One rule. Countless solutions.
Tap a tile and it flips between dark and glowing — and so do the tiles beside it. Light
the whole board, or clear it, depending on the level. The rule takes five seconds to learn and the boards
take rather longer to put down, because every tap ripples outward and the obvious move is usually the
wrong one.
The logic is real rather than lucky: every level has a genuine solution, the move counter runs against
the known best, and a reset lets you experiment without spoiling anything. Sixty hand-built grids climb
from small warmups to larger tangles across easy, medium and hard, with variants that change which
neighbours a tap affects, progress and best-move records kept, a limited hint that reveals one correct
tap, and a shuffle that hands you a fresh solvable board whenever you want one more. Offline, no account,
no advertising.
Why a board has to be built, and cannot just be scattered
A grid of lights is a system of linear equations in disguise. Each tile is either on or
off, each tap adds a fixed pattern to the board, and adding twice undoes it — which is arithmetic
modulo two, where 1 + 1 = 0. Whether a board can be lit at all is then the plainest question in
linear algebra: does the target lie in the span of the tap patterns? Row-reduce the matrix over
GF(2) and everything falls out at once — the rank, the number of reachable boards, and the
quiet patterns, sets of taps that change precisely nothing and therefore turn every solution
into several. The panel does that elimination for the size and rule you pick, exactly, with no
sampling.
33,554,432arrangements the board can be in
23rank of the tap matrix over GF(2)
2dimensions of quiet taps
1 in 4boards that can be lit at all
4distinct solutions each one has
8,388,608boards actually reachable
Not on this bench: no board, no tiles, nothing to tap and nothing solved. It
never looks at a particular arrangement and could not tell you a single move. It counts what the rule
makes possible, which is the reason levels in a game like this are built backwards from a finished
board rather than sprinkled and hoped over.