TECHNIQUE 1 OF 4
Read the complete cross before pressing
A press is not an instruction to turn a square off. It reverses every light in a fixed local pattern, so some lights may turn on while others turn off.
The rule
Pressing an interior square toggles five cells: itself and the four side neighbours. A non-corner edge press affects four, and a corner affects three. Diagonal cells are unchanged. A light that is on becomes off; one that is off becomes on.
A common mistake
Counting only the light under the pointer ignores most of the move. Judging progress solely by whether the number of lit cells decreases can also reject a move needed in a valid solution.
TRY IT 1 · lights-toggle-1
| C1 | C2 | C3 | C4 | C5 | |
|---|---|---|---|---|---|
| R1 | |||||
| R2 | |||||
| R3 | |||||
| R4 | |||||
| R5 |
What can you justify?
In the toggle sandbox, apply R1C1. Will R2C2 be on or off afterwards?
Written explanation
R2C2 starts off and is toggled 0 times. An even number leaves it as it began, so it finishes off. Diagonals do not belong to a press’s cross.
TRY IT 2 · lights-toggle-2
| C1 | C2 | C3 | C4 | C5 | |
|---|---|---|---|---|---|
| R1 | |||||
| R2 | |||||
| R3 | |||||
| R4 | |||||
| R5 |
What can you justify?
In the toggle sandbox, apply R3C3. Will R2C3 be on or off afterwards?
Written explanation
R2C3 starts off and is toggled 1 time. An odd number reverses it, so it finishes on. Diagonals do not belong to a press’s cross.
Pressing a lit corner can increase the number of lights
In a five-by-five Cross Lights practice board, R1C1 is on and every other light is off.
The tempting move
Predict that pressing R1C1 will finish the board because it is the only lit square.
Why it fails
The press also toggles R1C2 and R2C1. R1C1 turns off, but those two lights turn on. The resulting board has two lit squares.
What is actually justified
Predict the whole affected cross, including currently dark cells. This example describes one move's effect and makes no claim that the starting pattern is a generated or solvable game board.
Transfer the idea
On a five-by-five board, which cells change when you press R1C1? Does R2C2 change?
Check your reasoning
R1C1, R1C2 and R2C1 toggle. R2C2 is diagonal to the press and does not change. The cross is clipped by the board edges rather than wrapping to the opposite side.