Lights out
Every press flips a light and its neighbours. Turn them all off.
The maths Parity and arithmetic mod 2
5 lights still on.
How to play
Press any square. It flips, and so do the squares directly above, below, left and right of it. Your job is to turn every light off.
Pressing the same square twice puts everything back, so the order you press in never matters — only which squares you pressed, and whether you pressed each one an odd or even number of times.
Keyboard: arrow keys move, Enter or Space presses.
Why this is mathematics
Pressing the same button twice changes nothing, so only whether you pressed it an even or odd number of times matters, and the order never does. That makes this a system of equations where the only numbers are 0 and 1 — the smallest interesting arithmetic there is.