Toggle Grid· Advanced

Goal

Turn off every cell on the grid. Tapping a cell flips it and its orthogonal neighbors.

Rules

  • A tap toggles the chosen cell and up to four orthogonal neighbors (N, S, E, W). Edge and corner cells have fewer neighbors.
  • ↺Tapping the same cell twice returns it to its original state. Click order does not matter.
  • ★You win the moment every cell is off. Matching the optimal move count without hints earns a bonus.

How to Play

Tapping the center flips itself plus its four orthogonal neighbors.

Initial state — only the center is on
After tapping center — five cells flipped in a cross

Tip

  • Use the 'chase' technique: tap directly below any active cell in the row above to clear rows from top to bottom.
  • Tapping a cell twice reverts it, so experiment freely.
  • Hitting the optimal move count earns a bonus score.

Grid-toggle puzzles of this kind are classical GF(2) linear algebra problems, training constraint-based planning and abstract pattern reasoning.

  • Anderson & Feil (1998) Turning Lights Out with Linear Algebra, Mathematics Magazine 71(4) 300-303
  • Scherphuis (2023) The Mathematics of Lights Out, jaapsch.net