The 1995 handheld with a secret: presses commute, pressing twice undoes, and so the entire game is linear algebra over the two-element field. That one reframe hands you a solving technique, an exact count of solvable boards, and four ghostly 'quiet patterns' that press themselves and change nothing at all.
Each press toggles the cell you hit and its four orthogonal neighbours — a plus sign of five lights, or four along an edge, or three in a corner. Goal: total darkness. Press anywhere to feel the shape of the move.
The console lies to you. It looks like a dexterity toy — find the right sequence, in the right order, quickly. But every button is hard-wired to a fixed bundle of switches — five in the middle of the board, fewer at the rim — and flipping a switch twice puts it back. So pressing a button twice does nothing, which means no button is ever worth pressing more than once.
And if each button only ever contributes "on or off", the order you press them in cannot matter either — five flips here and five flips there land the same wherever you start.
Which strips the game to its bones: a "solution" is not a sequence at all, it is a set of buttons — which of the 25 you touch, and nothing else. The teal dots on the board track exactly that set. Twenty-five yes/no choices, and a rule that says what each choice does. That is algebra, not dexterity, and algebra can be solved rather than searched.