Cross-toggle lights: rules and printable materials

Toggle a chosen cell and its orthogonal neighbors to turn every light off.

Players

1–4 (cooperative)

Plan for

10–20 minutes

Bring

3×3 light grid, 9 counters and toggle log

Set the exact starting lights

Use columns A–C and rows 1–3 bottom to top. A counter means on; an empty cell means off. Start only A1, C1, B3 and C3 on. This particular printed start has been checked as solvable. Copy it exactly before searching; arbitrary arrangements should not be advertised as equally easy. All nine cells may be chosen, whether their own light is on or off.

Apply a complete cross

Choosing a cell reverses that cell and every orthogonal neighbor within the grid: on becomes off and off becomes on. Do not affect diagonals, wrap around an edge or leave the center unchanged. Choosing B2 reverses five cells, B1 reverses four, and A1 reverses A1, B1 and A2 only. Count the affected cells aloud before changing counters.

Use parity to plan

Choosing the same cell twice cancels those two moves. The order of chosen cells does not affect the final board because each affected light is simply reversed once per occurrence. Therefore a search can consider each cell either selected once or not selected, just 512 subsets. This is an optional reasoning method, not a requirement to do algebra or an invitation to use a hidden online solver.

Check the supplied solution

For the printed starting state, choose A1, B2 and C2 once each, in any order. After all three crosses, every light is off. The host key shows the chosen centers, not the cells that start on; do not confuse the two diagrams. Stop immediately when all lights are off. Extra toggles after solving are a new attempt, not part of the solved record.

Run a fair cooperative attempt

Give everyone an unscored cross demonstration, then reset the exact start. Share the move log and let a different person verify each cross before it is applied. No reflexes, silence or time pressure are needed. Keep counters large and away from small children; pencil circles can replace loose pieces. The kit is a manual state puzzle, without an automatic animation or solution checker.

Printable materials

Preview at 100% scale, with browser headers and footers off. Cut with suitable help. Keep host keys separate. This is a manual tabletop kit, not an online opponent, automatic judge or solver.