Light Switch: move the problem down the board.
Use row-by-row light chasing to make a complicated grid easier to reason about.
A Light Switch board can look chaotic because a single move changes several squares at once. The useful simplification is that every effect is local and predictable. A switch changes itself and its immediate horizontal and vertical neighbors. Nothing farther away is affected.
Start with a single cross
On an otherwise dark board, selecting the center lights up a cross. In the diagram below, filled circles are on and dots are off. Selecting the center a second time turns the entire cross off again.
· · · · · · · ● · · · ● ● ● · · · ● · · · · · · ·
This gives you the first rule: two selections of the same square cancel. The second rule is that switch order does not affect the final pattern. Selecting A then B has the same final effect as selecting B then A, because each selection reverses a fixed set of lights.
Clear the first row from below
Look at the first row only. For each lit square, select the square directly below it in the second row. A selection in row two affects exactly one light in row one: the square immediately above. It cannot disturb the other squares in that first row.
If the first row begins on, off, on, off, off, select row two at columns one and three. The first row is now dark. The lower rows have changed, but that is expected. You have moved the unresolved work downward.
Repeat without revisiting completed rows
After clearing row one, inspect row two and select directly underneath its lit squares in row three. Continue with rows three and four. Once a row is dark, this process does not change it again because later selections happen too far below it.
At the end, only the bottom row can remain lit. This is progress: you have reduced a two-dimensional pattern to one row of unresolved information. It is not yet a complete solver, because there is no sixth row to press underneath the bottom row.
What the remaining pattern means
A remaining bottom-row pattern means you need different choices in the top row before chasing downward. You can try a top-row pattern, run the same row-chasing process, and check the result. There are 32 possible on-or-off choices for five top-row switches, including pressing none.
For a solvable board, testing those top-row choices and chasing each one is a finite solving method. Keep each trial separate by starting from the same original board; combining partial trials makes the comparison meaningless. The live game does not include a trial-history tool, so this systematic method is easiest to explore with a written copy of the starting grid.
A useful practice goal
Do one careful chase and predict every change in the row above your selection. If the prediction is wrong, stop and check which neighbors a switch affects. Our new puzzles are generated by pressing switches on an all-dark board, which ensures a solution exists. The lesson is to replace random presses with a controlled process, even before you can finish every board efficiently.