Each press flips a square and its neighbours — find the presses that switch every light off.
The full guide, with a worked example and common mistakes: How to play Light Switch.
On some boards, yes; on others (5×5 with plus-shaped switches, for example) only about a quarter of all patterns can. Every puzzle the game makes is solvable.
They mark the squares you have pressed an odd number of times — handy for spotting double presses.
The solver finds the fewest presses by solving the light equations mod 2 and trying the few free choices.
Open the Light Switch Solver, set the lights and press Solve.