Light Switch: test a hand-made board before you chase it.
Use two marked-square counts to reject impossible 5 × 5 diagrams, then check your reasoning in an editable board exercise.
A diagram with just one light on looks easier than a large pattern. In Light Switch, that impression can be wrong: a single light in the top-left corner cannot be cleared under this site's rules. No longer sequence of legal presses fixes it.
Two small counting checks explain why. They are useful when you copy a puzzle onto paper, invent a starting diagram, or suspect a transcription error. The live game already constructs its boards from legal presses on an all-dark grid, so it does not need you to repair its generated starts.
Fix the rules before counting
Use exactly five rows and five columns. A press toggles its own square and its immediate horizontal and vertical neighbors. Edges do not wrap, diagonal lights are unaffected, and the goal is all lights off. Rows run from R1 at the top to R5 at the bottom; columns run from C1 on the left to C5 on the right.
These details matter. A different board size or a rule that toggles diagonals can invalidate the checks below. In the diagrams, ● means on and · means off.
Place two counting masks over the diagram
A mask is a list of positions to count. An X below marks a counted position; a dot marks a position to ignore. The X is not a light state and is not a switch to press. Read the same coordinates in your actual starting diagram.
Mask A
· X X X · X · X · X X X · X X X · X · X · X X X ·
Mask B
X · X · X X · X · X · · · · · X · X · X X · X · X
For each mask separately, count how many of its marked positions are currently on. Ignore off lights even when their position is marked. Also ignore on lights at unmarked positions. The resulting count is either even or odd. Zero is even.
Why an odd count proves impossibility
Every legal switch footprint contains an even number of marked positions in each of these masks: zero, two, or four. For example, a press at R1C1 changes R1C1, R1C2, and R2C1. Mask A counts the latter two positions; mask B counts R1C1 and R2C1. Each mask therefore has two of its positions toggled.
Toggling an even number of counted lights preserves whether their total is odd or even. The count itself can increase, decrease, or stay the same; its parity does not change. If two counted positions toggle, the on count changes by −2, 0, or 2. The same argument works for four counted positions.
The all-dark goal has zero counted lights in both masks. It has even parity in A and in B. A starting diagram with an odd count in either mask therefore cannot reach that goal. This is a property preserved by every move, rather than a prediction about the next few moves.
Compare three starting diagrams
Example A: only the top-left light is on
● · · · · · · · · · · · · · · · · · · · · · · · ·
R1C1 is unmarked in A, so the A count is 0. It is marked in B, so the B count is 1. The odd B count proves this diagram is impossible. Pressing the corner will change how it looks, but B will remain odd.
Example B: move that one light to R1C2
· ● · · · · · · · · · · · · · · · · · · · · · · ·
Now A counts 1 and B counts 0. Checking only B would miss this obstruction. An odd result in A is enough to reject the diagram, even though B is even. Use both masks as separate checks.
Example C: the center cross
· · · · · · · ● · · · ● ● ● · · · ● · · · · · · ·
A counts four of these five lights: R2C3, R3C2, R3C4, and R4C3. B counts two: R2C3 and R4C3. Both results are even. There is also a direct solution witness: pressing R3C3 once turns the entire cross off.
The total number of on lights is five, which is odd. That does not prevent a solution. You must count the marked positions in each mask, rather than assume that the whole board's lit count is preserved.
| Diagram | A | B | Conclusion |
|---|---|---|---|
| A: R1C1 only | 0, even | 1, odd | Impossible |
| B: R1C2 only | 1, odd | 0, even | Impossible |
| C: center cross | 4, even | 2, even | One center press solves it |
Check an edited diagram yourself
Use Try the parity check in the side panel to reach the exercise below the lesson. It starts with Example A. The editor changes one light at a time, unlike a game switch. This distinction lets you enter a diagram that the live game's generator would never produce.
Count A and B on paper, optionally enter your two predictions, then choose Check board. Load Example B and check that the failing mask changes. Load Example C and verify its counts of four and two. The feedback explains the parity result; it does not play the solving center press.
Change one light after a check: the old verdict is cleared. Retry example restores the last loaded diagram and clears predictions. Clear diagram turns every light off. None of these editing actions counts as a game move, changes a live game, saves a diagram, or submits it to the server.
Two checks to try without the editor
Only R1C3 is on. What do both masks say?
That position is marked in A and B, so the counts are 1 and 1. Both are odd. Either result alone proves the all-dark goal is unreachable from that diagram.
You press R1C1 in Example A. Does the odd B count disappear?
No. The three on/off changes leave R1C2 and R2C1 on. Only R2C1 is marked in B, so its count remains 1. A now counts both lights and has count 2; it changed from 0 while staying even.
Use the result for its stated purpose
An odd check is a reason to stop trying to solve that exact hand-made diagram and recheck its transcription or rules. It is not a reason to keep pressing until the odd count becomes even: legal game presses cannot do that.
When both counts are even, this exercise does not reject the diagram. The counts do not provide a switch sequence or a minimum move count. For Example C, the separate one-press witness supplies the actual solution. For other diagrams, a constructive method such as row chasing is still useful for finding the moves.
Both masks were checked against all 25 legal single-switch footprints using the site's exact cross rule; their marked counts are always even. The three printed examples were also checked independently by testing all 32 first-row choices in a row-chasing calculation. These results concern fixed diagrams and rules, not player ability, completion time, or health.