ·
X · X · X
X · X · X

1. Row 1: C1, C3, C5.
2. Row 2: C1, C3, C5.
3. Row 3: no press.
4. Row 4: C1, C3, C5.
5. Row 5: C1, C3, C5.

There are four rows with three presses each: twelve distinct switches. Follow the listed row order for the live experiment below. The pattern is supplied as a testable example; knowing it does not tell you how to solve an arbitrary starting board.

Count how often each light is touched

For each light, count selected switches at that same coordinate and at its horizontal or vertical neighbors. A selected switch one diagonal away does not count. These are toggle counts, not light states and not the number of switches selected in each row.

2 2 2 2 2
2 2 2 2 2
2 0 2 0 2
2 2 2 2 2
2 2 2 2 2

Check R1C1 first. Its own switch and R2C1 are selected, while R1C2 is not: two toggles. At R1C2, the selected neighbors R1C1 and R1C3 supply two toggles. At R3C3, R2C3 and R4C3 supply two. R3C2 receives none because it and all four neighboring switches are unselected.

Twenty-three lights are toggled twice; R3C2 and R3C4 are toggled zero times. Every count is even. Two toggles restore an on light to on and an off light to off; zero leaves it alone. Q therefore returns any starting light pattern to itself under these fixed rules.

This is an end-of-sequence statement. Intermediate boards usually look different. Nor does “unchanged” mean all lights are off: a board with thirteen lights on still has those same thirteen lights on after Q.

Watch the state return while the counter advances

Use Practice this example in the side panel, or Load guide example below the Light Switch game. It loads the original guide's fixed board, shown here with ● for on and · for off, and resets Moves to zero:

● ● ● · ·
● ● ● ● ·
· ● ● · ·
● ● ● · ·
· ● · · ·

1. Before pressing, compare all 25 lights with the diagram. There are thirteen on.
2. Follow Q's twelve switches in the listed order. Row 3 is skipped.
3. After the twelfth press, compare positions again. The entire starting board has returned, with thirteen on and Moves at twelve.
4. Now press R1C1, R2C3, and R4C2. All lights turn off, and Moves reaches fifteen.

The specified fifteen-press route does not clear the board early: the first all-dark state occurs on its last press. That matters because this game stops accepting board presses after a win. An abstract claim about a switch set is not permission to keep pressing a finished live board.

Choose Retry this board, rather than New puzzle, to compare from the identical starting state. The direct sequence R1C1, R2C3, R4C2 clears it in three presses. Q contributed twelve actual moves to the longer attempt even though its final effect was zero. The game counter does not refund cancelling moves or store a ledger of previous attempts.

Build a different solution set

Let S be that three-switch answer: R1C1, R2C3, R4C2. The fifteen-press route is Q followed by S. It clears the board because Q first returns the board to its starting state, then S clears it.

Two switches appear in both lists: R1C1 and R2C3. Delete both copies of each repeated switch. Their fixed toggle effects cancel even when other presses separate them. The remaining eleven switches form another working set T:

1. Row 1: C3, C5.
2. Row 2: C1, C5.
3. Row 3: no press.
4. Row 4: C1, C2, C3, C5.
5. Row 5: C1, C3, C5.

Retry the guide example and follow those rows in order. It finishes on the eleventh press. T contains no repeated switch, yet it is longer than the three-switch S. Removing repeated presses is useful, but a list with no repeats is not automatically the shortest solution.

Use the difference between two answers

S and T are different reduced answers to the same board. Keep switches that occur in exactly one list, removing those shared by both. This symmetric difference is Q. Both answers have odd total toggle counts at every originally on light and even counts at every originally off light. Combining their counts makes every total even, so their difference has zero net effect.

This gives a useful check for two claimed answers. If the switches present in only one list change any light overall, the lists cannot both clear the same starting board under the same rules. The zero-effect check establishes that they have the same effect; you still need to verify that at least one actually clears the intended board. Two wrong lists can have the same effect too.

Two checks before retrying

Keep the claim within its limits

Q does not fix an impossible board: it leaves that board unchanged too. It is not an all-purpose solution, an optimality proof, or an exhaustive list of zero-effect patterns. Here it provides a concrete explanation for different answers and a reproducible distinction between a board's state and the work counted by the game.

All diagrams and routes depend on five-by-five, non-wrapping cross toggles. Changing the board size or switch footprints requires a fresh coverage check. Intermediate states matter when a live game stops at a win, even though switch order does not affect the final abstract toggle result.

Analysis checked October 25, 2026. All 25 coverage counts and every intermediate board in the 3-, 11-, 15-, and 27-press routes were checked against the site engine and an independent coordinate-distance model.