Lights Out
Turn every light off. Pressing a cell toggles it and its neighbours.
moves: 0
The solver is Gaussian elimination over GF(2): the whole puzzle is one
matrix equation A·x = b (mod 2). On 5×5 the matrix is
singular — its null space holds the two famous “quiet patterns”, only ¼
of random boards are solvable, and the solver picks the fewest-press
solution among all four.