Light Switch: combine two patterns by cancelling their overlap.

Build a new solvable board from two known patterns, cancel shared switches, and replay six-press and four-press routes on the same fixed example.

H5 Free Fun · Published October 22, 2026 · 8 min read

If you already know how to clear two Light Switch patterns, can you use those answers to clear a combination of them? Yes, provided that “combine” means toggle their states together, rather than keep every light that is on in either picture.

This lesson constructs one new board from two small examples. We will check the combined lights, combine the switch lists separately, then retry the result in six and four presses. The useful skill is reusing a verified answer without confusing a light's state with a switch's effect.

Keep two kinds of diagram separate

We use this site's five-by-five cross rule: a press toggles its own light and the immediate horizontal and vertical neighbors. Edges do not wrap. In each diagram, ● means on and · means off. Rows count from top to bottom; columns count from left to right.

A light diagram shows the current state. A switch list records positions to press. A lit square need not belong to the solution list, and a switch in that list may start off. Copy each kind of information into its own note.

Start with two verified patterns

Pattern A

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

Pattern A is cleared by R1C1, R2C3, R4C2. It is the same starting pattern as the original guide example. You can check its origin by applying those three presses to an all-dark grid; applying them again clears it.

Pattern B

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

Pattern B is cleared by R2C3, R3C3, R5C5. It is constructed in the same way from an all-dark grid. The two solution lists share R2C3. Keep that shared switch separate from the positions where the two light patterns overlap.

Combine the lights one square at a time

At each coordinate, keep a light on only when the two patterns disagree. On plus off gives on; off plus on gives on. Two on states cancel to off, and two off states stay off. This operation is called exclusive OR, often written XOR.

For example, R1C1 is on only in A, so it stays on. R1C3 is on in both, so it becomes off. R1C4 is off in both and stays off. Working through all 25 coordinates gives Pattern C:

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

Practice this example in the side panel loads C into the live game. You can also choose Load combined-pattern example below the Light Switch board. Loading replaces the current board and resets Moves to zero. Retry this board restores C; New puzzle returns to a random starting pattern. Refreshing the practice entry reloads C.

Combine the answers, then remove duplicate presses

One way to clear C is to apply A's three-switch answer and then B's. Applying A's answer removes A's contribution, leaving exactly Pattern B. Applying B's answer removes the rest.

1. R1C1
2. R2C3
3. R4C2
4. R2C3
5. R3C3
6. R5C5

That route uses six presses. But R2C3 appears twice. Each press toggles the same fixed footprint, so two presses of that switch cancel. Switch order does not change the final state; the two copies cancel even though other presses separate them.

Remove both copies of R2C3, rather than keep one copy. The remaining route is:

1. R1C1
2. R3C3
3. R4C2
4. R5C5

These four presses clear C too. Combining lists by ordinary set union would keep R2C3 once and give a different result. The correct operation keeps switches that appear in exactly one reduced list, also called the symmetric difference.

Why combining answers works

Consider a single light. A switch either toggles it or does not. Its final state depends only on whether the total number of toggles is odd or even. It does not depend on the order of those toggles.

Pattern A records the odd-toggle effect of A's switch list; B records B's. Putting both lists together adds those effects at every coordinate. An effect present twice cancels. The same combined list therefore constructs C from darkness and clears C back to darkness. Deleting duplicate pairs of switches does not change that effect.

This gives a constructive answer, rather than a search through all possible switch sets. It requires the actual clearing lists for A and B. Two pictures alone do not supply their solutions, and a shared lit square is not automatically a repeated switch.

Compare the routes on the same board

1. Load the combined-pattern example. Check that its 25 lights match C and Moves is zero.
2. Replay the six-press route. After the first three presses, compare the board with B. Complete the route and record six moves.
3. Choose Retry this board. Replay the four-press route and record four moves, with every light off again.

Retry resets the game counter, not your memory or a saved attempt history. Every actual press counts, including the two redundant R2C3 presses in the longer route. Four is a checked improvement over six; this construction alone does not prove that four is the minimum.

Three checks before using the method again

The printed boards and coordinates use this site's five-by-five cross rule and all-dark goal. A different neighbor rule or wrapping at edges requires new diagrams and verified clearing lists. Cancellation still works for fixed toggle footprints; it is not a method for rules that move lights or change a switch's effect during play. On this board, it gives a practical way to build and solve a new pattern from answers you have already checked.